Precise Hydrodynamic Levelling Using Pressure Gauges with Application to Improvement of the Estonian National Levelling Network

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PRECISE HYDRODYNAMIC LEVELLING USING PRESSURE GAUGES WITH APPLICATION TO IMPROVEMENT OF THE ESTONIAN NATIONAL LEVELLING NETWORK

RÕHUANDURITEL PÕHINEV TÄPNE HÜDRODÜNAAMILINE LOODIMINE RAKENDATUNA EESTI RIIKLIKU KÕRGUSVÕRGU REKONSTRUEERIMISEL

AIVE LIIBUSK

A Thesis for applying for the degree of Doctor of Philosophy in Geodesy

Väitekiri filosoofiadoktori kraadi taotlemiseks geodeesia erialal

Tartu 2013

EESTI MAAÜLIKOOL ESTONIAN UNIVERSITY OF LIFE SCIENCES

PRECISE HYDRODYNAMIC LEVELLING USING PRESSURE GAUGES WITH APPLICATION TO IMPROVEMENT OF THE ESTONIAN NATIONAL LEVELLING NETWORK

RÕHUANDURITEL PÕHINEV TÄPNE HÜDRODÜNAAMILINE LOODIMINE RAKENDATUNA EESTI RIIKLIKU KÕRGUSVÕRGU REKONSTRUEERIMISEL

AIVE LIIBUSK

A Thesis for applying for the degree of Doctor of Philosophy in Geodesy

Väitekiri ﬁ losooﬁ adoktori kraadi taotlemiseks geodeesia erialal

Tartu 2013 Institute of Forestry and Rural Engineering Estonian University of Life Sciences

According to verdict No 27 of March 11, 2013, the PhD Committee for Engineering Science of the Estonian University of Life Sciences has accepted this thesis for the defence of degree of Doctor of Philosophy in Geodesy.

Opponent: Prof. Markku Poutanen Department of Geodesy and Geodynamics Finnish Geodetic Institute

Supervisors: Prof. Artu Ellmann Faculty of Civil Engineering Tallinn University of Technology

Ass. Prof. Harli Jürgenson Institute of Forestry and Rural Engineering Estonian University of Life Sciences

Language editor: Marguerite Oetjen

Defence of this thesis: Estonian University of Life Sciences, room 1A5, Kreutzwaldi 5, Tartu on April 22, 2013 at 12:00.

Publication of the thesis is supported by Estonian University of Life Sciences and Doctoral School in the Field of Building and Environmental Engineering.

LIST OF FIGURES ...... 8 LIST OF TABLES ...... 10 LIST OF PUBLICATIONS ...... 11 LIST OF ABBREVIATIONS ...... 12 INTRODUCTION ...... 14 1. REVIEW OF LEVELLING METHODS AND SPECIFICS OF THE STUDY AREA ...... 18 1.1. Methods of across-water levelling ...... 18 1.1.1. GNSS-levelling ...... 18 1.1.2. Geometric levelling ...... 19 1.1.3. Trigonometric levelling ...... 20 1.1.4. Hydrostatic levelling ...... 21 1.1.5. Hydrodynamic levelling ...... 22 1.1.6. Summary of achieved accuracies of across-water levelling ...... 23 1.2. The Estonian National Levelling Network ...... 24 1.2.1. Historical across-water levellings in Estonia ...... 25 1.2.2. Opportunities for across-water levelling in the modern Estonian National Levelling Network ...... 27 2. AIMS OF THE STUDY ...... 30 3. EQUIPMENT, METHOD AND DATA PROCESSING ...... 32 3.1. Equipment for sea level observations ...... 32 3.1.1. Staff gauges ...... 32 3.1.2. Float-based gauges ...... 33 3.1.2.1. Stilling-well gauges ...... 33 3.1.2.2. Modern geodetic instruments, adapted for sea level observations ...... 34 3.1.3. Automatic tide gauges ...... 36 3.1.3.1. Acoustic gauges ...... 36 3.1.3.2. Radar gauges ...... 37 3.1.3.3. Pressure gauges ...... 38 3.1.4. Conclusions on usable equipment ...... 41 3.2. Principles of hydrodynamic levelling ...... 43

5 3.3. Specifi cs of the study area ...... 46 3.3.1. Considerations of the sea surface topography of the Väinameri Basin ...... 47 3.3.2. Determination of height differences in the study area ...... 53 3.4. Water level registration with piezoresistive and capacitive pressure gauges ...... 54 3.5. Set up of pressure gauges and data acquisition ...... 56 3.6. Processing sea level series ...... 62 3.6.1. Detecting time-dependent drift ...... 64 3.6.1.1. Control readings and estimating parameters of drift trend ...... 65 3.6.1.2. Computing the drift-corrected data ...... 70 3.6.1.3. Reliability of the estimated drift corrections ..70 3.6.2. Filtering of sea level series ...... 76 4. RESULTS, THEIR VERIFICATIONS AND DISCUSSION ..78 4.1. Results of pressure gauge-based hydrodynamic levelling ...... 78 4.2. Internal verifi cations of the annual hydrodynamic levelling results ...... 80 4.2.1. Short-term “ice-tamed” sea level observations ...... 80 4.2.1.1. “Ice-tamed” observations in February 2011 ...81 4.2.1.2. “Ice-tamed” observations in March 2012 ...... 86 4.2.2. Hydrodynamic levelling with “thinned” data ...... 87 4.3. External verifi cations of the annual hydrodynamic levelling results ...... 89 4.3.1. Hydrostatic levelling for verifying across-water hydrodynamic levelling results ...... 90 4.3.2. Geometric levelling for verifying land-connected hydrodynamic levelling results ...... 95 4.3.3. GNSS-levelling for verifying across-water and land- connected hydrodynamic levelling results ...... 96 4.4. Combining the hydrodynamic and spirit levelling results into a closed loop ...... 99 4.5. Conclusions and discussion on verifi cations ...... 101 5. SUMMARY AND CONCLUSIONS ...... 106

6 REFERENCES ...... 112 APPENDICES...... 121 APPENDIX A. Transformation the acquired raw pressure gauge data to the same (arbitrary) height system ...... 122 APPENDIX B. Historical staff gauge series for hydrodynamic levelling ...... 125 APPENDIX C. Compilation of empirical land uplift WEst12LU model over the West-Estonian Archipelago ...... 128 APPENDIX D. Proﬁ le-wise veriﬁ cations of gravimetric GRAV-GEOID2011 model over marine areas ...... 132 SUMMARY IN ESTONIAN ...... 145 ACKNOWLEDGEMENTS...... 150 PUBLICATIONS ...... 151 CURRICULUM VITAE...... 223 ELULOOKIRJELDUS ...... 225

7 LIST OF FIGURES

Figure 1. Layout of the Estonia National Levelling Network in 2012 25 Figure 2. Locations of installed pressure gauges and connecting levelling lines around the Väinameri Basin 27 Figure 3. Basic structure of a stilling-well system (modifi ed from Pugh 1987) 34 Figure 4. Prism on a fl oat tracked by an Autolock total station 35 Figure 5. Schema of a bubbler gauge (modifi ed from Pugh 1987) 39 Figure 6. Principles of hydrodynamic levelling 43 Figure 7. GNSS-derived mean sea surface topography (SST) in the Väinameri Basin in 2010 and 2011 52 Figure 8. Pressure sensors Keller 36XW and Keller 46X 57 Figure 9. Typical set up of a pressure gauge station used in this study 60 Figure 10. Differences between the readings of two Keller 46X sensors (upper minus lower) in Sõru, Triigi and Kuivastu 63 Figure 11. The differences between the readings of pressure sensor and staff gauge and drift trends 68 Figure 12. Estimated daily height differences (∆H) of across-water CPs at the Virtsu–Kuivastu, Triigi–Sõru and Heltermaa–Rohuküla sections 72 Figure 13. Estimated daily height differences (∆H) of land- connected CPs at the Rohuküla–Virtsu, Kuivastu–Triigi and Sõru–Heltermaa sections 73 Figure 14. A sample of the ferry-induced data jumps in the Virtsu sea level series on July 5, 2010 76 Figure 15. Ice conditions in the Väinameri and nearby areas on February 23, 2011 and March 4, 2012 as seen on MODIS satellite images 81 Figure 16. Sea level observations by electronic distance meter Disto A6 82

8 Figure 17. Height connection between sea surface, contact point (CP) and tide gauge benchmark (TGBM) 83 Figure 18. One hour (data sampling interval 5m) water level discrepancies between the electronic distance meter (EDM) and the pressure sensor results on February 22–23, 2011 84 Figure 19. Discrepancies between height differences based on the sea level observations with different periods 85 Figure 20. Location of geodetic benchmarks, II order points, levelling lines and sea level gauges used in external veriﬁ cations of the annual hydrodynamic levelling results 90 Figure 21. Discrepancies between height differences based on different levelling methods 93 Figure 22. Daily misclosures of the Väinameri-encircling levelling loop (total length 253 km) in 2010 and 2011 101

9 LIST OF TABLES

Table 1. Accuracies of across-water levelling achieved in various case studies using different levelling methods 24 Table 2. Characteristics of different sea level gauges 42 Table 3. GNSS-derived and the DTU10MDT model-based mean sea surface topography at the locations of installed pressure gauges 49 Table 4. Characteristics of the Keller 36XW and Keller 46X pressure sensors 57 Table 5. Characteristics of pressure gauge stations installed around the Väinameri Basin 58 Table 6. Extract from the raw data ﬁ le recorded by pressure sensor 62 Table 7. The rates of drift trend of pressure sensors (and their standard deviations) based on control readings from staff gauges in 2010 and 2011 69 Table 8. Trend of measurements, joint drifts (and their standard deviations) in the paired pressure gauge stations at the end of years 2010 and 2011 74 Table 9. Hydrodynamic height differences (and their standard deviations) between the pressure gauge pairs 78 Table 10. Hydrodynamic height differences based on annual drift- corrected and short-term “ice-tamed” drift-free sea level observations (and their standard deviations) 85 Table 11. Hydrodynamic height differences (and their standard deviations) based on different data sampling intervals 88 Table 12. Height differences between paired pressure gauges (and their standard deviations) achieved by different levelling methods 91 Table 13. Height differences and misclosures of the Virtsu–Kuivastu– Virtsu and Triigi–Sõru–Triigi loops 94 Table 14. Heights of II order and contact points (CP) at the epoch 1997.56 and height differences between II order point and CP 98 Table 15. Misclosures of the Väinameri-encircling levelling loop by combining hydrodynamic and spirit levellings 100 10 LIST OF PUBLICATIONS

I Liibusk, A., Ellmann, A., Kõuts, T., Jürgenson, H. 2013. Precise hydrodynamic levelling by using pressure gauges. Marine Geodesy, 36. DOI: 10.1080/01490419.2013.771594 (in print).

II Liibusk, A., Ellmann, A., Kõuts, T. 2011. Use of high resolution sea level measurements for height transfer in the West-Estonian Archipelago. In Environmental Engineering, the 8th International Conference, May 19-20, 2011 Vilnius, Lithuania. Selected Papers: Vilnius Gediminas Technical University Press "Technika", pp 1374–1381.

III Liibusk, A., Jürgenson, H. 2008. Connections of Gulf of Riga islands to the Baltic Height System 1977. In Environmental Engineering, the 7th International Conference, May 22-23, 2008 Vilnius, Lithuania. Selected Papers: Vilnius Gediminas Technical University Press "Technika", pp 1378–1385.

IV Liibusk, A., Kõuts, T., Ellmann, A. 2012. Transfer of heights to islands in West-Estonian Archipelago using hydrodynamic levelling. In IEEE/OES Baltic 2012 International Symposium: IEEE/OES Baltic 2012 International Symposium, May 8-11, Klaipeda. IEEE Conference Proceedings. 8 pp.

V Liibusk, A., Jürgenson, H. 2008. Detecting the Baltic Sea Level Surface with GPS-measurements and Comparing it with the Local Geoid Model. In Observing our Changing Earth. International Association of Geodesy Symposia, Proceedings of the 2007 IAG General Assembly Perugia, Italy July 2-13, 2007: Springer-Verlag Heidelberg Proceedings 133:125–134.

The contribution of the author to the papers: Paper Study design Data Data Manuscript collecting processing preparation I AL, AE, TK AL, TK AL AL, AE, TK, HJ II AL, AE AL, TK AL AL, AE, TK III HJ, AL AL, HJ AL AL, HJ IV AL, AE, TK AL, TK AL AL, AE, TK V HJ, AL AL, HJ AL AL, HJ AE – Artu Ellmann; AL – Aive Liibusk; HJ – Harli Jürgenson; TK – Tarmo Kõuts.

11 LIST OF ABBREVIATIONS

ALS Airborne Laser Scanning ARP Antenna Reference Point AVISO Archiving, Validation and Interpretation of Satellite Oceanographic data BK77 Baltic Height System, year 1977 BOOS Baltic Operational Oceanographic System CARS2006 CSIRO (Commonwealth Scientific and Industrial Research Organisation) Atlas of Regional Seas, year 2006 (oceanographic SST model) CCD Charge Coupled Device CLS Collecte, Localisation, Satellites, subsidiary of CNES CNES National Centre for Space Studies, French Space Agency CorSSH Corrected Sea Surface Height CP Contact Point at sea level gauge DNSC08MDT Danish National Space Centre Mean Dynamic Topography Model, year 2008 DTU10MDT Mean Dynamic Topography Model, Technical University of Denmark (DTU), year 2010 DTU10MSS Mean Sea Surface Model, Technical University of Denmark (DTU), year 2010 EDM Electronic Distance Meter EGM2008 Earth Gravitational Model, year 2008 ELB Estonian Land Board ENLN Estonian National Levelling Network ENVISAT Environmental Satellite ERS European Remote Sensing (satellite) ESA European Space Agency EST-GEOID2011 GNSS-levelling fitted Geoid Model of Estonia, year 2011 EST-GEOID2003 GNSS-levelling fitted Geoid Model of Estonia, year 2003 EUMETSAT European Organisation for the Exploitation of Meteorological Satellites FS Full scale

12 GGM02 DOT GRACE (Gravity Recovery and Climate Experiment) Gravity Dynamic Ocean Topography Model, year 2002 GNSS Global Navigation Satellite System GOCE Gravity field and Ocean Circulation Explorer (satellite) GPRS General Packet Radio Service GRAV-GEOID2011 Gravimetric geoid model of Estonia, year 2011 GRACE/JPL GRACE/Jet Propulsion Laboratory Dynamic Ocean Topography Model GRS-80 Geodetic Reference System, year 1980 GSM Global System for Mobile Communications HIROMB High-Resolution Operational Model for the Baltic Sea IOC Intergovernmental Oceanographic Commission KTH08 Gravimetric Quasigeoid Model in Sweden, year 2008 MSL Mean Sea Level MSI Marine System Institute at Tallinn University of Technology NASA National Aeronautics and Space Administration NKG04 Nordic Gravimetric Geoid Model, year 2004 NKG2005LU Nordic Land Uplift Model, year 2005 NOAA National Oceanic and Atmospheric Administration PG Pressure Gauge RA-2 Radar Altimeter-2 Rio05 CMDT geodetic-oceanographic SST model by Rio and Hernandez, year 2005 RMS Root Mean Square Error SA Satellite Altimetry SLG Sea Level Gauge SST Sea Surface Topography SD Standard Deviation TGBM Tide Gauge Benchmark TGZ Tide Gauge Zero TUT Tallinn University of Technology, Estonia UTC Coordinated Universal Time WEst12LU West-Estonian Land Uplift Model, year 2012 WGS84 World Geodetic System, dating from 1984

13 INTRODUCTION

Levelling is a branch of surveying which is used to determine height differences with respect to benchmarks with known heights. Precise heights are important in many applications, e.g. in geodesy, engineering and oceanography. Nowadays, traditional spirit levelling is used to achieve the highest precision (sub-cm, typically) in height determination. To maintain the same height datum within a country (or continent) a nationwide levelling network needs to be established. The National Levelling Network is usually comprised of several interconnected loops, whereas the heights (either normal or orthometric) of benchmarks are determined from a common adjustment. For rigorous datum unification it is necessary to establish reliable connections between all parts of such a levelling network, both on the mainland and on adjacent islands.

Apparently, extension of a nationwide height reference system from mainland to islands (e.g. between Australia and the island of Tasmania), across the fjords (e.g. in Scandinavia) or between countries (e.g. France and Great Britain) may become very complicated due to the need for precise across-water measurements. The distances between the involved stations can range up to a few hundred kilometres. Various methods have been developed and practiced for across-water height determination, e.g. global navigation satellite system- (GNSS) based levelling, hydrostatic, hydrodynamic, and trigonometric levelling. Geometric levelling on the ice has also been used in sub-polar regions. All these methods differ from one another both by achievable precision and equipment required for conducting the measurements. In addition, the cost of various levelling methods may differ by magnitudes.

Notably, through the past decades simple oceanographic observations have been used for determining height (potential) differences between coastal stations. Such across-water levelling uses mainly multi-annual sea level series from sea level gauges (SLG), e.g. staff gauges, mareographs, pressure gauges, radar gauges. According to the Intergovernmental Oceanographic Commission (IOC 2006), the corresponding accuracy of sea level determination in individual sites could be from a few mm (e.g. some types of pressure gauges) up to several cm (e.g. staff gauges). Additionally, knowledge of sea surface

14 topography (SST) within the area of interest needs to be acquired to ensure the accuracy of the determination of height differences.

This study focuses on the usability and achievable accuracy of pressure gauges (PG) for hydrodynamic levelling. Automatic PGs are easy to use but they are known for time-dependent drift. Therefore, proper data filtering and processing algorithms need to be applied to acquired PG observations. Also an optimal duration of the PG series needs to be determined. Note that, traditionally, decade(s) long sea level series are used for hydrodynamic levelling. However, it may not be possible to use (stationary) long-term sea level series everywhere. Instead, a temporary SLG could be set up to collect data for hydrodynamic levelling. Therefore, due to limited budgets and the requested accuracy it is very important to determine the most optimal duration of sea level observations. This study tests performance of PGs and the developed methodology during a practical case study in the West-Estonian Archipelago. Height differences between the mainland and two major islands are determined and evaluated by alternative levelling techniques. The achieved results have practical application in the renovation of the Estonian National Levelling Network (ENLN) and for specifying land uplift velocities for Estonia.

Most of the results summarized in this Thesis have already been published (or are in print) in peer-reviewed scientific journals or volumes (cf. papers I–V). This Thesis is assembled as a self- comprehensive summary of the papers: it refers to them when appropriate. However, the present Thesis includes many complementary details that were not included in the publications, mostly due to limits set by publishers. These may be useful, since they support the achieved results and may enhance understanding of different aspects of the study.

The outline of the Thesis is as follows: Chapter 1 reviews the most common methods of across-water levelling and summarizes accuracies achieved in different studies in the northern part of Europe. The results illustrate the usability of different levelling methods for various lengths of water stretch to be bridged.

The present study results can be applied to the ongoing renovation of the ENLN, thus an overview of this network is presented. Loops of

15 precise levellings have also been established and measured on the two largest islands of Estonia (Saaremaa and Hiiumaa). Throughout history several attempts have been made to connect the island levellings to those of the Estonian mainland. Therefore, a brief overview of previous works is given in this Chapter. A similar and partly overlapping discussion can be found in paper II.

Chapter 2 states the main aims of the present study and recapitulates related research topics for achieving the aims.

Chapter 3 presents different types of available sea level gauges and geodetic instruments (see also paper III), which can be considered for hydrodynamic levelling.

This is followed by a brief overview of the principles of hydrodynamic levelling. This method was tested using six pressure gauges in a semi- enclosed water body. Since knowledge of the sea surface topography need to be integrated into the hydrodynamic levelling solution, it is important to know the physical characteristics of the study area. A discussion on the applicability of existing SST data models can be found in this chapter and in paper I.

The main emphasis of this study is on pressure gauges, which are known to be affected by time-dependent drift. This undesirable phenomenon needs to be eliminated from the data series. Measures to eliminate drift and adopted pre-processing principles of sea level series are discussed in Chapter 3 and analysed in papers I and IV as well.

Chapter 4 summarizes the results of hydrodynamic levelling achieved in the practical case study. Four different comparisons (short-term “ice-tamed” drift-free sea level observations, spirit, hydrostatic and GNSS-levelling) verify the results and accuracy of hydrodynamic levelling. The misclosure values of a closed loop (comprising hydrodynamic and spirit levelling sections) are analysed in the context of achievable accuracy of hydrodynamic levelling. Additionally, the usability of low frequency (12h interval between sequential samples) sea level data is evaluated. The resulting knowledge can be applied to PGs to reduce data sampling frequency and thus also power consumption in areas without stationary power supply.

16 Chapter 5 contains a general summary of this study. The most important results, problems and recommendations for future studies are pointed out in this section.

Appendices provide an overview of the results of related research topics. For instance, the results of 19-year-long historical staff gauge series are compared with the achieved PG hydrodynamic levelling results.

The outcome of this study and historical repeated levelling results are used for specifying regional land uplift velocities.

A new regional gravimetric geoid model is used for GNSS-levelling in this study. Therefore, additional verifications by means of profile-wise GNSS, airborne laser scanning (ALS) and satellite altimetry (SA) measurements are carried out to detect the accuracy of this geoid model in the marine and coastal areas. Profile-wise verifications of the geoid model are described in paper V, as well.

17 1. REVIEW OF LEVELLING METHODS AND SPECIFICS OF THE STUDY AREA

1.1. Methods of across-water levelling

Precise heights are needed for many applications in geodesy, engineering and oceanography. High-precision spirit levelling can be used on dry land. For across-water connections GNSS, geometric (e.g. levelling on the ice), trigonometric, hydrostatic and hydrodynamic levellings can be implemented. These methods are briefly reviewed below in the context of their accuracies and usability. Even though these methods are in use all over the world, priority in the references below is given to results obtained for the area of principal interest – the northern part of Europe.

1.1.1. GNSS-levelling

Geodetic GNSS measurements in conjunction with a regional geoid model can be used for levelling. However, in many regions the accuracy of gravimetric geoid models does not exceed 2…3 cm. Even though regional geoid models may be corrected by using GNSS- levelling points (resulting in a so-called height correction surface), both the levelling and GNSS-derived heights need to be consistent, i.e. originating from the respective adjustment. The GNSS-derived geodetic heights are obtained with respect to an adopted reference ellipsoid (such as GRS-80), whereas levellings refer to some initial point (“zero”) of a sea level-related vertical datum. For GNSS measurements a consistent network solution for the mainland and oversea points can be easily achieved through methods of satellite geodesy. However, in the case of the common adjustment of traditional levelling, the height differences between the mainland benchmarks and that of islands must be determined rigorously, e.g. by using hydrostatic or hydrodynamic levelling methods. Therefore, the issue of precise height transfer over waterways remains crucial even in the GNSS era.

For example, amongst the first researchers to apply this method across a stretch of water were Goldan and Seeber (1994), who connected the

18 island of Helgoland (North Sea) with the mainland of Germany, separated by a ~40 km wide waterway. They reported that the differences in GNSS-derived ellipsoidal heights can be determined with centimetre accuracy. Unfortunately, the relationship between the mainland height system was not established at the same level of accuracy due to systematic errors in the former geoid models over the German Bight.

Recently, a similar connection between the mainland of Sweden and the island of Gotland (distance about 70 km) was established with an estimated accuracy of ±3 cm (J. Ågren, pers. comm., 2010). The Gotland GNSS heights were converted to normal heights using the quasigeoid model KTH08 (Ågren et al. 2009).

The advantage of the GNSS-levelling method is that it is not affected by the distance between two points and it enables advantageously transferring the heights over hundreds of km. However, the accuracy of the resulting height differences depends mainly on the accuracy of the underlying geoid model. Note also that both the coverage and quality of the gravity data at shorelines could be quite heterogeneous and possibly contaminated with systematic errors, which affect subsequent geoid determination accuracy in the coastal regions.

1.1.2. Geometric levelling

Geometric (a.k.a. spirit levelling) is an accurate levelling method. However, the rather limited sight-line between the levelling instrument and staffs (a.k.a. rods) imposes restrictions on the use of this method for across-water measurements. Nevertheless, this method has been used for height transfer over narrow stretches of water. Interestingly, Kakkuri and Kääriäinen (1977) developed the method further. They carried out measurements in the Aland Archipelago, Finland in the 1960’s and 1970’s and proposed simultaneous observations with two optical levelling instruments (Zeiss Ni2) from opposite shores. Arguably, this eliminates most errors due to the refraction effect. Moreover, in order to compute the effect of refraction, the vertical thermal gradient was measured along the line of sight using a small boat. Although the maximum distance in their study ranged up to 4 km, reliable results were obtained only for up to 1.8 km-long water

19 crossings; that seems to be the ultimate limit for optical levelling instruments. To enable readings for such long distances, special types of targets (an aluminium plate, 50 cm wide and 60 cm high) were made and fixed to the levelling rod. Note that the simultaneous observations included up to 100 pointings and the measurements were repeated over several days. The height differences were determined with accuracy ±1 cm across 1.8 km stretches of water (ibid.). Note however, that modern digital instruments in conjunction with bar-coded levelling rods are more demanding than traditional (optical) line-of-sight measurements. In particular, the distance is more limited by the size of the CCD-array (charge-coupled device) and especially the size of the code element. By magnifying the size of the bar code element by 2x...10x, modern digital levelling instruments can take readings from the distance of 1.0 km (Takalo and Rouhiainen 2006).

Geometric levelling on the ice can also be considered for across-water height determination. Certainly, levelling on the ice can only proceed under Nordic winter conditions when sufficiently thick and “crack- free” ice-cover develops. Note however, that even a relatively thick (a few tens of cm) ice-cover is unable to entirely prevent weather-induced sea level fluctuations. Thus, it could be quite difficult to ensure ideal weather conditions for ice-levelling and therefore the method has seldom been used. Nevertheless, Bogdanov et al. (2000) report the ice- levelling results over the eastern end of the Gulf of Finland (eastern area of the Baltic Sea) for connecting the Kronstadt tide gauge1 with a benchmark on the mainland. This 6 km distance has been measured four times (1875, 1886, 1931 and 1947). Comparison of the results reveals a standard deviation of ±2.8 cm (ibid.). Similar measurements were carried out for 3 and 4 km distances by Linnamaa (1940) in Estonia. More details on these measurements can be found in Section 1.2.1. Due to practical considerations, however, it is difficult to maintain accuracy requirements for ice-levelling routes exceeding 5 km.

1.1.3. Trigonometric levelling

Reasonably good results have been reported by Takalo and Rouhiainen (2006) for trigonometric levelling across relatively narrow water bodies.

1 Kronstadt tide gauge marks the zero of the Baltic Geodetic Height system. The Kronstadt zero is the mean sea level of period 1825–1840.

20 Here the vertical angles and slope distance between two points are simultaneously measured with high precision total stations from the opposite side of the water. For each water crossing several rounds (a.k.a. series) of vertical angle measurements need to be taken. For instance, five series of observations were taken by Takalo and Rouhiainen (2006), achieving the accuracy r 4 mm km . However, due to refraction of the optical sight-line this accuracy cannot be maintained for distances longer than 1 km. The effect of refraction cannot be eliminated but the reliability of the results in long distances can be increased using simultaneous observations and taken several rounds. The accuracy of the optical method can be estimated from the measurements of the water crossing made over several days. Recall also the experiment by Kakkuri and Kääriäinen (1977) reviewed in Section 1.1.2.

1.1.4. Hydrostatic levelling

According to the method of hydrostatic levelling an elastic tube (or a set of interconnected tubes) filled with liquid (water or spirit) is laid between the shores of the water body to be bridged. The level of liquid, observed at both ends of the tube, indicates (in an ideal case) the same level surface. The method was used mainly from the 1950’s to 1970’s. For example, hydrostatic levelling was used across 2 km-wide Als Fjord in Denmark by Jessen (1968). In the Netherlands six islands (the Frisian Islands) and three sandflats were connected with the mainland by Waalewijn (1964). The across-water lengths were 3 up to 7 km. This method has been applied in Denmark on a number of occasions for ranges up to 20 km (e.g. Fehmarn Belt, Baltic Sea; for more details see Andersen 1992). The hydrostatic levelling was also used to connect the Kronstadt tide gauge and a mainland benchmark (cf. Tamme 1971, reviewed also in Bogdanov et al. 2000). The list can be continued with several similar works.

Precise hydrostatic levelling is technically sophisticated (e.g. due to the need to remove all air-bubbles in the tube). However, hydrostatic levelling is generally regarded as the second order accuracy2 (Crumrine and Palmer 1951, Hurst and Bilham 1986). Some authors have stated that hydrostatic levelling has achieved even the first order accuracy

2 Accuracy of height difference between directly connected benchmarks for the second order is r 1.3 mm km by Vaníÿek et al. (1980).

21 (r0.5 mm km by Tamme (1969)). All in all, it can be argued that the height transfer accuracy remains mainly within ±1 cm for distances up to 10 km (see also Section 4.3.1.). This method is no longer feasible, mainly due to its high cost but also due to sensitivity to temporal and spatial changes in environmental conditions.

1.1.5. Hydrodynamic levelling

In the case of longer (more than 10 km) distances and deep water conditions, the method of hydrodynamic levelling could be applied. Hydrodynamic levelling requires sea level observations for determining height (potential) differences between coastal points or over oceanic regions (e.g. Torge 2001). The observations have to be averaged and reduced due to the sea surface topography (SST), which is a deviation of the mean sea level (MSL) from an equipotential surface (e.g. marine geoid). This implies the development of a hydrodynamic model, which takes into account water velocity, currents, wind drag, water depth and bottom friction, water density, atmospheric pressure, Coriolis force and gravity (cf. Merry and Vaníÿek 1983, Pugh 1987, Hipkin 2000, Torge 2001). However, river discharge and seabed topography (cf. Dunn and Ridgway 2002) also contribute to the variability of the SST in coastal regions (Merry and Vaníÿek 1983). The height determination becomes very expensive (if possible at all) if all these parameters are acquired specifically for a single hydrodynamic levelling campaign. Therefore, it is possible to use global or regional SST models based either on oceanographic data (e.g. Carlsson 1998, Lisitzin 1974), satellite altimetry (e.g. Andersen and Knudsen 2011) or geodetic measurements (e.g. Ekman and Mäkinen 1996). The common disadvantage of these models is that their accuracy may often be poorer (especially in the coastal areas) than that of actual sea level observations.

Traditionally, long-term (several years to decades) sea level series observed by float-in-a-well tide gauges (a.k.a. mareograph) have been preferred for hydrodynamic levelling. Contemporary automatic SLG stations track water level changes continuously and are able to transfer data via data communication devices even in real-time. Importantly, this enables monitoring sudden water level changes that could otherwise remain unnoticed. A brief overview of contemporary automatic SLGs can be found in Section 3.1.3.

22 A common disadvantage of long-term hydrodynamic levelling, however, is gaps in data series. Data quality could vary due to malfunctioning of instruments and/or natural causes (e.g. vertical land movements, waves, local water circulation patterns, etc.) as well. In addition, the SLG equipment may experience mechanical damages (e.g. due to ship collisions, ice, vandalism) and consequently need to be replaced. Therefore, there are only a few sea level gauges with century-long continuous and reliable data series anywhere in the world. In general, the usable time span for across- water height connections is a few decades or less.

Hydrodynamic levelling has been tested in several studies. For instance, Cartwright and Crease (1963) and Wübbelmann (1992), reviewed in Torge 2001, used hydrodynamic levelling over the Dover Strait (about 70 km) and the Fehmarn Belt (about 20 km), respectively. They claim achieving ±1.0…1.5 cm accuracy for their results.

In addition, 19 years of sea level records (monthly mean values) together with an oceanographic model (Novotny et al. 2002) were used to connect the island of Gotland to the Swedish mainland (Norin et al. 2010). The uncertainty obtained for this 70 km distance was estimated to be ±3 cm (J. Ågren, pers. comm., 2010).

Recall that the present study tests applicability of contemporary automatic pressure gauges (cf. Section 3.4.) for obtaining geodetic accuracy (±1 cm) in hydrodynamic levelling.

1.1.6. Summary of achieved accuracies of across-water levelling

Different across-water levelling methods used in conjunction with the corresponding case studies were reviewed in Sections 1.1.1.–1.1.5. The achieved accuracies from different levelling methods and case studies are summarized in Table 1.

Apparently, only two levelling methods (GNSS-based and hydrodynamic) allow transferring the heights over stretches of water exceeding 10 km. Note that GNSS-levelling can be affected by the accuracy of the regional geoid model. Therefore, the focus in the sequel is on hydrodynamic levelling and its use for the improvement of the Estonian National Levelling Network.

23 Table 1. Accuracies of across-water levelling achieved in various case studies using different levelling methods. Across-water Maximum distance Achieved Reference levelling method between the stations average in the case studies accuracy (km) (cm) GNSS-geoid 70 ±3.0 J. Ågren, pers. comm., 2010 Geometric on the ice 6 ±2.8 Bogdanov et al. 2000 Geometric direct line 1.8 ±1.0 Kakkuri and Kääriäinen of sight measurements 1977 Trigonometric 1 ±0.4 Takalo and Rouhiainen 2006 Hydrostatic 10 ±1.0 Tamm 1981 Hydrodynamic 70 ±1.5 Cartwright and Crease 1963

1.2. The Estonian National Levelling Network

The first levelling network covering the entire Estonian territory was established in 1933–1943. The total length of the levelling lines reached 1800 km (Torim 1993). The measurements were repeated within the two following periods, as summarized by Rüdja (2004, Table 3.1): 1950–1969 (total length of levelling lines 2067 km) and 1970–1991 (1771 km). The third levelling period, 1970–1996 (altogether 1884 km), is somewhat differently defined by Torim (2009). The differences in the length of levelling lines are mainly caused whether the across-water levelling lines and the lines between SLGs and levelling network are accounted for or not.

The latest reconstruction of the Estonian National Levelling Network started in 2001. During the reconnaissance it was detected that more than 44% (1130 out of 2588) of previous benchmarks were destroyed or cannot be found (cf. Torim and Jürma 2007). As a result of the reconstruction, the ENLN presently (2012) includes ~2700 benchmarks. The maximum along-line distance between the benchmarks in the renovated network is 2.5 km, but on average it is 1.3 km. The levelling lines (total length of about 3700 km) form altogether 26 loops, 24 on the Estonian mainland and 2 on the West- Estonian islands (see Figure 1). The levelling field-works were carried out in 2001–2012 by Planserk AS, a contractor to the Estonian Land Board (ELB). According to the ELB (A. Torim, pers. comm., 2012), the adjustment of the entire ENLN would be finalized at the end of

24 2013. To complete the nationwide renovation of the high-precision levelling network, the loops in the islands of Saaremaa (levelled in 2010) and Hiiumaa (2009) need to be connected with the mainland and each other. Therefore, it is appropriate to review historical attempts with similar scope.

Figure 1. Layout of the Estonia National Levelling Network in 2012 (ELB). Two westernmost loops are on the islands of Hiiumaa and Saaremaa. Inset: location of Estonia in the Baltic Sea region.

1.2.1. Historical across-water levellings in Estonia

Throughout the past decades, the levellings in the West-Estonian islands have been connected with the mainland using different levelling (geometric, hydrostatic, hydrodynamic) methods. For instance, a double-run precise spirit levelling on the ice was performed between the mainland and the island of Muhu (Saaremaa)3 (cf. Figure 2) in the extraordinarily cold winter of 1940 (Linnamaa 1940). The length of the

3 As a matter of fact, the island of Muhu is separated from neighbouring Saaremaa by a relatively narrow strait (cf. Figure 2). The islands are inter-connected by a solid dam-bridge that allows traditional spirit levelling to be used for rigorous connection of the benchmarks on the two islands. Also the Kuivastu pressure gauge station is located in Muhu. However, since Saaremaa is to be connected to Hiiumaa, then, in order to avoid possible confusion, in further text the “mainland-Saaremaa” levelling section will be denoting the actual “mainland-Muhu” levelling section.

25 connecting levelling line was 3+4 km by using two sections thorough Kesselaid islet in the middle of the strait (cf. Figure 2). The first section (3 km) was between Muhu and Kesselaid; the second (4 km) was between Kesselaid and Virtsu. The 3 km line was measured under windy conditions, whereas the 4 km line measurement was taken in calm weather. The differences between the forward and backward measurements in the sections were 2.0 cm and 0.5 cm, respectively. In parallel, short-term visual sea level observations were performed in ice holes (using temporarily mounted staff gauges close to the endings of the levelling lines) during two consecutive days for a four-hour long period each day. The height differences based on sea level observations agreed with the levelling on the ice results within ±3.5 mm, although a large difference between the forward and backward measurements (2.0 cm) was detected in one levelling section (Linnamaa 1940).

Short-term (several hours to a few days) sea level observations between the mainland and Saaremaa (cf. Figure 2) were repeated in 1963 and 1979 (Tamm 1992). Also, additional connections between the island of Saaremaa and Hiiumaa were established in 1958 and 1971. These sea level observations were made from temporarily mounted staff gauges in ice holes (ibid.). Winter months were preferred for these short-term water observations due to regional ice-coverage, which reduces possible wind influence on the sea level. The accuracy of height transfer over water by means of these short-term visual water observations was claimed to correspond to the second (r1.5 mm km ) and third order (r4 mm km ) for different campaigns (Torim 2009).

Figure 2. Locations of installed pressure gauges and connecting levelling lines around the Väinameri Basin. Inset: location of the study area in Estonia.

In addition, an across-water trigonometric levelling was tested at the beginning of the 1960’s (Tamm 1992). Unfortunately the distances (up to 4 km) appeared to be too long for trigonometric levelling and thus the experiment did not provide satisfactory results (confirmed later also by Takalo and Rouhiainen (2006), see a discussion in Section 1.1.3.

In 1968 and 1978 hydrostatic levellings were used to connect the island of Saaremaa with the mainland (cf. Torim 2009). The island of Hiiumaa was connected by hydrostatic levelling with Saaremaa in 1976 and repeated in 1977. These hydrostatic levelling results will be used for verification of the present study results (cf. Section 4.3.1.).

1.2.2. Opportunities for across-water levelling in the modern Estonian National Levelling Network

Nowadays, the methods discussed in Sections 1.1.1.–1.1.4. and short- term sea level observations cannot be used for precise across-water levelling in the West-Estonian Archipelago due to the following reasons:

27 (i) geometric levelling on ice is not accurate enough to satisfy geodetic requirements. Also, the favourable weather conditions in conjunction with thick ice-cover over the entire study area occur only once every two to three years (on average); (ii) short-term sea level observations may be affected by unpredictable environmental conditions and therefore need to be duplicated by alternative measurement methods; (iii) hydrostatic levelling is expensive and labour-intensive; (iv) GNSS-based levelling depends on the local geoid model. Even though the accuracy of the new national geoid model (Ellmann et al. 2011) is estimated to be within ±1.3 cm on the mainland (Oja et al. 2011), accuracy is suspected to be variable in the coastal and marine areas. Nevertheless, this study also attempts to verify the accuracy of the local geoid model over marine areas (see Appendix D for more details). All in all, the accuracy of GNSS-based levelling within the study area was estimated to be 2 cm, which does not satisfy the requirements of precise levelling.

Note that the across-water distances between the mainland and the islands reach up to 22 km in this study. Thus, across-water geometric and trigonometric levellings cannot be used either. Therefore, hydrodynamic levelling could be the best choice for connecting the oversea levellings to the mainland part of the ENLN most rigorously.

For hydrodynamic levelling six pressure gauges (PG) were installed by the Marine Systems Institute (MSI, at the Tallinn University of Technology), a contractor for the ELB. PGs were mounted on opposite sides of the straits, at the ferry harbours of Rohuküla and Virtsu (on the mainland), Kuivastu and Triigi (on the island of Saaremaa), Sõru and Heltermaa (on the island of Hiiumaa) (see Figure 2) in 2008–2010. After installation the stations were integrated into the Baltic Operational Oceanographic System4 (BOOS) as well (cf. Lagemaa 2012). The six PGs are also presently amongst 11 sea level observation stations (operated by the MSI) on the coast of Estonia that are used for the High-Resolution Operational Model for the Baltic Sea (HIROMB) level forecasting system in Estonia (Lagemaa et al. 2011).

4 BOOS provides integrated marine services and manages the online exchange of observational and modelled oceanographic data.

28 More details about these PGs and their installation can be found in Section 3.5.

Note that PGs located on the mainland or on the same island are connected with precise levelling. These land-connected sections can be included into the ENLN directly, since the average levelling RMS for these lines is comparable to the random error Ƨ = 0.19 mm km ; systematic error Ƴ = 0.04 mm/km of the ENLB (Torim and Jürma 2011).

Further inclusion of hydrodynamic levelling results enables formation of an additional combined levelling loop, which is comprised of three across-water (Virtsu–Kuivastu, Triigi–Sõru and Heltermaa–Rohuküla) and three land-connected (Rohuküla–Virtsu, Kuivastu–Triigi and Sõru–Heltermaa) sections (see Figure 2). Apparently, this extra (27th) loop has a potential to strengthen the entire western part of the ENLN.

29 2. AIMS OF THE STUDY

The main objectives of this study are: • to determine whether deployment of contemporary pressure gauges could ensure geodetic accuracy in hydrodynamic levelling; • to determine optimal duration of sea level observations for hydrodynamic levelling to guarantee the required geodetic accuracy; • to apply the study results for improving the West-Estonian part of the Estonian National Levelling Network.

To achieve these aims the following aspects had to be researched as well: 1. Investigation of the suitability of existing SLGs for hydrodynamic levelling. Although the emphasis of this study is on pressure gauges, a few feasible alternative gauge types are to be investigated and field tested as well. 2. Earlier hydrodynamic levelling experiences to be reviewed and the methodology of hydrodynamic levelling to be adapted to the Väinameri Basin for determining height differences across 6…22 km-wide water bodies. 3. Accounting for the sea surface topography is needed to ensure the required accuracy for hydrodynamic levelling. Therefore, a special SST-related study needs to be conducted to consider specifics of the Väinameri Basin, which is the principle interest of the study. 4. A great deal of attention to be given to developing principles of post-processing high-frequency (with 5m sampling interval) sea level data. In particular, (i) data filtering thresholds to be developed and tested, (ii) time-dependent drift of pressure sensors to be detected and eliminated. 5. Averaging principles of the filtered and drift-corrected annual sea level series to be developed in order to obtain reliable height differences between paired sea level gauges. Methodology to be developed and applied to verify the obtained results with alternative height determination techniques.

30 6. To investigate a suitable way of integrating the obtained hydrodynamic levelling results into the Estonian National Levelling Network. Further, involving historical levelling data, the new results to be used for development of an empirical land uplift model over the West-Estonian Archipelago. 7. As a side-product of the study, the “thinned”5 pressure gauge data to be used for evaluating reliability of historical staff gauge sea level series. 8. Application of profile-wise GNSS, ALS and satellite altimetry data for evaluating accuracy of a regional high-resolution gravimetric geoid model.

5 The term “thinned data” here and in further text denotes 12h sampling interval data, which are extracted from the original high frequency (5m) sea level observations.

31 3. EQUIPMENT, METHOD AND DATA PROCESSING

3.1. Equipment for sea level observations

Mean sea level (MSL) at a given point is defined as a temporal average of sea level observations (collected during a sufficiently long period) for a specific epoch (Vaníÿek 1991). Sea level observations are mainly used for marine navigation and for early warning of floods. Thus, most commonly the SLGs are installed at harbours, where the necessary infrastructure exists for running an SLG.

The first staff gauge (a.k.a. sea level scale or tide pole) for continuous sea level observations was mounted in Amsterdam as early as 1682, but was discontinued after a few decades (Pugh 1987). The longest continuous sea level observations have been carried out in Stockholm, starting in 1774. Nowadays, these sea level series are valuable for sea level rise and land uplift research. A detailed overview of the oldest sea level series and their use is given by Ekman (2009).

The first self-reader float-in-a-well tide gauges began operating at Sheerness (United Kingdom) in the Thames estuary at the beginning of the 19th century (Palmer 1831, reviewed in Pugh 1987). The self-reader gauges recorded the sea level readings on the chart; the chart had to be replaced daily or weekly. Also regular checks of the gauge’s clock were needed for precise time-keeping of records. The self-reader gauges were used intensively for more than 150 years (till the end of the 20th century). In recent decades different new types of automatic sea level gauges have emerged for sea level observations. A brief overview of sea level determination methods and usable equipment is given below.

3.1.1. Staff gauges

The staff gauge is the simplest and lowest cost device for sea level observations. According to the IOC (1985), staff gauges are usually 3…5 m long poles made of metal (e.g. cast aluminium or enamelled steel, cf. Boiten 2008) or wood which is covered with glass-reinforced plastic material. The cm-scale on the pole is usually bi-coloured (mostly

32 black and white). Note that depending on the sea surface conditions the sea level height could be observed with variable accuracy (for the calm sea ±0.5 cm, whereas with 1.5 m waves up to ±5 cm or worse, cf. Pugh 1987). Apparently, with very stormy weather it could be impossible to take visual readings from a staff gauge at all.

However, averaging long-term (up to decades) sea level observations compensate (possibly erratic) readings which have been taken in stormy weather.

3.1.2. Float-based gauges

Float-based gauges are divided into two groups in this study: (i) Stilling-well gauges; (ii) Modern geodetic instruments, adapted for sea level observations.

A float on the water surface is used by both types of gauges. The differences are related to the float’s surroundings. In the first case, the walls of a well protect the float against the waves. In the second case, the float is affected by waves. Therefore, reliable results with geodetic instruments can be obtained only with calm weather.

3.1.2.1. Stilling-well gauges

Stilling-wells (a.k.a. float-in-a-well) were probably the most common of all sea level recording systems throughout the 20th century worldwide (cf. IOC 2006). The well system enables minimizing the influence of waves on the readings. A schematic view of a stilling-well gauge is presented in Figure 3. The well is a vertical concrete tube with diameter 0.3…1.0 m (Pugh 1987, IOC 2006) and is connected to the sea through the conical input or horizontal intake pipe (Boiten 2008). The float in the well is connected to a recording device. The recorder zero is connected to the contact point (CP). Note that the CP is a benchmark-type mark on the top of the well (cf. Figure 3). The recorder zero has to be checked periodically by using steel tape to measure the distance between CP and water level (Pugh 1987).

Figure 3. Basic structure of a stilling-well system (modified from Pugh 1987).

The main advantage of such a gauge is direct sea level measurements with accuracy ~1 cm (even 0.2…0.4 cm, as advocated by Boiten (2008)) in all weather conditions. However, mounting of a stilling-well gauge is laborious and expensive, requiring a considerable amount of costly engineering works.

3.1.2.2. Modern geodetic instruments, adapted for sea level observations

For short-term (e.g. a few days) sea level observations industrially manufactured SLGs could be replaced with geodetic instruments, such as a GNSS receiver or an Autolock total station.

By the beginning of the 1990’s the GNSS buoys were used by Rocken et al. (1990) and Kelecy et al. (1994) for satellite altimetry calibration. Principles of a GNSS buoy are quite straightforward, e.g. a dual- frequency GNSS receiver can simply be placed on a float (for more details see Cheng 2004). This type of sea level gauge is easy to set up. For sea level observation the GNSS data post-processing is preferred. The main disadvantage of the GNSS buoy is imprecise height connection between sea level and reference benchmark. It is affected by the accuracy of GNSS measurements, geoid model and determination of GNSS antenna height. Note that in this case the GNSS antenna height is defined as the vertical distance between the water surface and the antenna reference point (ARP). Accordingly,

34 inaccuracies up to 2 cm can occur when connecting sea level heights to a nearby benchmark. Within the frames of this study a self-made GNSS buoy was tested in the Gulf of Riga. More details about these experiments can be found in paper III.

Additionally, an Autolock total station can be used for short-term sea level observations. Here, a prism is placed on a float as shown in Figure 4. The separation of the centre of the prism from the water surface is determined and thereafter the initial position of the prism is tied to the nearby benchmark by using two-round angular/distance measurements both at the beginning and at the end of the session. During the entire session the prism vertical movements were tracked automatically by the automatic target recognition (so called “autolock”) function of the total station. The accuracy of sea level observations depends on the accuracy of the Autolock total station and the distance between the total station and the prism. The test measurements carried out during this study showed that an Autolock total station is a good alternative for industrially manufactured sea level gauges. It is easy to set up and use, and sea level changes can be detected with accuracy ~0.5 cm.

Figure 4. Prism on a float tracked by an Autolock total station. Nearby benchmark is used for height connection between sea surface and levelling network. Inset: Determining offset between the centre of the prism and the water surface.

35 Apparently, sea level observations with geodetic instruments are weather sensitive. Therefore, measurements can only be carried out with calm weather. Otherwise, a special construction must be mounted into the water or onto the pier. The stationary power supply can be used for a total station and GNSS receiver in port areas. In remote areas the observation duration depends on the batteries and a nearby infrastructure. Therefore, for long-term (from months to years) observations, industrially manufactured SLGs are preferred (see the next section).

3.1.3. Automatic tide gauges

According to IOC (2006), contemporary automatic SLGs can be divided into three main groups: (i) Acoustic gauges; (ii) Radar gauges; (iii) Pressure gauges.

However, this grouping is somewhat artificial, since for some automatic SLGs the best results may be reached when a gauge is placed over/in a stilling-well (cf. Section 3.1.2.). All of them can be used for hydrodynamic levelling, therefore a brief overview of the automatic SLGs is given below.

3.1.3.1. Acoustic gauges

The working principles of an acoustic gauge are described in detail by Pugh (1987). In brief, a reflector (or a simple float) has to be placed on the water surface, preferably in the stilling well. Acoustic equipment (which contains both the sender and receiver of the acoustic signal) is mounted above the stilling-well. This method is difficult to apply without a stilling-well because reflections from the surface may get directed away from the receiver with rough waves.

The time taken by a pulse of sound to travel (along the plumb-line) from the source to a reflecting surface and back again is used to compute the vertical distance (L) from the source of the reflector:

36 L = (t · cs) / 2 (1)

where t is the sound’s travel time and cs is the speed of sound in the measurement environment (here the lowermost layer of the atmosphere). Note that corrections must be made for the variations of cs with air temperature, pressure and humidity. For example, for dry air cs = 337.5 m/s (at 10 ºC and 1 atm = 1013.25 hPa), at 0 ºC cs = 331.5 m/s. Sea level changes can be measured with accuracy ~1 cm using an acoustic gauge (cf. IOC 2006).

A similar principle is used by Electronic Distance Meter (EDM), such as the well known hand-held Disto device. An EDM works by measuring the time it takes a pulse of laser light to be reflected off a target and returned to the sender. In this case, Eq. 1 must be modified 6 – instead of speed of sound (cs) the speed of light (cl) needs to be inserted into Eq. 1. Thus, EDM can be used for sea level observations as well (for a practical case study see Section 4.2.1.).

3.1.3.2. Radar gauges

Radar gauge technology is relatively new and has been used since the 1990’s (cf. IOC 2006). The radar is mounted to a pier several meters above the water surface and monitors sea level continuously (Woodworth and Smith 2003). There is no need to deploy floating reflectors. The radar emits a continuous microwave frequency (electromagnetic signal at 8…10 GHz). The sea level height is measured by the phase shift between the frequency of the emitted signal and the frequency of the reflected signal (Barjenbruch et al. 2002). The method is insensitive to effects of density and temperature variations in the atmosphere. Radar gauges are easy to install, operate and maintain. Unfortunately, however, these gauges cannot be used when the sea is under ice cover. Secondly, the power consumption of the equipment may be relatively large. Therefore, a stationary power connection must be guaranteed for the radar equipment. Sea level measurements can be made with accuracy ~1 cm by using a radar gauge.

6 Note that speed of light in air at 0 °C and 1 atm pressure is 299 792 km/s.

37 3.1.3.3. Pressure gauges

Unlike other previously mentioned gauges, PGs are mounted under water. The working principles of PGs are described by many authors (cf. Pugh 1987, Woodworth et al. 1996, Boiten 2008). The pressure due to the above water column is measured at a fixed point below the sea surface, further converting this into units of length using the following relationship (e.g. Pugh 1987):

D = (P – PA) / (U · g) (2) where D is the water column height above the fixed point below the sea surface, P is the measured pressure at the fixed point depth, PA is the atmospheric pressure acting on the water surface, U is the mean density of the overlying column of sea water and g is the gravitational acceleration. The pressure to the sensor increases as the water level increases. Note that the seawater density U is important in pressure measurements. If needed, this can be verified by taking a water sample from a nearby PG. The density corrections can be added to the sea level observations during data processing.

Commonly for all PGs, there is a need to establish a datum for the observed time series. This can be achieved in several ways as presented in IOC (2006): (a) from knowledge of the exact height of the pressure point during installation7; (b) using a datum level which triggers at a known sea level; (c) by having a parallel system (a.k.a. a “B” gauge) with a duplicate and more accessible pressure point fixed near the MSL.

PGs can be divided into two main groups: (i) Bubbler gauges; (ii) Transducer pressure gauges.

Bubbler gauges do not need vertical structures on which to attach the equipment. Parts of the equipment can be several hundred meters apart, one (sea bottom cylinder, called a pressure point or bubbler

7 Note that for a transducer, determining the exact depth of the diaphragm (pressure point) could be complicated. Therefore, this method is difficult to use.

38 orifice chamber) installed in the sea bottom and another (measuring and recording system) can be placed onshore (cf. Figure 5). By Boiten (2008), the compressed air or nitrogen gas from a compressor flows over the pressure reducer through the measuring system. Gas bubbles flow out through the gas outlet at the end of connecting tube. At this underwater pressure point the gas pressure is equal to the water pressure P. The water pressure is measured by manometer on the shore. The bubbler gauge can measure the sea level with 1 cm accuracy. However, the accuracy may degrade under large-wave conditions (IOC 2006).

Figure 5. Schema of a bubbler gauge (modified from Pugh 1987).

Transducer (a.k.a. pressure sensor, pressure probe, pressure transmitter) pressure gauges are easy to mount and simple to use. Unlike traditional float-in-a-well tide gauges, no special well is required for operating a PG (cf. Mueller et al. 1989). Attaching a sensor inside a protective tube or onto the back side of the staff gauge (cf. Section 3.5.) could be sufficient to ensure the immobility of the sensor and protect it from mechanical damage.

Pressure sensors use a diaphragm to measure strain due to applied force (i.e. pressure) caused by the stress of the column of water above the sensor. Due to the different operational principles, force collector pressure sensors can be divided into piezoresistive and capacitive pressure gauges. As this study employs both pressure gauge types, the

39 piezoresistive and capacitive pressure gauges are described in more detail in Section 3.4.

Note that pressure transducers are sensitive to temperature (cf. IOC 2006, Woodworth and Smith 2003). Therefore, an in-built or separate temperature sensor and its recordings are used to compensate the temperature-dependent drift (cf. Section 3.5.). Additionally, according to IOC (2006): “Drift in the various properties of pressure sensors is confined to changes in its datum value (i.e. there is usually no change in scale).” It means that even for a high-quality pressure sensor the instrumental drift can be an important issue which has to be taken under control through regular control readings from a nearby staff gauge. More details about the necessity of control readings for the determination of time-dependent drift of pressure sensors can be found in Section 3.6.1. Note that a pressure gauge station could include more than one pressure sensor. The concept of a multiple pressure transducer gauge was developed for precise datum control of sea level records by Woodworth et al. (1996). According to this concept one transducer is mounted under water and an additional, called “B” sensor is located at the MSL and fixed relative to the CP of the gauge. An accuracy of a few millimetres is achieved using this method. However, fixing the datum requires tides with water levels that fall below the “B” sensor. Therefore, the viability of this method diminishes in microtidal areas or lakes.

As pressure sensors are compact and consume a very small amount of power, they can be operated from batteries and solar panels for periods of a year or even longer. Therefore, they can be used in remote areas (e.g. on the oceanic islands) and in ice-covered polar regions. Pressure sensors are mainly applied in various scientific studies and monitoring (e.g. tsunami monitoring (Horsburgh et al. 2009) but also in industrial tanks and basins. The accuracy of the single transducer depends on full scale8 (FS) of the pressure sensor and it remains within 0.2…1.0 cm (cf. Section 3.5.).

8 Full scale is difference between the lowest and highest possible measurement point and provides a common term for defining specification parameters such as accuracy errors and overpressure ratings for devices which have many different pressure ranges.

40 3.1.4. Conclusions on usable equipment

In Sections 3.1.1.–3.1.3. seven different types of SLGs for sea level observations were reviewed. Accuracy of ~1 cm can be achieved with most SLGs (cf. Table 2). However, pressure gauges equipped with transducers are distinguished from others, • better determination of sea level accuracy (~0.5 cm); • ease of mounting and use; • small power consumption; • ice-resistance; • relatively low cost.

Therefore, the pressure sensors could be appropriate for precise sea level observations in sub-polar latitudes and areas where no permanent power supply can be established. Note that other SLGs (e.g. acoustic and radar gauges) are high power consumption devices (cf. Table 2); use of batteries in conjunction with solar panels may not be sufficient to ensure their work capacity for a long period. Therefore, deployment of pressure sensors seems to be an appealing choice for hydrodynamic levelling.

Table 2 summarizes characteristics of sea level gauges, including their advantages and disadvantages.

41 *

No No No No No Yes Yes Yes Low Low gauge ~0.3 cm Yes / No Battery or power cable

No No No No No Yes Yes Yes Yes Low Low ~1 cm Power cable

No No No No No No Yes Yes Low mainly ~1 cm Power cable Acoustic gauge Radar gauge Pressure

1 *

No No No No No Yes Yes Yes Yes Low Low ~0.5 cm Battery mainly Total station

No No No No No Yes Yes Yes Yes Low Low ~2 cm GNSS buoy Battery mainly Observation period: days up to week. days up to period: Observation

No No No No No Yes Yes Yes Low Low gauge ~1 cm Battery or power cable

No No No Yes Yes Yes Yes High of the present research. of the ~0.5 cm Staff gauge Stilling-well ~0.5K – 1K ~4K – 10K ~12K – 14K ~12K – 14K ~4K – 10K ~6K – 11K ~1K – 3K carried out with calm weather only. calm weather carried out with Characteristics (IOC 2006) of different sea level gauges. 2006) of different sea level (IOC Characteristics Extra well Power consumption Vertical structure for Affected by waves Affected by ice Low power consumption Time-dependent drift mount Easy to Labour input during

Sea level observations are Sea level observations The accuracy achieved in case studies Table 2. Characteristics of sea level gauge Installation requirements: Accuracy of sea level weather observation in ideal conditions of EURO-s) Cost (thousands Advantages / disadvantages: 1 * supply installation measurements

42 3.2. Principles of hydrodynamic levelling

Obtainable accuracy of hydrodynamic levelling depends on many different factors, e.g.: • connection between MSL and tide gauge benchmark (TGBM); • accuracy of sea level observations; • methodology of processing sea level series; • type of SLG to be used.

An SLG usually comprises a sea level tracking device (e.g. a cm- graduated staff gauge, float, radar, acoustic or pressure sensor, cf. Section 3.1.), data logger, power supply and a communication modem (if applicable). For connecting the SLG to a levelling network the following reference points are needed: tide gauge zero (TGZ), contact point (CP) and TGBM (cf. Figure 6).

Figure 6. Principles of hydrodynamic levelling. The height difference (¨H) is determined between paired contact points (CPA and CPB). Readings of the MSL values ( R A , R B ) are obtained by averaging. Other values are either calculated (heights: H1 , H2 , H A , HB ) or assigned (tide gauge zeros: TGZA and TGZB).

TGZ is a pre-determined point (e.g. a metrical reading on the staff gauge, if such is mounted), with respect to which the sea level fluctuations are measured. In principle, TGZ can be selected arbitrarily. For instance, such a point could be in the middle of the staff (a zero- reading, thus the sea level readings are either positive or negative) or at the bottom of the staff (in this case the readings are one-signed).

43 The CP is a benchmark-type reference mark on the SLG. For the float- type gauges the CP is usually located on the top of the well. For acoustic and radar gauges the CP can be located on the top of the container holding the equipment. For the pressure gauges the CP can be placed on the top of the nearby staff gauge.

In order to connect the TGZ with the national height datum, the vertical

(along the plumb-line) distance between the TGZ and the CP (cf. TA and TB in Figure 6) must be accurately determined. The CP is connected to a nearby (usually up to a few hundred meters from the SLG) TGBM by spirit levelling (cf. Figure 6). The TGBM is usually included into the national levelling network and thus the height of the mainland TGZ can be directly referred to the national height datum. The MSL at a given SLG can then be uniquely determined from the sea level fluctuations with respect to the TGZ. However, the height transfer across a waterway via sea level observations involves more than one SLG. Recall that the TGZ (e.g. bottom of the staff gauge, zero of the float, PG’s initial account) is determined at each SLG independently from other SLGs. In other words, the readings at each SLG are taken with respect to some arbitrary local initial value (i.e. TGZ), which generally is not coinciding with the level surface of the TGZ on the opposite side of the waterway. The solution to the problem of determining height differences between paired sea level stations (more correctly – between respective CPs) can be described as follows.

In hydrodynamic levelling it is important to identify the same level surface that was adopted at the initial SLG. First, at a mainland Station

A (see Figure 6) the CPA height (HA) can be determined precisely by connecting it to TGBMA by spirit levelling. At an island Station B the CPB height (HB) needs to be determined with respect to HA by using sea level observations. Observation equations for determining the heights of the MSL ( H1 and H2 , cf. Figure 6) at paired Stations A and B can be represented as follows:

A H1 (HA TA ) (R TGZ R A ) ƥA (3) and

B H2 (HB TB ) (R TGZ R B ) ƥB (4)

44 where TA and TB are vertical distances between the corresponding CP and TGZ at Stations A and B, respectively (cf. Figure 6). Thus, the first bracketed term on the right hand side of Eqs. 3 and 4 denotes the A B height of the corresponding TGZ. The readings R TGZ and R TGZ correspond to the TGZ location (determined at the installation of the SLG, independently from other SLGs) of Station A and B, respectively. The overbarred symbols denote values obtained by simple arithmetical averaging (of the total number of usable measurements n) over the given time period. The averaged readings R A and R B correspond to the MSL at Station A and B, respectively, i.e.

n i R 1 max R dcorr (5) n ¦i 1 i i

th where Ri is the sea level reading at the i time-epoch of measurements corr and di denotes relevant corrections (e.g. due to the drift of pressure sensors; for a more extended discussion see Section 3.6.1.) at the same instant. Symbols ƥA and ƥB denote a random variable (error of measurements at Stations A and B) with the mathematical expectation A of zero, i.e. E(ƥA ) = E(ƥB ) = 0. Note that the quantities TA, TB, R TGZ , B R A , R TGZ , R B , HA, H1 can be measured directly or obtained from simple averaging. The only unknowns are H2 and HB which need to be determined from solving the system of equations. Subtracting Eq. 4 from Eq. 3 yields:

A B HB H2 (H A TA ) H1 TB (R TGZ R A ) (R TGZ R B ) (6) where the two unknowns are grouped on the left hand side and the values of random measurement errors are henceforth neglected for the sake of brevity of discussion. Recall that in general the MSL does not coincide with an equipotential surface, i.e. the geoid. The height H2 can also be expressed via SST (cf. Figure 6). The height of the MSL at Station B can then be written as (see also Figure 6):

H2 H1 SSTA SSTB (7)

45 where SST A and SSTB are the mean sea surface topography values at Stations A and B, respectively. Now Eq. 6 can be expressed as:

A B H B (H A TA ) TB (R TGZ R A ) (R TGZ R B ) (SST A SST B ) (8)

Certain assumptions need to be introduced in order to determine HB. For instance, the mean SST values can be taken from existing global/regional SST models.

The above principles of hydrodynamic levelling are valid for all types of SLGs. Note that the above expressions are somewhat simplified. More elaborated expressions for hydrodynamic levelling can be found in Cartwright and Crease (1963). A discussion about the applicability of Eq. 8 for the selected study area follows in Section 3.3.2.

3.3. Specifics of the study area

The PG-based hydrodynamic levelling was tested in the Väinameri Basin, which forms an eastern part of the Baltic Proper9. It is a semi- enclosed (surrounded by an arc of islands and the mainland, see Figure 2) and rather shallow water body, with a mean depth of ~5 m. Its area is 2200 km² and includes hundreds of small islets.

The hydrodynamic conditions of the Väinameri are slightly different from the rest of the Baltic Sea – the wave heights are lower, water is less saline, water temperature variations are larger, and the ice cover is formed more frequently and lasts longer. For instance, the water temperature in the Väinameri is under +10 °C for about seven months per year and the ice coverage could last even up to 5…6 months in cold winters. In July and August the water temperature could increase up to +25 °C in the surface layer (cf. Section 3.6.). Väinameri is brackish sea with salinity of 4…6‰, even 2…3‰ at the shoreline. Such low salinity seawater starts to freeze in temperature around -0.3 ºC.

9 The Baltic Proper covers the part of the Baltic Sea without the Gulf of Bothnia, Gulf of Finland and Gulf of Riga.

46 Note that the Väinameri, similarly to the rest of the Baltic Sea, is almost tide-less, since the tides stay below a decimetre level (Raudsepp et al. 1999). Instead, the sea level fluctuations are primarily forced by the wind stress and atmospheric pressure changes. The extreme daily fluctuations of the Väinameri sea level can reach 200 cm (Suursaar et al. 2008), which is usually related to a passing area of low atmospheric pressure10 accompanied by very strong W and SW winds. During unidirectional winds the daily sea level changes may reach ±50 cm (Suursaar 2011). The influence of the wind stress on the sea level, however, is assumed to be rather insignificant when averaged over a longer period (e.g. annual sea level series).

The Väinameri Basin is a rather dynamic water body. The water exchange processes are forced by the nearby Baltic Proper and the Gulf of Riga. The main driver for water exchange and corresponding current speeds in the Väinameri straits is local wind speed and direction. Maximum flow velocities up to 1.0 m/s in the Väinameri straits were measured by Suursaar et al. (2004). Importantly, in the Väinameri the currents can change their direction (even become opposite) depending on the direction and speed of wind. A general description of the current system in the Väinameri is presented by Suursaar et al. (2001). Therefore, considering all the above it is reasonable to expect that when averaged over a longer period the SST in the Väinameri Basin is also insignificant (most likely remaining within 5 cm, if at all). This will be discussed in more detail in the next section.

3.3.1. Considerations of the sea surface topography of the Väinameri Basin

In hydrodynamic levelling the SST values are needed for rigorous determination of across-water height differences. The availability of global or regional SST models could be appealing for use in estimating the SST over the region of interest. For example, Filmer and Featherstone (2012) used 5 different SST models to re-evaluate the Australian Height Datum offset in the island of Tasmania (distance to mainland ~200 km). The tested models were:

10 Atmospheric pressure change 1 hPa = 1 mbar corresponds approximately to 1 cm sea level change.

47 Oceanographic-only: (i) CARS2006 by Ridgway et al. (2002). Geodetic-oceanographic: (ii) Rio05 CMDT by Rio and Hernandez (2004); (iii) GGM02 DOT by Tapley et al. (2005); (iv) GRACE/JPL. Geodetic-only: (v) DNSC08MDT by Andersen and Knudsen (2009).

Discrepancies up to 14.5 cm between the results based on different SST models were detected (cf. Filmer and Featherstone 2012). Therefore, the choice of SST model must be made very carefully and in some cases it may even be appropriate to exclude it from the final solution due to poor accuracy of the models (cf. Section 4.2. in paper I).

Nevertheless, for the sake of experiment a satellite altimetry-based SST model DTU10MDT (Mean Dynamic Topography model) by Andersen (2011) was tested for this study. The model DTU10MDT has been obtained by combining the Mean Sea Surface model (DTU10MSS) and the global geoid model based on the Earth Gravitational Model EGM2008 (Pavlis et al. 2008, also Pavlis et al. 2012). The model DTU10MSS has been derived from 17 years of data from the European Remote Sensing (ERS) and Environmental Satellite (ENVISAT) altimetry missions. The model accuracy is estimated to be ~10 cm in the Baltic Sea (O. B. Andersen, pers. comm., 2012). The MDT model used has a resolution of 1 arc-minute, which corresponds to 1.8 km by 0.9 km cell size within the study area. The DTU10MDT- derived mean SST values ( SST DTU10MDT) are shown in Table 3, column 8. SST differences (ƅSSTDTU10MDT) within the PG pairs (3 across-water and 3 land-connected sections; see Figure 2) are originally presented in paper I, Table 2. The across-water and land-connected ƅSSTDTU10MDT remain within ±1 cm and ±2.5 cm, respectively. Even though the across-water and land-connected SST differences appear to be more or less comparable with the expected accuracy of the hydrodynamic levelling, the absolute SST values within the study area are dubious.

2010 2011 and SST SST between Difference Difference )) are )) are

ƫ 3 , ƶ 2011

in 2011 2011 in GNSS- derived SST mean SST

3 2010

in 2010 GNSS- derived SST mean SST

2 )) and geoidal height (N( height geoidal )) and Appendix D). ƫ , ƶ

DTU10MDT SST 0.076 -0.095 -0.026 -0.069 -0.069 -0.026 -0.095 0.076 -0.070 -0.024 -0.094 0.072 -0.105 -0.022 -0.127 0.048 -0.105 -0.004 -0.109 0.038 -0.097 -0.057 -0.154 0.047 -0.097 -0.006 -0.103 0.052 Model based mean SST DTU10MDT ) mean sea surface topography at the locations of at sea surface topography ) mean

T 1.797 1.797 1.796 1.099 1.718 1.641 1.578 Vertical Vertical distance and TGZ DTU10MDT between CP SST ), geodetic height of CP (h( ), geodetic height

1 ) ƫ , 2011 msl ƶ T 20.453 20.459 20.510 20.448 20.386 20.410 model N( GRAV- from the , GEOID2011 Geoidal height 2010 msl T

) ƫ , ƶ CP h( height of Geodetic

and and

2011 msl T 2010 msl between T Difference Difference ) and the DTU10MDT model-based ( model-based the DTU10MDT ) and 2011

SST 2011 msl , was used, respectively. T Vertical Vertical distance between MSL and CP in 2011 in CP 2010 calculations. Unit is metre. calculations. 2011 msl T 2011 SST

and SST 2010 msl 2010 msl 1.898 1.829 0.069 22.256 22.256 0.069 1.829 1.898 22.262 0.070 1.827 1.897 21.627 0.105 1.139 1.244 22.202 0.105 1.758 1.863 21.992 0.097 1.663 1.760 22.004 0.097 1.600 1.697 T Vertical Vertical T distance between MSL and CP in 2010CP and and 2010 SST GNSS-derived( 1 2 3 4 5 6 7 11 8 10 9 Sõru Triigi Virtsu Virtsu gauge pressure pressure Kuivastu Rohuküla Heltermaa Location of 23º30'29.1''E 23º23'36.6''E 22º43'02.1''E 22º31'18.9''E 23º02'47.6''E 23º25'29.3''E 58º34'34.0''N 58º34'27.0''N 58º35'29.2''N 58º41'28.6''N 58º51'59.0''N 58º54'17.6''N For better comparison a 40 cm offset was removed from gravimetric GRAV-GEOID2011 model (for more details see the text below and For better comparison a 40 cm offsetremoved was from the global SST model DTU10MDT. Computed by Eq. 9. used for used for installed pressure gauges. Vertical distance between MSL and CP ( and MSL between distance Vertical gauges. installed pressure Table 3. 1 2 3

49 Alternatively, the mean SST value ( SST (ƶ, ƫ)) at an SLG (with the geodetic coordinates ƶ and ƫ) can also be estimated from GNSS measurements in conjunction with a precise regional geoid model by using the following formula (cf. Poutanen 2000):

SST (ƶ, ƫ) = h(ƶ, ƫ) – N(ƶ, ƫ) – Tmsl (9) where h(ƶ, ƫ) is the geodetic height of the CP (obtained from GNSS measurements), N(ƶ, ƫ) is the geoidal height and Tmsl denotes the vertical distance between the MSL reading R and the CP (cf. Figure 6).

The first two terms on the right hand side of Eq. 9 can be considered to be “static” components of the SST. In this study the following two datasets were deployed for computing SST by Eq. 9: (i) The geodetic heights h(ƶ, ƫ) of the CPs were obtained (cf. Table 3, column 5) by using the nearby II order points of the Estonian National Geodetic (GNSS) Network. The GNSS measurements on these points were carried out in 1997 with dual-frequency GPS receivers Ashtech Z-XII. The GNSS sessions lasted 24 hours (4 x 6 hours). The Bernese software was used for data processing and the accuracy of the height component was estimated to be 5…10 mm (Rüdja 2004). During the renovation of the ENLN each PG was connected to a nearby national geodetic point by precise levelling. Due to relatively short connections (mostly <6.5 km) the levelling errors are presumably not significant. (ii) Geoidal heights N(ƶ, ƫ) at each PG were computed by using a recent regional gravimetric geoid model GRAV-GEOID2011 (Ellmann et al. 2011), cf. Table 3, column 6. This model has been computed by the least-squares modification of Stokes’s formula, whereas a GOCE-satellite (Gravity field and steady-state Ocean Circulation Explorer) based geopotential model was used as the reference. The resolution of the GRAV-GEOID2011 model is 1' x 2' (1.8 km x 1.8 km) and its accuracy has been estimated to be ±1.3 cm on the mainland of Estonia (Oja et al. 2011).

The remaining term ( Tmsl ) in Eq. 9 may change its value depending on the MSL value for the selected time period. In other words, if for some reason (e.g. due to slightly different direction of dominating winds)

50 there appear to be differences in the annual MSL values, then the value of the corresponding SST changes accordingly. Interestingly, the 2010 and 2011 sea level series demonstrate that within the given study area year-to-year differences in Tmsl may reach a dm range. Therefore, this yields changes in SST “absolute” values as well. Hence, several years (decades) of sea level series are preferred to accurately determine the SST absolute value at locations of interest.

2011 Note that within the study area Tmsl (for 2011) is on average 9 cm 2010 smaller than Tmsl (for 2010) (cf. Table 3, column 4). Thus, the MSL in 2011 was 9 cm higher than in 2010. Note that this agrees with O. B. Andersen’s estimation for DTU10MDT absolute accuracy as well. Note that large discrepancies (from 7 to 10 cm, on average 9 cm, cf.

Table 3, column 11) between the SST 2010 and SST 2011 values were detected at this study sites. This could be caused by annual variability of meteorological and hydrological conditions. Recall that annual sea level changes are mainly caused by precipitation, ice and snow conditions in winter, river runoff and water inflow from the North Sea to the Baltic Sea, i.e. a steady wind over the Nordic area could change the distribution of water between the North Sea and the Baltic, altering the entire Baltic Sea level (cf. Ekman 2009). The meteorological and hydrological information encompassing the Baltic Sea should be analysed to detect the exact influence on the 9 cm sea level rise in 2011. This is outside of the scope of this study; factors influencing the (temporal) changes of annual averaged sea level will not be explored further here.

Next, by plotting the annual SST values at six SLG stations a westward downslope can be detected in the study area (cf. Figure 7), especially between Rohuküla and Heltermaa, where the downslope is about 1 cm per 4 km. Recall that currencies are affected by winds in the Väinameri Basin (cf. Section 3.3.). Therefore, dominantly northbound currents through the strait between Rohuküla and Heltermaa could carry water against the mainland coast and thus could have caused the detected slope of the sea surface.

A B Figure 7. GNSS-derived mean sea surface topography (SST) in the Väinameri Basin in 2010 (A) and 2011 (B). Note that the SST could also be affected by possible systematic errors in the gravimetric GRAV-GEOID2011 model. SST contour interval is 2 cm.

On the other hand, the SST also depends on the quality of the underlying gravimetric geoid model. This seems to be a more likely explanation for the virtual slope of the sea surface. Note that the coverage of the terrestrial gravity data used for the regional geoid model computation is quite heterogeneous (Ellmann et al. 2011, Figure 1) within the Väinameri region and in its vicinity. More specifically, geoid modellings over the West-Estonian Archipelago are mostly influenced by two independent datasets, which cover the immediate vicinity of the study area. Quite dense historical gravity data are available over the dry land, whereas over marine regions the data originate from the international Baltic Sea 1999 aerogravity survey (Forsberg 2001). Thus it cannot be excluded that possible discrepancies between these datasets may cause artificial tilt in the used regional geoid model. Therefore, additional verifications of the gravimetric GRAV-GEOID2011 model were carried out in the Väinameri Basin by using profile-wise GNSS, ALS and SA measurements to study the hypothesis. Some uncertainties (up to 4 cm) were detected in the regional geoid model near Heltermaa using profile-wise GNSS and ALS measurements. The verifications and the results are described in more detail in Appendix D.

As a consequence, the disagreements between the GNSS-based SST

(ƶ, ƫ) and the global SST DTU10MDT (see Table 3, columns 8–10) could be due to several reasons. First, the used DTU10MDT model is global and therefore it would be too optimistic to expect revelation of high- resolution specifics over the Väinameri. Second, the regional gravimetric geoid model could include systematic errors in the marine

52 area as the verifications indicated (cf. Appendix D). Unfortunately, no specially designated high resolution SST model for the Väinameri exists to present knowledge. As discussed in Section 1.1.5., this would require time consuming and very laborious efforts, which are not feasible within the framework of the present study. However, in hydrodynamic levelling the SST differences in a relative, rather than in absolute sense (cf. last term in Eq. 8) are of interest. Note that the relative differences between SST 2010 and SST 2011 were almost constant in the across-water PG pairs (cf. Table 3, column 11). In this situation, disregarding the computed SST (ƶ, ƫ) (both the GNSS-derived and global SST model- based) values could be safer, since their involvement may yield errors exceeding the range of the PG errors. Therefore, the absolute SST values are neglected from hydrodynamic levelling calculations (cf. Eq. 8) (see also next section).

3.3.2. Determination of height differences in the study area

As discussed in previous sections, for a relatively small and semi- enclosed water body, such as the Väinameri Basin, it could be safer to assume that SST A =SST B. Also, within the Väinameri the station-to- station differences in gravity, temperature and salinity are also negligible for the purpose of height transfer (cf. Section 3.3.). Subsequently, the height determination for the across-water Station B

(CPB) (cf. Figure 6 and Eq. 8) can be further simplified to:

A B HB (H A TA ) TB (R TGZ R A ) (R TGZ R B ) (10)

A warning is due here. The adopted simplification holds only for sufficiently long (at least a year’s duration) data series, in order to filter out or minimize the seasonal component of the water circulation. This simplification cannot be used unconditionally for any area of interest, especially when the hydrodynamic levelling is proceeded over a sea, across an ocean, or in areas with complicated hydrodynamic conditions. Instead of simplified Eq. 10 a more rigorous Eq. 8 must be used in those regions.

Thus Eq. 10 can be used to determine the height of the island TGBMB (e.g. at Kuivastu, see Figure 2), which then serves as initial height for

53 island (spirit) levellings. For this the corresponding height difference

(ƅHAB) between across-water CP pairs (e.g. here Virtsu–Kuivastu, whereas the HA of the Virtsu CP is assumed to be assigned) is computed by (cf. Eq. 10):

A B H B H A ƅH AB TB TA (R TGZ R A ) (R TGZ R B ) (11)

The Väinameri loop (total length 253 km) comprises 3 across-water (clock-wise Virtsu–Kuivastu, Triigi–Sõru, Heltermaa–Rohuküla) and 3 land-connected sections (Kuivastu–Triigi, Sõru–Heltermaa, Rohuküla– Virtsu), see Figure 2. Note that the across-water and land-connected sections alternate. Accordingly, the height of the subsequent one (HC) can be passed by spirit levelling from CPB to CPC (i.e. from Kuivastu to Triigi). Therefore, the height of Triigi CP is:

HC = HB + ƅHBC (12)

where ƅHBC is the spirit levelled height difference between Kuivastu and Triigi. Now, HC serves as initial height for determining across- water HD (i.e. for Sõru in this study) by Eq. 10.

Different types of SLGs (cf. Section 3.1.) can be used for determining readings R in Eq. 10. However, automatic tide gauges equipped with pressure sensors seem to be the most suitable to use in Estonian conditions (see Section 3.1.4.). Therefore, piezoresistive and capacitive pressure gauges were chosen and set up around the Väinameri Basin. Accordingly, the next sections review the main characteristics of piezoresistive and capacitive pressure sensors that were used in this case study.

3.4. Water level registration with piezoresistive and capacitive pressure gauges

The focus of this study is on the usage of pressure gauges (cf. Section 3.1.3.). The main emphasis is on the piezoresistive and capacitive measurement technologies. These are the force collector-type pressure sensors, which measure the pressure force changes caused by the stress

54 of the column of water above the sensor. Usually there is also a compensation mechanism (a.k.a. vent tube) to account for variations of the atmospheric pressure on the diaphragm. The default output of the PG could be both pressure values and the water column height in units of length (cm), cf. Eq. 2.

PGs are generally accurate SLGs. However, they are sensitive to some external factors that could cause problems in their proper operation or even damage the PG. According to Freeman et al. (2004) the main problems associated with PGs are as follows: (i) Water leaking into the housing, which can be prevented by using welded seals, O-ring seals, potted electronics and soldered contacts. (ii) Water freezing in the transducer could rupture the diaphragm. Therefore, the transducer should be set to the depth below the ice formation level to avoid its freezing. (iii) The transducer’s overpressure caused by strong pressure waves through the water column, which could rupture the diaphragm as well. This problem is solved by using PGs with a wider pressure range. (iv) The small-diameter vent tube is susceptible to blockage by the moisture accumulation in the tube. The moisture barrier is used at the end of the vent tube to keep the air in the vent tube dry.

Note that all the mentioned drawbacks were taken into account by choosing and setting up the pressure sensors in this study (T. Kõuts, pers. comm., 2012) (cf. Section 3.5.). However, PGs are also affected by time-dependent drift caused by possible congestion of the sensor’s diaphragm or by a change of rigidity of the diaphragm. Therefore, time-dependent drift is discussed in more detail in Section 3.6.1.

Transducers with piezoresistive technology Piezoresistive technology has been used in pressure sensors since the 1960’s. The operational principles of piezoresistive pressure sensors are based on the ability of silicon crystals, polysilicon thin film, bounded metal foil or sputtered thin film to generate an electrical charge when it is mechanically pressured by the weight of the water column above.

The advantage of piezoresistive technology is wider pressure measurement scale than that of capacitive sensors (cf. Section 3.5.).

55 Therefore, it is suited to measure both low and medium pressures. An exhaustive review of pressure sensors can be found in Bao (2000).

Transducers with capacitive technology The capacitive PG technology was developed in the 1980’s. A simple description for capacitive technology is given by Bao (2000): “The capacitive pressure sensor consists of a silicon chip with an etched thin diaphragm that is hermetically bonded to a glass plate face-to-face by electrostatic bonding. The diaphragm serves as one electrode of the capacitor and the other electrode is a metal film attached to the glass under the cavity. The distance between the two electrodes is a few microns which is controlled by the shallow cavity etch on the front surface of the silicon or ceramic wafer.” Thus, the capacitive sensor uses a diaphragm and pressure cavity to create a variable capacitor to detect strain due to applied pressure. This technology is better suited for low pressures.

3.5. Set up of pressure gauges and data acquisition

The design and construction of six installed PG stations was performed by the MSI, Dr. Tarmo Kõuts as project leader. The project itself was initiated and funded in 2009 by the Estonian Land Board, to validate a method of high frequency sea level measurements for transferring of heights from the mainland to the islands. These PG stations are equipped with piezoresistive Keller 36XW or capacitive Keller 46X sensors (see Figure 8 for their appearance and Table 4 for their characteristics, cf. Section 1.2.2.). Two different sensor types were used based on recommendation from manufacturer Keller AG Ltd to compare performances of these sensors. Note that SLGs with Keller 36XW were installed about one year earlier than Keller 46X (cf. Table 5). The latter sensors were selected with more sensitive FS (cf. Table 4). For both sensor types, the accuracy of the water column height is ±0.1% of FS pressure range. In units of length this corresponds to ±1.0 cm and ±0.3 cm for Keller 36XW (FS is 1000 mbar) and Keller 46X (FS is 300 mbar), respectively. Variations in atmospheric pressure are compensated using sensors of relative pressure and leading the atmospheric pressure to the other side of the diaphragm through a special capillary vent tube (combined with the power and signal cable, cf. Figure 8).

Figure 8. Pressure sensors Keller 36XW (sub-plot A) and Keller 46X (sub-plot B). Note the capillary vent tube/power cable at the back of the sensor for compensating variations in the atmospheric pressure. Photos: Keller AG Ltd

Table 4. Characteristics of the Keller 36XW and Keller 46X pressure sensors. Pressure sensor Keller 36XW Keller 46X Type Piezoresistive Capacitive Length (mm) 121 44.5 Diameter (mm) 22 38 Full scale (FS) pressure range 1000 300 (mbar) Accuracy ±0.1% FS ±0.1% FS (in units of length) (±1.0 cm) (±0.3 cm) Compensated temperature 0…50 °C 10…50 °C range Operating temperature -20…80 °C 0…80 °C Iceproof Yes No The characteristics presented in the table are based on the specifications by Keller AG Ltd as typical specifications.

57 of staff Height difference gauge (m) and the top and the between CP the autor of c (m) (m) 5 Height between difference point ision control levellingsision control pier check- TGBM and

4 pendix A) were carried pendix out in nus TGBM. nus TGBM. (m) -1.004 -1.073 -0.017 -1.664 -1.273 -0.016 -1.099 -1.066 -0.024 -0.756 -0.350 -0.018 -1.646 -0.888 -0.021 -1.692 -1.131 -0.018 TGBM Height and CP between difference eved with high prec eved with high

a a a c c c c b b b b b

CP r of Geodesy (cf. Ellmann 2010) and Precise between levellings 12.02.2009 13.02.2009 12.02.2009 07.03.2012 07.07.2011 07.03.2012 06.03.2012 20.05.2010 20.05.2010 19.05.2010 19.05.2010 20.05.2010 TGBM and

in km) 3 (0.52) (0.27) (0.42) (0.26) (0.11) (0.13) TGBM TGBMs and CPs were achi Reference number of (distance to CP TUT. Height difference: check-point mi TUT. Height difference: check-point at the level on the zero Reading of staff gauge installation different benchmarks not included in the new ENLN, see Ap Tallinn University of Technology (TUT) Chai b (m) 3.000 3.000 1.220 2.685 1.220 PR8118 1.610 3.000 SR294 3.000 1.300 PR8851 1.380 SR8797 SR8704 3.000 1.440 SR8148 gauge of staff Length

ed to all stations in May 2010 by in May 2010 stations all ed to (1) (1) (1)

(2) (2) (2) Planserk AS, type Used Keller Keller Keller a sensor levellings (but using pressure 36XW 36XW (amount) 36XW Keller 46X Keller 46X Keller 46X height differences (CP minus TGBM) between differences (CP minus TGBM) height Figure 9) were mount coordinates 23º30'29.1''E 23º23'36.6''E 22º43'02.1''E 22º31'18.9''E 23º02'47.6''E 23º25'29.3''E The WGS84 58º54'17.6''N lumn 8) performed by 1 In since 01.2009 58º34'34.0''N 01.2010 58º34'27.0''N 01.2010 58º35'29.2''N 02.2010 58º41'28.6''N 10.2008 58º51'59.0''N 01.2009 operation Characteristics of pressure gauge stations installed around the Väinameri Basin. around stations installed gauge pressure of Characteristics 1 2 3 4 5 6 7 8 9 10 11 10 9 6 7 8 5 4 3 2 1 name Station (see levellings dates in co this study. Note that several technical control this study. Note that several technical control 2008–2012Institute (MSI) as well. by the Marine System PG ceased to work in April 2012. PG ceased to work in included Levelling Network (ENLN). Tide gauge benchmark (TGBM) to the new Estonian National 9). Figure (cf. of staff gauge top the on point CP is a contact (variations within 1 mm) same Almost the The on the pier check-points (cf. Table 5. Virtsu Kuivastu Triigi Sõru Heltermaa Rohuküla 1 2 3 4 5

58 The water temperature is determined by an internal temperature sensor which ensures automatic temperature compensation of the sensing cell. The algorithm of temperature compensation is described by Vetterli (2012). All pressure sensors were individually calibrated by the manufacturer; the calibration data matrix is stored into the Electrically Erasable Programmable Read-Only Memory of each sensor and used until new calibration data is inserted. The microprocessor of the PG in operation receives pressure from the sensing cell and temperature from the PT100 thermocouple and calculates the pressure value by solving the calibration data matrix. In order to keep the specified accuracy, the manufacturer recommends repeat calibration once a year. Within the compensated range the pressure values take into account the thermal expansion of the piesoresistive crystals and the capacitive diaphragm. Note that the compensated range is different for Keller 36XW and Keller 46X (cf. Table 4). For the Keller 46X, the minimal operating and compensated temperatures are 0 °C and +10 °C, respectively. More detailed discussion and examples about the influence of water temperature to PG readings are provided in Section 3.6.

However, both types of pressure sensors are suited for using in harsh environmental conditions (e.g. under ice), and due to their low power consumption can be operated just on a battery and a solar panel. The power consumption depends also on the data sampling interval, which can be set from a few minutes to hours.

All six PG stations around the Väinameri Basin (cf. Figure 2) have been in operation simultaneously for more than two full annual cycles (2010 and 2011) (cf. Table 5). Only the Rohuküla station ceased to work in April 2012. Note that the Virtsu, Rohuküla and Heltermaa stations were equipped with the Keller 36XW sensors; the Kuivastu, Triigi and Sõru stations were equipped with the Keller 46X sensors. The sensors were duplicated in Kuivastu, Triigi, Sõru stations (cf. Table 5). The duplicate sensor was mounted at the height of ~50 cm from the bottom sensor (cf. Figure 9). These concurrent sensors were foreseen as back-up to ensure that the PG continues to collect sea level values if the main (lower) sensor should malfunction. The twin sensor system can be used for studying sea water density variations as well. However, it should be noted aright that the PG sea level series appeared to be too noisy to detect such small scale variations (see Section 3.6.).

Figure 9. Typical set up of a pressure gauge station used in this study. Note that the pressure sensor(s) are mounted on the backside of the staff gauge (in the right-hand figure). Photos: MSI

Each installed PG station in this study consists of an individually calibrated pressure sensor attached to a 3 m long staff gauge11. The sensor was mounted on the backside of the staff gauge at the depth of ~1.3 m (~0.8 m for duplicate sensor) below the average water level (see the initial zero level on the staff gauge in Table 5, column 6). Note that the cavities were carved into the wooden staff gauge for accommodating the pressure sensors and capillary vent tube/power cable (cf. Figure 9). The staff gauges with sensors were securely fastened to a pier. The front side of the staff gauge is a cm-graduated scale, which allows determining the sea level reading visually at any arbitrary instant. To allow precise levelling, a round-head contact point was welded to the top of its metallic frame (cf. Figure 9). Note that an additional check-point was mounted on piers by Tallinn University of Technology’s (TUT) in May 2010 to check their vertical stability (cf. Figure 9). A separate protective box containing a data logger, a modem and power supply was placed close to the staff gauge, and a solar panel was mounted at each PG (cf. Figure 9).

11 As an exception, due to shallow waters in the harbour the length of the Triigi staff gauge was reduced to 2.685 m (cf. Table 5, column 5).

Sea level readings (cf. Water Level [cm] in Table 6) in all PGs are taken every 5m during a 30s time span, i.e. 12 times per hour. The measurement frequency is 4 Hz, thus the water column height for each 30s epoch is computed by averaging 4 x 30 measurements. The resulting single value represents the entire 30s long observation epoch. Thus, 12 x 24h = 288 averaged readings can be obtained daily at each PG. Note that all sea level readings in the raw data file are given with respect to the initial TGZ12 defined on the staff gauge (cf. Table 5, column 6) at the time of installation.

Additionally, some basic parameters: water temperature (Water Temp [deg]), maximum and mean wave height (Max Height [m] and Mean Height [m]), wave period (Mean Period [s]) are also calculated from raw data and recorded (cf. Table 6). The file holds technical information concerning the battery voltage feeding the station (Battvolt [V]), GSM signal strength (Signal strength [dBm]) and the code of the GSM service provider (Current provider). All the observation data are transmitted in real time into the central database using GPRS (General Packet Radio Service) protocol and stored on a memory card as backup at the station.

The raw 2 x 12 month (2010 and 2011) PG data (and the staff control readings for each station) for the present study were obtained from Dr. T. Kõuts, MSI. Note that the water level readings in the raw data files (cf. Table 6) are not drift-corrected, i.e. the drift corrections detected by visual control readings from the staff gauge (see the discussion in Section 3.6.1.) are not saved into the raw files. The principles of processing sea level series are described in next section.

12 A note of warning should be given for using such PG data for other applications (e.g. determining rigorously sea level heights for any given instant at a station). The TGZ heights were initially determined (essentially, an attempt was made to define the staff reading, which would correspond to the 0-height) by the MSI from nearby benchmarks, which have heights in the Baltic Height System 1977 (BK77) catalogues or in the ELB digital database. Unfortunately, the used benchmarks belong to lower (III) order Soviet levelling network or they are the III order GNSS geodetic points. None of them are included in the new ENLN. Due to the use of such benchmarks, errors in historical data and land uplift in the obtained TGZ heights are suspected to be inconsistent. This is confirmed by differences (from -1.3 cm up to -4.3 cm) between initially determined TGZ heights and that of obtained from the hydrodynamic/land-connected levelling loop adjustment. Appendix A provides guidance for transforming the acquired raw PG data to the same (arbitrary) height system.

61 Table 6. Extract from the raw data file recorded by pressure sensor.

Water level readings are given with respect to initial tide gauge zero (TGZ) on staff gauge (cf. Table 5 and Appendix A) at the installation. Note that raw water level readings are not drift- corrected in the data files. Drift corrections are added during data processing. Wave height and period is characterized in columns Max Height, Mean Height and Mean Period. Battvolt indicates the battery voltage feeding the station. Signal strength is GSM (Global System for Mobile Communications) signal strength. Current provider denotes the GSM service provider.

3.6. Processing sea level series

For reliable hydrodynamic levelling results the sea level measurements should be performed over an adequate time period to filter out data blunders and obtain statistically meaningful results. As a working hypothesis an annual water cycle period is assumed to be sufficient for achieving geodetic accuracy for hydrodynamic levelling. To prove the hypothesis, several verifications are carried out in Sections 4.2.– 4.4. The internal precision can be revealed by comparing the hydrodynamic levelling results of two subsequent (annual) results. The applied data processing principles are explained below.

First, the sea level series from twin sensor stations (Sõru, Triigi, Kuivastu) were analysed to determine the stability of the sensors. The drift corrections (see Section 3.6.1.) for both sensors were taken into account before comparison. As the physical distance between two sensors is fixed (cf. Figure 9), the difference between readings (i.e. water column height) must be constant (~50 cm) within the measurement noise as well. The differences between two sea level readings (upper minus lower sensor) are presented with black dots in Figure 10. Note that on a few occasions the 2010 deviations from the expected constant (~50 cm) peaked up to 10 cm in Triigi, whereas up to 5 cm in Sõru and Kuivastu (see Figure 10).

62 A sudden increase of height differences was observed in Sõru and Triigi stations in summer 2011 (see Figure 10). Curiously, this is correlated with maximum water temperature (+25 ºC) (cf. light grey dots in Figure 10) in the West-Estonian Archipelago. There is no clear explanation, but it is possible that the warm water could cause a proliferation of algae that could somehow congest the sensor’s diaphragm.

Figure 10. Differences (black dots) between the readings of two Keller 46X sensors (upper minus lower) in Sõru, Triigi and Kuivastu. Light grey dots denote the water temperature measured by the lower sensor. Dark grey dots denote the differences of water temperature measured by upper and lower sensor. Note that a different vertical scale is applied for the Sõru graph.

The temperature differences (see dark grey dots in Figure 10) between twin sensors reached up to 5 ºC in summer due to intense sunshine warming the upper layers of water. Note that the larger temperature differences coincide with a general increase of water temperature, soon

63 followed by unreasonable differences (reaching up to 90 cm) between the sea level readings in Sõru and Triigi in July 2011. The water temperature (light grey dots in Figure 10) and temperature differences between twin sensors (dark grey dots in Figure 10) have been more stable (with an exception, though13) in winter-time: the Väinameri Basin is usually covered by fast ice from December to April.

All in all, the influence of water temperature on the PG reading was revealed by twin sensor analysis. Warm water promotes the proliferation of algae, which may congest the sensor’s diaphragm and could cause rapid increase of the PG drift trend. Therefore, use of pressure sensors for long-term sea level observations could be challenging. Alternatively, pressure sensors should be cleaned at least once a year. Cleaning requires the removal of the staff gauge and therefore the connection with previous measurements must be carried out meticulously. Note that the pressure sensors used in this study were not cleaned due to the relatively short duration of the campaigne. However, cleaning the pressure sensor would not replace the need for staff control readings. Therefore, control readings from a nearby cm- graduated staff gauge were taken to control and calibrate PG readings (cf. Section 3.6.1.).

3.6.1. Detecting time-dependent drift

Many earlier studies (e.g. Chiswell and Lukas 1989, Testut et al. 2006, Polster et al. 2009, Horsburg et al. 2009) note the occurrence of time- dependent drift for pressure gauges, e.g. deep-ocean bottom and sea surface pressure sensors. All PGs are inclined to possess drift over time. The drift could be affected by temperature fluctuations, power supply, sensor leakage, proliferation of algae, concentration of

13 Note that water temperature up to -5 ºC was measured by the lower sensor in Sõru and Kuivastu at the end of January 2010 (see light grey dots in Figure 10). It could mean that the lower sensor was covered with ice (recall that brackish water freezes in temperature -0.3 ºC). Such underwater ice could be caused by low sea level (55…75 cm below the MSL in Väinameri Basin from January 10–28, 2010) in conjunction with continuous easterly winds accompanied by cold air-temperature (-17…-25 ºC from January 20–24, 2010). Such conditions could be favourable for bottom ice formation. For instance, the cold could gain access to the sensor surroundings through the metal frame that holds the staff gauge (cf. Figure 9). However, no remarkable influence on the subsequent sea level readings was detected for the PG station in Sõru. Note that similar conditions and bottom ice formation behind a reservoir dam is described by Devik (1948).

64 microscopic floating particles in the water and/or other marine or environmental processes that might cause inaccuracies in water level readings. Note that most of the mentioned factors can be eliminated or minimized (cf. Section 3.4.). For instance, the influence of temperature fluctuations on the readings can be minimised by calibration coefficients supplied by the manufacturer. To protect the sensor against marine processes, it may be placed into a plastic/copper jacket (Horsburg et al. 2009). But there are still some factors that could cause the drift and which are impossible to predict precisely (e.g. environmental conditions).

The drift values of pressure sensors could reach up to several cm per year. In order to monitor the drift behaviour, visual control readings from the adjacent staff gauge should be taken as frequently as possible.

The control drift values (di) are detected from the difference of two read readings, i.e. the readings of staff gauge RStaff( t i ) and pressure gauge read read RPG( t i ) at the same instant ( t i ) as follows:

read read di = RStaff(t i ) – RPG( t i ) (13)

Note that in the following data processing the main (lower) sensor sea level readings were initially used. Malfunctioning of the lower sensor in Triigi and the upper sensor in Sõru was noticed in 2011. Therefore, the Triigi data for 2011 in the subsequent data processing originates from the recordings of the upper sensor data.

3.6.1.1. Control readings and estimating parameters of drift trend

The staff control readings were taken at variable intervals – mostly once a month or less frequently in this study. The number of control readings varied from station to station. For instance, 8 visual readings were taken in Sõru in the year 2010, whereas 20 were taken both in Heltermaa and Rohuküla in 2010 (see Table 7). Such differences in the number of control readings were due to limited budget, therefore the most distant stations were visited less frequently (T. Kõuts, pers. comm., 2012). Occasionally stormy weather conditions or the presence of significant waves also disrupted the ability to take control readings with the requested accuracy of ±0.5 cm; in such infavourable cases the control readings were registered with accuracy ±1 cm or less.

In this study the drift of all PG sensors was assumed to be time- dependently linear. Therefore, also in calculating drift corrections for all water level records the drift behaviour was modelled by using linear trend14. First, the linear regression components: slope parameter (a) of the trend line and the intercept (b) values were calculated for every PG as follows:

i i i n max (t read d ) maxt read max d ¦i 1 i i ¦¦i 1 i i 1 i a i i (14) n max(t read )2 ( max t read )2 ¦¦i 1 i i 1 i

i i i i ( maxd max (t read )2 ) maxt read max (t read d ) ¦¦i 1 i i 1 i ¦¦i 1 i i 1 i i b i i (15) n max(t read )2 ( max t read )2 ¦¦i 1 i i 1 i

where n is number of control readings at a PG station, di is obtained th from Eq. 13 and i = 1….imax denotes an i staff control reading at a PG station.

Thereafter the computed parameters a and b were inserted into the corr standard linear regression formula to calculate drift corrections ( di ) for PG series for any given time epoch ti (day from beginning of the calendar year) within the corresponding calendar year(s) as follows:

corr di = ati + b (16)

For visualisation (used also in future computations), the conjoint two- year trendline (separate estimates for the two annual periods can be found in paper IV) was chosen to give a better overview about drift linearity in 2010–2011 (cf. Figure 11, containing also numerical estimates of the regression parameters a and b). Recall that b is the corr intercept in Eq. 16, i.e. the value of di for the first water level reading in the PG at the beginning of observations. Note that theoretically (without the measurement noise of the control readings) the drift correction for the first water level reading is expected to be

14 Nonlinear drift trend cannot be excluded either. For instance, see 4th degree polynomials in Figure 11 (cf. dashed lines). Due to a small number of staff control readings reliable estimation of nonlinearity may be questionable.

66 zero. Nevertheless, a small drift correction (a few millimetres, cf. regression parameters in Figure 11) is obtained even for the moment of installation.

This is due to the fact that the trend line parameters estimated by Eqs. 14 and 15 are constrained by the well-known least square principles: n Ƶ2 min , the sum of the squares of corrections (Ƶ2 ) give a sum ¦i 1 i i which is a minimum for the most likely corrections, where Ƶi is the deviation of the actual control reading from the estimated drift trend line as follows:

read Ƶi (at i b) di (17)

The Ƶi values also allow estimation of the standard deviation (SD) of the obtained annual (or multi-annual) drift trend:

(Ƶ Ƶ)2 SD ¦ i (18) (n 1) where Ƶ is average of the deviations of the actual control readings and n is number of control readings.

Note that the largest discrepancies between actual drift values (di) and drift trend line were detected in Rohuküla and Heltermaa, where the extreme outliers reached 2.3 and 2.0 cm (cf. Figure 11), respectively. In other stations outliers remained at 1.5 cm level. Note that an outlier up to 10 cm was detected in Sõru in November 2011, which was due to stability problems of the upper sensor (cf. Section 3.6.). However, the SDs (cf. Eq. 18) derived from the deviations of the actual control readings (Ƶi ) remain mostly within 1 cm over two years (cf. Figure 11), confirming that the choice of linear drift trend is a reasonable representation of drift values based on actual control readings (di). Thus, the errors caused by control readings and linear drift trend should remain within the accuracy of the PGs (cf. Table 4).

67 the the

f. Eq. 18). The Eq. f. tude of main (lower) of main tude degree polynomials, which in most occasions th derived from the deviations of the actual control reading (c derived from the deviations The differences between the readings of pressure sensor and staff gauge and drift trends. White dots and bordered lines denote denote lines and bordered dots White trends. drift and gauge staff and sensor of pressure readings the between The differences Figure 11. drift trends as 4 denote lines Dashed upper sensors respectively. of control readings and drift trend follow closely the estimated linear trend. Linear regression formulas (cf. Eq. 16) indicate the drift trend direction and magni trend the drift 16) indicate (cf. Eq. formulas regression Linear linear trend. follow closely the estimated and upper (enclosed formula) sensors. Standard deviations (SD) are sensors. Standard formula) and upper (enclosed units of regression parameters and SD are centimetres. are centimetres. and SD parameters regression units of

68 The 2010 and 2011 rates of drift trends and their SDs are separately presented in Table 7 as well (see also paper IV). The trends of Virtsu, Sõru and Heltermaa sensors were more or less stable over two years. The larger changes in the drift trends were revealed for the other three stations (Kuivastu, Triigi and Rohuküla). The drift of the Kuivastu sensor was markedly slowed down during the measurements, i.e. the trend decreased from +4.8 cm/year in 2010 to 0.0 cm/year in 2011. Note that two of the three problematic stations (Kuivastu and Triigi) are equipped with Keller 46X capacitive sensors.

Table 7. The rates of drift trend of pressure sensors (and their standard deviations) based on control readings from staff gauges in 2010 and 2011. Unit is centimetre per year. 2010 2011 Station Number Main Upper Number Main Upper name of control (lower) sensor of control (lower) sensor readings sensor readings sensor from staff from staff gauge gauge Virtsu 18 -2.5±0.81 - 10 -2.3±0.5 - Kuivastu 11 +4.8±0.3 +1.8±0.7 6 0.0±0.6 +0.6±0.8 Triigi 9 +5.6±0.9 +1.4±0.9 8 +2.6±0.5 +1.8±0.4 Sõru 8 +1.2±1.2 +3.2±3.3 6 +1.1±1.0 -8.7±5.5 Heltermaa 20 -0.5±1.1 - 10 +2.3±1.3 - Rohuküla 20 -5.7±1.2 - 13 -4.7±0.9 - 1 The drift trends and their standard deviations are computed by Eqs. 16 and 18, respectively.

Different drift trends in similar environmental conditions may be caused by barnacles and/or algae that may congest the diaphragm of the pressure sensor. This situation is typical for shallow loughs, e.g. such as the Triigi area. Additionally, the condition of the seafloor and the concentration of microscopic floating particles in the water accumulating on the membrane could influence the drift magnitude as well. For instance, the seafloor is soft and muddy at Rohuküla, and the PG is exposed to frequent ferry traffic. Therefore, permanent and intense water and bottom sediment mixing takes place at this station. Although the PG diaphragm is very well protected and sealed, the microscopic floating particles could possibly accumulate on the diaphragm and consequently stimulate the rate of drift. Therefore, it is crucial to determine the drift values accurately and to consider them in further data processing.

69 Additionally, different trend directions were revealed for different PG types (Figure 11). The drift trends of the piesoresistive Keller 36XW appear to be negative (or near zero, see Heltermaa in Figure 11), whereas the capacitive Keller 46X exhibited positive drift trends. Thus, different measurement technologies (piesoresistive and capacitive, Section 3.4.) can react differently to the water column pressure and environmental conditions.

3.6.1.2. Computing the drift-corrected data

The drift-corrected reading (R) for every water level observation (Ri) corr was calculated using Eq. 5. The drift correction (di ) for every observation refers to the conjoint two-year drift trend15 (Eq. 16) and linear regression coefficients in Figure 11. The annual average drift- corrected readings ( R ) were inserted into Eqs. 3 and 4 to calculate drift-corrected MSL heights ( H1 and H2 cf. Figure 6) in a pair of PG stations for 2010 and 2011.

3.6.1.3. Reliability of the estimated drift corrections

In order to analyse the reliability of the estimated drift corrections, the daily averaged values of R A and R B (with and without drift corrections, cf. Eq. 5) were inserted into Eq. 10. A daily estimation of

ƅHAB with and without the drift correction was calculated using Eq. 11. The results are shown in Figure 12 (across-water pairs) and Figure 13 (land-connected pairs). The trends without drift corrections are presented to demonstrate the necessity of control readings and corrections. Clearly, the drift-corrected data series in the across-water

15 Note that instead of the conjoint two-year drift trend (e.g. by Eq. 16) the drift corrections can be computed in between subsequent control readings, i.e. by:

t t read dcorr d (d d ) i i1 i i1 i1 i1 read read t i1 t i1 where di is an individual control reading, i.e. the difference between the reading of pressure read sensor and staff gauge collected in the instant ti . Note that such control-to-control corrections can be used on the assumption that all individual staff control readings are correct. Recall that attempts were made to take the staff control readings with accuracy ±0.5 cm. However they could include random errors caused by weather conditions and/or human errors. Therefore, the conjoint two-year linear trend estimates were preferred and used in this study (cf. Eq. 16).

70 pairs (Virtsu–Kuivastu, Triigi–Sõru and Heltermaa–Rohuküla, cf. Figure 12) indicate improvements over the data series without drift correction. Theoretically, the drift-corrected data series should, in an ideal case, yield a horizontal zero-trend for daily ƅHAB throughout the entire observation period. In reality, however, the actual trend lines of the daily ƅHAB deviate somewhat from the zero-trend, cf. Figure 12 and Figure 13. Note that the following reasons for tilted daily ƅH trend lines cannot be excluded: (i) seasonal tilt of the sea level; (ii) inaccuracy of some control readings. Therefore, additional discussion about drift trends and their influence on the height differences is presented below.

Note that the ƅHAB values are based on the data collected within paired stations (Station A and B, cf. Eq. 11). Thus, the ƅHAB value becomes affected by data (RA and RB) collected at both stations corr (Station A and B) and their drift corrections ( di ), cf. Eq. 5.

For instance, the drift correction by the end of 2010 is +4.8 cm/year in Kuivastu (cf. Table 7). But when coupled with the Virtsu (drift value -2.5 cm/year) then the joint drift of the SLG pair reaches +7.3 cm/year (cf. Table 8), which almost corresponds to the estimated linear trend of uncorrected measurements +7.0 cm/year16 in Figure 12. The detected discrepancy between linear trend of measurements (drift- affected values) and joint drift of paired stations is 0.3 cm/year (cf. Table 8).

In Sõru station, the drift correction by the end of 2010 is +1.2 cm/year, but when coupled with the Triigi station (drift reaching +5.6 cm/year, cf. Table 7) the joint drift influence reaches +4.4 cm/year (cf. Table 8), which more or less corresponds to the estimated linear trend of uncorrected measurements -5.0 cm/year in Figure 12. The detected discrepancy in the trend values is 0.6 cm/year.

16 Note that in reverse direction (Kuivastu–Virtsu) the trend value is the same, but with opposite sign (-7.0 cm/year).

wise movement) the the wise movement) sented in Table 8. sented in Table 8. H) of across-water CPs at the Virtsu–Kuivastu, Triigi–Sõru and Heltermaa–Rohuküla sections (cf. Triigi–Sõru Virtsu–Kuivastu, CPs at the H) of across-water ƅ values are shown for Kuivastu, Sõru and Rohuküla (moving clockwise along the levelling loop). White and black dots denote loop). White and black dots along the levelling Rohuküla (moving clockwise Sõru and values are shown for Kuivastu, AB H ƅ Estimated daily height differences ( differences height daily Estimated trend values are the same, but with opposite sign. Calendar months are denoted on the horizontal axis. Trend statistics are pre statistics are axis. Trend horizontal denoted on the months are Calendar sign. with opposite are the same, but values trend the outcome with and without drift corrections, respectively. In the case of reverse directions (corresponding to counter clock to counter directions (corresponding reverse In the case of respectively. corrections, drift and without with the outcome Figure 12. 11). The Eq.

istics are istics r clockwise . In the case of reverse directions (corresponding to counte (corresponding directions of reverse . In the case H) of land-connected CPs at the Rohuküla–Virtsu, Kuivastu–Triigi and Sõru–Heltermaa sections sections and Sõru–Heltermaa Kuivastu–Triigi CPs at the Rohuküla–Virtsu, H) of land-connected ƅ values are shown for Virtsu, Triigi and Heltermaa (moving clockwise along the levelling loop). White and black dots dots and black White levelling loop). along the clockwise Heltermaa (moving and Triigi Virtsu, values are shown for AB H ƅ Estimated daily height differences ( differences height daily Estimated (cf. Eq. 11). The The 11). Eq. (cf. Figure 13. denote the outcome with and without drift corrections, respectively outcome with and without drift the denote movement) the trend values are the same, but with opposite sign. Calendar months are denoted on the horizontal axis. Trend stat on the denoted months are Calendar same, but with opposite sign. values are the trend movement) the 8. in Table presented

2 010 and Discrepancy aired stations (column 3 minus 3 minus (column aired stations

1 stations 2010 2011 2010 2011 2010 2010 2011

2011 Drift- corrected

2011 Drift- affected measurements (drift-affected values) and jointmeasurements (drift-affected drift of p

2010 Drift- Trend of measurements Trend of measurements Joint drift of paired corrected of paired stations; for more details see text below. see text paired stations; for more details of

2010 Drift- affected 4 minus column 8 for 2011). minus column 8 4 (km) (km) Direct distance computing the joint drift ancy value is calculated between linear trend of 1 10 9 3 4 5 6 7 8 2 Trend of measurements, joint drifts (and their standard deviations) in the paired pressure gauge stations at the end of years 2 years of end the at stations gauge pressure paired in the deviations) standard their (and drifts joint measurements, of Trend stations column 7 for 2010 and Table 7 is the source for Table 7 is The absolute discrep Paired pressure gauge Paired pressure Table 8. Across-water pairs Virtsu–Kuivastu Triigi–Sõru Heltermaa–Rohuküla Land-connected pairs 7 22 +7.0±1.3 +7.3±0.8 -2.3±0.6 -8.2±2.8 -2.7±1.7 -8.1±2.5 -0.2±1.4 -5.2±1.2 +0.3±0.8 +3.0±1.1 +7.0±2.2 -0.6±1.1 Rohuküla–Virtsu 3.0 0.3 Kuivastu–Triigi 0.9 16 +1.5±1.0 0.7 +4.4±1.2 0.6 -2.0±1.3 -5.0±2.0 -0.4±1.3 -2.4±1.3 Sõru–Heltermaa 65 -1.6±1.6 -3.2±1.2 -2.4±0.9 +1.4±1.6 -1.3±1.3 1 +1.7±1.0 1.5 0.9 2 65 1.0 45 +5.5±2.6 +0.8±0.9 +2.6±1.2 +2.2±1.7 +4.1±2.9 +2.7±2.0 1.9 +0.5±2.1 +2.0±2.1 +2.3±1.9 +2.4±1.9 -1.7±1.2 +1.2±1.3 1.2 1.5 1.1 2011. Unit is centimetre per year. centimetre per 2011. Unit is

74 The largest discrepancies occur for the Heltermaa–Rohuküla pair in 2010. The drift correction is -5.7 cm/year and -0.5 cm/year by the end of the observation period at Rohuküla and Heltermaa, respectively (cf. Table 7). The joint drift of paired stations thus reaches -5.2 cm/year (cf. Table 8). The joint drift influence does not match the estimated trend of uncorrected measurements as of -8.2 cm/year in Figure 12. The detected discrepancy in the trend values reaches 3.0 cm/year here. As for the two previous pairs, the variation could be due to measurement uncertainties and/or interpretation of the linear trend of drift corrections. Note that the two largest outliers (2.3 and 2.0 cm) from linear trend lines were revealed in Heltermaa and Rohuküla (cf. Figure 11). It cannot be entirely excluded that some residual trend could be present due to complicated environmental conditions or seasonal tilt (e.g. due to prevailing winds) of the sea level for this longest stretch (22 km) of water to be bridged. Recall that at the conjoint two-year trend estimation its linearity was assumed. Control- to-control or polynomial fit would result in slightly different estimators. Possible subsidence of one (or both) CP(s) during the observation period is unlikely, since the repeated levellings between TGBM and CP (cf. Table 5) did not reveal any significant changes in the heights.

The above discussion also applies to land-connected pairs, especially in 2011, cf. Figure 13, where drift-corrected data improvements are not so significant. Recall, however, that the land-connected Kuivastu–Triigi stations are 65 km apart. Therefore, it could be suspected that the water circulation processes, e.g. waves could cause a time lag between such distant stations.

However, the measurements’ uncertainties could be affected by drift determination, or caused by possible nonlinearity of drift trends. Recall that linear drift trends were adopted in all stations due to too few control readings in some stations (e.g. Sõru in Figure 11). The influence of drift trend on the final height differences (ƅH) could be up to 3 cm (cf. Table 8). However, this difference could be affected by possible water tilt between two stations as well. Therefore, the separate verifications are carried out to specify the accuracy of hydrodynamic levelling. Drift-corrected final height differences (ƅH) are verified in Section 4.3 using the results of hydrostatic, spirit and GNSS-based levellings.

75 3.6.2. Filtering of sea level series

The drift-corrected data were further filtered in order to remove data blunders and gross errors. Recall, that the maximum amount of daily readings was 288 at each PG (cf. Section 3.5.). In practise, the data series may contain gaps and unreasonable peaks. In addition, the data quality could become poor due to stormy weather conditions (e.g. rough waves, extreme atmospheric pressure changes). After drift corrections such disturbed data were removed using a sequence of steps. The principles used for data filtering were as follows.

Firstly, the occurrence of data gap in one station yielded the removal of the same time-epoch from the paired station as well. Such disruptions were mostly caused by battery voltage drops or power outages lasting from several minutes to a few days.

Secondly, the occasional data jumps (defined as a single reading differing from its adjacent readings by some threshold) by 2…6 cm were identified (cf. Figure 14), studied and eliminated. For instance, data analysis revealed that such jumps might be caused by sea vessels manoeuvring close to the PG. In particular, Figure 14 illustrates unfiltered sea level series in the stations of Virtsu and Kuivastu. Indeed, the occurrence of outliers (i.e. prominent data peaks in Virtsu) coincides with the scheduled departures/arrivals of ferries from/to harbours. Thus, in the second stage the filtered initial data were smoothed, i.e. epoch-to-epoch jumps exceeding 2 cm were removed from the data series.

Figure 14. A sample of the ferry-induced data jumps in the Virtsu sea level series on July 5, 2010. For the clarity of the comparison the observations (shifted by a constant -7 cm) in the across-water pressure gauge in Kuivastu are shown as well.

76 Thirdly, specific weather conditions (e.g. unidirectional winds) could cause a temporal tilt in the sea level. Therefore, such data-days with height differences (between the paired stations) exceeding 10 cm (from the annual average) were also removed during the third step. Note that 10 cm is the optimal quantity that enables filtering out large tilts but keeps a sufficient number of data-days for the calculations of height differences.

Recall that the daily sea level changes are usually less than ±50 cm in the Väinameri (cf. Section 3.3.). Hence, the daily sea level changes larger than ±50 cm (i.e. indicating stormy conditions) were filtered out from the sea level series as well.

After filtering the sea level series, up to 30% of the observation days were eliminated (see Tables II and III in paper IV). The largest number of eliminations was associated with the land-connected Rohuküla–Virtsu and Kuivastu–Triigi pairs, both some 65 km apart from each other. It appears that the filtering thresholds are more likely to occur for longer hydrodynamic levelling sections caused mainly by different wind conditions.

77 4. RESULTS, THEIR VERIFICATIONS AND DISCUSSION

4.1. Results of pressure gauge-based hydrodynamic levelling

The drift-corrected across-water and land-connected heights (HB) for each day and the corresponding height differences (ƅH) between CPs were computed by Eq. 10 and Eq. 11, respectively. The averaged daily results were shown in Figure 12 and Figure 13. The yearly averages of 2010 2011 ƅH and ƅH for 2010 and 2011 are presented in Table 9.

Table 9. Hydrodynamic height differences (and their standard deviations) between the pressure gauge pairs. Unit is centimetre.

Hydrodynamic height differences Pressure gauge pair Direct distance 2010 1 2011 (km) ƅH ƅH Across-water Virtsu–Kuivastu 7 1.4 ± 1.1 1.2 ± 0.8 Triigi–Sõru 16 65.2 ± 1.3 64.8 ± 1.3 Heltermaa–Rohuküla 22 -4.0 ± 1.7 -2.9 ± 1.4 Land-connected Rohuküla–Virtsu 65 20.1 ± 1.2 19.1 ± 1.6 Kuivastu–Triigi 65 -68.3 ± 1.7 -68.5 ± 2.6 Sõru–Heltermaa 45 -14.0 ± 2.1 -14.2 ± 1.9 1 The annually averaged results (2010) are highlighted since they are considered to be the most representative across-water height differences obtained from hydrodynamic levelling, see the further discussion below.

Due to the averaging of annual data series, the height differences in Table 9 are related to the middle of the corresponding year, thus to the epochs 2010.5 and 2011.5, respectively.

The hydrodynamic height differences were divided into two groups. The first includes across-water PG pairs (Virtsu–Kuivastu, Triigi–Sõru, Heltermaa–Rohuküla). These three pairs are important for the reconstruction of the Estonian National Levelling Network. The second group consisting of three land-connected PG pairs (Rohuküla– Virtsu, Kuivastu–Triigi, Sõru–Heltermaa) enables studying the

78 performance of hydrodynamic levelling for longer distances (up to 65 km). Note that the environmental conditions could be quite different for such distant locations, although the wind effect can be efficiently minimized by filtering the sea level series (cf. Section 3.6.2.).

2010 2011 The yearly average values of ƅH and ƅH are similar for all pairs. However, the maximal discrepancy between the results remains only within ±1 cm, which corresponds to the specification-based PG accuracy (cf. Table 4). In selecting the final height differences from the two sets in Table 9 the following options can be considered: (i) Adopting either the 2010 or 2011 solution; (ii) Taking the average of the two annual solutions.

For selection, the following aspects should be taken into consideration. Recall that: • More control readings from staff gauges were collected in 2010 than in 2011 (cf. Table 7); • The first year (2010) measurements with Keller 46X sensors appeared to be more stable than in 2011 (see Figure 10); • The stability analyses indicated that, over time, the diaphragm of the PG could have become contaminated with microscopic floating particles, barnacles and/or by a proliferation of algae.

For the reasons stated, the height differences of solution 2010 2010 (ƅH ) could be more reliable and therefore were selected to be the final results of this study (see highlighted results in Table 9). The 2011 alternative height differences ( ƅH ) were used for comparison. The largest discrepancies (~1 cm) between annual solutions refer to the Heltermaa–Rohuküla and Rohuküla–Virtsu pairs (cf. Table 9). Note that Rohuküla station is involved in both pairs, which may indicate some uncertainties in the Rohuküla drift-corrected sea level series. Recall that the largest discrepancy of the estimated drift corrections was detected with reliability analysis in the Heltermaa–Rohuküla pair as well (see Table 8). Still, the average standard deviation for all six pairs remains within ±1.6 cm for distances up to 65 km in both years (2010 and 2011) (cf. Table 9). Comparisons of the standard deviations confirm (as is expected) that the smallest ones are associated with shorter distances (cf. Table 9) where environmental conditions are expected to be similar. Based on the latter results, an internal precision

79 as of ±1.5 cm could be estimated for the present hydrodynamic levelling height differences.

Further, several validations and comparisons were made to control the results and the accuracy of hydrodynamic height differences. To verify the obtained results (cf. Table 9) a series of internal and external validations were undertaken. The two internal verifications were as follows: (i) Short-term “ice-tamed” hydrodynamic levelling; (ii) Hydrodynamic levelling with “thinned” data.

The first experiment used data collected under very favourable weather conditions during 4- and 6-day periods. For such short-term observations, the possible influence of the drift can be neglected. Therefore, these 4- and 6-day sea level observations will be called “drift-free” in the further text. The second experiment was designed to determine the possibility of reducing the data sampling interval without essentially damaging the hydrodynamic levelling results.

The external verifications include the hydrodynamic levelling results with independent hydrostatic, spirit and GNSS-levelling datasets and their combinations. Details of the validations are described in following sections.

4.2. Internal verifications of the annual hydrodynamic levelling results

4.2.1. Short-term “ice-tamed” sea level observations

Recall that the hydrodynamic levelling results (cf. Table 9) were obtained by averaging two sets of continuous 12-month sea level series. Supposedly, such a large amount of data (covering the annual water cycle) should be sufficient for ensuring the geodetic accuracy (±1 cm) of the MSL determination at each PG. On the other hand, the determination of time-dependent drift values may still involve uncertainties (see a discussion in Section 3.6.1.). Therefore, it could be useful to compare the obtained results with those obtained during optimal weather conditions. Apparently, the influence of weather-

80 dependent (wind, waves and atmospheric pressure) sea level fluctuations is minimized with an ice-covered sea surface. Two very calm weather periods in February 2011 (duration 6 days) and March 2012 (duration 4 days) were selected for short-term sea level observations. Note that during these periods the study area was entirely covered with ice. Recall that similar short-term ice hole sea level observations were carried out in the West-Estonian Archipelago in 1940, and in the 1960’s and 1970’s (cf. Section 1.2.1.).

4.2.1.1. “Ice-tamed” observations in February 2011

In February 2011 the Väinameri Basin became covered with a 50+ cm thick layer of fast ice (see satellite image in Figure 15A). The adjacent gulfs (the Gulf of Riga, the Gulf of Finland) were also covered with pack ice and the open seawater was further than 10 km away from the study area. A high pressure continental weather system covered the Baltic Sea entirely during the second half of February. Thus the weather conditions were very stable within the study area from February 20–25, 2011. During this 6-day period the atmospheric pressure was almost the same and changed evenly in all stations (cf. Table 4 in paper I). Therefore, it could be expected that the weather- induced sea level slope between PGs would be nonexistent or minimal. This allowed collecting the so called “ice-tamed” sea level observations at each PG.

A B Figure 15. Ice conditions in the Väinameri and nearby areas on February 23, 2011 (A) and March 4, 2012 (B) as seen on MODIS satellite images. White area between mainland and islands denotes fast ice with thickness 50+ cm, grey area denotes pack ice with thickness at least 10 cm; the darkest area denotes open water. Photos: MSI

81 A field expedition was organized in the middle of the selected period (February 22–23) in order to determine precise control readings at PG stations. At every station the ice was removed from around the staff gauge (cf. Figure 16). The water in ice holes was calm and the control readings from staff gauge were taken visually with accuracy of ±0.5 cm.

Moreover, an EDM device (Disto A6) was mounted on the top of staff gauge17 to track fluctuations of the sea level in the ice holes (see Figure 16). For this a thin (0.2 cm) layer of polystyrene foam was placed in the open water as a reflector.

Figure 16. Sea level observations by electronic distance meter Disto A6.

17 The top of the staff gauge was levelled with respect to CP using spirit levelling (cf. Table 5 and Figure 17).

Figure 17. Height connection between sea surface, contact point (CP) and tide gauge benchmark (TGBM). Electronic distance meter (EDM) is used to determine fluctuations of the sea level and verify the readings of the pressure sensor.

The EDM measurements were carried out simultaneously within each pair of PG stations. In all six stations the sea level was EDM-tracked at least for 1 hour with the data sampling interval 1m. Later on, these EDM control results were compared to the readings of the PG sensors; their discrepancies are presented in Figure 18. Note that the discrepancies remain mainly within ±0.3 cm. The EDM accuracy (±0.2 cm) is slightly better than the sea level accuracy ±0.3 cm and ±1.0 cm associated with the Keller 46X and Keller 36XW sensors, respectively (cf. specification in Table 4). A few larger discrepancies can be explained with differences in the data sampling interval, which for the PG series was 5m and for the EDM one reading per minute.

The EDM control results enabled precise detection of the PG drift values; they were then applied for the duration of the short-term measurements. Accordingly, practically drift-free solutions were achieved for short-term observations even in the PGs with high annual drift (e.g. 5.7 cm/year in Rohuküla and Triigi stations, cf. Table 7, corresponding to 0.16 mm/day only). The drift-free (6-day) height 6day differences ( ƅH ) between the CPs within each pair were computed and then compared with the annual (drift-corrected) hydrodynamic levelling results (cf. Table 10). The discrepancies between the results are presented in Figure 19. Note that the “ice-tamed” drift-free results agree reasonably with the annual results. The largest discrepancy 1.6 cm (note white squares in Figure 19) is associated with the Heltermaa–

83 Rohuküla section. Other discrepancies in across-water connections remain below 1.0 cm. The detected discrepancies in land-connected PG pairs do not exceed 1.0 cm. These comparisons reveal a reasonable agreement between short-term “ice-tamed” drift-free and annual drift- corrected results.

Keller 36XW Keller 46X

Figure 18. One hour (data sampling interval 5m) water level discrepancies between the electronic distance meter (EDM) and the pressure sensor results on February 22– 23, 2011. The zero reference line denotes the EDM results.

84 Table 10. Hydrodynamic height differences based on annual drift-corrected and short-term “ice-tamed” drift-free sea level observations (and their standard deviations). Unit is centimetre. Hydrodynamic height differences Pressure gauge “Ice-tamed” drift-free Annual (the source is Table 9) pair 6day 4day 2010 2011 ƅH ƅH ƅH ƅH Across-water Virtsu–Kuivastu 0.6±0.4 0.7±0.4 1.4±1.1 1.2±0.8 Triigi–Sõru 65.0±0.2 65.0±0.2 65.2±1.3 64.8±1.3 Heltermaa– -2.4±0.5 -3.1±1.6 -4.0±1.7 -2.9±1.4 Rohuküla Land-connected Rohuküla–Virtsu 19.4±0.7 21.8±0.4 20.1±1.2 19.1±1.6 Kuivastu–Triigi -69.2±0.8 -71.7±0.8 -68.3±1.7 -68.5±2.6 Sõru–Heltermaa -13.4±0.3 -12.8±0.6 -14.0±2.1 -14.2±1.9

Figure 19. Discrepancies between height differences based on the sea level 2010 2011 observations with different periods (annual: ƅH , ƅH and short-term: 6day 4day ƅH , ƅH ) and data sampling interval 12h (historical staff gauge-based: 19year 2010 2011 Hand PG-based H, H ). The zero line denotes the results of the annual 12h 12h 12h (2010) hydrodynamic levelling as the reference. The vertical error bars denote the individual standard deviation values of the hydrodynamic levelling results (2010), cf. Table 9.

85 4.2.1.2. “Ice-tamed” observations in March 2012

The second short-term “ice-tamed” (4-day) observation period was selected in March 2012 at a time when the Väinameri Basin was covered with a 20- cm thick layer of pack ice (cf. Figure 15B). The weather was calm over the entire Väinameri area from March 4–7, 2012. However, prior to the field observations, the weather was more variable than in February 2011. Therefore, due to winds before March 4 and the thinner ice cover, the sea surface conditions over longer distances (Rohuküla–Virtsu, Kuivastu–Triigi and Sõru–Heltermaa) were probably not as stable as during the February 2011 campaign.

A field expedition was organized for March 6–7 in order to determine simultaneous precise control readings within pairs of PG stations. As earlier, the control readings in all six stations were taken by using Disto A6 (cf. Figure 18). The 4-day MSL values were calculated from the PG data and thereafter used for hydrodynamic levellings. The comparisons between 4day the results of 4-day “ice-tamed” drift-free ( ƅH ) and annual 2010 2011 hydrodynamic levellings ( ƅH , ƅH ) are presented in Figure 19. The maximum discrepancies (up to 3.4 cm) were related to land-connected pairs (distances up to 65 km). As mentioned, due to winds before March 4, the sea level slope could become more evident over large distances. Note also that the sea surface outside the Väinameri Basin was ice-free in March 2012 (cf. Figure 15B), demonstrating how challenging it can be to catch a suitable time period for short-term “ice-tamed” sea level observations.

The comparisons between short-term “ice-tamed” drift-free and annual drift-corrected hydrodynamic levelling prove that application of linear drift trends is justified for annual observations (cf. discussion in Section 3.6.1.). The annual drift-corrected values yield a similar outcome to drift- free results performed under very favourable conditions. The discrepancies remain mainly within 1 cm (cf. Figure 19), i.e. within the accuracy range of both types of used pressure sensors. However, the results also indicated that short-term sea level observations in calm weather conditions are viable for hydrodynamic levellings only in short distances (up to 20 km). Note discrepancies (black squares) associated with longer distances in Figure 19. The experience of this study indicates that it is complicated to predict favourable conditions for “ice-tamed” measurements. Therefore, annual sea level observations should be preferred for rigorous determination of height differences.

86 4.2.2. Hydrodynamic levelling with “thinned” data

An advantage of a PG is that the data sampling interval can be easily changed. In this study the results obtained with the original data sampling interval 5m were used to validate sea level series with data sampling interval 12h, which is the same interval used for most of the historical staff gauge data in Estonia (cf. Appendix B). In the following experiment discrepancies between high-frequency (originally 5m sampling rate) and “thinned” (12h) sea level series were analysed. The resulting “thinned” data series could be useful for reducing the power consumption of the PG battery, i.e. in polar areas, when the duration of seasonal daylight may not be sufficient for daily recharging of batteries using solar panel. The results may also be useful for estimating the reliability of the historical staff gauge data, when the readings were mostly taken with a 6h or 12h interval.

The 12h “thinned” data were obtained by picking the drift-corrected 6 am (UTC – Coordinated Universal Time) and 6 pm PG readings of the original 5m data18. Thereafter the occurrence of the filtering thresholds was checked and relevant actions taken (cf. Section 3.6.2.). Note that after filtering, the number of 5m data days is 5…8 % larger than that for the 12h data days (see paper IV, Tables II and III). It follows, that data-series with frequent data sampling intervals are less affected by anomalous events in the sea level series. This is also confirmed by the larger standard deviation values of the results obtained for the 12h thinned data (see Table 11).

The results show that the annual mean height differences between 5m h 2010 2011 2010 and 12 data remain within ±0.3 cm (cf. ƅH , ƅH and ƅH12h , 2011 h ƅH in Table 11, where the subscript 12 is assigned for “thinned” 12h data).

18 Recall that the daily height differences ƅH for the PG pairs were obtained by averaging 288 readings of the original 5m data.

87 Table 11. Hydrodynamic height differences (and their standard deviations) based on different data sampling intervals. Unit is centimetre. Hydrodynamic height differences Annual 2010 Annual 2011 Historical staff gauge Pressure gauge 2010 2011 2010 1 ƅH 2011 1 ƅH 19year ² 12h 12h ƅH pair ƅH ƅH 12h original “thinned” original “thinned” (time period) Across-water Virtsu–Kuivastu 1.4±1.1 1.4±1.2 1.2±0.8 1.2±0.9 - Triigi–Sõru 65.2±1.3 65.2±3.3 64.8±1.3 65.0±1.7 - Heltermaa– -4.5±3.6 Rohuküla -4.0±1.7 -4.3±2.0 -2.9±1.4 -3.1±1.5 (1956–1975) Land-connected 22.8±3.5 Rohuküla–Virtsu 20.1±1.2 20.0±2.0 19.1±1.6 18.9±2.3 (1966–1985) Kuivastu–Triigi -68.3±1.7 -68.1±3.8 -68.5±2.6 -68.3±3.5 - Sõru–Heltermaa -14.0±2.1 -14.3±2.6 -14.2±1.9 -14.3±2.3 - 1 The source is Table 9. 2 The results are based on the 19-year-long daily sea level series. The results include land uplift corrections (-0.2 cm for Heltermaa–Rohuküla and -1.4 cm for Rohuküla–Virtsu) from Figure C2 in Appendix C.

All in all, there is a surprisingly good agreement between 5m and “thinned” (12h) data, suggesting that the study knowledge can be applied to SLGs to reduce their daily power consumption. For instance, it could be useful in polar areas without stationary power supply, where solar panels are required for re-charging batteries. Note that sea level observations in polar areas have become more important due to the melting polar ice and sea level rise. Therefore, the knowledge gained from this study could be useful and applicable in that context. However, the experiment was carried out in almost tide- less conditions. Presumably, the more frequent data sampling interval (e.g. 1h) should be preferred in areas with significant tides.

Additionally, relying upon the good agreement between 5m and “thinned” sea level series, the historical sea level series with data sampling interval 12h were tested for hydrodynamic levelling (cf. Appendix B). These comparisons are useful to validate the quality of historical staff gauge data. Note that there has been scepticism towards the reliability of historical data and connections between staff gauge and TGBM within the given study area (e.g. Jevrejeva et al. 2001). Therefore, the 19-year-long sea level series from the Virtsu, Rohuküla

88 and Heltermaa historical staff gauge stations (cf. Figure 20) were 19year processed to calculate the height differences between PGs (cf. ƅH12h in Table 11). More details about historical sea level series, their 2010 2011 connection with PGs and comparison with annual ( ƅH , ƅH ) results can be found in Appendix B and paper IV. Some uncertainties in the historical sea level series were confirmed with this validation. 2010 Discrepancies up to 3.7 cm (cf. Table 11) between annual ( ƅH , 2011 19year ƅH ) and 19-year low frequency ( ƅH12h ) sea level series were detected. The large discrepancies are most likely due to human error that could have occurred during digitalization of historical record books, compromising their reliability. Additionally, in some periods the height connection between historical staff gauges and their TGBM could include inaccuracies, e.g. the staff gauge was damaged by ice and/or the control levelling was made only for some time afterwards. Some other reasons for detected discrepancy ranges are discussed in Appendix B.

All in all, it seems that the tested Estonian historical staff gauge data can be used for oceanographic purposes but are not suited to satisfy contemporary geodetic requirements where the accuracy of 1 cm level is needed.

4.3. External verifications of the annual hydrodynamic levelling results

Based on the PG sea level series, an average accuracy as of ±1.5 cm was achieved for hydrodynamic levelling (cf. standard deviation in Table 9). It should be emphasised that this is an internal accuracy, which needs to be confirmed by alternative height determination methods.

The external verifications include comparisons of the present hydrodynamic levelling results (cf. Sections 4.3.1.– 4.3.3.) with the following independent datasets: i) Historical hydrostatic levelling results; ii) Contemporary precise spirit levelling results; iii) GNSS-levelling using precise GNSS results in conjunction with the latest regional gravimetric GRAV-GEOID2011 model.

Figure 20. Location of geodetic benchmarks, II order points, levelling lines and sea level gauges used in external verifications of the annual hydrodynamic levelling results.

The location of geodetic benchmarks, II order (GNSS) points, historical and contemporary levelling lines and sea level gauges (PGs and historical staff gauges) used in external verifications of the annual hydrodynamic levelling results are presented in Figure 20. Note that for an additional verification the spirit, hydrostatic and hydrodynamic levelling results were integrated into a combined solution (see the mini- loops formed between Virtsu–Kuivastu–Virtsu and Triigi–Sõru–Triigi in Figure 20).

4.3.1. Hydrostatic levelling for verifying across-water hydrodynamic levelling results

The historical hydrostatic height differences were compared with the obtained across-water hydrodynamic results (cf. Table 12). Recall that hydrostatic levellings between the Estonian mainland and the island of Saaremaa took place in 1968 and 1978 (cf. Figure 20 and Section 1.2.1.). The length of tube connections varied from 3.6 to 6.0 km by using two sections through Kesselaid islet. For the 1968 hydrostatic levelling the tubes were laid on the sea bottom (Tamme 1972). As the

90 depth of the strait reaches 20 m in some places, the temperature of the environment (air, water) surrounding the tube could be heterogeneous. Depending on the profile of the sea bottom and actual weather conditions, the differences in temperature can reach 5…7 ºC along the levelling tube. Consequently, the fluid density in the tubes may also vary along the line; that, together with air pressure differences at the tube ends, may yield a quite unpredictable total error in height differences. Therefore, the hydrostatic levelling between the islands of Saaremaa and Hiiumaa was tested in the winter of 1976, which allowed placing the spirit-filled tubes (total length 10 km) on the ice, thus reducing large temperature and density differences in the tube.

Table 12. Height differences between paired pressure gauges (and their standard deviations) achieved by different levelling methods. Unit is centimetre. Direct Hydrodynamic Hydrostatic Spirit GNSS- Pressure distance levelling (year) levelling1 levelling levelling2 gauge pair (km) (the source is (year) (year) (year) Table 9) Across-water Virtsu– 7 1.4±1.1 0.1±1.0 - 0.1±2.0 Kuivastu (2010) (1968) (1997) 16 64.2±1.0 - Triigi–Sõru 65.2±1.3 (1976) 64.1±2.0 (2010) 63.2±1.0 (1997) (1977) Heltermaa– 22 -4.0±1.7 - - -1.3±2.0 Rohuküla (2010) (1997) Land-connected Rohuküla– 65 20.1±1.2 19.63±0.24 20.4±2.0 Virtsu (2010) - (2005) (1997) Kuivastu– 65 -68.3±1.7 -69.3±0.2 -68.5±2.0 Triigi (2010) - (2010) (1997) Sõru– 45 -14.0±2.1 -12.8±0.2 -14.9±2.0 Heltermaa (2010) - (2009) (1997) 1 The results include land uplift corrections (+0.4 cm for the Virtsu-Kuivastu and +1.0 cm for the Triigi–Sõru sections), cf. Figure C2 in Appendix C. 2 Gravimetric GRAV-GEOID2011 model (Ellmann et al. 2011) was used for GNSS-levelling. The results include land uplift corrections, cf. Figure C2 in Appendix C. 3 The Rohuküla-Virtsu pair includes land uplift correction -0.2 cm (cf. Figure C2); for the other land- connected pairs the land uplift influence is insignificant due to the short period between the spirit levelling (proceeded 2009–2010) and hydrodynamic levelling (epoch 2010.5). 4 Levelling standard error Ƭ = 0.27 mmkm (Planserk 2010) from loops misclosures was used.

Even though the hydrostatic levelling accuracy was formally estimated to be better than ±0.2 cm (Tamme 1969), it appears to be too optimistic an estimate. For instance, the hydrostatic levelling between the islands of Saaremaa and Hiiumaa was repeated in winter of 1977

91 and the results differed by 1.0 cm from the 1976 results (Tamm 1992). Therefore, it can be concluded that the accuracy of the historical hydrostatic levellings could be at 1.0 cm level.

Note that hydrostatic levelling between the island of Hiiumaa and the mainland has not previously been carried out due to the long distance (22 km).

The hydrostatic levellings took place more than 30 years ago. Thus for rigorous comparison the land uplift corrections must be taken into account. A recent Fennoscandian land uplift model NKG2005LU (Ågren and Svensson 2007) was used in paper I, Section 6.2. Note however, that it seems that the NKG2005LU values for Estonia have been extrapolated, i.e. no Estonian geodetic nor sea level data have been used at the compilation of the NKG2005LU model. Therefore, specified land uplift velocities (from repated levellings) were calculated for the entire West-Estonian Archipelago within the framework of this study (cf. Appendix C). The NKG05LU model was used to verify this empirical land uplift WEst12LU model in the West-Estonian Archipelago. The mean difference between two models reached 0.3 mm/year. Note that the maximum discrepancies reaching up to 1.2 mm/year (cf. Figure C3) are associated with fringe areas of levelling (cf. Figure C1), which are also extrapolated from the WEst12LU model. Note that the discrepancies between the two models remained only within 0.25 mm/year in the vicinity of the Väinameri Basin.

The land uplift velocities of WEst12LU and NKG05LU models are matching reasonably well in the West-Estonian Archipelago. However, since the land uplift WEst12LU model (cf. Figure C2) has a higher resolution, it was used to correct historical levelling results in this study.

Note that the WEst12LU model based rates of across-water height difference velocities are +0.1 mm/year, +0.3 mm/year and -0.05 mm/year for the Virtsu–Kuivastu, Triigi–Sõru and Heltermaa– Rohuküla pairs, respectively. For land-connected height differences the rates are -0.4 mm/year, +0.1 mm/year, -0.05 mm/year in Rohuküla– Virtsu, Kuivastu–Triigi and Sõru–Heltermaa pairs, respectively. Accordingly, the uplift corrections +0.4 cm and +1.0 cm (over the past 42 and 34 years) between the initial benchmarks Bm 234 – Bm 244 and

92 Bm 264 – Bm 418 (cf. Figure 20) were taken into account to calculate hydrostatic results to epoch 2010.5, respectively. It appears that within the Triigi-Sõru pair the maximum difference between the sections containing hydrodynamic and hydrostatic levelling reached 1.5 cm, cf. Table 1219 and Figure 21.

Figure 21. Discrepancies between height differences based on different levelling 2010 2011 Hydrostatic methods (hydrodynamic: ƅH , ƅH ; hydrostatic: ƅH ; spirit: Spirit GNSS ƅH and GNSS: ƅH ). The zero line denotes the results of the annual (2010) hydrodynamic levelling as the reference. The vertical error bars denote the individual standard deviation values of the hydrodynamic levelling results (2010), cf. Table 9.

Certainly, all the above comparisons include not only the hydrostatic and precise spirit levelling errors, but errors of hydrodynamic levelling as well. Note that present hydrodynamic and historical hydrostatic levellings refer to different benchmarks, which are separated by several kilometres (cf. Figure 20). Connections between CPs were established by combining historical and new spirit levellings. This allowed the formation of closed mini-loops separately for Virtsu–Kuivastu–Virtsu and Triigi–Sõru–Triigi (cf. Table 13). Note that the misclosures of closed levelling mini-loops after inclusion of the land uplift correction remain within ±1.5 cm. It can be expected therefore, that the individual errors of the involved levelling methods most likely do not exceed this estimate either (cf. Figure 21).

19 The average (63.7 cm) of the 1976 and 1977 hydrostatic levelling height differences (64.2 cm and 63.2 cm, respectively in Table 12, see row 4, column 4) was used.

93 Table 13. Height differences and misclosures of the Virtsu–Kuivastu–Virtsu (left hand side) and Triigi–Sõru–Triigi (right-hand side) loops. Unit is metre. (km) (km) (year) (year) Height Height method method Distance Distance Levelling Levelling Levelling Levelling difference difference Land uplift Land uplift Benchmark Benchmark Bm 234 Bm 264 -8.603 9.9 Spirit -2.190 2.1 Spirit (2005) (2010) Virtsu CP Triigi CP 0.014 6.7 Hydro- 0.652 15.9 Hydro- dynamic dynamic (2010) 0.000 (2010) 0.000 Kuivastu Sõru CP CP 10.474 9.3 Spirit 4.959 0.7 Spirit (2010) (2009) Bm 244 Bm 418 -9.7471 4.8 Spirit -4.829 3.4 Spirit (1963) (1971) Bm n-ta FR IX 3.1 Hydro- -1.0213 9.9 Hydro- 0.004 static static

(1968) (1976) 2

Bm 240 FR VIII 2

1.5391 1.6 Spirit 14.746 9.9 Spirit -0.010 (1963) (1971) Bm 239 -0.004 Bm 215 -1.814 4.0 Hydro- -12.292 9.7 Spirit static (1979) (1968) Bm 238 Bm 264 8.1501 7.5 Spirit (1963) Bm 234 Total distance: 46.9 51.6 Misclosure 0.017 0.025 Misclosure with land uplift 0.013 0.015 correction: 1 Height differences based on the 1977 levelling catalogue: map sheet O–34–ǢVIII (Orissaare) in scale 1:200000. 2 Land uplift corrections from the land uplift model (cf. Appendix C) are used for historical levellings between Bm 244 – Bm 234 and Bm 418 – Bm 264 over 42 and 34 years, respectively. Note that, uplift model NKG05LU gives the corrections -0.002 m and -0.003 m for Bm 244 – Bm 234 and Bm 418 – Bm 264, respectively. 3 Hydrostatic height difference -1.026 m and -1.016 m was achieved between FR IX and FR VIII in 1976 and 1977, respectively (Tamm 1981). An average height difference (-1.021 m) is used in this table.

94 4.3.2. Geometric levelling for verifying land-connected hydrodynamic levelling results

All PGs are connectable to the ENLN by using precise levelling results between the corresponding TGBM and CP (cf. Table 5, columns 8 and 9). There are two-to-three precise levellings between TGBM and CP, which confirm that the constructions of staff gauges (cf. Figure 9) have been stable throughout the observation period, thus no deformations were detected in PGs.

The TGBMs of the PG stations are included in the ENLN and measured by precise spirit levellings in 2005–2010 as part of the renovation of the national levelling network by Planserk AS, a contractor to ELB. The average RMS for the national levelling lines in West-Estonia are: Ƨ = 0.19 mm km ; Ƴ = 0.04 mm/km (Torim and Jürma 2011). Accordingly, the results of this high-precision spirit levelling are suitable for verifying the results of hydrodynamic levelling within land-connected PG pairs. Moreover, the results of spirit levelling enable verification of hydrodynamic levellings for distances up to 65 km. Note that in this study the longest across-water section is three times shorter (22 km).

The spirit levellings between Rohuküla and Virtsu were carried out in 2005. Therefore, the land uplift correction (in total -0.2 cm for the five years from Figure C2) was taken into account in this pair (cf. Table 12). For the other land-connected pairs (i.e. Sõru–Heltermaa and Kuivastu– Triigi sections were levelled just a few years ago in 2009 and 2010, respectively) the land uplift influence is insignificant.

The hydrodynamic height differences between the land-connected PG pairs were estimated by Eqs. 10, 11 and presented in Table 9. The spirit levelling and the annual drift-corrected hydrodynamic levelling results agree within 1.2 cm (cf. Table 12 and Figure 21). Additional comparisons between spirit and short-term (6-day) hydrodynamic levelling can be found in paper I, Table 5.

All in all, agreement between the results of spirit and annual hydrodynamic levellings is satisfactory for distances up to 65 km (cf. the land-connected pairs in Figure 21).

95 4.3.3. GNSS-levelling for verifying across-water and land- connected hydrodynamic levelling results

The GNSS-levelling method can be used for comparing both the across-water and the land-connected height differences, although a suitable gravimetric geoid model is needed for this exercise. The normal heights H(ƶ, ƫ) of the CPs were obtained by using nearby located national II order GNSS points (see Figure 20 and Table 14 for their location and characteristics), where GNSS measurements were carried out in 1997. The normal heights for the used GNSS points H(ƶ, ƫ) were calculated by using geoidal heights N(ƶ, ƫ) from the gravimetric GRAV-GEOID2011 model (cf. Table 14, column 4). The normal heights were transferred to CPs using precise spirit levelling (cf. Table 14, column 7). A more detailed overview of GNSS measurements and GRAV-GEOID2011 is presented in Section 3.3.1. and paper I, Section 4.2.

Note that heights in Table 14 refer to the epoch 1997.56. For the sake of rigorous comparison, the across-water and land-connected height differences were transformed to epoch 2010.5 using land uplift corrections presented in Section 4.3.1. The final height differences can be found in Table 12, the last column. The detected discrepancies between the results of hydrodynamic and GNSS-levelling vary from 0.2 up to 2.7 cm, cf. Table 12 and Figure 21. The largest discrepancy is associated with the Heltermaa–Rohuküla pair (cf. Figure 21), where the GNSS-levelling is unfortunately the only independent (external) verification for the hydrodynamic levelling results. The large discrepancy in this pair could be caused by the accuracy of the GRAV- GEOID2011 model. Recall that the overall accuracy of GNSS-levelling remains within 2 cm and the accuracy is affected by the geoid model (see also Section 1.2.2.). Nevertheless, the geoid model accuracy could be worse in marine areas due to heterogeneous coverage and the quality of the gravity data at the shorelines. Therefore, additional verifications of the used geoid model need to be carried out in the Väinameri Basin. Note that traditional point-based GNSS-levelling cannot be used for geoid model verification in marine areas. Accordingly, profile-wise airborne laser scanning and space-borne (GNSS and satellite altimetry) methods were chosen (cf. Appendix D). Although the accuracy and the resolution (one point per 8 m for GNSS and one point per 8 km for SA) of these three methods are

96 different, they all enable direct tracking of the geoid surface by knowing the height of actual sea level during the measurements. However, due to datum offsets the absolute verification could be a bit complicated with these methods. But assuming that their accuracy is constant during the measurements, the relative geoid undulations can be detected.

All in all, with GNSS and ALS-based verifications, the uncertainties ±3…4 cm were detected in GRAV-GEOID2011 model near Heltermaa (cf. Figure D3 and Figure D5). At the other PGs the discrepancies between geoid model and profile-wise measurements were around 2 cm. Due to low resolution, the small offsets from the geoid model near the coastal area could not be detected using SA measurements. A more detailed overview of all profile-wise verifications and their results can be found in Appendix D.

In particular, it is concluded that detected discrepancies (up to 2.7 cm) between hydrodynamic and GNSS-levelling could be caused by accuracy of the geoid model as well. The verifications confirmed that GNSS-levelling cannot be used for precise across-water levelling in the West-Estonian Archipelago.

97 metre. ) ƫ , ƶ 1.803 1.803 1.117 1.754 1.606 1.594 H( (via geoid model) of CP model) of CP Normal height Normal

(Sõru) (Triigi) (Virtsu) (Kuivastu) (Rohuküla) (Heltermaa) (Heltermaa) point and CP CP point and

(name of station) Height difference between II order GNSS (km) (km) Distance between II order GNSS point and CP point and ) ƫ , ƶ point H( (via geoid order GNSS model) of II Normal height Normal

3 ) ƫ , ƶ ( CP N of II order GNSS point Geoidal height

2 ) ƫ , ƶ point 43.488 20.439 23.049 14.2 26.888 20.458 6.430 -21.246 3.1 26.229 20.493 5.736 6.2 29.086 20.442 -4.627 8.644 1.9 33.074 20.366 -4.619 12.708 6.1 26.452 20.408 -6.890 6.044 -11.102 1.5 -4.450 h( ffset was removed from gravimetric GRAV-GEOID2011 model. ffset was removed Geodetic height of II order GNSS ts are presented in Figure 20. coordinates The WGS84 23º41'45.7''E 22º22'09.9''E 22º38'46.4''E 22º32'02.3''E 22º57'32.5''E 23º26'12.9''E Heights of II order and contact points (CP) at the epoch 1997.56 and height differences between II order point and CP. Unit is II order point between differences and height epoch 1997.56 at the (CP) contact points and Heights of II order 1 1 2 3 4 5 6 7 8 5298 58º37'59.5''N 5296 58º35'07.4''N 5292 58º34'21.0''N 6201 58º42'12.0''N 6223 58º52'36.8''N 6236 58º54'30.7''N point GNSS II order Reference The location of II order poin The location of Reference: Rüdja (2004), Table F.2. o better comparison a 40 cm For number of Table 14. 1 2 3

98 4.4. Combining the hydrodynamic and spirit levelling results into a closed loop

Certainly, all the above discussed comparisons include not only the hydrodynamic levelling errors, but errors of alternative height determination methods as well. Therefore, an adequate accuracy estimation for hydrodynamic levelling could be based on the misclosures of the closed levelling loop. The Väinameri-encircling levelling loop (total length 253 km) comprises 3 across-water and 3 land-connected sections (see Figure 2 and Table 15).

For the combinations of spirit and hydrodynamic (solutions 2010 and 2011 separately) levellings the misclosure values of the 253 km long levelling loop remain under 0.8 cm (cf. Table 15, columns 1 and 2). Thereafter the least squares adjustment by elements was applied to obtain the adjusted height differences (see Table 15, columns 4 and 5). The weighting of measurements applies the inverse distance principle (the longer the levelling section, the smaller the corresponding weight in the adjustment), whereas the height differences to be adjusted are divided into two groups. The spirit levelled results are estimated to be 4…5 times more reliable than those of hydrodynamic levelling. Thus, the spirit levelling results form one group and the hydrodynamic levelling results the second. For the assigned weights see Table 15, column 3.

The standard deviation of the daily loop misclosures is ±1.5 cm for both years (cf. Figure 22). It is the same accuracy range that was estimated with different verifications in Section 4.3. Note that the height differences were not changed substantially during adjustment (cf. Table 15). Regardless, the accuracy of the adjusted hydrodynamic height differences in Table 15, columns 4 and 5 could be estimated to be ±1.5 cm.

Additionally, Figure 22 illustrates daily misclosures of the levelling loop for solution 2010 and 2011. Altogether 176 (note that Triigi’s station was malfunctioning from July to September) and 238 data-days remained after the removal of all data gaps for 2010 and 2011, respectively. Note that a data gap in any PG yielded removal of the same time period from other PGs as well.

1.0 -3.2 64.6 19.8 -69.3 -12.8 hydrodynamic Adjusted height differences (2011 solution + spirit)

1.3 -4.1 65.1 19.8 -69.3 -12.8 hydrodynamic difference (2010 Adjusted height solution + spirit)

(8) (3) (1) (7) (5) (10) (inverse 7 64 16 22 97 47 Length of (km)

levelling section distance weight) 1.2 -2.9 64.8 (solution 2011) Hydrodynamic height difference 0.8 ± 1.5 253 0.0 ± 1.5 0.0 ± 1.5

19.8 -69.3 -12.8 difference Spirit height

1.4 -4.0 65.2 (solution 2010) Hydrodynamic height difference

spirit Misclosure 0.2 ± 1.5 1 2 3 4 5 Misclosures of the Väinameri-encircling levelling loop by combining hydrodynamic and spirit levellings. Unit is centimetre. centimetre. Unit is levellings. spirit and hydrodynamic combining by loop levelling Väinameri-encircling the Misclosures of Virtsu Triigi – – Heltermaa – levelling section Hydrodynamic / Table 15. Virtsu–Kuivastu Kuivastu Triigi–Sõru Sõru Heltermaa–Rohuküla Rohuküla

100 Note that the daily misclosures may reveal some seasonal weather patterns in 2010 (cf. Figure 22). The smallest misclosure values are associated with the ice-covered winter period (January–April 2010) (see also paper I) but the same seasonal pattern cannot be detected for 2011. However, the 3rd degree polynomials reveal similar seasonal cycles for both years (cf. Figure 22). Therefore, the use of shorter than annual sea level series could be risky for hydrodynamic levelling.

Both misclosures of the levelling loop changed with time. The trends are -1.2 cm/year and -1.7 cm/year in 2010 and 2011, respectively. These could be related to the time-dependent drift of the PGs. As discussed in Section 3.6.1., the control readings from a staff gauge need to be taken frequently (i.e. at least once a month) to guarantee the requested accuracy of hydrodynamic levelling (±1 cm) using PGs.

Figure 22. Daily misclosures of the Väinameri-encircling levelling loop (total length 253 km) in 2010 and 2011. Continuous lines denote the corresponding linear trends of misclosures. 3rd degree polynomials indicate seasonal cycle trends. Calendar months are denoted on the horizontal axis.

4.5. Conclusions and discussion on verifications

Using annual sea level series an internal precision as of ±1.5 cm was achieved for the PG-based hydrodynamic levelling results, cf. Section 4.1. Recall that hydrodynamic levelling results are mainly affected by environmental conditions, whereas the PGs suffer from time- dependent drift. Therefore, several validations and comparisons were made to verify the obtained results and accuracy.

First, the annual hydrodynamic levelling results (Table 9) were compared with short-term (6- and 4-day) sea level observations, i.e. with practically “drift-free” data series. Moreover, these observations

101 (6-day in February 2011 and 4-day in March 2012) were collected and field checked during two consequent winter seasons, with thick coverage of ice and calm weather conditions. It was assumed that during the selected periods the influence of weather dependent (wind, waves and atmospheric pressure) sea level fluctuations is minimized. The results of comparisons confirmed that the discrepancies between annual and short-term “ice-tamed” sea level observations remain mainly within ±1.0 cm for distances up to 22 km (cf. Figure 19). The larger discrepancies (at 2 cm level) are related to longer distances (up to 65 km). Note that during short-term observations the average standard 6day deviation of height differences was only ±0.6 cm (cf. ƅH and 4day ƅH in Table 10), which is associated with “ice-tamed” calm weather conditions. The results confirmed that discrepancies between averaged annual and short-term sea level observations are reasonable.

Second, high-frequency (5m) sea level observations were thinned to a 12h data sampling interval to detect the capability of low-frequency sea level observations to adequately detect across-water height differences. 2010 2011 The discrepancies between high-frequent ( ƅH , ƅH ) and sparse 2010 2011 ( ƅH12h , ƅH12h ) data sampling intervals remained within ±0.3 cm (cf. Table 11). The experiment illustrated that final results were not notably affected by data sampling interval in this tide-less, semi-enclosed water body. Consequently, data sampling interval could be successfully increased in automatic SLGs. However, in tidal areas an hourly data sampling interval (e.g. 1h) should be feasible in SLGs. This is useful in limited power conditions, e.g. in the sub-polar regions in wintertime when short daylight may not be enough to fully recharge the PG batteries.

In this way also usability of historical sea level observations for hydrodynamic levelling can be analysed. The “thinned” PG data were compared to historical long-term (19-year) observations of paired staff gauges. Discrepancies up to 3.7 cm (cf. Table 11) were detected. Such a large discrepancy and standard deviation ±3.6 cm (for 19-year sea level observations) could be caused by many factors, e.g. (i) non-reliability of historical sea level series, which were digitalized many decades later by different personnel. Therefore, the large discrepancies are most likely due to human error. (ii) Over the decades, the height connection between historical staff gauges and their TGBM could include some

102 inaccuracies. For example, in winter and spring the ice could have damaged the staff gauge, and new levelling connections were not made till some time later.

All in all, adequate verification was not achieved between the annual hydrodynamic and 19-year-long sea level series in the Väinameri Basin area. Historical staff gauge series are suitable for oceanographic purposes but one should be cautious using them for geodetic purposes where the accuracy of 1 cm is needed.

Third, three alternative levelling methods (spirit, hydrostatic and GNSS-levelling) were used to externally verify the accuracy of hydrodynamic levelling. Spirit levelling is the most accurate levelling method of these three. Although the verification could be carried out between land-connected pairs only, this verification is certainly the most adequate. The differences between annual hydrodynamic and spirit levelling remained within ±1.5 cm for distances up to 65 km (cf. Figure 21).

Historical hydrostatic levelling results were used for verification of across-water connection. The hydrostatic levelling accuracy is (optimistically) estimated to be at 1 cm level. The discrepancies between hydrodynamic and hydrostatic levelling remained within ±1.5 cm (cf. Figure 21). Recall that across-water distances for hydrostatic levelling were only up to 10 km (cf. Table 13).

Additionally, the Virtsu–Kuivastu–Virtsu and Triigi–Sõru–Triigi closed mini-loops (~50 km) were formed combining the spirit, hydrodynamic and hydrostatic levelling results (cf. Figure 20). The misclosures of land-uplift-corrected levelling loops remained within ±1.5 cm as well (cf. Table 13).

GNSS-levelling enabled verification of both land-connected and across-water height differences. The largest discrepancies (up to 2.7 cm in Heltermaa–Rohuküla pair) were detected in this verification (cf. Figure 21). However, the discrepancies compared to hydrodynamic levelling remain within ±1.3 cm in Virtsu–Kuivastu and Triigi–Sõru pair. All in all, GNSS-levelling is affected by the accuracy of the regional geoid model, which needs further testing in the West-Estonian Archipelago.

103 Fourth, 3 across-water and 3 land-connected sections were combined into the Väinameri Basin-encircling loop (total length 253 km). For the combinations of spirit and hydrodynamic (solution 2010 and 2011) levellings the misclosure values remained under 0.8 cm. Additionally, the daily misclosures of the levelling loop for solution 2010 and 2011 were calculated. Their standard deviations were ±1.5 cm for both years. Note that seasonal effect on the hydrodynamic levelling was detected by daily misclosures. Therefore, to eliminate seasonal effect, at least annual sea level observations are recommended to be carried out for hydrodynamic levelling.

In conclusion, all verifications confirmed that the accuracy of PG- based hydrodynamic levelling is at ±1.5 cm level in the distances up to 65 km. Recall that this result was achieved for an almost tide-less and semi-enclosed water body, which is quite similar to large lakes, e.g. the Great Lakes in North America, Lake Peipus in Estonia or other large lakes in Eurasia. Note that SST was neglected in this study because the available SST models near the coastal area appeared to be less accurate than the accuracy of hydrodynamic levelling results.

Short-term “ice-tamed” drift-free measurements revealed that even better accuracy (±1.0 cm) could be achieved using sea level series from pressure gauges (cf. 6-day observation in Table 10 and spirit levellings in Table 12). Such privileged “ice-tamed” sea level observations are possible only in subarctic latitudes (e.g. Scandinavian fjords, coastlines of Canada, Alaska and Northern Russia and in frozen lakes). However, such “ice-tamed” and ideal calm weather periods might take place only once every two to three years.

Note that for ensuring accurate PG-based hydrodynamic levelling the control readings from a nearby staff gauge must be taken at least monthly with accuracy ±0.5 cm. It could be costly and laborious to visit remote PGs so often. Therefore, future studies might include application of some technical resource, possibly telemetry. It should be feasible to facilitate frequent staff gauge readings and minimise transport expenses. For example, webcams could be tested. However, there are several potential problems for their use: • Webcams placed in front of the staff gauges could be inconvenient because they need special constructions;

104 • It is complicated to guarantee the security against vandalism of both webcams and SLGs; • Water drops or cobwebs on the camera lens could disturb the view; • Webcams become useless with ice-coverage.

However, PGs have one main advantage compared with other SLGs (e.g. float, radar, acoustic, cf. Section 3.1.): they can be used in sub- polar latitudes throughout the year. PGs can measure the sea level changes with accuracy ±0.5 cm (accuracy depends on the full scale of pressure sensor) even in ice cover conditions.

105 5. SUMMARY AND CONCLUSIONS

The main objective of this study was to investigate the usability and obtainable accuracy of hydrodynamic levelling by PGs. The study demonstrated that PGs are useful not only for maritime and oceanographic purposes, but also for geodetic applications, e.g. in connecting island levellings to each other and to those on the mainland. In particular, the study has a practical outcome: the results can be used to improve the Estonian National Levelling Network by strengthening its western part with additional connections.

However, there are some drawbacks that influence the accuracy of hydrodynamic levelling. (i) The pressure sensors are affected by time-dependent drifts. The control readings from staff gauges showed that the drift values can reach up to 6 cm per year. Hence, regular control readings from nearby staff gauges have to be taken (either visually or telemetrically) to estimate the drift corrections throughout the entire observation period. (ii) The hydrodynamic levelling results can also be affected by the specifics of the study area. In particular, the mean and seasonal SST must be taken into consideration. This could be the most challenging part of hydrodynamic levelling, since the accuracy and resolution of existing global and regional SST models could be insufficient (especially for the coastal zone) to ensure the geodetic accuracy of hydrodynamic levelling. Therefore, in some circumstances it could be even safer to disregard such SST values if no high-resolution SST model exists for the region of interest. Also, the time period of sea level observations should be sufficient to eliminate the seasonal and weather-induced fluctuations of the SST from the equipotential surface.

The study revealed that, depending on the specifics of the study area, at least, the entire annual water cycle may be necessary to determine reliable hydrodynamic height differences. With longer observation series the results may not necessarily become more reliable, since barnacles and algae may congest the PG diaphragm over time, thus worsening the quality of longer-term PG measurements.

106 All the mentioned factors were taken into consideration in this study and the results of hydrodynamic levelling were validated with case studies in the West-Estonian Archipelago. Six pressure gauges (Virtsu, Kuivastu, Triigi, Sõru, Heltermaa and Rohuküla) with inter-connecting lines of the Estonian National Levelling Network form a closed loop consisting of three across-water and three land-connected levelling sections encircling the Väinameri Basin. Such a constellation sets rigorous constraints for the hydrodynamic levelling experiment. The sea level observations lasted 2 x 12 months (2010, 2011). Thus, two consecutive annual water cycles were entirely covered. The sea level series were pre-processed before estimating height differences between paired PG stations. Pre-processing included the following phases: (i) drift corrections were added to the raw sea level data, (ii) the influences of external factors, i.e. ferry traffic near the station and weather- induced sea surface slopes were filtered out. The data processing and filtering principles were developed and explained in Section 3.6. The height differences between the PG pairs were calculated by using the annual MSL values.

Note that the annual (2010) hydrodynamic height differences between Virtsu–Kuivastu, Triigi–Sõru and Heltermaa–Rohuküla are the final results of this study (cf. Table 9). Solution 2010 was selected because: • more control readings from staff gauges were taken in 2010 and therefore, the results are more reliable then in 2011; • the stability analyses indicated that the first year data series are less affected by congestion by microscopic floating particles, barnacles and/or by algae. • the 2010 misclosure (0.2±1.5 cm) of the Väinameri Basin- encircling levelling loop was smaller than that of 2011.

The final results of height differences between both across-water and land-connected PG pairs were verified using six alternative methods and levelling results by the following concurrent and earlier studies: (i) 6- and 4-day “ice-tamed” drift-free sea level observations; (ii) “thinned” (interval 12h) sea level series were compared with original PG sea level series (interval 5m). Note that observation interval 12h corresponds to the historical staff gauge observations in Estonia that were taken into comparison as well;

107 (iii) high-precision spirit levelling results (accuracy r 0.27 mm km ) were used for the land-connected comparisons between PGs; (iv) historical hydrostatic levelling results (accuracy ±1.0 cm per connection) were used for the across-water comparisons between PGs; (v) GNSS-levelling height differences (accuracy ±2.0 cm) were used for both land-connected and across-water sections; (vi) misclosure of the Väinameri Basin-encircling levelling loop was calculated by combining hydrodynamic and spirit levellings.

The numerical results of the annual PG-based hydrodynamic levelling agree with the aforementioned verification datasets within ±1.5 cm (cf. Figure 19 and Figure 21). Furthermore, the discrepancies between (i) short-term “ice-tamed” drift-free and annual sea level observations and (ii) short-term “ice-tamed” drift-free and spirit levelling remained mainly within ±1.0 cm (cf. Figure 19). This indicates that the time- dependent drift of PGs and influence of weather conditions could be the main drawbacks affecting the accuracy of hydrodynamic levelling. Although the accuracy ±1.0 cm could be achieved using short-term sea level observations, the annual sea level series should be preferred. Note that short-term sea level observations may be strongly affected by incidental weather conditions, which could cause water tilt between the SLGs. With a short observation period such anomalous events will not average out and thus may provide erratic estimates for height differences. Such short-term and seasonal disturbancies can be eliminated or minimized by using annual sea level series.

However, two larger discrepancies (up to 3.7 cm) with the present hydrodynamic levelling results were detected for the historical staff gauge observations and GNSS-levelling results. There could be some unreliability in the historical sea level series, but decades later it is hard or even impossible to detect exact reasons. For GNSS-levellings, the gravimetric GRAV-GEOID2011 model was used (Section 4.3.3.). The accuracy of this model was estimated via GNSS-levelling points to be ±1.3 cm on the Estonian mainland. In the marine area the accuracy of this model was uncertain. Therefore, three separate profile-wise GNSS, ALS and satellite altimetry verifications were carried out as a side- product of the study. The accuracy of these methods is different but relative changes of the geoid surface can be detected effectively. The

108 verifications confirmed some uncertainties (±3…4 cm) in the geoid model in the Väinameri Basin. Moreover, the comparisons revealed that existing SST values cannot be used in the Väinameri Basin, as there could be problems with the geoid model, as well. There are indications that the magnitude of uncertainties of both (SST and geoid model) may exceed the accuracy of hydrodynamic levelling. Further dedicated research should be carried out for specifying the geoid model over the marine area.

It can be concluded that geodetic accuracy (±1.0 cm) for height determination can be achieved using hydrodynamic levelling with contemporary pressure sensors, provided that the data collecting and processing procedures are also handled properly. The control readings from staff gauges were few in some PG stations in this study. Therefore, since the stretches of water varied from 7 km up to 65 km in the experiments, then it can be concluded that PG-based hydrodynamic levelling can be used for sections up to 65 km with an expected accuracy of ±1.5 cm. However, its performance for distances longer than 65 km needs to be investigated. Apparently, a complex of challenging factors should be considered for a hydrodynamic levelling section stretching across the open sea. Here the salinity variations (affecting density and SST) and lags in the tidal phase and magnitude may cause larger discrepancies.

In some conditions hydrodynamic levelling could be the only feasible option for height determination. Compared to alternative levelling methods, hydrodynamic levelling has certain advantages. Hydrodynamic levelling is: • economically more feasible and less laborious than hydrostatic levelling; • more accurate than the widely used GNSS-levelling. Recall that GNSS-levelling depends on the accuracy of the regional geoid model; • usable in all latitudes, since PGs are not affected by ice conditions.

Compared to other SLGs the PGs have certain advantages. They are small, cheap, easy to mount and use. They can be used in harsh environmental conditions, e.g. with ice coverage. In all cases the time- dependent drift of a PG can and must be taken under control, taking

109 control readings from a nearby staff gauge at least once a month with accuracy ±0.5 cm.

However, in order to improve the accuracy of hydrodynamic levelling, some recommendations for future investigations are due: • Pressure sensors and their time-dependent drift needs more study to use for geodetic purposes. Therefore, some automatic (e.g. telemetry) and independent method should be used to collect staff control readings periodically. Note that PG drift values are important for sea level research by other institutions in the future. For instance, dozens of PGs have been installed on the coast of Estonia from 2010 by the Estonian Meteorological and Hydrological Institute. The sea level series of these stations have importance but only then when the drift corrections have been collected accurately and periodically (i.e. once per month). Otherwise, these sea level series are useless for geodetic purposes. • SST models need more study and verifications in the coastal areas and enclosed stretches of water.

Note that height differences between the islands of Estonia and the mainland have not been determined over the last three-four decades. Moreover, there was no previous direct height connection between the island of Hiiumaa and the mainland. Therefore, this study has the following important consequences: • The results of hydrodynamic levelling achieved in this study can be used for improving the Estonian National Levelling Network. • The new height system can be adjusted for islands based on the across-water height differences. This allows correction of the geoid model in the islands, thus also improving the accuracy of GNSS-levelling. • Enables further specification of fitting parameters between the gravimetric GRAV-GEOID2011 model and the current/new official height system. • New height connections between the islands and the mainland can be used to specify land uplift velocities in Estonia. • Establishment of the rigorous height system in all parts of a country has importance for engineering works as well. For instance, the designing and building of an across-strait

110 connection (i.e. bridge or tunnel) between the island of Muhu and the Estonian mainland is being discussed. • Assigning rigorous heights to the high frequency sea level series enables calibration of satellite altimetry results over the Baltic Sea.

In summary, the conclusions reached in this Thesis will provide vital information for the renovation of the Estonian National Levelling Network. Furthermore, the methodology and devices described may provide useful knowledge for research in areas with diverse geographical and environmental conditions.

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120 APPENDICES Appendix A. Transformation the acquired raw pressure gauge data to the same (arbitrary) height system

At the installation of PGs (2008–2010, cf. Table 5) the TGZ heights were initially determined using technical levelling from nearby benchmarks by the MSI. Essentially, an attempt was made to define the staff reading, which would correspond to the 0-height in the Baltic Height System 1977 (BK77), which is the “official” national height system until the full renovation of the ENLN. Such TGZ readings were presented in Table 5, column 6. The benchmarks used initially for the TGZ reading determination, however, are not included in the new ENLN. They belong either to the low-order or trigonometric levelling or III order national GNSS network (their heights were obtained via geoid EST-GEOID2003 model, cf. Table A1).

Table A1. Differences between initial tide gauge zero (TGZ) height values and that obtained from the hydrodynamic/land-connected levelling loop adjustment. Station Initial benchmark used for determinining Height of Differences5 name the heights of the TGZ1 by the MSI benchmark (adjusted (benchmark type / levelling technique) used by the minus MSI (m) initial) (cm) Virtsu 52-971-2002 1.436 -2.1 (Local II order point / trigonometric levelling) Kuivastu 52-961-90294 3.468 -1.3 (II order wall benchmark / geometric levelling) Triigi 52-921-4647 5.0003 -4.3 (III order GNSS point / height obtained via EST- GEOID2003) Sõru 62-013-90418 6.682 -1.9 (III order wall benchmark / geometric levelling) Heltermaa 301 2.5354 -2.0 (a bolt in the basement of lightning mast / geometric levelling) Rohuküla 62-362-4168 4.7763 -3.0 (III order GNSS point / height obtained via EST- GEOID2003) 1 The readings of the tide gauge zero (TGZ) level on the staff gauge are presented in Table 5, column 6. 2 Benchmark reference IDs as presented in Estonian Land Board (ELB) digital database: www.maaamet.ee/rr/geo/ 3 A previous EST-GEOID2003 model was used for obtaining the used height value. 4 The BK77 height of a bolt in the basement of nearby lightning mast is determined by a local land surveyor (M. Matto, report nr MB08_125; also in the MSI report, 2010). 5 The BK77 height (H = 5.726 m) of the fundamental benchmark FR AM20 near Rohuküla was used as initial for the hydrodynamic/land-connected levelling loop (free) adjustment. The detected differences (adjusted minus initial) are thought to be due to the use of different types of initial benchmarks, errors in historical data and land uplift.

122 Additionally, the BK77 heights of low-order benchmarks were published by the Soviet geodetic authorities in the 1970’s. Note that there were several across-water height connections (cf. Section 1.2.1.) between the mainland and Saaremaa and between Saaremaa and Hiiumaa in the 1970’s and earlier. However, it is unclear which height differences were used by the Soviet authorities for calculations of islands’ heights. Additionally, not much is known about corrections applied and the adjustment made to obtain these heights. Furthermore, the Hiiumaa levellings were not connected to the mainland, which prevented closing the levelling loop around the Väinameri in the 1970’s. The heights of benchmarks have been changed in time due to land uplift as well. These inaccuracies have caused the BK77 catalogue heights have become obsolete. Therefore, the heights determined for TGZs are suspected to be inconsistent. The connections between the CP and nearby TGBM (established in 2004–2010, also included into the new ENLN) were subsequently (2009–2011) re-levelled by Planserk AS and TUT’s Chair of Geodesy (see Table 5). Where possible, the initial benchmarks used by the MSI (in Kuivastu, Triigi, Sõru, Heltermaa) were included in the levellings (cf. Ellmann 2010) as well.

The water level recordings in raw PG data files (cf. Table 6) refer to initial TGZ readings (see Table 5, column 6). The closed hydrodynamic/land-connected loop adjustment (cf. Section 3.2.) was used to calculate new TGZ heights for the epoch 2010.5. The fundamental benchmark FR AM20 (BK77 height is 5.726 m) near Rohuküla was used as an initial benchmark for the adjustment. Thus, new heights were achieved for CPs in the same (arbitrary) height system. Thereafter TGZ values were specified from the CP heights.

Note that discrepancies up to -4.3 cm (cf. Table A1) occur between initial TGZs and that obtained from the hydrodynamic/land- connected levelling loop adjustment. These discrepancies and drift corrections (cf. Figure 11) need to be accounted for when attempting to use the raw PG data files (cf. Table 6). Note that BOOS and/or MSI on-line (on-line.msi.ttu.ee/kaart.php) data are drift-corrected (using the latest control values) but they refer to the initial TGZ readings (T. Kõuts, pers. comm., 2011). Therefore, when pursuing geodetic accuracy for the BOOS or MSI on-line data, accounting for differences presented in Table A1 is needed to transfer the PGs data

123 into the same (arbitrary) height system. Note that after renovation of the ENLN the differences presented in Table A1 should be specified in order to relate the sea level data to the new realisation of the national height system.

124 Appendix B. Historical staff gauge series for hydrodynamic levelling

There is a long history of sea level measurements utilizing staff gauges in Estonia and in the Väinameri region in particular; for a review see Jevrejeva et al. 2001. Altogether 7 staff gauges (see Figure 2 in paper IV) were erected around the Väinameri Basin and observed within the period of 1894–2008. Most were operational for only a few decades and had longer or shorter gaps in sea level series, and sea level observations were taken mainly two or four times a day.

Jevrejeva et al. (2001) used the sea level series for specifying the postglacial rebound rates in Estonia. They noticed also possible stability problems of staff gauges and TGBMs. For example, in some cases the TGBM height has been changed by a couple of centimetres over 35 years, seemingly without any particular reason. Inconsistencies in the sea level series were noted as well. Therefore, the use of decades- long sea level series for hydrodynamic levelling should proceed cautiously. However, there have been a couple of earlier experimental attempts to use historical staff gauges for hydrodynamic levelling in the West-Estonian Archipelago. For instance, 13- and 4-year long continuous sea level series were used by Eipre (1964) and Tamm (1992), respectively. The hydrodynamic height differences between staff gauges on the islands of Saaremaa and Hiiumaa were estimated for 1945–1958 by Eipre and for 1962–1966 and 1979–1983 by Tamm. For verification of their results, the short-term (a few days) sea level observations from ice holes were carried out in the 1960’s and 1970’s by Tamm (1992). The observations from ice holes agreed with the aforementioned results within ±1…2 cm (Tamm 1992). Note that similar differences were achieved between annual and short-term “ice- tamed” observations using PGs (cf. Section 4.2.1.).

In the present study applicability of a longer timespan of staff gauge based sea level series was studied for hydrodynamic levelling. The 19- year-long periods (1966–1985 for Rohuküla–Virtsu and 1956–1975 for Heltermaa–Rohuküla, cf. Figure 20) – without significant data gaps – were available for calculating hydrodynamic height differences 19year (ƅH12h ).

125 The historical sea level readings were taken visually two, three or four times daily for Rohuküla, Heltermaa and Virtsu staff gauges. For example, at 6 am, 12 pm and 6 pm in 1950–1957 and at 6 am and 6 pm after 1957 in Rohuküla station. In Heltermaa the readings were taken 4 times daily (at 12 am, 12 pm, 6 am, 6 pm) in 1958–1987. Note that time refers to UTC. Since only two daily readings were taken in Rohuküla after 1957 then for a “fair” comparison two readings (at 6 am and 6 pm) were selected for Heltermaa and Virtsu stations as well. Thereafter 19-year MSL were calculated at each staff gauge station.

For comparing the historical hydrodynamic levelling results with contemporary PG results, the historical staff gauges were connected to PGs by selecting historical spirit levelling sections through common nearby benchmarks (Bm 1230, FR AM20 and Bm 235; their distances from the PGs are less than 10 km) in Heltermaa, Rohuküla and Virtsu (see Figure 20). The detected height differences between historical staff gauges and PGs (CP of PG minus that of historical staff gauge) are as follows: -19.9 cm; -14.1 cm and +31.6 cm in Heltermaa, Rohuküla and Virtsu, respectively.

The middle epoch (1976 and 1966) of the 19-year sea level observations was used for calculating land uplift corrections within the Rohuküla–Virtsu and Heltermaa–Rohuküla pairs, respectively. For comparison with PG results, the land uplift corrections -1.4 cm and -0.2 cm for the pairs were taken into account to transfer the historical data to epoch 2010.5. Note that the land uplift corrections are derived from the WEst12LU model, see Appendix C for a more extended discussion on compilation of this model. Thus, the historical sea level series were connected to TGZ of PGs by taking into account the estimated height differences and corrections. That enabled to calculate the Rohuküla–Virtsu and Heltermaa–Rohuküla height differences 19year (ƅH12h ) (cf. Table 11).

2010 2011 The discrepancies between annual PG results ( ƅH , ƅH ) and 19year ƅH12h sea level series reached up to 3.7 cm (cf. Rohuküla–Virtsu pair in Table 11). The large discrepancy and standard deviation (±3.6 cm based on the daily height differences calculated over 19 years) could be caused by many factors, but most likely it is due to unreliability of historical sea level series. Note that all the data were digitalized many decades later by different personnel. Therefore, the detected

126 discrepancies are most likely due to human error. Additionally, in winter periods the ice could move the staff gauge, creating inaccuracies in the sea level readings. Note that typically the staff gauge heights were re-measured once or twice a year.

All in all, the quality of decades-long historical sea level series seems to be acceptable for oceanographic purposes. However, one should cautiously use historical sea level series for geodetic purposes where 1 cm accuracy is requested. Therefore, the historical sea level series (even if available for all across-water connections) cannot be used for the present reconstruction of the ENLN.

127 Appendix C. Compilation of empirical land uplift WEst12LU model over the West-Estonian Archipelago

Estonia is located in the south-east periphery of the Fennoscandian post-glacial rebound area. The land uplift in north-west Estonia (including the West-Estonian Archipelago) reaches up to 2.5 mm/year, whereas land subsidence (-0.8 mm/year) has been detected in south- east Estonia (cf. Vallner et al. 1988). Historically, precise repeat levelling series were used for determining the land uplift in Estonia; several land uplift maps were constructed by Vallner et al. (1988), Randjärv (1993) and Torim (2004). It should be noted that the hydrostatic levelling results (cf. Section 1.2.1.) between the island of Saaremaa and the mainland and between the islands of Saaremaa and Hiiumaa have been used for compilation of the earlier land uplift maps. Recall that previously, due to the long distance, there was no direct height connection between the island of Hiiumaa and the mainland. Therefore, the outcome of this study (hydrodynamic levelling results) was used for specifying land uplift velocities over the western part of Estonia.

Figure C1. Layout of levelling lines (bold lines) and benchmarks incorporated into the compilation of the land uplift model in West-Estonia. FR AM20 denotes the location of the initial benchmark in the adjustment.

128 For computing the land uplift velocities the height differences of the ongoing and previous national levellings (see Section 1.2.) were used. For the West-Estonian region 10 common fundamental (ground) benchmarks (5 in mainland and 5 in Saaremaa) were available and incorporated into the present solution. In addition, 29 wall benchmarks were incorporated into the computation of the land uplift velocities. Locations of the involved benchmarks are shown in Figure C1. The total length of spirit levelled lines in conjunction with hydrodynamic levelling sections ~1000 km (see bold lines in Figure C1).

Data processing for land uplift velocities relative to the mean sea level included the following phases: 1. The relative land uplift velocities between two levellings (mainly, the second (1950–1969) versus ongoing (2001–2013), cf. Section 1.2.) were calculated for the West-Estonian network (see Figure C1). The spirit levelled height differences between the benchmarks were obtained from the ELB. The results of annual (2010) hydrodynamic levelling were used for three across-strait connections to connect the island loops with the mainland. 2. The calculated relative velocities between the benchmarks were adjusted all together over West-Estonia using the least square method based on the well known criteria: >pƵ2 @ min . Weights (p) for all land uplift velocities in this study were calculated as follows (Holdahl 1978, Randjärv 2008):

p = (r · t 2)/ M2 (C1)

where r is the root mean square (RMS) of unit weight (in these calculations r = 1 was uniformly adopted for all land uplift velocities at different locations), t is time period in years between two levellings and M is the RMS of levellings computed by:

2 2 M SD1 SD2 (C2)

where the standard deviations SD1 and SD2 were calculated for historical and ongoing levellings, respectively by:

SD Ƨ2L Ƴ2L (C3)

129 where Ƨ and Ƴ are random and systematic errors of levelling and L is the distance in km between the two benchmarks. For the ongoing and historical levelling Ƨ = 0.19 mm km , Ƴ = 0.04 mm/km and Ƨ = 0.43 mm km , Ƴ = 0.06 mm/km were adopted, respectively (cf. Torim and Jürma 2011).

3. After the network adjustment the land uplift velocities relative to the mean sea level were calculated for every benchmark (the fundamental benchmark FR AM20 was kept fixed, cf. Figure C1). The land uplift velocity (with respect to the mean sea level) as of 1.35 mm/year for FR AM20 was derived from the Fennoscandian 5' x 10' (approx. 9 km x 9 km) resolution land uplift model NKG2005LU (Ågren and Svensson 2007).

4. The obtained land uplift velocity model (Figure C2) was gridded with resolution 0.5' x 1' (0.9 km x 0.9 km) by using the kriging technique (included to ArcGIS ver 10.0 software package). The resulting model is referred to as WEst12LU.

Figure C2. Empirical land uplift WEst12LU model based on repeated levellings in West-Estonia. The dots denote the location of benchmarks and corresponding land uplift velocity. The results of hydrodynamic levelling (2010) were used for across- strait connections.

130 Verification of empirical land uplift WEst12LU model For verification, the model WEst12LU (Figure C2) was compared with the NKG05LU model. Note that at the compilation of the NKG2005LU model no geodetic nor sea level data from Estonia were used (cf. Vestøl 2006, Lambeck et al. 1998, Ågren and Svensson 2007). Thus the NKG05LU model values over Estonia are obtained from extrapolation. The mean difference between the two models (NKG05LU minus WEst12LU) as of 0.3 mm/year was detected with the standard deviation 0.3 mm/year as well (cf. Figure C3). The largest detected discrepancies (reaching up to 1.2 mm/year, e.g. on the southernmost part of Saaremaa) are concentrated in border areas of West-Estonian levellings (cf. Figure C1 and Figure C3) where no data are available, i.e. the uplift rates are extrapolated also in the WEst12LU model. In the area of interest, i.e. within the immediate neighbourhood of the Väinameri Basin the discrepancies between the models remain generally within 0…0.25 mm/year.

All in all, the land uplift velocities of WEst12LU and NKG05LU models are matching reasonably well in the West-Estonian Archipelago. However, WEst12LU model (cf. Figure C2) has a higher resolution and therefore was used in this study to correct historical height differences, i.e. hydrostatic, spirit and GNSS-levellings carried out in the last few decades.

Figure C3. The differences between land uplift models NKG05LU and WEst12LU (NKG05LU minus WEst12LU). Statistics of differences: min: -0.3, max: 1.2, mean: 0.3, standard deviation: 0.3.

131 Appendix D. Profile-wise verifications of gravimetric GRAV- GEOID2011 model over marine areas

The gravimetric GRAV-GEOID2011 model (Ellmann et al. 2011) was used for GNSS-levelling across the straits in this study. The accuracy of the regional gravimetric GRAV-GEOID2011 model has been estimated to be 1.3 cm in the mainland of Estonia (cf. Oja et al. 2011 and Section 3.3.1.) but its offshore accuracy remains unknown. Therefore, three profile-wise verifications by means of GNSS, Airborne Laser Scanning (ALS) and satellite altimetry (SA) measurements were carried out to validate the accuracy of the gravimetric geoid model over the Väinameri Basin.

Verifications by GNSS measurements In 2004 and 2006 GNSS measurements on board ferry-boats were undertaken to assess the NKG04 geoid model (Forsberg et al. 2004) accuracy in the Gulf of Finland and across the Baltic Proper (for more details see paper V). The comparisons demonstrated good agreement over large portions of the tested GNSS profiles. The detected discrepancies did not exceed 15 cm even in areas with relatively steep geoidal slope (160 cm per 100 km).

Based on the experiences cited in paper V, the same method was used over the ice-covered Väinameri on February 22–23, 2011 (cf. Figure 15A). However, instead of the ferry a motor vehicle was deployed. The GNSS kinematic measurements with tracking interval 1 Hz were carried out in calm weather conditions on the official ice roads between Virtsu–Kuivastu, Triigi–Sõru and Rohuküla–Heltermaa20 (cf. thick lines in Figure D1). The car speed during the measurements was approximately 20…25 km/h, corresponding to data sampling interval as of 1 point per 7 meters.

Two GNSS antennas/receivers (Trimble R8 and Spectra Precision Epoch 50) were mounted on the car roof (cf. Figure D2). The height of GNSS antennas from the ice surface was determined (with the full car load) before and after GNSS measurements. The separation between the water and the ice surface was determined indirectly. Recall

20 The road length, 26 km between Rohuküla and Heltermaa, makes it the longest ice road in Europe.

132 that the density of ice is ~920 kg/m³ whereas that of brackish water is ~1004 kg/m³. Therefore, approximately one-tenth of the volume of the ice is above the water surface. The ice thickness at PG stations reached 50 cm (less in the middle of the strait) (cf. Section 4.2.1.), thus the along-route GNSS results include the offset (-3 cm) due to the separation of the ice surface from the water surface.

Figure D1. Profiles measured by GNSS (thick lines) and ALS (thin line) over the Väinameri Basin, respectively. The GNSS and VRS base stations were used as references for GNSS data post-processing. The gravimetric GRAV-GEOID2011 model with contour interval 1 cm is placed in the background. For a better comparison a40 cm offset has been removed from the GRAV-GEOID2011 model.

Figure D2. Profile-wise GNSS kinematic measurement on the ice. Note two GNSS antennas mounted on the car roof.

133 Kinematic GNSS measurements were carried out to compute the heights and coordinates of the moving vehicle. For this temporary GNSS base stations were set up on the pier at Rohuküla, Sõru and Kuivastu (see the location in Figure D1). On average, the duration of static GNSS measurements in base stations was two hours. The coordinates of the temporary base stations were calculated with respect to the continuously operating GNSS station (reference ID: 62-422- 5069 at Kärdla, which belongs to the Trimble VRS Now network in Estonia, vrsnow.ee). Additionally, a few virtual reference stations (VRS1, VRS2, VRS3 in Figure D1) were artificially created from the VRS Network in the middle of every route and incorporated into the data post-processing as well. The coordinates of profile-points were computed by Trimble Total Control software ver. 2.73 for kinematic data post-processing, where the virtual and temporay base stations served as the initial. On average, RMS for all kinematic points as of ±0.9 cm was achieved from data post-processing.

Note that the gravimetric GRAV-GEOID2011 model does not coincide with the official height system (BK77) in Estonia. For a better comparison, the offset 40 cm21 was removed from the GRAV- GEOID2011 model (cf. Figure D1). The actual sea level determined at all PGs was uniformly -32 cm below the MSL (cf. Table 4 in Paper I) during GNSS measurements. Therefore, +32 cm was added to post- processed GNSS results. Theoretically, the sea level-corrected22 GNSS results must be equal to the values of the geoid model. Practically, both GNSS measurements and the geoid model contain errors.

The differences between model GRAV-GEOID2011 and the sea level- corrected GNSS measurements (geoid minus GNSS results) are presented in Figure D3. Note that there are some sudden jumps in GNSS data: the recorder had to cross wooden boards that were laid over cracks and uneven areas of the ice, making it difficult to obtain consistent readings. The Kuivastu–Virtsu and Sõru–Triigi along-route differences between the geoid model and sea level-corrected GNSS measurements remain within +2.5…-1 cm. The difference is a bit larger in the Rohuküla–Heltermaa profile, reaching up to -3 cm at the coast near Heltermaa. Note that the geoid model changes very rapidly,

21 The difference between gravimetric GRAV-GEOID2011 model and the BK77 fitted EST- GEOID2011 model varies within 38…42 cm in the West-Estonian Archipelago. 22 The sea level corrections are based on the results of this study (cf. Appendix A).

134 7 cm per 4 km near Heltermaa (cf. contours in Figure D1). Assuming that the accuracy of GNSS measurements is constant for the entire profile, the differences between the geoid model and GNSS measurements should be constant in Heltermaa and Rohuküla as well. However, some larger differences occurred near the coast of Heltermaa, possibly caused either by uncertainties of the used geoid model or ice conditions. Note that Heltermaa is surrounded by two islets and the ice road passes by the coast of one islet (cf. Figure D1). The water is shallow in this area and remains within 1…2 m. Therefore, the ice could be even thicker than 50 cm in that area and the separation between ice surface and water level could be larger than the adopted 3 cm corrections.

Figure D3. Differences (geoid minus GNSS) between gravimetric GRAV- GEOID2011 model and profile-wise sea level-corrected (+32 cm) GNSS measurements in the Väinameri Basin. A 40 cm offset has been removed from GRAV-GEOID2011 model, the GNSS heights include offset -3 cm due to separation of the ice surface from the water surface. 4th degree polynomials are denoted by the black lines. Standard deviations of geoid-profile discrepancies are as follows: Kuivastu–Virtsu 1.4 cm, Sõru–Triigi 1.7 cm, Rohuküla–Heltermaa 2.1 cm.

135 All in all, a reasonable agreement (±2.5 cm, excl. the ending of the Rohuküla–Heltermaa route) between the gravimetric GRAV- GEOID2011 model and profile-wise GNSS measurements was detected for all GNSS profiles. Presumably, by using GNSS-levelling the heights can be transferred across the Väinameri with accuracy ±2.5 cm, which is somewhat worse than that achieved by hydrodynamic levelling. However, there should be additional research of the gravimetric GRAV-GEOID2011 model in the Väinameri area.

Verifications by ALS measurements Profile-wise ALS measurements were designed and carried out (May 22, 2012, with sunny weather and a calm sea surface at an altitude of 2400 m) by the ELB to confirm gravimetric geoid changes in the centre of the Väinameri Basin, where a suspicious “lump” in the geoid model was detected (cf. Figure D1). Note that in this particular area only a few gravity data points were available over the sea surface for geoid modelling (cf. Ellmann et al. 2011, Figure 1).

Laser scanner Leica ALS50-II mounted to the ELB aircraft Cessna 208B Grand Caravan was used. Additionally, the aircraft was equipped with an inertial measurement unit (IMU) and GNSS to locate and orient the laser returns in three-dimensional space. The scanning frequency and pulse repetition frequency were 31.9 Hz and 93.2 kHz, respectively. Point density in the nadir region was approximately 0.45 points per square meter. Laser wavelength 1064 nm, i.e. near-infrared spectrum was used for recording water surface returns. Note that infrared light is effectively absorbed by water bodies (Wolfe and Zissis 1993).

The accuracy of ALS-measurements depends on: (i) the laser calibration; (ii) range measurement; (iii) the GNSS positioning. Overall, the accuracy of an elevation is typically better than ±10 cm over the ground surface (cf. Krabill et al. 2002). According to Huising and Pereira (1998) and Pereira and Wicherson (1999), the vertical accuracy of ALS measurements in coastal and flood areas remains within ±20 cm. The accuracy ±12 cm was achieved with control measurements on the roads by ELB (A. Gruno, pers. comm., 2012). To the present knowledge no earlier sea surface ALS scanning has been reported, therefore prior information on the expected accuracy over the sea surface was absent.

136 The coordinates and heights of the aircraft trajectory and sea level height were calculated by the ELB. A continuously operating GNSS station at Kärdla and a VRS base station VRS4 (cf. Figure D1) were used for kinematic GNSS data post-processing (processed by A. Gruno, ELB). Additionally, IMU data were added to specify the positioning results. For profile-wise comparison, only nadir range ALS data were used. For this, a 4 m wide strip (±2 m from opposite sides of the nadir-trace) was extracted from a standard 2700 m (corresponding to off-nadir angle 27.5º) wide scanning strip to eliminate possible errors.

The actual sea level for every ALS point was interpolated using adjusted PG data in Triigi and Heltermaa (cf. Figure D1). Note that during the flight the actual sea level from the 2010 MSL was -13 cm and -10 cm in Triigi and Heltermaa, respectively. The 4th degree trend polynomial was calculated from the sea level-corrected ALS geodetic heights (cf. white line in Figure D4). The SD = 7.1 cm based on the differences between sea-level-corrected ALS data and 4th degree trend polynomial was achieved.

Figure D4. Sea level-corrected ALS data across the Väinameri. The white line indicates 4th degree trend polynomial from sea level-corrected ALS data between Triigi and Heltermaa. Standard deviation of ALS-profile discrepancies is 7.1 cm.

The offset 40 cm was removed from the GRAV-GEOID2011 model for a better comparison between geoid model and 4th degree polynomial from sea level-corrected ALS data (cf. black and dark grey lines in Figure D5). Note that a gentle “lump” (from latitude 58°38' to 58°46') in the geoid surface has been confirmed by the sea level- corrected ALS data as well.

137

Figure D5. Profile-wise gravimetric GRAV-GEOID2011 model and 4th degree polynomial from sea level-corrected ALS data between Triigi and Heltermaa. A 40 cm offset has been removed from GRAV-GEOID2011 model. Differences (geoid minus ALS) between gravimetric GRAV-GEOID2011 model 4th degree polynomial from sea level-corrected ALS data in the Väinameri Basin are presented on the right- hand scale.

The differences between geoid model and ALS data remain within +1…+7 cm (cf. light grey line and right-hand scale in Figure D5) and increase quite linearly from Triigi to Heltermaa. Note that from latitude 58°47' the differences start to increase more rapidly, possibly because the plane turned (cf. northernmost curved ending of the plane trajectory in Figure D1). The change in direction could cause roll, yaw and pitch of the plane, affecting its stability, which in turn could have caused inaccuracies in ALS measurements. Therefore, ALS results after latitude 58°47' are most likely erratic. Notably, the ALS track mimics the GRAV-GEOID2011 model quite well, since the differences in the open sea remain below +4 cm.

Further studies can be conducted for profile-wise fitting (complementing the usual point-wise GNSS-levelling fitting) of gravimetric geoid models to the actual height datum over marine areas.

Verifications by satellite altimetry data Additionally, satellite altimetry mission ENVISAT (Environmental Satellite) data were used to get more information about gravimetric geoid surface changes across the Väinameri Basin and nearby areas. ENVISAT (operational from March 1, 2002 to April 8, 2012) was a European Space Agency (ESA) satellite, which carried 10 earth- observing instruments to provide atmospheric, oceanic, land, and ice measurements, including the Radar Altimeter-2 (RA-2). ENVISAT flew in a polar orbit at an altitude of about 800 km, with a 35-day repeat cycle and an inclination of 98.6°. ENVISAT provided observations with a ground-track spacing of ~40 km in the Baltic Sea

138 area (cf. Figure D6A). Note that for another SA mission Jason-2, ground-track spacing is ~160 km in the Baltic Sea area (cf. Figure D6B). Jason-2 is operated by NASA (National Aeronautics and Space Administration), CNES (National Centre for Space Studies), NOAA (National Oceanic and Atmospheric Administration) and EUMETSAT (European Organisation for the Exploitation of Meteorological Satellites). There are no Jason-2 tracks over the Väinameri Basin (cf. Figure D6B). Therefore, ENVISAT data were used in this study.

A B Figure D6. Ground-tracks of ENVISAT (A) and Jason-2 (B) over the coastal areas of Estonia. Photos: Google maps/CLS

RA-2 is a nadir-looking pulse-limited radar altimeter operating at two frequencies: Ku- (13.575 GHz) and S- (3.2 GHz) bands. The surface footprint size is uncertain and its nominal diameter varies approximately between 2 km and 10 km (cf. Chelton et al. 2001). These variations are caused by waves. Note that the Väinameri Basin is a small water body with many small islets. Therefore, in the coastal areas, a number of footprints are partly over water and partly over land. The power received in a given gate will thus be linked to the relative proportion of the sea and land areas in the corresponding footprint. In the coastal zone (a few tens of km from the coast) data are often discarded because the modelling land effects on the altimetric waveforms are unknown and/or lack adequate corrections for various effects such as path delays, coastal tides, high frequency atmospheric signals. Therefore, the land flags were rejected and the corrected sea surface heights (CorSSH) were computed by AVISO (Archiving, Validation and Interpretation of Satellite Oceanographic data). The CorSSH is calculated as:

139 CorSSH = h – AR – Ʈ (D1) where h is satellite altitude that refers to the distance of the center of mass of the satellite above a reference ellipsoid (cf. Figure D7). The orbit accuracy for ENVISAT is estimated to be 2 cm (cf. Ghazavi 2008), which is achieved by the Doppler Orbitography and Radio- positioning Integrated by Satellite (DORIS) instrument. Note that DORIS measures the Doppler frequency shift between radio signal transmissions from ground beacons to satellite. AR (altimeter range) is the distance from the center of mass of the satellite to the surface of the Earth, as measured by RA-2 with precision 2 cm (Ghazavi 2008). Ʈ includes corrections of orbit, dry and wet troposphere, ionosphere, sea state bias, ocean tide and loading tide, solid Earth tide, pole tide, combined atmospheric correction, major instrumental correction (AVISO 2012).

Figure D7. A schematic illustration of the principle of satellite altimetry and the corrections applied to the altimeter observations of sea surface height. The range corrections affect the range through the speed of the radar pulse and sea-state bias. The geophysical corrections removed the largest known contributor to sea level in order to enhance the oceanographic contributor. Modified from a CNES figure.

Note that TOPEX/Poseidon and GRS-80 ellipsoid is used for CorSSH and GRAV-GEOID2011 model, respectively. The TOPEX/Poseidon ellipsoid axis are ~70 cm shorter than GRS-80, cf. Table D1. Conversation between two ellipsoidal heights can be approximated by an empirically-derived formula (cf. Keysers et al. 2012):

140 2 2 h2 – h1 = – ((a2 – a1) · cos(ƶ) ) + ((b2 – b1) · sin(ƶ) ) (D2)

where ƶ is latitude of point, h1 and h2 are elevations, a1 and a2 are equatorial axes of ellipsoids, b1 and b2 are polar axes of ellipsoids, where indices 1 and 2 denote ellipsoids TOPEX/Poseidon and GRS-80, respectively.

For the latitude 58º40' the Eq. D2 yields the offset (h2 – h1) of 71 cm, which was removed as the constant from all used CorSSH values.

Table D1. Parameters of the TOPEX/Poseidon and GRS-80 ellipsoids. Unit is metre.

Ellipsoid Equatorial axis a Polar axis b TOPEX/Poseidon 6378136.300 6356751.601 GRS-80 6378137.000 6356752.314

CorSSH data of 2010 were used in this study. An ice-free period, i.e. the cycles 89–97 from April to December, were selected. However, cycles 94 and 95 were missing in the ENVISAT series due to changes of the ENVISAT orbit between October 22 and November 02, 2010.

Note that sea level-corrected CorSSH are expected to follow the geoid surface. Therefore, the exact sea level values (using adjusted PG data of this study) were accounted for in every flyover. The actual sea level values were extrapolated outside of the Väinameri as well and added to CorSSH. The accuracy of sea level-corrected CorSSH remains within ±6 cm (includes errors of MSL, altimeter range, orbit and corrections). The discrepancies between GRAV-GEOID2011 and CorSSH for every flyover (cycles 89–97) are presented in Figure D8. Note that standard deviation remains mainly within ±8 cm, except for cycle 93 (±19.1 cm). This larger SD could be affected by windy weather during flyovers on September 18, 19 and 22, 2010.

Additionally, average discrepancies for 5 cycles (89–93) were calculated (cf. Figure D9). Note that after orbit changes the ground tracks of cycles 96 and 97 did not conform to previous tracks. Therefore, these cycles were not used for calculations of average discrepancies between GRAV-GEOID2011 and CorSSH. The SD of discrepancies remained within ±5.5 cm, which is the accuracy of sea level-corrected SA as well. However, SA does not provide as high resolution of the changes of

141 gravimetric GRAV-GEOID2011 model surface as profile-wise ALS and GNSS measurements. Note that the distance between footprints of SA is ~8 km (1 Hz data were used) and only some points without land effect fall into the Väinameri Basin (cf. Figure D9). However, large discrepancies between the regional gravimetric geoid model and SA data were not detected.

All in all, this verification illustrated that the SA data is not as accurate as the used regional gravimetric geoid model. SA observations enable verification of large water areas and detect extreme offsets in geoid surface. On the other hand, this exercise demonstrates that the high- resolution regional geoid models in conjunction with high-frequency PG data can be useful for calibration of the SA results.

Cycle 89 (28.04-24.05.2010) SD ±6.4 cm Cycle 90 (02.06-28.06.2010) SD ±6.5 cm

Cycle 91 (07.07-02.08.2010) SD ±8.3 cm Cycle 92 (11.08-06.09.2010) SD ±5.5 cm

142

Cycle 93 (15.09-11.10.2010) SD ±19.1 cm Cycle 96 (01.11-25.11.2010) SD ±9.8 cm

Cycle 97 (01.12-25.12.2010) SD ±7.3 cm Figure D8. Discrepancies (geoid minus CorSSH) between gravimetric GRAV- GEOID2011 model and MSL-corrected CorSSH data based on ENVISAT. GRAV- GEOID2011 model with contour interval 10 cm is placed in the background. Unit is centimetre.

143

Cycles 89-93 (28.04-11.10.2010) SD ±5.5 cm Figure D9. Discrepancies (geoid minus CorSSH) between gravimetric geoid model GRAV-GEOID2011 and MSL-corrected CorSSH data based on ENVISAT cycles 89–93. GRAV-GEOID2011 model with contour interval 10 cm is placed in the background. Unit is centimetre.

144 SUMMARY IN ESTONIAN

Käesoleva doktoritöö eesmärgiks oli uurida rõhuanduritel põhineva hüdrodünaamilise loodimise täpsust. Uuringud kinnitasid, et rõhuandureid saab lisaks merendusotstarbele kasutada ka geodeetiliste ülesannete lahendamiseks. Töö tulemusi on võimalik rakendada Eesti riikliku kõrgusvõrgu rekonstrueerimisel, et siduda mandri kõrgusvõrguga Saaremaa ja Hiiumaa.

Rõhuanduritel põhineval hüdrodünaamilisel loodimisel tuleb siiski arvestada järgmisi aspekte: (i) Rõhuandurite mõõtmistulemused on mõjutatud ajalisest triivist, mis antud töös kasutatud anduritel ulatus kuni 6 cm aastas. Triivi suuruse ja suuna määramiseks on võimalik kasutada rõhuanduri lähedale paigaldatud veemõõdulatti ja võtta sellelt perioodiliselt (nt kord kuus) kontroll-lugemeid. (ii) Hüdrodünaamilise loodimise tulemusi võivad mõjutada keskkonnatingimused. Seetõttu tuleks arvesse võtta keskmine ja aastaaegadest sõltuv merepinna topograafia. See võib aga osutuda problemaatiliseks, kuna nõutava täpsuse (1 cm) tagamiseks on olemasolevad merepinna topograafia globaalsed ja regionaalsed mudelid ebatäpsed. Seega, kui uuritava ala kohta pole kasutada täpset merepinna topograafia mudelit, siis mõningatel puhkudel (nt rannikualadel) on otstarbekam topograafia parandeid vältida. Nimetatud juhtudel peaksid aga meretaseme vaatluste aegread olema piisavalt pikad, et elimineerida aastaaegadest ning ilmastikust tingitud topograafia kõikumised ekvipotensiaalpinna suhtes.

Doktoritööst järeldus, et sõltuvalt uuritava mereala iseärasustest tuleks kõrguskasvude määramiseks hüdrodünaamilise loodimisega kasutada aastast veemõõdu perioodi. Pikemate vaatlusseeriate korral ei pruugi tulemuste usaldusväärsus suureneda, kuna koorikloomad ja/või vetikad võivad aja jooksul rõhuanduri membraani ummistada ning pikaajaliste mõõtmiste kvaliteeti halvendada.

Käesolevas töös arvestati kõiki eelpool mainitud aspekte ning hüdrodünaamilise loodimise tulemusi valideeriti Lääne-Eesti saarestikus. Uurimistöös kasutati kuut rõhuanduritel töötavat veemõõdujaama (Virtsu, Kuivastu, Triigi, Sõru, Heltermaa ja

145 Rohuküla). Jaamad moodustavad ümber Väinamere suletud polügooni, mis koosneb kolmest mööda maad ja kolmest üle vee looditud sektsioonist. Veetasemed mõõdeti kõigis jaamades kahe aasta (2010, 2011) vältel. Enne jaamadevaheliste hüdrodünaamilise loodimise teel saadud kõrguskasvude arvutamist töödeldi veemõõdujaamade andmed. (i) Lisati toorandmetele triivi parandid ning (ii) filtreeriti veemõõdu aegridadest välja väliste tegurite (nt laevaliiklus rõhuanduri lähedal) ja tuultest tingitud merepinna kallete mõju. Andmetöötluse ja filtreerimise printsiipe on selgitatud peatükis 3.6. Jaamadevahelised kõrguskasvud arvutati aasta keskmise veetaseme põhjal.

Töö tulemuseks on hüdrodünaamilise loodimisega 2010. aasta veemõõduandmete põhjal määratud kolme lõigu (Virtsu–Kuivastu, Triigi–Sõru ja Heltermaa–Rohuküla) kõrguskasvud (vt tabel 9). Ühtlasi valiti need väärtused lõplikeks, kuna: • 2010. aastal koguti veemõõdulattidelt rohkem kontroll-lugemeid kui 2011. aastal ja seetõttu on triivi parandi määramise tulemused usaldusväärsemad; • stabiilsusanalüüsid näitasid, et rõhuandurite esimese aasta aegread on vees leiduvast hõljumist, koorikloomadest ja/või vetikatest vähem mõjutatud; • Väinamerd ümbritseva suletud loodimispolügooni sulgematus (0.2±1.5 cm) oli 2010. aasta andmete põhjal väiksem kui 2011. aastal.

Hüdrodünaamilise loodimise kõrguskasvude kontrollimiseks kasutati kuut erinevat meetodit ning loodimistulemusi varasematest mõõtmistest: (i) Teostati 6- ja 4-päevased veevaatlused tingimustes, kus kogu Väinameri oli kaetud jääga ning anduri triiv puudus. (ii) Hõrendatud intervalliga (12h) veemõõdu aegridu võrreldi 5m andmetega. Võrdlustesse kaasati ka veemõõdulattide ajaloolised aegread (latilugemite võtmise intervall 12h). (iii) Kõrgtäpsete loodimiste tulemusi (täpsus ±0.27 mm km ) kasutati mööda maad ühendatud veemõõdujaamade vaheliste hüdrodünaamiliste kõrguskasvude kontrollimiseks. (iv) Hüdrostaatiliste loodimiste tulemusi (täpsus ±1.0 cm) kasutati üle vee ühendatud jaamade vaheliste kõrguskasvude võrdlemiseks.

146 (v) GNSS-loodimiste kõrguskasve (täpsus ±2.0 cm) sai rakendada nii mööda maad kui üle vee ühendatud veemõõdujaamade vaheliste kõrguskasvude võrdlemiseks. (vi) Arvutati ümber Väinamere moodustunud loodimispolügooni sulgematus.

Rõhuanduripõhiste hüdrodünaamiliste loodimiste väärtused sobisid eelpool loetletud meetodite tulemustega ±1.5 cm täpsusega (vt joonis 19 ja 21). Veelgi enam, erinevused (i) talviste lühiajaliste, anduri triivist mõjutamata ja aastaste veetaseme jälgimiste ning (ii) talviste lühiajaliste, anduri triivist mõjutamata ja kõrgtäpsete loodimiste vahel jäid enamasti ±1.0 cm sisse (vt joonis 19). See viitab, et rõhuandurite ajaline triiv ja ilmastikutingimused (tuul) võivad olla peamised hüdrodünaamilise loodimise täpsust mõjutavad tegurid. Kuigi jääga kaetud veekogus tehtud lühiajaliste veevaatlustega on võimalik saavutada ±1.0 cm täpsus, tuleks siiski eelistada aastaseid vaatlusseeriaid. Nimelt võivad lühiajalised mõõtmised olla tugevalt mõjutatud ilmastikuoludest, mis põhjustavad jaamadevahelist vee kallet. Mainitud kallet on võimalik elimineerida või minimeerida, kasutades aastapikkusi aegridu.

GNSS-loodimiste ja veemõõdulattidelt kogutud ajalooliste vaatulsseeriate tulemuste ning hüdrodünaamilise loodimise kõrguskasvude vahel esines siiski ka kuni 3.7 cm erinevusi. Suurte vahede põhjuseks võivad olla ebausaldusväärsed ajaloolised vaatlusseeriad, mida aastakümneid hiljem on raske täpsustada. GNSS- loodimisteks kasutati gravimeetrilist geoidi GRAV-GEOID2011 (vt peatükk 4.3.3.). Mudeli täpsus mandri-Eestis on hinnanguliselt ±1.3 cm. Kuna merealadel on mudeli täpsus määramata, siis käesoleva töö raames teostati selleks kolm profiilipõhist kontrollmõõtmist, kasutades GNSS-i, aerolaserskaneerimise (ALS) ja satelliitaltimeetria (SA) andmeid. Nimetatud meetodite täpsus võimaldab edukalt määrata geoidi pinna suhtelist muutust. Verifitseerimised kinnitasid ±3…4 cm ebatäpsusi geoidi mudelis Väinameres osas. Võrdlustest ilmnes, et geoidi mudeli ebatäpsusest tulenevalt ei saa Väinamere piirkonnas kasutada olemasolevaid merepinna topograafia väärtusi. Mereala geoidi mudeli täpsustamiseks tuleks läbi viia täiendavad uuringud.

Rõhuanduritel põhineva hüdrodünaamilise loodimisega on võimalik saavutada täpsus kuni ±1.0 cm eeldusel, et andmete kogumine ja töötlemine on teostatud korrektselt. Käesolevas töös oli mõnedest

147 jaamadest võetud vähe kontroll-latilugemeid. Seega võib kokkuvõttena väita, et kuni 65 km laiuste veetakistuste ületamisel saadi hüdrodünaamilise loodimise täpsuseks ±1.5 cm. Pikemate vahemaade loodimine üle vee vajab lisauuringuid. Üle avamere loodimisel tuleb arvestada soolsuse (mõjutab vee tihedust ja merepinna topograafiat) ja loodetega, mis võivad põhjustada suuri ebatäpsusi loodimiste lõpptulemustes.

Hüdrodünaamiline loodimine võib sageli osutuda kõrguste üle vee kandmise ainuvõimalikuks (täpseks) viisiks, sest võrreldes teiste meetoditega on see • majanduslikult odavam ja vähem töömahukas kui hüdrostaatiline loodimine; • täpsem kui laialdaselt kasutatav GNSS-loodimine, mille täpsus sõltub suuresti kasutatava geoidi mudeli täpsusest; • kasutatav kõikidel laiuskraadidel, kuna see ei sõltu jääkatte olemasolust.

Võrreldes teiste veemõõdujaamadega on rõhuandurite eeliseks nende väiksus, odavus ja lihtne paigaldatavus. Täpseteks mõõtmisteks saab ja tuleb anduri triiv hoida kontrolli all, võttes selleks lähedal asuvalt veemõõdulatilt kontroll-lugemeid täpsusega ±0.5 cm vähemalt kord kuus.

Rõhuanduritel põhineva hüdrodünaamilise loodimise täpsuse suurendamiseks tuleks järgnevates töödes uurida ja püüda täpsemalt määrata • rõhuandurite triiv, kasutades selleks automatiseeritud (nt telemeetrilist) kontroll-lugemite võtmist rõhuanduri lähedal olevalt veemõõdulatilt. Triivi väärtused on vajalikud ka teistele meretaseme aegridade kasutajatele. Näiteks on Eesti Meteoroloogia ja Hüdroloogia Instituut paigaldanud alates 2010. aastast Eesti rannikualadele kümneid rõhuanduritel töötavaid veemõõdujaamu. Nende jaamade aegridu on võimalik kasutada, kuid ainult siis, kui triivi parandid on kogutud täpselt ja perioodiliselt (nt kord kuus). Vastasel korral ei saa tulevikus nende jaamade aegridu kasutada geodeetilistel eesmärkidel; • rannikuäärse ja poolsuletud veekogu merepinna topograafia.

148 Kõrguskasve mandri-Eesti ja saarte vahel pole määratud üle 30–40 aasta. Siiani puudus ametlikult kõrguslik side ka Hiiumaa ja mandri vahel. Seega on käesoleva töö tulemustel mitmeid olulisi rakendusi. • Rõhuanduritel põhineva hüdrodünaamilise loodimise kõrguskasve mandri ja saarte vahel saab kaasata Eesti riikliku kõrgusvõrgu rekonstrueerimisse. • Kasutades üle vee loodimisi, saab täpsustada saarte uut kõrgussüsteemi. See omakorda võimaldab korrigeerida geoidi mudelit saartel ja seega suurendada GNSS-loodimise täpsust. • Tulemused võimaldavad täpsutada gravimeetrilise geoidi mudeli GRAV-GEOID2011 ja kehtiva/uue ametliku kõrgussüsteemi vahelisi sobitusparameetreid. • Saarte ja mandri vaheliste uute kõrguskasvude kaasabil saab täpsustada maakoore vertikaalliikumisi Eestis. • Üleriigiline täpne kõrgussüsteem on oluline ka insener-tehnilistel töödel. Näitena võib tuua arutelu püsiühenduse (st silla või tunneli) rajamise kohta Muhu ja mandri vahele. • Täpsete kõrguste lisamine veemõõduandmetele võimaldab kalibreerida satelliitaltimeetria tulemusi Läänemerel.

Kokkuvõttena võib öelda, et doktoritöö sisaldab olulist informatsiooni Eesti riikliku kõrgusvõrgu rekonstrueerimiseks. Lisaks leiab tööst kasulikke lisateadmisi kirjeldatud metoodika ja seadmete kohta, et neid rakendada maailma erinevates piirkondades ja keskkonna tingimustes.

149 ACKNOWLEDGEMENTS

This work was carried out at the Department of Geomatics, Estonian University of Life Sciences. The study was financially supported by target-based funding from the Estonian Science Foundation Grants No. 5731 and 8749.

First and foremost I would like to express my gratitude to my supervisors. I am thankful to Dr. Harli Jürgenson for directing me to PhD studies. My special thanks go to my mentor Professor Artu Ellmann, Tallinn University of Technology for his immense help, encouragement, guidance and patience during the last years of my studies.

Many thanks are due to Dr. Tarmo Kõuts, Marine Systems Institute at Tallinn University of Technology for providing pressure gauge data and for his valuable comments related to sea level observations and specifics of used pressure gauges.

I would like to thank Dr. Ants Torim and Helju Jürma from the Estonian Land Board for helping me to collect and systematise the historical levelling data. Many thanks go to Anti Gruno, Estonian Land Board, for providing the ALS data used in this study. I wish to express my thanks to staff members from the Estonian Meteorological and Hydrological Institute for providing the historical sea level series.

I am obliged to Aado Tamm for technical assistance and helping in data processing of sea level series. I am thankful to Kristina Türk and to all my students for helping me in the fieldworks.

I am grateful to all my colleagues from the Department of Geomatics of the Estonian University of Life Sciences for their help and support, especially to head of the department Siim Maasikamäe. I am very thankful to Tarmo Kall for fruitful discussions and guidance throughout all my studies.

I also greatly appreciate Professor C.K. Shum and his research team from Ohio State University (OSU) in USA for providing the opportunity to stay and study at OSU and to receive guidance about satellite altimetry.

Last but not least, I would like to express my gratitude to my family and friends for their understanding and persistent encouragement throughout my PhD studies.

150 I

PUBLICATIONS Liibusk, A., Ellmann, A., Kõuts, T., Jürgenson, H. 2013. PRECISE HYDRODYNAMIC LEVELLING BY USING PRESSURE GAUGES

Marine Geodesy, 36. DOI: 10.1080/01490419.2013.771594 (in print). ACCEPTED MANUSCRIPT

Precise hydrodynamic levelling by using pressure gauges Aive Liibusk1, Artu Ellmann2, Tarmo Kõuts3, Harli Jürgenson1

1Department of Geomatics, Estonian University of Life Sciences, Tartu, Estonia 2Faculty of Civil Engineering, Tallinn University of Technology, Tallinn, Estonia 3Marine Systems Institute, Tallinn University of Technology, Tallinn, Estonia Corresponding author: Aive Liibusk, Estonian University of Life Sciences, Kreutzwaldi 1, Tartu 51014, Estonia. Phone: +372 7313 196, fax: +372 7313 156. E-mail address: [email protected]

Received: 16 Mar 2012. Accepted: 17 Jan 2013 Accepted author version posted online: 25 Feb 2013

This study investigates applicability of hydrodynamic levelling by means of contemporary pressure gauges for achieving geodetic accuracy in height determination. The main problems associated with pressure gauges are rigorous connection to national levelling network and data processing, e.g. determination of time-dependent drift and data filtering principles. The equipment and methodology developed was tested in a test area in the Baltic Sea. It can be concluded that the year-long sea level series may provide ±2.0 cm accuracy for hydrodynamic levelling within the water stretches up to 65 km. This is confirmed by alternative height determination methods and additional field experiments.

Keywords: hydrodynamic levelling; pressure gauges; time-dependent drift

Introduction

For many applications in geodesy, engineering and oceanography a nationwide common height reference system need to be implemented and maintained. Traditional spirit levelling is used to achieve the highest precision (sub-cm, typically) in height determination. National levelling network usually comprises of several inter-connected loops, whereas the heights (either normal or orthometric) of benchmarks are determined from a common adjustment. For rigorous datum unification it is necessary to establish reliable connections between all parts of such a levelling network, both in mainland and on adjacent islands.

Apparently, extension of a nationwide height reference system from mainland to islands may become very complicated due to the need for precise across-water measurements. Various methods have been developed for the purpose. They differ from one another both by achievable precision and the amount of work and resources required for conducting the measurements. Contemporary height determination methods providing a cm-range precision are: (1) global navigation satellite system (GNSS) based levelling,

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(2) hydrostatic levelling, (3) hydrodynamic levelling.

This study focuses on the hydrodynamic levelling. Since the results are verified against the first two height determination methods, it is appropriate to review these as well.

(1) Geodetic GNSS-measurements in conjunction with a regional geoid model can be used for vertical positioning. However, in many regions the accuracy of gravimetric geoid models is not exceeding 2–3 cm. Even though regional geoid models may be corrected by using GNSS-levelling points (resulting in a so-called height correction surface), both the levelling and GNSS heights need to be consistent (i.e. originating from the respective adjustment). For the GNSS points a consistent solution can be easily achieved. However, in case of the common adjustment of traditional levelling, the height differences between the mainland benchmarks and that of islands need to be determined rigorously, i.e. by using any of the other two (i.e. (2) and (3)) levelling methods. Therefore, the issue of precise height transfer over waterways remains crucial even in the GNSS era.

(2) According to the method of hydrostatic levelling an elastic tube (or a set of interconnected tubes) filled with liquid (water or spirit) is laid between the shores of the waterway to be bridged. The level of liquid, observed at both ends of the tube, indicates (in an ideal case) the same level surface. This method has been applied on a number of occasions in Denmark for ranges up to 20 km (e.g. Fehmarn Belt, Baltic Sea, for more details see Andersen 1992). The hydrostatic levelling was also used to connect the Kronstadt tide gauge (the zero of the Baltic Geodetic Height system) and a mainland benchmark (Tamme 1971, also in Bogdanov et al. 2000). Precise hydrostatic levelling is technically sophisticated (e.g. due to the need to remove all of the air-bubbles in the tube) and economically expensive. Thus this method is no longer feasible, mainly due to its high cost but also due to sensitivity to temporal and spatial changes in environmental conditions.

(3) In case of longer (more than 20 km) distances and deep water conditions, the method of hydrodynamic levelling could be applied. Hydrodynamic levelling is connoted with sea level observations for determining height (potential) differences between coastal points or over oceanic regions (e.g. Torge 2001). The observations have to be averaged and reduced due to the sea surface topography (SST), which is a deviation of the mean sea level (MSL) from an equipotential surface (e.g. marine geoid). Traditionally, long-term (from several years up to decades) sea level series by float-in-a-well tide gauges (a.k.a. mareograph) have been preferred for hydrodynamic levelling. Contemporary automatic tide gauge stations (TG) track the water level changes continuously and even in real-time. Importantly, this enables monitoring sudden water level changes that could otherwise remain unnoticed.

Common disadvantages of the hydrodynamic levelling, however, are gaps in data series. Data quality could vary due to the malfunctioning of instruments and natural causes (e.g. vertical land movements, waves, local water circulation patterns etc.) as well. In addition,

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the TG equipment may experience mechanical damages (e.g. ship collisions, ice, vandalism) and consequently need to be replaced. The replacement could lead to physical shifts in the tide gauge’s zero, thus also causing systematic biases in the sea level series. Therefore, there are only a few tide gauges with century-long continuous and reliable data series all around the world. Mostly, the time span that can be used for across-water height connections is a few decades or less. For instance, 19 years of sea level records (monthly mean values) together with an oceanographic model (Novotny et al. 2002) were used to connect the island of Gotland to Swedish mainland (Norin et al. 2010). The uncertainty obtained for this 70 km distance was estimated to be ±3 cm (Jonas Ågren, pers. comm., 2010).

Studies by Cartwright and Crease (1963), and Wübbelmann (1992) apply hydrodynamic levelling over the Dover Strait (about 70 km) and the Fehmarn Belt (about 20 km), respectively. They claim achieving 1.0–1.5 cm accuracy for their results.

This study, however, tests applicability of year-long sea level observations by means of contemporary automatic pressure gauges (PG) for obtaining geodetic accuracy for hydrodynamic levelling.

The outline of the paper is as follows. First, theoretical principles of hydrodynamic levelling are explained. The next section reviews main characteristic of the pressure sensors, which are used in our pressure gauges. Section 4 deals with the specifics of the case study area – the Väinameri Basin in the eastern part of the Baltic Sea. Data processing principles are reviewed in Section 5. The emphasis is on the estimation of the PG drift and its elimination and also the data filtering procedures. Section 6 contains numerical verifications of the obtained results through spirit, GNSS and hydrostatic levelling experiments. The paper is concluded by a brief summary and relevant discussion.

2. Principles of hydrodynamic levelling

The mean sea level at a TG is determined by periodic or continuous sea level observations. For connecting the TG to a levelling network the following reference points are needed: tide gauge zero (TGZ), contact point (CP) and tide gauge benchmark (TGBM).

TGZ is a pre-determined point with respect of which the sea level fluctuations are measured. In principle, TGZ can be selected arbitrarily. The CP is a benchmark-type reference mark on the TG. For the pressure gauges the CP can be placed on the top of the nearby erected staff gauge.

In order to connect the TGZ with the national height datum, the vertical distance between the TGZ and the CP must be accurately determined. The CP is connected to a nearby TGBM by precise spirit levelling. The TGBM is usually included to the national levelling network and thus the height of the mainland TGZ can be directly referred to the national

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height datum. The MSL at a given TG can then be uniquely determined from the sea level fluctuations with respect to the TGZ. However, the height transfer across a waterway via sea level observations involves more than one TG. The readings at each TG are taken with respect to some arbitrary local initial value (i.e. TGZ), which generally is not coinciding with the level surface of the TGZ on the opposite side of waterway. The solution to the problem of determining height differences between paired sea level stations (more correctly – between respective TGZs) can be described as follows.

Figure 1. Hydrodynamic levelling between paired tide gauges. The height difference between respective contact point (CP) and tide gauge benchmark (TGBM) can be measured by spirit levelling.

Readings of the MSL values (୅ǡ୆) are obtained by averaging. Other values are either calculated (heights: ଵ, ଶǡ ǡ ) or assigned (tide gauge zeros: TGZA and TGZB).

In hydrodynamic levelling it is important to identify the same level surface that was adopted at the initial TG. First, at a mainland Station A (see Fig. 1) the CPA height (HA) can be determined precisely by connecting it to TGBMA by spirit levelling. At an island Station B the CPB height (HB) needs to be determined with respect to HA by using sea

level observations. Observation equations for determining the heights of the MSL ( ଵ

and ଶ) at paired Stations A and B can be represented as:

୅ ଵ ൌ ሺ ୅ െ୅ሻ െ൫୘ୋ୞ െ୅൯൅Ԗ୅ (1)

and ୆ ଶ ൌ ሺ ୆ െ୆ሻ െ൫୘ୋ୞ െ୆൯൅Ԗ୆ (2)

where TA and TB are vertical distances between the corresponding CP and TGZ at Stations A and B, respectively (cf. Fig. 1). Thus, the first bracketed term on the right hand side of ୅ ୆ Eqs. 1 and 2 denotes the height of the corresponding TGZ. The readings ୘ୋ୞ and ୘ୋ୞ correspond to the TGZ location (determined at the instalment of the TG) of Station A and B, respectively. The overbared symbols denote values obtained by simple arithmetical

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averaging over the given time period. The averaged readings ୅ and ୆ correspond to the MSL at Station A and B, respectively, i.e.

ଵ ഥ ൌ σ୬ୀ୧୫ୟ୶ ሺ ሻ ൅ሺሻ (3) ୬ ୧ୀଵ ୧ ୧

where R(ti) is the reading at the i-th time-epoch of measurements (ti) and d(ti) denotes relevant corrections (e.g. due to drift of pressure sensors, for a more extended discussion

see Section 5.1) at the same instant. Symbols Ԗ୅ and Ԗ୆ denote a random variable (error of

measurements at Stations A and B) with the mathematical expectation of zero, i.e. E(߳஺) = ୅ ୆ E(Ԗ୆) = 0. Note that the quantities TA, TB, ୘ୋ୞, ୅, ୘ୋ୞, ୆, HA, ଵ can be measured

directly or obtained from simple averaging. The only unknowns are ଶ and HB which need to be determined from solving the system of equations. Subtracting Eq. 2 from Eq. 1 yields:

୅ ୆ ୆ െ ഥଶ ൌ ሺ ୅ െ୅ሻ െ ഥଵ ൅୆ െ൫୘ୋ୞ െഥ୅൯൅ሺ୘ୋ୞ െഥ୆ሻ (4)

where the two unknowns are grouped on the left hand side and the values of random measurement errors are henceforth neglected for the sake of brevity of discussion. The

height ଶ can also be expressed via SST. The height of the MSL at Station B can then be written as (see also Fig. 1):

ଶ ൌ ଵ െ୅ ൅୆ (5)

where ୅ and ୆ are the mean sea surface topography values at Stations A and B, respectively. Now Eq. 4 can be expressed as:

୅ ୆ ୆ ൌ ሺ ୅ െ୅ሻ ൅୆ െ൫୘ୋ୞ െ୅൯൅൫୘ୋ୞ െ୆൯ െ ሺ୅ െ୆ሻ (6)

Certain assumptions need to be introduced in order to determine HB. For instance, the mean values can be taken from existing global/regional SST models. Note that the above expressions are somewhat simplified. More elaborated expressions for hydrodynamic levelling can be found in Cartwright and Crease (1963). A discussion about the applicability of Eq. 6 in our study area is postponed to Section 4.2.

The above principles of hydrodynamic levelling are valid for all types of tide gauges. In remote locations with minimum infrastructure the TGs are required to be compact, robust, reliable and autonomous. Since automatic pressure gauges correspond to the requirements, then the emphasis of the following sections is given on their main characteristics and usage.

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3. Sensors used in pressure gauges

Different types of pressure gauges exist. In this study the force collector type (i.e. piezoresistive and capacitive) pressure sensors were used. Such pressure sensors use a diaphragm to measure strain due to applied force (i.e. pressure). Note also that the pressure at depth in a column of water depend on the mean density of the above water column and the acceleration due to gravity (g). Differences in water density from place to place may be important, particularly if large differences in salinity and/or temperature occur. Thus, the g differences and large variations of the salinity and temperature during the measurements need also be taken into account.

The focus of this study is on the usage of piezoresistive and capacitive measurement technologies. Piezoresistive technology is suited to measure both low and medium pressures. Capacitive technology is better suited for low pressures. An exhaustive review on pressure sensors can be found in Bao (2000).

In our study the piezoresistive Keller 36XW and capacitive Keller 46X sensors were selected for sea level observations, see Fig. 2. Variations in air pressure are compensated by leading the atmospheric air to the other side of diaphragm through a special capillary cable. The default output of PG is the water column height in units of length (cm).

Figure 2. Pressure sensors Keller 36XW (A) and Keller 46X (B). Note the capillary cable for compensating variations in the atmospheric air-pressure. (Photos: Keller Ltd.).

Both types of pressure sensors can be used in harsh environmental conditions, and due to their low power consumption can be operated just on a battery and/or a solar panel. The power consumption depends also from the data sampling interval, which can be set from a few minutes to hours.

Pressure sensors are mainly used in various short-term (from a few weeks to a few months) scientific studies and monitoring but also in industrial tanks and basins. Unlike to traditional float-in-a-well tide gauges, no special well is required for operating a PG. Attaching a sensor inside a protective tube or onto the back side of the staff gauge could be

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sufficient to ensure the immobility of the sensor and protecting it from mechanical damage. Although PGs have a number of advantages (inexpensive, easy to install, compact) compared to other measurement techniques, they also possess some drawbacks that may jeopardise their use for high-precision height determination. Firstly, it is quite difficult to precisely connect the diaphragm of the pressure sensor to the CP with direct length measurements. This problem can be overcome by collocating the PG with a staff gauge. After installation the PG initial reading of the sea level is taken visually from the staff gauge and entered into the data handling system ( server). Note that with ideal and very calm weather conditions a cm accuracy for the staff gauge reading can be achieved. In the presence of weak waves the visual reading accuracy decreases down to 2-3 cm, yielding thus a corresponding discrepancy for the PGs initial reading. However, this discrepancy value can be detected later by taking staff gauge readings with calm sea surface when cm accuracy can be achieved.

Secondly, the pressure sensors can be influenced by time-dependent drift. To account for the drift effect frequent (at least once a month) control readings from staff gauge need to be taken and compared with the reading of the pressure sensor at the same time moment. We return to this issue with some more details in Section 5.1.

The characteristics of the used pressure sensors are compared in Table 1. The main differences (apart from the shape) between these two sensors are the measurement principles and accuracy and also the range of operating and compensated temperature. The water temperature is determined by an internal thermometer. For the Keller 46X, the minimal operating and compensated temperatures are 0 °C and +10 °C, respectively. Within the compensated range the pressure values consider the thermal expansion of the piesoresistive crystals and the capacitive diaphragm. Suitability of these sensors for the year-round usage is tested by a practical experiment in the West-Estonian Archipelago. It should be noted that our experiments did not reveal any peculiar changes in Keller 46X’s data series when the temperature fell below the compensated range (+10 °C).

Table 1. Characteristics of the Keller 36XW and 46X pressure sensors. Pressure sensor Keller 36XW Keller 46X Type Piezoresistive Capacitive Length [mm] 121 44.5 Diameter [mm] 22 38 Full scale (FS) pressure range 1000 300 [mbar] Accuracy ±0.1% FS ±0.1% FS (in units of length) (±1.0 cm) (±0.3 cm) Compensated range 0…50 °C 10…50 °C Operating temperature -20…80 °C 0…80 °C

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4. Characteristics of the study area

4.1 Constellation of the pressure gauges

The latest modernisation of the precise national levelling network of Estonia started in 2001. The levelling lines (total length of about 3700 km) form altogether 20 loops – 18 of them are located in the Estonian mainland and 2 within the West-Estonian Archipelago, see Fig. 3.

Figure 3. Layout of the national levelling network of Estonia in 2011. Two westernmost loops are on the islands Hiiumaa and Saaremaa.

To complete the nationwide renovation of the high-precision levelling network also the loops in the West-Estonian islands of Saaremaa (levelled in 2010) and Hiiumaa (2009) need to be connected with the mainland. As it was discussed in the introduction the only feasible method seems to be using hydrodynamic levelling.

It should be noted that in the selected study area there is a long history of the sea level measurements, for more details see e.g. Jevrejeva et al 2001, who used the sea level series for specifying the postglacial rebound rates in Estonia. Most of the stations in the area of interest were simple staff gauge stations, which ceased to be operational decade(s) ago. Moreover, the locations of historic sea level stations were not optimal for establishing a reliable across-water connection between the Estonian mainland the island Saaremaa and between the islands Saaremaa and Hiiumaa.

Therefore, in 2009–2010 PGs were installed in six selected locations: two on mainland Estonia (Rohuküla, Virtsu) and two on both islands, Saaremaa (Kuivastu, Triigi) and Hiiumaa (Sõru, Heltermaa), see Fig. 4. Note that the stations are located on the opposite sides of three straits of the Väinameri Basin.

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Figure 4. Locations of pressure gauges around the Väinameri. Three hydrodynamic and three spirit levelling sections form a 253 km long levelling loop around the Väinameri. Inset – location of the study area in the Baltic Sea region.

All six PGs are located in sheltered ferry harbours. The Virtsu, Rohuküla and Heltermaa stations are equipped with the Keller 36XW sensors and the Kuivastu, Triigi and Sõru stations are equipped with the Keller 46X sensors. The station-to-station distances within the pairs vary from 7 km (between Virtsu and Kuivastu) up to 22 km (Rohuküla and Heltermaa), see the triple-dashed lines in Fig 4. Within the mainland and both islands the CPs are connected by national high-precision levellings, see bold lines in Fig 4. Thus, three hydrodynamic and three spirit levelling sections form a 253 km long levelling loop around the Väinameri (Fig. 4).

4.2 Considerations on the sea surface topography

The Väinameri forms an eastern part of the Baltic Sea. It is an enclosed (surrounded by an arc of islands and the mainland) and a rather shallow water body, with a mean depth of ~5 m. Its area is only 2200 km² but it also contains hundreds of islets. The Väinameri is connected with the Baltic Sea through a system of straits, see Fig. 4. The hydrological conditions of the Väinameri are slightly different from the rest of the Baltic Sea – the wave heights are lower, the water is less saline, the water temperature variations are larger, also the ice cover is thicker and lasts longer. For instance, the water temperature in the Väinameri is under +10 °C about seven months per year and the ice coverage lasts for 3–4 months during cold winters. The Baltic Sea is almost tide-less, the tides stay well below a decimetre level (Raudsepp et al 1999). Thus, within the study area the tide range remains almost the same at any given instant. Instead, the sea level is primarily influenced by the wind stress, air pressure fluctuations and river run off. It should be noted that the seasonal

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variations in the sea level are mainly due to large scale meteorological effects, therefore not generating significant and long-lasting surface slope over such a small area. The maximum daily fluctuations of the sea level can reach 200 cm (Suursaar et al 2008), which is usually related to a passing area of low pressure accompanied by very strong westerly winds. During unidirectional winds the daily sea level changes may reach ±50 cm (Suursaar 2010). The influence of the wind stress, however, is assumed to be rather insignificant when averaged over a longer period.

The sea surface topography values are needed to determine height differences over waterways. Various regional and global models of the mean SST exist. Some of them are computed by using oceanographic (e.g. Carlsson 1998, Lisitzin 1974) and geodetic (e.g. Ekman and Mäkinen 1996) methods and some are derived from satellite altimetry data (e.g. Andersen and Knudsen 2011). Such models can be safely used on the open sea, however, they could be quite inaccurate in coastal areas. Unfortunately, no specially designated high resolution SST model for the Väinameri exists to our present knowledge.

Nevertheless, for the sake of the experiment a satellite altimetry-based SST model DTU10MDT (Mean Dynamic Topography model) by Andersen (2011) was tested for this study. The MDT10 model has been obtained by combining the Mean Sea Surface model (DTU10MSS) and the global geoid model based on the Earth Gravitational Model EGM2008 (Pavlis et al. 2008). The DTU10MSS model has been derived from 17 years data from the European Remote Sensing (ERS) and Environmental satellite altimetry (ENVISAT) missions. The model accuracy has been estimated to be better than 10 cm in most areas of the world (Andersen and Knudsen 2011). The MDT model used has a resolution of 1 arc-minute, which corresponds to 1.8 km by 0.9 km resolution within the study area. The DTU10MDT-derived mean SST differences within the PG pairs (3 across- water and 3 land-connected) are shown in Table 2, column 1. The across-water SST differences remain within 1 cm, which is comparable with the expected accuracy of the hydrodynamic levelling.

Table 2. The satellite altimetry DTU10MDT model based and GNSS-levelling derived mean SST differences (ǻSST) between the across-water and land-connected pressure gauge pairs. Units in cm.

Pairs of pressure gauges ǻSSTDTU10MDT ǻSSTGNSS

Virtsu-Kuivastu -0.4 -1.4

Triigi-Sõru -1.0 -1.5 water Across- Heltermaa-Rohuküla 0.5 3.5

Rohuküla-Virtsu 2.4 0.2

Kuivastu-Triigi -2.4 -0.3 Land-

connected connected Sõru-Heltermaa 0.9 -0.7

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In principle, the mean value at a TG (with the geodetic coordinates ĳ and Ȝ) can also be estimated from GNSS-measurements accompanied by a precise regional geoid model by using the following formula:

തതതതതሺɔǡ ɉሻ ൌሺɔǡɉሻെ୫ୱ୪ െ ሺɔǡ ɉሻ (7) where ሺɔǡ ɉሻ is the geodetic height of the CP (obtained from GNSS-measurements), the geoidal height is ሺɔǡ ɉሻ and ୫ୱ୪ denotes the vertical distance between the MSL reading and the CP. Apparently, several years of sea level series may be needed to accurately determine the തതതതതvalue. Nevertheless, an attempt was made to estimate the തതതതതfrom the year-long sea level observations (i.e the Tmsl values in Eq. 7) of this study. The two following datasets were involved for the purpose:

(1) The geodetic heights ሺɔǡ ɉሻ of the CPs were obtained by using nearby located points of the Estonian national geodetic (GNSS) network. The GNSS measurements on these points were carried out in 1997 with dual-frequency GPS-receivers Ashtech Z-XII. The GNSS sessions lasted 24 hours (4 x 6 hours). The Bernese software was used for data processing and the accuracy of the height component was estimated to be 5–10 mm (Rüdja 2004). Each PG was connected to a nearby national geodetic (GNSS) point by precise levelling. Due to relatively short connections (mostly < 5 km) the levelling errors are presumably not significant. (2) Geoidal heights ሺɔǡ ɉሻ at each PG were computed by using a recent regional gravimetric geoid model GRAV-GEOID2011. This model has been computed by the least-squares modification of Stokes’ formula, whereas a GOCE-satellite (Gravity field and steady-state Ocean Circulation Explorer) based geopotential model was used as the reference. The resolution of the GRAV-GEOID2011 model is 1´ x 2´ (1.8 km x 1.8 km) and its accuracy has been estimated to be ±1.3 cm (Ellmann et al 2011).

The GNSS-levelling differences (ǻSSTGNSS) within the PG pairs are also shown in Table 2, the last column. The detected disagreements between the corresponding ǻSSTDTU10MDT could be due several reasons.

First, the used DTU10MDT model is global and therefore it would be too optimistic to expect a revelation of high-resolution specifics over the Väinameri coastal zone. Second, our separate study (unpublished) revealed discrepancies as much as 2–3 cm between the regional GRAV-GEOID2011 and the global 5 arc-min resolution EGM08 (used at the compilation of the DTU10MDT) geoid models at the locations of the PG. Comparisons with GNSS-levelling points within the entire Väinameri region revealed a standard deviation as of 3 cm between the two geoid models. Note also that the coverage of the terrestrial gravity data used for the regional geoid model computation is quite heterogeneous (Ellmann 2005, Fig. 2) within the Väinameri region and in its vicinity. In

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this situation the computed mean SST values need to be disregarded, since their involvement may yield errors exceeding the range of the PG errors.

Therefore, for a relatively small and enclosed water body, such as the Väinameri, it could

be safer to assume that ୅ = ୆. Also, within the Väinameri the station-to-station differences in gravity, temperature and salinity are also negligible for the purpose of height

transfer. Subsequently, the height determination of the across-water Station B (CPB) can be further simplified (cf. Eqs. 5 and 6) to:

୅ ୆ ୆ ൌ ሺ ୅ െ୅ሻ ൅୆ െ൫୘ୋ୞ െ୅൯൅൫୘ୋ୞ െ୆൯ (8)

Note that the adopted simplification holds only for sufficiently long (at least a year) data series, in order to filter out the seasonality component of the water circulation. The

obtained height HB can be used to determine the height of the island TGBMB, which then serves as initial data for island levellings. In the case of the chain (or loop) of PGs, the

height of each subsequent one (HC) can be passed by spirit levelling from TGBMB to CPC,

and then by hydrodynamic levelling to CPD and so forth. These are the principles that will be used in our numerical studies and data processing.

4.3 Typical set-up of a pressure gauge

Each installed PG in this study consists of an individually calibrated pressure sensor attached to a 3 m long staff gauge. The front side of the staff gauge is a cm-graduated scale, which allows determining the sea level visually at any arbitrary instant. The contact point (CP) is welded to the top of its metallic frame, Fig. 5. A separate installation box protecting a data logger, a modem and the power supply was placed nearby. Also a solar panel was mounted at each PG. The staff gauges with sensors were securely fastened to a pier. The sensor was mounted on the backside of the staff gauge at the depth of ~1.5 m below the average water level (Fig. 5). During the measurements, the water column heights above the sensors ranged from 0.5 to 2.5 m.

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Figure 5. Staff gauge with the recess at the bottom (circled) to hold the pressure sensor. The arrow indicates the contact point (CP) on the top of the staff gauge.

Sea level readings were taken every 5 minutes during a 30 second time span, i.e. 12 times per hour. The measurement frequency was 4 Hz, thus the water column height for each 30s epoch was computed by averaging 4 x 30 measurements. The resulting single value represents the entire 30s long observation epoch. Thus, 12 x 24h = 288 averaged readings can be obtained at each PG daily. Additionally, some basic parameters (water temperature, maximum and mean wave height, wave period and battery voltage) were calculated from raw data and recorded as well. All the observation data were transmitted in real time into the central database using GSM/GPRS protocol and stored on the memory card at the station as backup.

5. Processing of the sea level series

The main goal of this study is to develop a methodology for the precise height determination by using hydrodynamic levelling. The measurements should be performed over an adequate time period to allow filtering out data blunders and obtaining statistically meaningful results. Accordingly, this study uses 12 months PG data from the year of 2010. As a working hypothesis – this annual water cycle period is assumed to be sufficient for achieving geodetic accuracy for hydrodynamic levelling. The data processing includes estimating drift corrections, filtering of the sea level series and computing the across-water height differences. The applied principles are explained below.

5.1 Estimating corrections due to the pressure sensor drift

Aging of the sensor components may have long-term effects on the measurement results. During long-term measurements the diaphragm of the pressure sensor may experience

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various phenomena, which are not directly related to pressure in water. For instance, pressure sensors could barnacled which may cause stability issues. Secondly, pressure sensors are influenced by temperature changes of water. This influence to the final readings is minimal and it is solved by calibration coefficients supplied by manufacture. The drifts of pressure sensors could be caused by local vertical movements of staff gauge as well. All the mentioned factors add up in time and the drift values could increase up to several cm per year. In order to monitor the drift behaviour, visual control readings from staff gauge should be taken as frequently as possible (at least once a month). Recall that a cm- graduated staff gauge can be used in conjunction with PG to control and calibrate the latter. Comparison with the pressure sensor readings for the same moment reveals the drift value.

In this study, the drift values at six PGs were determined as described above. The control readings were taken at variable intervals – mostly once a month or less frequently. The number of control readings varied from station to station. For instance, 8 visual readings were taken in Sõru in the year 2010, whereas 20 visual readings were taken both in Heltermaa and Rohuküla in 2010. The control readings from staff gauge revealed linearity of the drift trends, which allowed interpolating the drift values for each observation day. The drifts values at six PGs are shown in Fig. 6.

Figure 6. Detected drift trends at six PG-s during 2010. Calendar months are denoted on the horizontal axis.

Note that different PGs reveal differences in the trend magnitude and direction (cf. Fig. 6). The drift trends of the piesoresistive Keller 36XW appear to be negative, whereas the capacitive Keller 46X exhibited positive drift trends. Two PGs (Heltermaa and Sõru) were more or less stable during the entire observation period, whereas the drift values for the rest may reach up to 5–6 cm per year. Different drift trends in similar environmental conditions could also be caused by barnacles and algae that may congest the diaphragm of the pressure sensor. This situation is typical for shallow loughs, e.g. such as Triigi area. Additionally, the condition of seafloor and the concentration of microscopic floating particles in the water accumulating on membrane could have influence to the drift magnitude as well. For instance, the seafloor is soft and muddy at Rohuküla. There is

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frequent ferry traffic near Rohuküla’s pressure gauge. Therefore, permanent and intense water mixing takes place at this station. Although the diaphragm is very well protected and sealed, the microscopic floating particles could possibly accumulate on the diaphragm of pressure sensor and consequently stimulate the rate of drift. Therefore, it is very important to determine the drift values accurately and to consider them in further data processing. In this study the sea level series collected by pressure gauges are drift corrected before filtering.

Figure 7. Estimated daily heights of across-water CPs at the Virtsu-Kuivastu, Triigi-Sõru and Heltermaa-Rohuküla sections, cf. Eq. 8. The HB values are shown for Kuivastu, Sõru and Rohuküla (as moving clockwise along the levelling loop). White and black dots denote the outcome with and without drift corrections, respectively. The trend values [cm/year] by the end of theobservation period and the corresponding standard deviations [cm], with and without drift corrections, are also shown. In case of counter clockwise movement the trend values are the same, but with opposite sign. Calendar months are denoted on the horizontal axis.

In order to analyse the reliability of the estimated drift corrections, the daily averaged values of ୅ and ୆ (with and without drift corrections, cf. Eq. 3) were inserted into Eq. 8.

This provided a daily estimation of HB, with and without the drift correction, cf. Fig. 7. The trends without drift corrections are presented here to demonstrate the necessity of control readings and corrections. Clearly, the drift-corrected data series indicate improvements over the data series without drift correction. Theoretically, the drift-corrected data series

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should yield a zero-trend for daily HB throughout the entire observation period. In reality, however, the actual trend lines of daily HB deviate somewhat from the zero-trend, cf. Fig. 7.

Acceptably, the drift-corrected trends of daily HB in Virtsu-Kuivastu and Triigi-Sõru sections remain almost horizontal, by the end of the year reaching around -0.5 cm. Conversely, the Heltermaa-Rohuküla trend-line reaches -2.7 cm by the end of the year. In case of anti-clockwise movement the trend values are the same but with opposite sign in the pair of station. Thus the results for Rohuküla-Heltermaa, Sõru-Triigi, Kuivastu-Virtsu are +2.7 cm, +0.4 cm and +0.6 cm (cf. Fig. 7), respectively. Note, however, that such a large discrepancy (2.7 cm) could also have been caused by other factors. Recall that this section is the longest (22 km) of the three. Therefore, the following reasons cannot be excluded: (i) seasonal tilt of the sea level; (ii) some control readings could be inaccurate; (iii) possible subsidence of one (or both) CPs during the observation period. All these may need further investigations.

For instance, in order to study the influence of possibly erratic drift corrections to the height difference a 6-days field experiment was carried out. This yielded with a “drift-free” solution, for more details see Section 6.1.

5.2 Processing of the sea level series

The maximum amount of daily readings was 288 at each PG, cf. Section 4.3. In practise, the data series may contain gaps and unreasonable peaks. Also the data quality could become poor due to stormy weather conditions (e.g. due to rough waves, extreme air pressure changes). Such disturbed data were removed using a sequence of steps. The principles used for raw data filtering were as follows. Firstly, the occurrence of data gap in one station yielded also the removal of the same time-epoch from the paired station as well. Such disruptions were mostly caused by battery voltage drops or power outages lasting from several minutes to a few days.

Next, the occasional data jumps (defined as a single reading differing from its adjacent readings by 2–6 cm, e.g. Fig. 8) were identified, studied and eliminated. For instance, data analysis revealed that such jumps might be caused by sea vessels manoeuvring close to PG. In particular, Fig. 8 illustrates unfiltered sea level series in the stations of Virtsu and Kuivastu. Indeed, the occurrence of outliers (i.e. prominent data peaks in Virtsu) coincides with the scheduled departures/arrivals of ferries to harbours.

Thus, in the second stage the filtered initial data were smoothed, i.e. epoch-to-epoch jumps exceeding 2 cm were removed from the data series. After the peak removal the basic statistics of the data series remained practically the same. For instance, the daily MSL estimate changed less than 1 mm only.

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Figure 8. A sample of the ferry-induced data jumps in the Virtsu sea level series in July 5, 2010. For the clarity of the comparison the observations (shifted by a constant - 7 cm) in the across-water pressure gauge in Kuivastu are shown as well.

Also, specific weather conditions (e.g. unidirectional winds) could cause a temporal tilt in the sea level. Therefore, such data-days with height differences (between the paired stations) exceeding 10 cm (from the annual average) were also removed during the third step.

Recall that the daily sea level changes are usually less than ±50 cm in the Väinameri (see Section 4.2). Hence, the daily sea level changes larger than ±50 cm (i.e. indicating stormy conditions) were filtered out from the sea level series as well. As a result of the aforementioned data filtering procedures on the average 290 data-days (cf. also Table 3) for each PG pair remained for further processing. The largest number of eliminations was associated with the Triigi-Sõru pair due to Triigi’s power outage in July-August 2010. A relatively large number of eliminations (~100 data-days) was associated with the Rohuküla-Heltermaa pair. Note that the distance between these stations is 22 km, which may explain the more frequent occurrence of the aforementioned thresholds.

5.3 Results

The drift-corrected across-water heights for each day were computed by Eq. 8 and the results are presented on Fig.7. The standard deviation (SD) of the water level series within each PG pair was computed by:

ଵ ൌ ට σ୬ୀ୧୫ୟ୶ሺ ሺ ሻെ ഥ ሻଶ (9) ୬ ୧ୀଵ ୆ ୧ ୆

where ഥ୆ is the annual mean value and HB(ti) is the daily mean of the height differences. The standard deviation value could be a reasonable indication of the achieved accuracy for the height differences between the paired PG stations.

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The standard deviation for the Virtsu-Kuivastu section is ±1.1 cm. Such a remarkably good result is related to the shortest distance (7 km) between the stations. The worst standard deviation (±1.7 cm) is associated with the Heltermaa-Rohuküla section (22 km), cf. Table 3.

The corresponding height differences (see Table 3) between CP-s of the paired across- water stations are computed as:

ο ൌ ୆ െ ୅ (10)

Table 3. Hydrodynamic height differences (ǻH) and their standard deviation between the pressure gauge pairs.

Across-water pairs Length of the ǻH Standard deviation HA and HB section (without SST) [cm] (# of data-days after filtering) [km] [cm]

Virtsu-Kuivastu (338) 7 +1.4 ±1.1

Triigi-Sõru (254) 16 +65.2 ±1.3

Heltermaa-Rohuküla (265) 22 -4.0 ±1.7

6. Verification of hydrodynamic levelling results

Three experiments were carried out to validate the accuracy of the achieved hydrodynamic levelling results: (1) “Ice-tamed” sea level observations; (2) Comparisons with spirit, GNSS and hydrostatic levelling; (3) Combining the hydrodynamic and spirit levelling results into a closed loop.

The setup and the results of each experiment are explained below.

6.1 „Ice-tamed“ sea level observations

Recall that the final results (cf. Table 3) were obtained by using 12-months continuous sea level series. Such a large amount of data should be sufficient for ensuring the geodetic accuracy of the MSL determination at each PG. On the other hand, the determination of time-dependent drift values may still involve uncertainties (see a discussion in Section 5.1). Therefore it could be useful to compare the obtained results (the year-long cycle) with those obtained during very favourable weather conditions. However, it could be difficult to find a time period with ideal weather conditions simultaneously over the entire study area.

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Apparently, the influence of weather dependent (wind, waves and air pressure) sea level fluctuations is minimized during the periods with the fast ice coverage in winter-time.

All six PGs continued to operate also in 2011. In February-March 2011 the Väinameri became covered with 50+ cm thick layer of fast ice, see Fig. 9. Also the adjacent gulfs were covered with pack ice. In such a way the open seawater was further than 10 km away from the study area. Fortunately, a high pressure continental weather system covered the entire Baltic Sea during the second half of February. Thus, the weather conditions were very stable within the study area in February 20-25 2011 (cf. Table 4). During this 6-days period the air pressure was almost the same and changed evenly in all stations, cf. Table 4. Therefore, it can be expected that the weather induced sea level slope between PGs is nonexistent or minimal. This allowed us to collect the so-called “ice-tamed” sea level observations at each PG.

Figure 9. Ice conditions in the Väinameri (February 23, 2011) as seen on MODIS satellite image. The dots indicate the locations of pressure gauges. Note that the study area was covered with fast ice (white)with a thickness 50 cm. Adjacent areas are covered with pack ice. Inset – location of the study area in the eastern part of the Baltic Sea.

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Table 4. Characteristics of the sea observations and air pressure in February 20–25, 2011.

Pressure The MSL height and Ice Min / max air Number of gauge standard deviation thickness pressure usable readings station [cm] [cm] [hPa] 1 2 3 4 Virtsu -35.4 ± 2.8 50 1030.4 / 1038.2 1688 Kuivastu -35.4 ± 2.8 50 1030.4 / 1038.2 1688 Triigi -35.2 ± 3.2 55 1030.5 / 1037.4 1686 Sõru -35.5 ± 3.6 55 1030.5 / 1037.4 1686 Heltermaa -35.4 ± 3.8 50 1030.3 / 1037.7 1686 Rohuküla -35.4 ± 3.8 50 1030.6 / 1038.2 1686

Also a field expedition was organised in the middle of the selected period (February 22– 23) in order to determine simultaneous precise control readings within station pairs. The water in ice holes was very calm and the control readings from a staff gauge were taken with an accuracy of 0.5 cm. Simultaneous control readings allowed to estimate precisely the PG drift values. Thus, practically a “drift-free” solution was obtained for the entire 6- days long period.

During the 6-days observation period the sea level fluctuations were minor and changed evenly at all stations, see Table 4, column 1. The “drift-free” height differences between the CPs within each pair were also computed by Eq. 8. This allowed a comparison between the 6-days “drift-free” and the annual hydrodynamic levelling results (Table 3). The “drift- free” (ǻH6-days) and the year-long (ǻH2010) hydrodynamic levelling results (without considering the SST values in Table 2) for the land-connected PG-pairs are presented in Table 5, columns 3 and 4, and for the across-water PG pairs in Table 6, columns 2 and 3, respectively.

The “drift-free” results agree reasonably with those in Table 3. The largest discrepancy 1.6 cm, cf. Table 6 and Fig. 10A, is associated with the longest section (Heltermaa-Rohuküla). Other discrepancies remain below 1.0 cm. The detected discrepancies between the annual and “ice-tamed” results for the land-connected PG pairs are not exceeding 1.0 cm, cf. Table 5 and Fig. 10B. This proves that there is quite a reasonable agreement between the annual hydrodynamic levelling results and that of the idealistic, “drift-free” solution.

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Table 5. Height differences (ǻH) between the land-connected pressure gauge pairs obtained by spirit, hydrodynamic and GNSS-levelling. Pressure Spirit levelling Hydrodynamic GNSS-levelling gauge pairs levelling ǻHS Length of ǻH2010±std ǻH6-days Along- ǻHGNSS Direct [cm] levelling [cm] [cm] coast [cm] length line (# of data- length [km] [km] days after [km] filtering) 1 2 3 4 5 6 7 Rohuküla- 19.8 98 20.1±1.2 19.4 65 20.3 37 Virtsu (241) (Estonian mainland) Kuivastu-Triigi -69.3 64 -68.3 ±1.7 -69.2 65 -68.6 39 (island of (181) Saaremaa) Sõru-Heltermaa -12.8 47 -14.0±2.1 -13.4 45 -14.8 36 (island of (285) Hiiumaa)

Table 6. Height differences (ǻH) between the across-water pressure gauge pairs obtained by hydrodynamic, hydrostatic and GNSS-levelling. Pressure Direct Hydrodynamic Hydrostatic levelling GNSS- gauge pairs length levelling levelling [km] ǻH2010 ǻH6-days ǻHyear Land uplift ǻHGNSS cf. Table [cm] (includes land correction [cm] 3 [cm] uplift [cm] correction) [cm] 1 2 3 4 5 6 Virtsu-

Kuivastu 7 1.4 0.6 -0.21968 +0.2 0.0 (CPA – CPB) 63.61976

Triigi-Sõru 16 65.2 65.0 62.61977 +0.3 63.7

(CPA – CPB) ------

63.1average Heltermaa- 22 -4.0 -2.4 – – -0.6 Rohuküla

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Figure 10. Discrepancies between different levelling methods in the across-water (A) and land- connected (B) sections. The zero line denotes the results of the annual (2010) hydrodynamic levelling as the reference. The vertical error bars denote the individual standard deviation values of the hydrodynamic levelling results between the pressure gauge pairs, cf. Table 3 and Table 5. “wrt” denotes “with respect to”.

6.2 Comparisons with spirit, GNSS and hydrostatic levelling

The land-connected PG pairs, i.e Rohuküla-Virtsu, Kuivastu-Triigi and Sõru-Heltermaa (see Fig. 4), were connected with high-precision spirit levellings in 2005–2010. These measurements are a part of the ongoing renovation of the national levelling network. The average RMS for the national levelling lines are: Ș = 0.18Ȁξ; ı = 0.03 Ȁ (Estonian Land Board, www.maaamet.ee), i.e. they can be safely used to verify the hydrodynamic levelling results.

The hydrodynamic along-coast height differences (and their standard deviations) between the land-connected PG pairs are also estimated by Eqs. 8 and 10 (cf. Table 5, columns 3 and 5). The corresponding spirit-levelled height differences are shown in column 1. The spirit levelling and the “drift-free” hydrodynamic levelling results agree within 0.6 cm; cf. Table 5, columns 1 and 4 and Fig. 10B. In other words, under ideal conditions the used PGs are able to provide comparable to spirit levelling results.

Agreement between the results of spirit and year-long hydrodynamic levellings is satisfactory, being at 1 cm level; cf. Table 5, columns 1 and 3 and Fig. 10B. As discussed before, this could be due to ambiguities in the drift estimation. Also some residual water tilt due to specifics of the observation year (e.g. prevailing winds from certain directions) cannot be entire excluded.

The GNSS-levelling method can also be used for comparing both the across-water and the land-connected height differences. Note that geoidal heights were computed by using the regional gravimetric geoid model GRAV-GEOID2011, cf. Section 4.2. The detected discrepancies vary from 0.1 up to 3.4 cm (cf. Table 5, columns 3, 6 and Table 6, columns 2, 6). Recall that the overall accuracy of GNSS-levelling remains within 2–3 cm (see also Section 4.1). Note that the largest discrepancies are associated with the Heltermaa- Rohuküla pair (cf. Fig. 10A), where the GNSS-levelling is unfortunately the only

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independent verification for the hydrodynamic levelling results. At the same time the GNSS-levelling results reveal a good agreement (~0.5 cm) with the across-water PG pairs Virtsu-Kuivastu and Triigi-Sõru, cf. Table 6, columns 4 and 6 and Fig. 10A.

Further, the historic hydrostatic levelling results were compared with across-water hydrodynamic results. Hydrostatic levellings between the Estonian mainland and the Saaremaa and between the islands of Saaremaa and Hiiumaa were proceeded in the 1960- ies and the 1970-ies. Hydrostatic levelling between the island Hiiumaa and the mainland has not previously been carried out due to the long distance (22 km).

The island Saaremaa was connected with the mainland in 1968 by using underwater tubes (Tamme 1972). The hydrostatic levelling between the islands of Saaremaa and Hiiumaa was proceeded first in winter of 1976, whereas the spirit-filled tubes (with the total length of 10 km) were placed on the top of ice-cover. Even though the hydrostatic levelling accuracy was formally estimated to be better than ± 0.2 cm (Tamme 1969), but it appears to be too optimistic estimate. Namely, the hydrostatic levelling between the islands Saaremaa and Hiiumaa was repeated in 1977. The 1977 results differed from the 1976 results by 1.0 cm (cf. Table 6, column 4). Therefore it can be concluded that the accuracy of the historic hydrostatic levellings could also be at 1.0 cm level.

Note that the rate of absolute land uplift within the West-Estonian Archipelago is 1–2 mm/year. The empirical land uplift model NKG05LU (Ågren, Svensson 2007) was used to correct the historic hydrostatic levelling data for the land uplift phenomenon, cf. Table 6, columns 4 and 5. Due to the short distances between PGs the relative land uplift rates are expected to be insignificant. In particular, the Kuivastu area has been risen by 0.2 cm with respect to Virtsu in 42 years. The uplift range of Sõru with respect to Triigi was detected to be 0.3 cm in 32 years.

It appears that the maximum difference between the hydrodynamic and hydrostatic levelling is 2.1 cm, cf. Table 6, columns 2 and 4 and Fig. 10A. Note that present hydrodynamic levellings and historic hydrostatic levellings refer to different benchmarks, which are separated by several kilometres. Connections between CPs were established by using historic and new spirit levellings. In other words, a closed loop consisting of hydrodynamic, hydrostatic and precise spirit levellings was formed separately for Virtsu- Kuivastu-Virtsu and for Triigi-Sõru-Triigi. Thus, the detected discrepancies could include errors of historic hydrostatic and spirit levellings as well. The “drift-free” hydrodynamic results agree slightly better with that of the hydrostatic levelling, cf. Table 6, columns 3 and 4. It can be concluded that the current hydrodynamic and historic hydrostatic levellings agree within 1–2 cm, which seems to be a realistic estimate for the precision of both methods.

Note that all height differences between land-connected PG pairs remain within the range of the individual standard errors of hydrodynamic levelling (cf. Fig. 10B), even though the

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along-coast distances reach up to 65 km, cf. Table 5. The across-water discrepancies appear to be more scattered, but still within ±2.0 cm, with one exception, though.

6.3 Combining the hydrodynamic and spirit levelling results into a closed loop

Certainly, all the above discussed comparisons include not only the hydrodynamic levelling errors, but errors of alternative height determination methods as well. Therefore, an adequate accuracy estimation for hydrodynamic levelling could be based on the misclosures of closed levelling loop. This all-around Väinameri loop (total length 253 km) comprises 3 across-water and 3 land-connected sections, see Table 7 and Fig. 4.

Table 7. Misclosures of the around Väinameri levelling loop by combining hydrodynamic and spirit levellings.

Hydrodynamic ǻH2010 ǻH6-days Length of Adjusted Adjusted

/spirit levelling [cm] ǻHSpirit [cm] levelling ǻH2010+ ǻH6-days+ sections [cm] section ǻHSpirit ǻHSpirit [km] [cm] [cm] (inverse distance weight) 1 2 3 4 5 Virtsu-Kuivastu 1.4 0.6 7 (5) 1.3 0.4 Kuivastu-Triigi -69.3 64 (8) -69.3 -69.3 Triigi-Sõru 65.2 65.0 16 (3) 65.1 64.7 Sõru-Heltermaa -12.8 47 (10) -12.8 -12.8 Heltermaa- -4.0 -2.4 22 (1) -4.1 -2.7 Rohuküla Rohuküla-Virtsu 19.8 98 (7) 19.8 19.7 Misclosure 0.2 0.9 254 0.0 0.0

For the combinations of spirit and hydrodynamic (either ǻH2010 or ǻH6-days) levellings the misclosure values of the 253 km long levelling loop remain under 1.0 cm. Thereafter the least squares adjustment by elements was applied to obtain the adjusted height differences, see Table 7, columns 4 and 5. The weighting of measurements applies the inverse distance principle (the longer the levelling section, the smaller the corresponding weight in the adjustment), whereas the height differences to be adjusted are divided into two groups. The spirit levelled sections could be 4–5 times more reliable than those of hydrodynamic levelling. Thus, the spirit levelling results form one group, whereas the hydrodynamic levelling results form the second group. For the assigned weights see Table 7, column 3.

Additionally, Fig. 11 illustrates daily misclosures of the levelling loop. Altogether 196 data-days remained after the removal of all data gaps. Note that a data gap in any PG yielded removal of the same time period from other PGs as well. Interestingly, the daily misclosures reveal a seasonal weather pattern. The smallest misclosure values are associated with the ice-covered winter period (January–April 2010). The standard

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deviation of the loop misclosure was only ±0.8 cm during these four winter months. With the open water the daily loop misclosures increase. The largest deflections from the 0- misclosure are associated with the autumnal storms. The resulting standard deviation of the drift-corrected annual (2010) series of the misclosure reach ± 2.1 cm (cf. Fig. 11). It is the same range that we estimated between Heltermaa-Rohuküla in Section 5.3, cf. Table 3. Note that the height differences were not changed substantially during adjustment, cf. Table 7, columns 1 and 4. Regardless, the accuracy of the adjusted hydrodynamic height differences in Table 7, column 4 could be estimated to be ±2.0 cm. This is in agreement with the results in Table 3.

Figure 11. Daily misclosures of the 253 km levelling loop around Väinameri. White and black dots denote misclosure values with and without drift corrections, respectively. Continuous lines denote the corresponding third degree polynomial trend of misclosures. Calendar months are denoted on the horizontal axis.

7. Summary and discussion

This study demonstrates that the pressure gauges are useful not only for maritime and oceanographic purposes, but also for geodetic applications. In particular, the main objective of this study was to develop and examine a methodology for precise height determination by using hydrodynamic levelling. Contemporary piezoresistive and capacitive pressure sensors were used for automatic year-round sea level observations. The PGs need to perform measurements simultaneously in the opposite sides of the waterway to be bridged or along coast.

The pressure sensors could be affected by time-dependent drifts. Our tests showed that the drift values can reach up to 5 cm per year. Hence regular control readings from a staff gauge need to be taken (either visually or telemetrically) to estimate the drift corrections throughout the entire observation period. The hydrodynamic levelling results can also be affected by the specifics of the study area. In particular, the mean and seasonal sea surface topography need to be taken into consideration. This could be the most challenging part of hydrodynamic levelling, since the accuracy and resolution of existing global and regional SST models could be insufficient (especially for the coastal zone) to ensure the geodetic

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accuracy of hydrodynamic levelling. Therefore, in many circumstances it could be even safer to disregard such SST values if no high-resolution SST model exists for the water body of interest. Also the length of sea level observations should be sufficient to eliminate the seasonal and weather-induced fluctuations of the SST from the level (equipotential) surface - at least the entire annual water cycle, or preferably over a few consecutive seasons. On the other hand, in coastal waters the barnacles and algae may congest the diaphragm of the pressure sensor more quickly, thus affecting the accuracy of the measurements.

The validity and achievable accuracy of the proposed method and the equipment used was validated with a case study in the West-Estonian Archipelago. The six mounted PGs formed a closed loop consisting of three across-water and three land-connected levelling sections. Such a constellation sets rigorous constraints for the hydrodynamic levelling experiment. The sea level observations lasted 12 months, thus the annual water cycle period was entirely covered. The data processing comprised estimating the drift corrections, filtering sea level series and computing the across-water heights. The data processing and filtering principles were developed and explained in Section 5. The height differences between the PGs were calculated by using the annually averaged sea level data.

The final height differences between across-water and also land-connected PG pairs were verified with three alternative levelling methods and results from earlier studies: x high-precision spirit levelling results between the land-connected PG pairs, x historic hydrostatic levelling results (accuracy ±1.0 cm) for the across-water comparisons, x the GNSS-levelling height differences (accuracy ±2.0–3.0 cm) for both land- connected and across-water sections.

All in all, the numerical results of the annual hydrodynamic levelling agree with concurrent results within ±2.0 cm. Furthermore, an additional field experiment was carried out to monitor the sea level during the fast ice coverage in winter-time. In this very favourable case it can be expected that the weather-induced sea surface slope is non-existent or minimal. The 6-days “ice-tamed” and the annual hydrodynamic levelling results (cf. Tables 5 and 6) agreed mostly within ±1.0 cm. Even though such privileged “ice-tamed” sea level observations are possible only in subarctic latitudes (e.g. Scandinavian fjords, coastlines of Canada, Alaska and Northern Russia also frozen lakes) the comparisons indicate that the year-long hydrodynamic levelling could provide satisfactory results in other geographical locations as well.

Finally, a closed, all-around Väinameri loop (253 km) was formed to inspect the misclosures of the loop for different data combinations. The misclosure of the entire loop was estimated to be 0.2 cm for the year-round observation period and 0.9 cm for the 6-days “ice-tamed” observation period.

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Since the stretches of water in varied from 7 km up to 65 km our experiments, then it can be concluded that this method can be used for sections up to 65 km with an expected accuracy as of ±2.0 cm. Its performance for distances longer than 65 km needs to be investigated, though. Apparently, a complex of challenging factors should be considered for a hydrodynamic levelling section stretching across the open sea. Here the salinity variations (affecting density and SST) and lags in the tidal phase and magnitude may cause larger discrepancies.

Nevertheless, it can be concluded that geodetic accuracy for height determination can be achieved by using hydrodynamic levelling with contemporary pressure sensors, provided that the data collecting and processing procedures are also handled properly. In some occasions the hydrodynamic levelling could be the only feasible option for height determination. Compared to alternative levelling methods the hydrodynamic levelling has certain advantages, such as: x Hydrodynamic levelling is economically more feasible and less laborious than hydrostatic levelling. x Hydrodynamic levelling is more accurate than the widely used GNSS-levelling. The GNSS-levelling also depends on the accuracy of the regional geoid model. Recall also, that due to heterogeneity (both the accuracy and availability) of gravity data within the coastal zone it could be a real challenge to develop high- resolution and accurate (better than ±2.0 cm) geoid models in many places of the world.

Acknowledgements Two anonymous reviewers are thanked for their constructive comments on the manuscript. This study is supported by the Estonian Science Foundation grant ETF 8749: Determination of height reference frame on the Estonian coastal sea using water lever monitoring and laser scanning data. The Estonian Land Board financed the installation and operation of pressure gauges and their connection to the national levelling network.

References Ågren, J., and R. Svensson. 2007. Postglacial land uplift model and system definition for the new Swedish height system RH 2000. LMV-Rapport 2007:4. Gävle: Lantmäteriet. Andersen, N. 1992. The hydrostatic levelling across the Fehmarn Belt in 1987. Kobenhavn: Kort- og Matrikelstyrelsen. Andersen, O. B. 2011. The DTU10 Mean Sea Surface for and with CryoSat-2. Paper presented at CryoSat validation workshop, Italy, Rome, February 1–3. Andersen, O.B., and P. Knudsen. 2011. The Mean Sea Surface DTU10MSS - Comparison With GPS And Tide Gauges. Proceedings of ESA Living Planet Symposium, Norwey, Bergen. June 28 – July 2, 2010. Bao, M.-H. 2000. Handbook of transducers and actuators. Micro mechanical transducers: pressure transducers, accelerometers, and gyroscopes, ed. S. Middelhoek, Vol. 8. Amsterdam: Elsevir.

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Bogdanov, V.I., M.Yu. Medvedev, V.A. Solodov, Yu.A. Trapeznikov, G.A.Troshov, and A.A. Trubitsina. 2000. Mean monthly series of sea level observations (1777- 1993) at the Kronstadt gauge. Report 2000:1. Kirkkonummi: Finnish Geodetic Institute. Carlsson, M. 1998. Mean Sea-Level Topography in the Baltic Sea Determined by Oceanographic Methods. Marine Geodesy 21:203–217. Cartwright, D. E., and J. Crease. 1963. A comparison of the geodetic reference levels of England and France by mean of the sea surface. Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences 273(1355):554–580. Ekman, M., and J. Mäkinen. 1996. Mean sea surface topography in the Baltic Sea and its transition area to the North Sea: A geodetic solution and comparisons with oceanographic models. Journal of Geophysical Research 101(C5):11993– 110999. Ellmann, A. 2005. Two deterministic and three stochastic modifications of Stokes’s formula: a case study for the Baltic countries. Journal of Geodesy 79:11–23. Ellmann, A., T. Oja, and H. Jürgenson. 2011. Application of space technologies to improve geoid and gravity field models over Estonia. Geodeet 41:22–25. (In Estonian). Jevrejeva, S., A. Rüdja, and J. Mäkinen. 2001. Postglacial rebound in Fennoscandia: new results from Estonian tide gauges. Proceedings of IAG Symposia 123: 193-198. Canada, July 31 – August 4. Lisitzin, E. 1974. Sea level changes. Oceanography, Vol 8. Amsterdam: Elsevier. Norin, D., L.E. Sjöberg, and J.M. Johansson. 2010. National Report of Sweden to the NKG General Assembly 2010 – geodetic activities in Sweden 2006-2010. Paper presented at 16th General Assembly of the Nordic Geodetic Commission, Norway, Sundvollen, September 27–30. Novotny, K., G. Liebsch, R. Dietrich, and A. Lehmann. 2002. Sea-Level Variations in the Baltic Sea: Consistency of Geodetic Observations and Oceanographic Models. Proceedings of IAG Scientific Assembly 125:493–498. Hungary, September 2–7. Pavlis, N.K., S.A. Holmes, S.C. Kenyon, and J.K. Factor. 2008. An Earth Gravitational Model to Degree 2160: EGM 2008. Paper presented at EGU General Assembly, Austria, Vienna, April 13–18. Raudsepp, U., A. Toompuu, and T. Kõuts. 1999. A stochastic model for the sea level in the Estonian coastal area. Journal of Marine Systems 22:69–87. Rüdja, A. 2004. Geodetic datums, reference systems and geodetic networks in Estonia. PhD diss., Finnish Geodetic Institute. Suursaar, Ü., J. Jaagus, A. Kont, R. Rivis, and H. Tõnisson. 2008. Field observations on hydrodynamic and coastal geomorphic processes off Harilaid Peninsula (Baltic Sea) in winter and spring 2006-2007. Estuarine Coastal and Shelf Science, 80(1):31–41. Suursaar, Ü. 2011. Sea Level Variations Along the Estonian Coast of the Baltic Sea. In Sea Level Rise, Coastal Engineering, Shorelines and Tides. Oceanography and Ocean Engineering, ed. L.L. Wright, 105-122. New York: Nova Science Publisher Inc. Tamme, L. 1969. Ɉɩɵɬ ɩɪɢɦɟɧɟɧɢɹ ɝɢɞɪɨɫɬɚɬɢɱɟɫɤɨɝɨ ɧɢɜɟɥɢɪɨɜɚɧɢɹ ɞɥɹ ɜɵɫɨɤɨɬɨɱɧɨɣ ɩɟɪɟɞɚɱɢ ɜɵɫɨɬ ɰɟɪɟɡ ɡɧɚɱɢɬɟɥɶɧɵɟ ɜɨɞɧɵɟ ɩɪɟɝɪɚɞɵ. Ⱦɢɫɫɟɪɬɚɰɢɹ, ɂɧɫɬɢɬɭɬɟ Ɏɢɫɢɤɢ ɢ Aɫɬɪɨɧɨɦɢ Ⱥɇ ɗCCɊ. Tamme, L. 1971. ɉɟɪɟɞɚɱɚ ɜɵɫɨɬ «Ʉɪɨɧɲɬɚɞɬ — Ʌɨɦɨɧɨɫɨɜ» ɦɟɬɨɞɨɦ ɝɢɞɪɨɫɬɚɬɢɱɟɫɤɨɝɨ ɧɢɜɟɥɢɪɨɜɚɧɢɹ , Ƚɟɨɞɟɡɢɹ ɢ ɤɚɪɬɨɝɪɚɮɢɹ. 5:30–35. Tamme, L. 1972. Oɛ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɵɯ ɪɚɛɨɬɚɯ ɩɨ ɩɟɪɟɞɚɱɟ ɜɵɫɨɬ ɦɟɬɨɞɨɦ ɝɢɞɪɨɫɬɚɬɢɱɟɫɤɨɜɨ ɧɢɜɟɥɢɪɨɜɚɧɢɹ. Bɵɩ 169, Ɇɨɫɤɜɚ:ɐɇɂɂȽȺɢɄ. Torge, W. 2001. Geodesy. 3rd Edition. Berlin-New York: Walter de Gruyter. Wübbelmann, H. 1992. Das hydrodynamische Nivellement am Beispiel eines Pegelnetzes am Fehmarn-Belt. Wiss. Arb., University of Hannover.

180 II Liibusk, A., Ellmann, A., Kõuts, T. 2011. USE OF HIGH RESOLUTION SEA LEVEL MEASUREMENTS FOR HEIGHT TRANSFER IN THE WEST-ESTONIAN ARCHIPELAGO

Reprinted from: Environmental Engineering. The 8th International Conference: Selected Papers. Vilnius Gediminas Technical University Press “Technika”, 1374–1381. ISSN 2029-7106 print / ISSN 2029-7092 online ENVIRONMENTAL ENGINEERING ISBN 978-9955-28-829-9 (3 Volume) The 8th International Conference ISBN 978-9955-28-827-5 (3 Volumes) May 19–20, 2011, Vilnius, Lithuania http://enviro.vgtu.lt Selected papers © Vilnius Gediminas Technical University, 2011

USE OF HIGH RESOLUTION SEA LEVEL MEASUREMENTS FOR HEIGHT TRANSFER IN THE WEST-ESTONIAN ARCHIPELAGO

Aive Liibusk1, Artu Ellmann2, Tarmo Kõuts3

1Estonian University of Life Sciences, Department of Geomatics, Kreutzwaldi 1, 51014 Tartu, Estonia. E-mail: [email protected] 2Tallinn University of Technology, Faculty of Civil Engineering, Ehitajate rd. 5, 19086 Tallinn, Estonia. E-mail: [email protected] 3Tallinn University of Technology, Marine Systems Institute, Akadeemia rd. 15a, 12618 Tallinn, Estonia. E-mail: [email protected]

Abstract. Renovation of the national high-precision levelling network has been completed for most of the Estonian territory. However, levelling loops on two large islands Saaremaa and Hiiumaa need to be connected with those of the mainland levellings. The transfer of heights over sea is performed by analyzing high resolution sea level measurement data of automatic stations equipped with pressure sensors. All together, three pairs of water level stations were installed in 2009-2010 in selected locations, in opposite coasts of each strait – 2 on mainland and 2 on each of islands. The time series of measured sea levels with some complementary data-sets are processed to detect as precisely as possible the local mean sea level on opposite sides of the straits. To fulfill this goal the sea level data were analyzed in order to assess the suitability of such height transfer methodology. It was found that elimination of the environmental and ferry-traffic induced disturbances homogenize the datasets remarkably and more consistent local mean sea level could be calculated. The differences in sensor readings were compared on a pair-of-station basis to assess the temporal stability of the sea level stations. Relatively short distances between the water level stations (maximum 22 km) and the fairly enclosed Väinameri were main reasons why sea level changes in different stations appeared to be well correlated and in same order of magnitude during the entire nine-month long measurement period. Three height transfers and the adjacent high-precision levellings form a closed 253-km long loop. Based on the tentative height differences of these sections the detected misclosure of the entire loop is 14 mm. This is a very promising result, since the data processing method tested is just a preliminary approach. More refined studies and longer sea level time series may yield even better accuracy for the height transfers.

Keywords: automatic tide gauges, pressure sensors, levelling, levelling network.

1. Introduction time period to allow filtering out of unreasonable sea level changes. That helps to obtain statistically This study focuses on issues related to processing of representative time series – the main goal is to get as sea level time series in order to analyse the possibilities precise as possible local mean sea level. of using automatic sea level gauges for height In this study we test the usability of data from connections over sea. The study results may be suitable modern automatic sea level stations (based on pressure for connecting high-precision levelling loops on the sensors) for this task. Totally, six automatic sea level islands of Saaremaa and Hiiumaa with the national stations were installed in 2009-2010 in selected locations levelling network in the Estonian mainland. (two on mainland and two on either island, Saaremaa and Previously, the connection was established by using: Hiiumaa), on opposite sides of the straits. The sea level (i) short term visual sea level observations, (ii) levelling stations are mounted to the piers, which are located in ferry over the ice and (iii) hydrostatic levelling (in the 1960’ies harbors. Each station has levelling point on the top of staff gauge, which was connected to the closest benchmarks of the and 1970’ies). Hydrostatic levelling is no longer feasible national levelling network. due to its high cost and sensitivity to temporal and spatial Note that in some stations the length of sea level changes in environmental conditions. An alternative way time series is currently shorter than 12 months, thus the for transfer of geodetic heights over straights is using full annual cycle has not been reached yet. This is crucial synchronized water level measurements. Such to fully catch the periodic component for the mean sea measurements should be performed over an adequate level in the Baltic Sea (Raudsepp et al. 1999). Therefore a

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throughout analysis is needed to evaluate the suitability and achievable accuracy of the sea level based height transfer over the straits. Such preliminary assessment can be useful in further data processing with longer data series and for evaluation the performance of sea level stations in operation. The methods of data analysis, cleaning and processing will be described in more detail in the sections below. The outline of the paper is as follows. First, the structure of the Estonian national levelling network and methods of previous height connections to West-Estonian Islands are reviewed. Next, the equipment and principles used at the water level stations are discussed in detail. Then the focus turns on the water level data processing. The achieved data processing results are used to calculate Fig 1. Layout of Estonian levelling polygons (Estonian the misclosure of the across-sea levelling loop. A brief Land Board) summary concludes the paper.

2. Estonian Levelling Network

The first levelling network covering the entire Estonian territory was established in 1933–1943. Then the total length of the levelling lines reached 1700 km nationwide. The measurements were repeated within the two following periods: 1956–1970 (total length of lines 1993 km) and 1970–1996 (altogether 1395 km). Throughout the past decades, the levellings in west Estonian islands have been connected with the mainland using different methods. For instance a geometric levelling over the ice was performed between the mainland and island Saaremaa (benchmarks Bm 234 – Fig 2. Locations of sea level stations, serving for height Bm 244, see Fig 2) in 1940. The length of the connecting transfer from mainland to the islands in the Väinameri Sea levelling line was 7 km. However, this ice-levelling was negatively influenced by extremely disadvantageous In 1967 and 1968 hydrostatic levelling was tested in weather conditions and wind-induced vertical ice Estonia for the first time. Note that the length of these undulations. In parallel, short-term visual water level “tube” connections varied from 3.6 to 6.0 km. Test observations were performed in ice holes (at both ends of measurements were performed between Muhu and the levelling line) during two consecutive days for four Saaremaa islands and at a small island between Muhu and hour long period each day. The data obtained by the mainland. The estimated accuracy of the method reached levelling as in conjunction with the water level 1 mm/km (Tamm 1970). By means of this method the observations allowed to connect the levellings of the island Saaremaa was connected with the mainland in island and the mainland with a mean deviation of +/- 3.5 1968 and repeated in 1978 (Bm 234 – Bm 244). The mm (Linnamaa 1940). Hiiumaa island was connected with Saaremaa in 1976 Short-term water observations between Bm 234 – and 1977 (Bm FRVIII – Bm FRIX). Again, the Bm 244 were repeated in 1963 and 1979, whereas a new hydrostatic levellings (except the one in 1968) were connection between the island Saaremaa and Hiiumaa performed in winter conditions, to avoid placing the tubes (Bm FRVIII – Bm FRIX,) was established in 1968 and in water. As the depth of the strait reaches 20 m in some 1971. Special immersed constructions were used for places, the temperature of the environment (air, water) those water observations to enable monitoring of surrounding the tube could be heterogeneous. Depending temporal water level changes. These observations lasted on the profile of the sea bottom and actual weather from several hours up to 2-3 days. Winter months were conditions the differences in temperature can reach 5-7º C preferred for the short-term water observations, due to along the levelling line. Consequently, the fluid density in regional ice-coverage. As well known, the ice reduces the tubes may also vary along the line; which, together wind impact on water tilt. The precision of height transfer with air pressure differences at the tube ends may yield over water by means of these short-term visual water quite unpredictable total error in height differences. observations has been estimated for different campaigns In 1996, preparations were started to reconstruct the to 2-4 mm/km, which yields the accuracy of the mainland Estonian geodetic network. The reconstruction of precise – Saaremaa connection to be within the range 12-24 mm national levelling network started in 2001. The objective (Torim 2009). of the works was modernization of the levelling network

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in accordance with the requirements of the national automatic compensation of water level measurements for geodetic network. changes in air pressure. Compensation of temperature The reconnaissance works detected that more than effects is performed electronically inside the pressure 50% (1275) of previous benchmarks (2403) are destroyed sensor. Output of the sensor is already water column or not usable due to unsatisfactory location, stability or heights in cm and 4 Hz data sampling is used. According type. As a result of the reconstruction, the Estonian to Carrera et al. 1996 water pressure sensors in general levelling network now includes 2264 benchmarks. An may be able to determine the water column height with a average along-line distance between the benchmarks in 0.01 m accuracy. In order to obtain proper water levels, the renovated network is 1.3 km. The levelling lines (total waves should be filtered out – that is performed using a length of about 3330 km) form 20 loops, 18 in the 30 s averaging upon the entry of the data into the Estonian mainland and 2 on the West – Estonian islands datalogger. As complementary information basic wave (approx. 320 km), see Fig 1. The levelling works were parameters are calculated and stored from raw pressure completed in autumn 2010. To complete the nationwide renovation of the high-precision levelling network also data – significant and maximums wave height and wave the loops in the islands of Saaremaa (levelled in 2010) period at the sea level station. The water level readings and Hiiumaa (2009) need to be connected with the are recorded every 5 minutes, stored on memory card of mainland. For this, the only feasible method seem to be the data logger, but also transmitted on-line into using sea level measurements, from which local mean sea databases with web-based user interface. For each day, level could be estimated. 288 readings are obtained, which results in fairly large Automatic sea level stations were developed and quantities of water observation data, allowing statistical installed by the Marine Systems Institute (Tallinn analysis of the data. University of Technology) on opposite sides of the The benchmark welded to the top of the staff gauge straits, at the harbours of Virtsu, Kuivastu, Triigi, Sõru, is connected with the levelling network in accordance Heltermaa and Rohuküla (see Fig 2). with high-precision levelling requirements. The sensor inside the staff is visually connected to staff readings and 3. Automatic water level stations through these to the levelling network. This means that the sensors inside the staff have been initialised by visual To ascertain the possibilities of using high resolution observation. In calm conditions it should be possible to sea level data in transferring the heights over water, we read a pole to 0.02 m, but the accuracy deteriorates in the scrutinized time series from water level stations installed presence of waves (Pugh 1996, Woodworth et al. 1996). on the Väinameri coasts. Data from 1 January to 30 The reading obtained in relation to the mean water level September 2010 from six automatic water level stations was entered into the sensor. Depending on the setting of were available for the present study. the first reading (in essence an arbitrary value), in relation Each of the water level stations contains of (i) one or to which the sensor will store the data, the sensor’s two individually calibrated pressure sensors readings contained an error (we can call it residual or the manufactured by the Swiss enterprise Keller Ltd.; (ii) 3 m initial unknown). The purpose of entering the readings long wooden staff with the plastic scale to determine was to keep them as close as possible to the existing visually the sea level at any instant and (iii) a benchmark Baltic Height System 1977 (BH77). Due to Fennoscanian welded to the top of metallic frame of the staff. postglacial rebound and possible deformation of the Stations in Virtsu, Rohuküla and Heltermaa harbors nearby benchmarks, however, the discrepancies between (Fig 2) are equipped with a Keller 36xw sensor (Fig 3) the initial values different water level stations from the and in Kuivastu, Triigi and Sõru with two Keller 46x_e BH77 may reach +/-10 cm. pressure sensors (Fig 4). Both models of pressure sensors The specifics of the pressure sensors lead to a drift (36xw and 46x_e) gain very similar performance, having in their readings, as a result of which the difference also similar specifications record. The reason to equip between the readings of the sensor and the staff changes three last stations with two sensors is mainly over time (Fig 6). Drift values were detected by experimental; two sensors are placed vertically in fixed distance from each other (50 cm). Aim of this comparing the visual reading from the staff and the measurement is to detect the role of water density sensor reading for the very same time-epoch. The results changes in water level measurement error and also to of such comparisons, i.e the monthly-averaged drift study the sensors performance in time. values for each water level station are presented in The pressure sensors have the vertical measuring Table 1. range of 5 m. The sensors were mounted on the backside Proceeding from the above, pressure sensor readings of 3 m long staff gauges at the depth of 1.5 m below the cannot be directly connected to the height network by this waterline (Fig 5). The sensors measure the relative method if the requirements of high-precision levelling are hydrostatic pressure of the water column above the sensor to be met. However, time series from the automatic diaphragm whereas on the other side of the diaphragm is stations currently in use provide important information air pressure, taken from the atmosphere down to the with regard to further processing of the data. sensors using a special capillary. Last feature provides

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Heltermaa 10.0 8.0 6.0 4.0 2.0 [cm] 0.0 -2.0 -4.0 -6.0 11.02. 12.04. 11.06. 10.08. 09.10. 08.12. 06.02. 07.04. 06.06. 05.08. 04.10. 03.12. 01.02. 2009 2009 2009 2009 2009 2009 2010 2010 2010 2010 2010 2010 2011 Ti me Rohuküla 6.0 4.0 2.0 0.0 -2.0

[cm] -4.0 Fig 3. Keller 36xw pressure sensor currently in use in the -6.0 harbours of Heltermaa, Rohuküla and Virtsu -8.0 -10.0 28.03. 22.05. 16.07. 09.09. 03.11. 28.12. 21.02. 17.04. 11.06. 05.08. 29.09. 23.11. 17.01. 2009 2009 2009 2009 2009 2009 2010 2010 2010 2010 2010 2010 2011 Time Virtsu 1.0 0.0 -1.0 -2.0 -3.0 [cm] -4.0 -5.0 -6.0 -7.0 29.01. 30.03. 29.05. 28.07. 26.09. 25.11. 24.01. 25.03. 24.05. 23.07. 21.09. 20.11. 19.01. 2009 2009 2009 2009 2009 2009 2010 2010 2010 2010 2010 2010 2011 Tim e Kuivastu

10.0 9.0 8.0 Fig 4. Keller 46xe pressure sensor currently in use in the 7.0 6.0 harbours of Kuivastu, Triigi and Sõru 5.0

[cm] 4.0 3.0 2.0 1.0 0.0 -1.0 14.10. 18.11. 23.12. 27.01. 03.03. 07.04. 12.05. 16.06. 21.07. 25.08. 29.09. 03.11. 08.12. 2009 2009 2009 2010 2010 2010 2010 2010 2010 2010 2010 2010 2010 Ti me Triigi -1.0 -2.0 -3.0 -4.0 -5.0 [cm] -6.0 -7.0 -8.0 -9.0 14.10. 18.11. 23.12. 27.01. 03.03. 07.04. 12.05. 16.06. 21.07. 25.08. 29.09. 03.11. 08.12. 2009 2009 2009 2010 2010 2010 2010 2010 2010 2010 2010 2010 2010 Tim e Sõru -7.0

-8.0

-9.0

-10.0

[cm] -11.0 -12.0

Fig 5. Staff gauge (water gauge), front view (A) and side -13.0 view, the recesses of which hold pressure sensors of the -14.0 automatic station (units is cm). The benchmark on the top 17.05. 06.06. 26.06. 16.07. 05.08. 25.08. 14.09. 04.10. 24.10. 13.11. 03.12. 23.12. 12.01. 2010 2010 2010 2010 2010 2010 2010 2010 2010 2010 2010 2010 2011 of staff gauge is for levelling. Type B is in use at Virtsu, Ti me Rohuküla and Heltermaa and C at Kuivastu, Triigi and Fig 6. Instrumental trends of the sea levels sensors over Sõru. Photo shows installed sea level station at Kuivastu 0.5 to 1.5 years period. Data points on the graphs show harbour. (Kõuts 2010) difference between measured by pressure sensor and visual readings of the staff gauges

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Table 1 Sensor dynamic corrections in relation to staff reading. various reasons. In most cases, such disruptions were Unit is cm caused by battery voltage drops or power outages. In addition to “gaps”, the water level data series readings contain occasional unreasonable “jumps” (Fig 8a, Virtsu). This means that one reading differs from its adjacent readings by 2-10 cm. Data analysis revealed that such

Month Month Rohuküla Virtsu Kuivastu Triigi Sõru Heltermaa isolated jumps may mostly be caused by sea vessels manoeuvring close to the water level station, prompting 01.10 -2 -3 4 -7 -7 2 pressure changes in water. Such jumps are the most 02.10 -3 -3 4 -7 -7 2 frequent in the Virtsu harbour and less frequent in Rohuküla and Triigi. 03.10 -3 -3 4 -6 -7 2 04.10 -4 -3 5 -6 -7 2 05.10 -4 -3 5 -5 -8 2 06.10 -5 -3 5 -5 -8 2 07.10 -5 -3 6 -4 -9 2 08.10 -6 -3 6 -3 -9 2 09.10 -6 -3 6 -3 -10 2

4. Raw data from automatic stations

Automatic sea level stations sample water column height data 4 times per second, from which 30 s average sea levels are calculated every five minutes. It makes 12x24=288 measurement results per station in 24 hours. a) Data are transmitted and stored in server in ASCII text format (see sample on Fig 7). For every month a separate data file is formed. The file contains information about the date, time of the recording (UTC), water level (cm, with respect to the initial value, which was set at the installation of the WSL), water temperature, maximum and mean wave height and wave period. In addition, the file holds technical information concerning the battery voltage feeding the station and GSM signal strength and service provider.

b) Fig 8. Sea level measured in three stations Rohuküla, Virtsu and Kuivastu are presented. Panel a) shows Virtsu data with sea level jumps from June 16, 2010, ranging from 3 to 6 cm (caused by ship wake). Panel b) shows the same data, but without sudden jumps. The numbers on graphs indicate the mean water level ± standard deviation (grey numbers) and daily water level change ± standard deviation (blue numbers). Numbers on the 3rd and 4th columns show the correlation of the sea level fluctuations Fig 7. An extract from an automatic station measurement between the stations. Last column is number of recorded file sea level readings per day (or after the filtering in panel b)

In the period from 1 January to 30 September 2010 5. Pre-processing of raw sea level data some “gaps” can be found in the automatic station raw data time series. These gaps last from several minutes to a Basically two approaches exist, using water level few days, when the stations have not stored data for observations for the transfer of heights over sea. Firstly,

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short term synchronized water level observations on both 282 daily readings. Judging by the numerics the removal sides of the straits, when duration of those is only couple of 19 single readings from the daily time series did not of days to weeks. The observation site is comfortably significantly change the mean water level and the daily chosen near the closest benchmark (Tamm 1992). Time water level change values, whereas the inter-station for sea level observations is chosen so that wind effect on correlations improved. local water level regime is minimal, usually wintertime Thirdly, the days could be distinguished when with ice cover. Still there are disturbing factors changing differences in wind-caused water level change between water level in the straits, such as salinity (density) two stations exceeded 10 cm and their standard deviation gradient of the sea water, currents etc. which make such exceeded 3 cm. Such sea surface tilts were eliminated short term observations not necessarily representative for from the observation data as well. estimation of local mean sea level. The Väinameri Sea, at shores of which the sea level Other way is to use long time series of sea level stations are installed, is an enclosed and rather shallow measurements, based on which long term mean sea level sea, with a mean depth only ~5m. In the Baltic Sea, the could be estimated. Length of time series needed for this tidal factor is practically nonexistent, staying below a purpose start from 10 years, there are two reasons behind decimetre level (Raudsepp et al. 1999). Presumably its to have that long time series. Firstly, seasonal variability range is the same for the all the stations for any given of mean sea levels, up to 20 cm by means of monthly moment. Instead, the sea level is primarily influenced by averages. Secondly, long term trends, from land uplift, wind, air pressure, currents and river run off in some water level rise of the World Ocean, long term changes in extent. Maximal daily fluctuations of the sea level can the Baltic Sea, trends of salinity etc. All these features reach 2 m and even more in some extreme cases. In should be covered by time series and can not be fulfilled extreme weather conditions, i.e. under strong westerly or if time series are shorter. easterly winds, the water level may change more than +/- In our study the estimation of the local mean sea 0.5 m with respect to the mean water level (Suursaar level is a compromise in between these two. The time 2010). Such daily water level changes were filtered out series of sea levels to be analyzed are much longer than from the time series as the fourth step. days and weeks – thus data are statistically more reliable. Finally, the differences in the time series of the In other hand, such time series are much shorter than used water level stations were studied. As the distances for estimation of long term mean sea levels – thus the between all the six stations were small (maximum 22 long term trends in time series can be safely neglected. km), it was assumed that in a shallow and enclosed water The most important with this method, is to find proper body the sea level fluctuations should be correlated in all dataset homogenization procedure and relevant stations. The sea level topography between the stations parameters, so that local mean sea level will be estimated was disregarded, since that was difficult to determine in with sufficient probability. Importantly, such epochs the West-Estonian archipelago. At the present stage of the (from few days to months) in the time series need to be study it is assumed that the mean sea level topography is used when the water level behaves similarly in paired equal for all the sea level stations. water level stations. In order to homogenizise dataset As a result of the aforementioned data smoothing number of peculiarities and effects need to be filtered out. and filtering procedures 250 data-days for the Virtsu and The most important types of peculiarities to be filtered Kuivastu pair, 183 data-days for Triigi and Sõru and 186 out are water level tilts across the straits. For this certain data-days for Rohuküla and Heltermaa were left for the threshold tilt value (to be explained later) is defined. estimate of local mean sea level and height transfer. The Aiming at transfer of heights from mainland to the largest number of eliminations was associated with the islands, 6 water level stations were arranged into three Rohuküla-Heltermaa pair of sea level stations. As these pairs: Virtsu-Kuivastu, Triigi-Sõru and Rohuküla- stations are the farthest away from each other (22 km) Heltermaa. At the first stage, the sea level data of these and they experienced the largest along strait sea surface paired stations were synchronised to the same time epoch. tilts, which were filtered out. The raw data synchronisation principle was as follows. If a station had no data for the given time-epoch, then also 6. Determining the local mean sea level the data from other station were removed. After such eliminations the overall remainder from the nine-month Based on homogenized datasets of the sea levels, the observation period (273 days) was 271 data-days at local mean sea level is estimated (hi_A) and corresponding Virtsu, Kuivastu, Rohuküla and Heltermaa and 202 days standard deviations calculated for each station, see Table at Triigi and Sõru. 2. A comparison of the statistics before and after data In the second stage the synchronised initial data smoothing revealed that the standard deviations had were smoothed, i.e. jumps over 2 cm (considered to be improved by 3-4 cm. This is due to the removal gross errors, since they exceeded more than twice the inadmissible sea level fluctuations due to applied filtering sensor’s measurement precision) were removed from the criterion. Note that the unrealistic standard deviation data-series. Fig 8 presents (a) unsmoothed and (b) (0.425m) at the Sõru water level station was due to the smoothed data series at three stations (Rohuküla, Virtsu fact that the under-water sensors appeared to be covered and Kuivastu) for 17 June 2010. After the removal of with underwater ice formed around staff gauge in January these gross errors 263 readings were retained out of initial

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2010. These faulty readings were removed from the time Triigi is very well protected from the open sea conditions series as well. by breakwater. As a result of the raw data smoothing, the mean The local mean sea levels (hi_A) were then corrected readings changed within the range of 3 cm. However, by the monthly correction factors due to the sensor drift when the mean readings in the pairs of water level station trend, see Table 1. The corrected readings (hi) can be were compared before and after data smoothing, the said used for determining of absolute local mean sea level differences had changed only slightly (within the range of during the nine-month period at each sea level station. +/-0.5 cm). An exception was the Triigi-Sõru pair, which Importantly, this can be related to the actual staff reading could not be compared due to the large standard deviation (ri). This allows connect the mean sea level value on the in the Sõru station. Last could be explained with the fact staff with the closest national levelling benchmark and that the Sõru station is quite open towards open sea, when also can be used for the height transfer between the water level stations on both sides of the straits.

Table 2. Elements of local mean sea level for the period from 1 January to 30 September 2010 at the stations (Unit is meter) Rohuküla Heltermaa Virtsu Kuivastu Triigi Sõru Mean sensor reading – before processing –0,106±0,193 –0,143±0,171 –0,096±0,198 –0,200±0,185 –0,130±0,184 0,039±0,425* (hi_B) Mean sensor reading –0,119 –0,152 –0,106 –0,114 after processing ±0,157 ±0,143 –0,061±0,156 –0,168±0,147 ±0,158 ±0,160 (hi_A) Number of days after processing 186 186 250 250 183 183 Corrected mean sensor reading (hi) –0,152 –0,125 –0,084 –0,108 –0,151 –0,181

Staff 0-reading (ri), 1,440 1,380 1,220 1,220 1,610 1,300 * sea level readings disturbed by underwater ice

6. Connection of the islands station was computed from Sõru’s zero level and the foot levelling results. The third height transfer was obtained All the staff gauges were connected to the closest from the comparison of the staff readings in Heltermaa national levelling benchmarks. The methodology of the and Rohuküla. It resulted with the reading 1.426 m at the high-precision levelling was strictly followed. This Rohuküla station. Thus, the detected misclosure is 14 mm allows determining precisely the height differences for the entire 253-km loop. (deltah) between the adjacent water level stations, which The presented data processing method is just a first are located either in the same island or in the mainland. approach and the procedure could be specified further. Three sea-level based height transfers and three Therefore we expect that more detailed analysis and height differences from foot levelling results allow to calculation methods for local mean sea level would result form a closed loop, see Fig 2. Obviously, the misclosure a 1 cm precision for height transfers using measured sea of this entire loop may indicate the overall quality of the levels. height transfers. As initial for subsequent determination of the height differences the zero (mean sea level during the 9-month 7. Conclusions and discussion observation period) of the Rohuküla staff was taken (1.440 from Table 1). Then the height difference at the The advantage of high resolution sea level zero level of the Virtsu WLS was computed by using the measurements producing data for local mean sea level new data from the national levelling network. estimate is continuous and large amount of data, which The zero level at the Kuivastu was obtained from the makes the end product statistically reliable and allows comparison of the staff readings in Virtsu and Kuivastu. finding the most suitable periods for height transfers. When transferring heights over water we assumed that The processing of sea level data of six automatic the used staff readings (obtained after filtering) are stations installed on the opposite sides of straits in the located on the same level surface Väinameri, resulted in the dataset where wind and other The foot levelling from Kuivastu to Triigi was used forcing impacts on water level was reduced to a to obtain the zero level at the Triigi WSL. The height minimum. As a consequence, the across strait sea level transfer from Triigi to Sõru was similar to Virtsu- tilt between the water level stations is minimal and can be Kuivastu connection. The zero level at the Heltermaa disregarded in transferring heights over water.

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The drift values of the sensors of sea levels stations References were detected by repeated comparisons of the sensor readings and visual sea level observations from staff Carrera, G.; Tessier, B.; O’Reilly, C. T. 1996. Statistical gauge. The benchmark on top of the staff gauge is Behavior of Digital Pressure Water Level Gauges. Marine levelled to the nearest benchmark of height network. The Geodesy, 19: 137 – 163. initial results of the experiment showed that it may be Kõuts, T. 2010. High precise sea level measurements in possible to connect the largest islands of West-Estonia to Väinameri for heigh system transfer from mainland to islands. Project report 2010, Marine Systems Institute, the mainland based on the data from the existing - Tallinn University of Technology, 72p. (In Estonian) visually connected automatic stations. The method under Linnamaa, T. 1940. The connection of the levelling-nets of the study yielded a misclosure of 14 mm for the 253-km long island Saaremaa and the main land. Geodeet, 23: 66 – 69. loop consisting all the three height transfers. Considering (In Estonian) the sensor accuracy, 1 cm for single measurement and the Pugh, D. T. 1996. Tides, surges, and mean sea-level. sensor connection accuracy, about 2 cm, the error of Chichester, UK: John Wiley & Sons Ltd. 486 p. closure obtained as a result of this study is very Raudsepp, U.; Toompuu, A.; Kõuts, T. 1999. A stochastic promising. model for the sea level in the Estonian coastal area. Note that the water level stations are still Journal of Marine Systems, 22, 69 – 87. operational, more data are to be collected. Thus from the Tamm, A. 1992. The levellings between the islands and main further studies more reliable results can be expected. In land. Geodeet, 2(26): 13 – 15. (In Estonian) this respect the most promising are the data for the period Torim, A. 2009. The levellings in Estonia between 1950 and of ice-coverage, when the water masses are not directly 1996. Geodeet, 38/39(62/63): 11 – 15. (In Estonian) influencing by the wind-induced disturbances. Tamm, A. 1970. The using of correlation and dispersion analyse to study the hydrostatic levelling data. Diploma Acknowledgements work, Tartu. (In Estonian) Suursaar, Ü. 2010. Sea Level Variations Along the Estonian Coast of the Baltic Sea. Sea Level Rise, Coastal This study is supported by the Estonian Science Engineering. Shorelines and Tides. Oceanography and Foundation grant ETF 7356 and grant ETF8749. Estonian Ocean Engineering. Nova Science Publisher Inc. New Land Board financed the installation of the used sea level York. stations. Dr. Ants Torim and Priit Pihlak from Estonian Woodworth, P. L.; Vassie, J. M.; Spencer, R.; Smith, D. E. Land Board are acknowledged for fruitful discussions. 1996. Precise Datum Control for Pressure Tide Gauges. Marine Geodesy, 19:1 – 20.

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190 III Liibusk, A., Jürgenson, H. 2008. CONNECTIONS OF GULF OF RIGA ISLANDS TO THE BALTIC HEIGHT SYSTEM 1977

Reprinted from: Environmental Engineering. The 7th International Conference: Selected Papers. Vilnius Gediminas Technical University Press “Technika”, 1378–1385. May 22-23, 2008 ENVIRONMENTAL th The 7 International Conference ENGINEERING Faculty of Environmental Engineering Vilnius Gediminas Technical University Saulơtekio ave 11, LT-10223 Vilnius, Lithuania Phone: +370 5 2745090; Fax.: +370 5 2744731; e-mail: [email protected]

CONNECTION OF GULF OF RIGA ISLANDS TO THE BALTIC HEIGHTS SYSTEM 1977

Aive Liibusk, Harli Jürgenson

Estonian University of Life Sciences, Institute of Forestry and Rural Engineering, Department of Geomatics, Kreutzwaldi 5, Tartu 51014, Estonia E-mail: [email protected] [email protected]

Abstract. Since 1933, when the national heights network was established in Estonia, there have been problems with the connection of the heights of small islands with mainland heights. In 1939-1940, leveling over the ice was used (Muhu Island). In 1962-1966 and 1979-1983, hydrostatic leveling and measurements of water level were employed (Muhu Island). In 2003, using the new geoid model and GPS-leveling techniques, a difference of approximately 10 cm from the height catalogue values for the island of Kihnu was established. Due to the fact that hydrostatic leveling is expensive and leveling over the ice is technically very complicated, we omitted these options. New water level measurements were carried out in 2006 and 2007, both in winter and in summer. The seawater level was observed and tied to benchmarks. The observation results from the summer and the winter led to findings that were quite similar to those from GPS/leveling. The results are used for precise geoid determination.

Key words: leveling, GPS, height system, tide gauge, sea water level, geoid

1. Introduction have been installed on Estonia’s coastline. Readings from tide gauges, even where they are available on the islands, In order to connect small islands with the national are taken at different times and at long intervals (every 3, heights network (Baltic Heights System - BK77), various 6, 12 or even 24 hours!). The use of data of such methods have been used over time. The largest islands of frequency, however, presupposes very long observation Estonia (Saaremaa and Hiiumaa) were connected with the periods (several years) [4]. mainland in the winter of 1939-40 using leveling over the The objective of the present study was to find and ice across Suur Straits (8 km) [1, 2]. As the ice moves investigate possibilities of simplifying water level (undulates) even during a longer spell (3-4 days) of observation methods and to test the methods in windless weather, the said measurement method may be connecting the island of Kihnu. regarded as unsatisfactory for high-precision leveling. In the 1960s the heights of the larger islands off the east 2. Methods coast of the Baltic Sea were connected with mainland heights using the hydrostatic measurement method [2]. The benchmark in the southern part of Kihnu Island That represented a method employing the principle of (in the Gulf of Riga) and in the harbor of Munalaid in joined vessels, where liquids of different densities are southwest Estonia were selected for the conduction of the discharged into pipes placed on the seabed. This method experiments (Fig. 1). The distance between the two water is one of the most precise for leveling where heights need level measurement stations was 18 km. to be transferred over bodies of water. At the same time, The measurements were performed in two different the last mentioned leveling method is expensive and seasons to represent different conditions of seawater. The labor-consuming, which is why it is not much employed. first series of measurements took place in winter, on Water level readings from tide gauges and March 7, 2007, when the whole of the Gulf of Riga was mareographs have been used the most frequently to covered with ice. Due to ice cover, seawater is in its most connect islands [3]. Over a long timeline, it represents a tranquil state in wintertime. precise measurement method. However, a disadvantage is The second series of measurements was performed that mareographs are expensive and not many of them in summer (June 25 and 26, 2007).

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Fig 1. Tide gauge positions. The distance between the tide Fig. 2. Temporary tide gauge in an ice-hole. gauges is ~18 km. 2.1.2. RTK GPS measurement 2.1. Height transfer from water observations 2.1.1. Tide gauges As a second measurement method, RTK GPS was used to observe water level. A dual-frequency GPS Observation of water level from tide gauges has been receiver (Trimble R8) was placed onto a float in the water a method used most frequently throughout history, and (Fig. 3). A base station (Trimble R8) was situated at a has proved to be fairly precise. 200-meter distance from the measurement point. The As there are no stationary mareographs in the region, GPS receiver placed on the float recorded data in real we opted for short-term water level observations. In order time at an interval of 1 second. The GPS receiver on the to use independent tide gauges, we set up our own tide float was not tied to the benchmark. During the gauges into the coastal waters near mainland Estonia performance of the GPS test primary attention was paid to (Munalaid) and a small island (Kihnu). The installed tide relative changes in seawater level and to their comparison with the relative changes in the seawater level as obtained gauges represented metal rods that were hammered from tide gauges [5]. solidly into the seafloor. Then millimeter-scale rulers were fixed onto the rods (Fig. 2). The first requirement in selecting rod locations was that they be located close to the benchmarks, which would enable tying the peak of the metal rod hammered into the seafloor to the local benchmark. With the help of the ruler fixed onto the metal rod, the normal height leveled for the rod was connected with seawater surface height using the mean value from the observations. The second requirement in selecting rod positions was that they be situated in a place maximally sheltered from the wind, and windless days be selected for measurements, which would lessen the effect of waves and water accumulation on measurement results. For winter measurements the tide gauge was placed Fig. 3. GPS receiver placed onto a float. in a hole drilled into the ice (Fig. 2). In the choice of rod locations, care was taken to ensure that the water be not 2.1.3. Total station measurements frozen to the bottom and that the ice be not attached to As a third water level observation method, we used a stones, which would result in the ice being lifted up. In Robotic total station. The objective was to further order to find a place suitable for winter measurements, it simplify water level observations. In order to do that, it was necessary to go out onto the ice dozens of meters off was necessary to place a prism into the water on a float, the shore. switch the total station into the mode of automatic In order to observe the water level, readings from tracking of the prism and record the readings at a desired both tide gauges (in the coastal waters near the mainland interval. In order for the experiment to be successful, the and the island) were taken during the same period (e.g. 1 difference between the center of the prism and the water hour) and at the same interval (1-5 min.). level needed to be measured and the measurements needed to be tied to the benchmark on land.

194 Measurements of the benchmark on land needed to be 'H 'h 'N 0.528 (0.330) 0.198m. performed using a complete two-round technique both at the beginning and at the end of the session. The The normal height for the national densification advantage of the method lies in that the prism moved by network point 501A at Kihnu was calculated as follows: the water is tracked automatically. This is performed by the automatic target recognition or autolock function of H H 'H 2.457 (0.198) 2.259m. the total station. The measurements are as precise as 501A 496A trigonometric leveling. As only one station is involved the degree of precision is primarily determined by the After connecting Point 501A with benchmark no. precision class of the total station. A 3” total station can 243 [7], the new normal height obtained for the provide a 2 mm precision level without much problem. benchmark at Kihnu was: We did not use a total station in Kihnu H H H measurements; however, we tested it on Lake Võrtsjärv, 243 _ GPS 501A ' 501A243 and the findings obtained there attest to the user- 2.259 0.486 2.745m. friendliness of the device and the reliability of the results. The results obtained here revealed the problem that 2.2. GPS-leveling the height of the Kihnu benchmark taken from the 1977 heights catalogue ( H 2.631m ), is ~12 cm smaller This represents a well-known method where 243 than the height obtained from GPS leveling gravimetric geoid height differences are subtracted from ellipsoid height differences. The level of precision of the ( H 243 _ GPS 2.745m ). The origin of the height taken results is primarily contingent on the geoid precision, but from the 1977 catalogue is not precisely known; use was also on the precision of the GPS measurements. In this made of time series from stationary mareographs. article, GPS coordinates of national densification network A difference of 11-12 cm also strikes the eye when points [6] and the gravimetric geoid calculated by Harli we compare the differences between the gravimetric and Jürgenson [7] are used. the geometric geoid all across Estonia (Fig. 4). Elsewhere in Estonia the differences are ca 49-51 cm whereas on 3. Connection of the island of Kihnu using GPS Kihnu it is 38 cm! [7] leveling

At Kihnu and Munalaid GPS points of the national densification network were situated close to wall benchmarks (No. 243 and 230 respectively). They were connected to the benchmarks by means of leveling. The difference between geodetic heights 'h at national densification network points 501A (at Kihnu) and 496A (at Munalaid) was:

'h h501A h496A 22.104 22.632 0.528m.

At the same points the gravimetric geoid difference was:

'd N 501A N 496A 20.340 20.670 0.330m. Fig 4. Difference between the gravimetric and the geometric Thus, the height difference between Kihnu and geoid (cm) [7]. Munalaid was:

4. Connection of the island of Kihnu using water level measurement session the interval needs to be shortened, observations in winter as at times the water moved up and down in the ice hole in a matter of minutes. In order to verify the incompatibility of the height The second measurement session was 1 hour long, described in the previous chapter, we carried out checks and the interval for taking the readings was set at 1 on the height differences using water level observations. minute. On March 7, 2007, we performed seawater level Subsequently, data concerning the measurement day measurements in winter conditions simultaneously at from mareographs surrounding the Gulf of Riga (Pärnu, Kihnu and at Munalaid using tide gauges set up at the Daugavgriva and Kolka) were taken from the website of seafloor. We carried out two measurement sessions. The the Baltic Operational Oceanographic System first session lasted 2 hours. We took readings from the (www.boos.org) (Fig. 5), from which it appears that on ruler mounted onto the rod at 15-minute intervals. It March 7, 2007, water levels in the Gulf of Riga were appeared during the first session, however, that in a short fluctuating in an analogous manner (Fig. 6).

195 As seawater level in the Gulf of Riga, in the Pärnu- Kihnu Kolka direction (distance ca 135 km), was evenly tilted by a mere 2-4 cm during the measurements, water surface -0.365 -0.370 tilt was not taken into account between Manilaid and -0.375 Kihnu (distance ca 18 km), which is in the same -0.380 -0.385 direction. The water level at Daugavgriva was 10 cm -0.390 higher than the average, which was evidently due to water -0.395 -0.400 accumulation in the southern corner of the Gulf, one of Sea BK77 level (m)

the reasons for which is the Daugava River discharging 14.05 14.25 14.35 14.50 15.05 15.20 15.35 15.50 16.05 into the Gulf of Riga. Time

Munalaid

-0.250 -0.255 -0.260 -0.265 -0.270 -0.275 -0.280 -0.285 -0.290 -0.295 Sea Level BK77(m) -0.300 -0.305 14.05 14.25 14.45 15.00 15.15 15.30 16.00 16.05 Time

Fig. 7. Fluctuations of sea level at Kihnu and Munalaid on March 7, 2007, at 14:00-16:00. Data recording interval 15 min.

Kihnu

-0.360 -0.365 Fig. 5. The locations of the mareographs of Pärnu, Daugavgriva -0.370 and Kolka around the Gulf of Riga. -0.375 -0.380 -0.385 -8 -0.390 -10 -0.395 -12 -0.400

-14 BK77 (m) level Sea -0.405 -0.410 -16 -0.415 -18 -0.420 -20 -0.425 -22

-24 17.45 17.53 17.58 18.01 18.06 18.12 18.16 18.20 18.32

Mean sea level (cm) Time -26 -28 Munalaid -30 -32 -0.245 -0.250 -0.255

00.00 02.00 03.00 04.00 05.00 07.00 08.00 09.00 10.00 12.00 15.00 16.00 17.00 18.00 19.00 20.00 21.00 22.00 23.00 -0.260 Time -0.265 -0.270 Pärnu Kolka Daugagriva -0.275 -0.280 -0.285

Sea level BK77 (m) -0.290 Fig. 6. Fluctuations in the mean sea level in the mareographs of -0.295 -0.300 Pärnu, Kolka and Daugavgriva on March 7, 2007.

17.45 17.50 17.55 18.06 18.25 18.35 Time In order to obtain a better overview of the winter measurements we prepared Figures 7 and 8. A mean was Fig. 8. Fluctuations of sea level at Kihnu and Munalaid on calculated from individual water level readings, and a March 7, 2007, at 17:45-18:40. Data recording interval 1 min. height difference with the Kihnu benchmark No. 243 and

Munalaid benchmark No. 230 respectively was added to Added to the figures are linear lines to facilitate the the mean. As the result, the normal height of the water reading of the diagrams and the assessing of the extent to level obtained was in the BK77 Heights System. which water level fluctuated during the measurement session in either measurement station. During the first 2- hour measurement session (Fig. 7) water level at Kihnu

196 rose by 0.7 cm while at Munalaid it dropped by 3.5 cm The results of the winter water level measurements within the same period. During the second measurement have been summarized in Table 1. Entered into the table session (Fig. 8) water level at Kihnu remained unchanged are the mean sea levels from the measurement sessions in while it dropped by 4.6 cm at Munalaid. Such short-term relation to the Kronstadt zero at Kihnu and Munalaid in movements of water level in different directions are the Baltic Heights System (BK77). In order to calculate natural and inevitable with sea. the sea level, the heights of Benchmark No. 243 (at We would like to call attention to the fact that in Kihnu) and Benchmark No. 230 (at Munalaid) taken from Figure 8 one can see a change in water level that is the 1977 heights catalogue have been used as initial characteristic to sea, where the water level rose by 6.5 cm heights. The last row of the Table shows the new height within 5 minutes. In this particular case, such an abrupt calculated for the Kihnu benchmark No. 243, which is change may have been caused by the waves that occurred connected with the Munalaid benchmark No. 230 by in ice-free waters several kilometers away from the means of water observations: measurement point. Such changes confirm that taking readings from stationary mareographs at an interval of 1, H 243 _ new H 243 'H (1)(2) . 3 or 6 hours would not yield high-precision results in short-term measurements, as the readings are of random As can be seen from Table 1, the new height for the nature. Given the said extremities, the frequency of taking Kihnu benchmark No. 243, calculated from the water readings from tide gauges in water level measurements observations ( H 2.742m ), is of the same should be high – at an interval of at least 5 minutes. As a 243 _ new result, it is possible to gain a more precise assessment of magnitude as the height of the benchmark obtained by the mean water level even over short measurement means of GPS leveling ( H 243 _ GPS 2.745m ). sessions.

Table 1. Mean sea level in relation to the Kronstadt zero in the BK77 system (m).

Mõõtesessioon 2h, intervall 15 min Mõõtesessioon 1h, intervall 1 min Keskmine Munalaid (1) -0.279 -0.276 -0.278 Kihnu (2) -0.382 -0.395 -0.389

'H (1)(2) 0.103 0.119 0.111

H 243 _ new 2.734 2.750 2.742

5. Connection of the island of Kihnu using water level 26. Such a tilt in water surface may be considered observations in summer insignificant over so long a distance (135 km), and thus the respective water surface tilt correction was not taken into account in the subsequent calculations. On June 25 (at 21:30-22:00) and June 26 (at 7:30- 14 14:30), 2007, repeat measurements were performed at 12 10 Munalaid and Kihnu. In order to do that, new metal rods 8 were hammered into the seafloor near the coast, and 6 4 rulers were mounted onto the rods. On that occasion, the 2 0 readings-taking interval during all the summer sessions -2 -4 was 1 minute. -6 -8 Mean levelsea (cm) In addition to the tide gauges set up to conduct the -10 -12 experiments, general fluctuations in the water level on the -14 Gulf of Riga were observed using data from mareographs -16 -18 at Pärnu, Kolka and Daugavgriva. The fluctuations at 0:00 3:00 5:00 8:00 13:00 16:00 18:00 20:00 22:00 10:00 13:00 16:00 19:00 21:00 23:00 these places are presented in Fig. 9. As can be seen from Time the Figure below, the difference in water level between Daugagriva Kolka Pärnu the mareographs of Kolka and Pärnu was 1-5 cm at Fig. 9. Mean sea level fluctuations in Pärnu, Kolka and 21:00-22:00 on June 25 and 0-6 cm at 7:00-15:00 on June Daugavgriva mareographs on June 25 and 26, 2007.

197 Kihnu 0.39 0.38 -0.155 0.37 -0.160 0.36 -0.165 0.35 0.34 -0.170 0.33

-0.175 Height (m) 0.32 -0.180 0.31 0.30 -0.185 0.29 -0.190

Sea level BK77 (m) -0.195 11:15 11:16 11:17 11:18 11:20 11:21 11:22 11:24 11:25 11:26 11:28 11:29 11:31 11:33 11:34 11:35 11:37 11:38 11:40 -0.200 Time -0.205 -0.210 Height (m) Linear (Height (m)) Poly. (Height (m)) 7:31 7:34 7:36 7:39 7:44 7:48 7:55 8:00 8:06 8:12 -0.18 Time Munalaid -0.19

-0.040 -0.20 -0.045 ) m ( -0.050 -0.21

-0.055 Sea level (m) BK77 -0.060 -0.22 -0.065 ea level BK77 S -0.070 11:16 11:18 11:20 11:21 11:23 11:24 11:26 11:27 11:29 11:30 11:32 11:33 11:34 11:36 11:38 11:39 Time -0.075

7:30 7:35 7:40 7:45 7:50 7:55 8:00 8:05 8:10 8:15 Time Fig. 11. Sea level fluctuations at Kihnu on June 26, 2007. Data recording interval 1 second using GPS method (upper Fig. 10. Sea level fluctuations at Kihnu and Munalaid at 7:30- diagram), 1 minute using tide gauge (lower diagram). 8:15 on June 26, 2007. Data recording interval 1 min.

0.395 Of the summer measurements, diagrams have been 0.385 presented for three measurement sessions that are the 0.375 most telling. In the morning session of June 26 one can 0.365 recognize an abrupt drop in water level (by 4 cm) within a 0.355 0.345 few minutes (Fig. 10), which is analogous to that 0.335 observed during the winter measurements. At the same 0.325 time, the mean rise in water level within half an hour was (m) Height 0.315 barely 0.6 cm at Kihnu and 2.7 cm at Munalaid during the 0.305 0.295 same period. 0.285 In the summer measurements, an experiment of 0.275 observing the water level using real-time GPS was also 0.265

performed in parallel with taking readings from tide 13:30 13:35 13:38 13:41 13:43 13:45 13:48 13:50 13:52 13:54 13:58 14:01 14:06 14:08 14:11 14:13 14:15 14:18 14:20 14:22 14:24 14:26 14:29 gauges. Fig. 11 and 12 present diagrams of data collected Time from the GPS method and from the tide gauge method. Height (m) Linear Poly. (Height (m)) When using the GPS method, data was recorded at a 1- second interval (upper diagrams in Fig. 11 and 12). The -0.17 -0.18 lower diagrams of the figures show the data gathered -0.19 from tide gauges at an interval of 1 minute. It appears -0.20 from the GPS-measurement diagrams that the sea level -0.21 fluctuated within a very wide range (up to 2.5 cm). Such -0.22 great fluctuations here are due mainly to two factors: the -0.23 Sea level (m) BK77 -0.24 degree of precision of height determination using GPS (± -0.25 2 cm + 1 ppm) and the low intensity of the waves on the sea. At the same time, if we draw a sixth-degree 13:30 13:37 13:40 13:43 13:46 13:49 13:51 13:57 14:02 14:06 14:09 14:13 14:15 14:20 14:23 14:26 14:30 polynomial through the heights from the GPS Time measurements entered into the diagram, a curve is formed Fig. 12. Sea level fluctuations at Kihnu on June 26, 2007. Data that shows smooth rising and falling of the water level, recording interval 1 second using GPS method (upper thus reducing short-lived protrusions. diagram), 1 minute using tide gauge (lower diagram).

198 As the floated GPS was not tied to the benchmark, (BK77), analogously with the winter measurements. The the heights obtained are not in the BK77 system. The only results of the first measurement session (at 21:30-22:00 thing that was observed in using the GPS method was on June 25, 2007) in the table differ greatly from the relative change in comparison with the results from the measurement results from the second day (by ca 3 cm). tide gauges. The results gained from the two different The reason may be the evening low tide of the seawater, water observations methods agree well with each other. which at short distances and in the short run may have a During the measurement session at 11:15-11:40 the water fairly diverse effect on the water level. At the same time, level rose by 2.8 cm according to the GPS method and by the new heights for the Kihnu benchmark No. 243, 2.3 cm as observed from the tide gauge data. During the obtained from winter measurements (2.742 m) and from second measurement session at 13:30-14:30 the water summer measurements (2.753), may be regarded as level dropped by 2.7 cm according to either method. The coming very close to each other. The difference in the results obtained are promising, as the GPS method would heights of the benchmark, calculated from the results simplify the measurement process and enable data obtained from water observations performed in two collection in greater quantities. different seasons and under different circumstances, is Table 2 summarizes the results of five summer water only 1.1 cm. level observation sessions in relation to Kronstadt zero

Table 2. Mean sea level in relation to Kronstadt zero (m).

Measurement session 21:30-22:00 7:30-8:15 10:35-11:00 11:15-11:50 13:30-14:30 Mean Munalaid (1) 0.015 -0.057 -0.087 -0.077 -0.097 -0.061 Kihnu (2) -0.131 -0.181 -0.193 -0.199 -0.211 -0.183 H ' (1)(2) 0.146 0.124 0.106 0.122 0.114 0.122 H 243 _ new 2.777 2.755 2.737 2.753 2.745 2.753

6. Results and conclusions from the catalogue how the benchmark height had been determined. The present article presents two different methods of In the study, a new attempt was made at connecting connecting the heights of small islands with mainland the Kihnu Island benchmark using short-term sea level heights. The tests conducted during the study are built measurements. Sea level was monitored using both the around the case of the island of Kihnu. The height of the tide gauge method and the GPS method. Based on the wall benchmark on Kihnu Island, H 243 2.631m , was results of the test measurements, the two measurement taken from the 1977 heights catalogue; however, it did methods, which are substantially different, yielded very not agree with the result of GPS-leveling. It is not clear similar results. The results of the different methods have been summarized in Table 3. Table 3. Heights of Kihnu benchmark No. 243 (m) BK77. The results obtained are promising, yet so far they are based on an insufficient amount of data. Therefore Kihnu benchmark initial normal 2.631 one has to be very cautious about them. Unquestionably, height a one-hour measurement session with a 1-minute Kihnu benchmark normal height by 2.745 recording interval in water level observations is GPS leveling insufficient for transferring normal heights from mainland Kihnu benchmark normal height by 2.742 to island, as the behavior of sea surface on a short-term sea level observations in winter basis is fairly different in different places. In works Kihnu benchmark normal height by 2.753 requiring a smaller degree of precision one can disregard sea level observations in summer water surface topography and water surface tilt; at the Kihnu benchmark normal height as a 2.747 same time, however, data from mareographs situated mean of sea level observations in close to the measurement area need to be collected so it winter and in summer would be possible to take them into account in case of major deviations. From Chapter 3 of the present article we found that Nevertheless, the measurements performed during the height of the Kihnu benchmark obtained from the the present study confirmed that in order to simplify

1977 heights catalogue, H 243 2.631m , was ~12 cm further water observations use should be made of the GPS smaller than the height obtained from GPS leveling, method and/or automated tacheometry. As the measurements performed corroborated to the H 2.745m . A height difference of the same 243 _ GPS existence of a 12-cm difference between the geometric magnitude was confirmed by the results from repeated and the gravimetric geoid, the results obtained can be sea level observations in winter and in summer. used to correct the official Estonian combined geoid model Est-Geoid2003.

199 References tide gauges. International Association of Geodesy Symposia, Vol. 123, 2001. 193-198 p. 1. Torim, A. Renovation of the national basic height 5. Ben-Michael, C., Even-Tzur, G. Monitoring Sea network. Tõravere, 1997 (in Estonian). Level Using GPS – The Difference between the 2. Tamm, A. Levelings between the island and the Mediterranean and the Red Sea Levels as a Test Case. mainland. Geodeet, 1992, No 2, p. 13-15 (in XXIII FIG Congress, Munich, Germany, Estonian). October 8-13, 2006. 3. Tamm, A. ɉɟɪɟɞɚɱɚ ɜɵɫɨɬɵ ɧɚ ɨɫɬɪɨɜɚ Ɂɚɩɚɞɧɨ- 6. Planserk AS. Report of geodetic works. Lääne County ɗɫɬɨɧɤɨɝɨ ɚɪɯɢɩɟɥɚɝɚ ɦɟɬɨɞɨɦ ɜɨɞɧɨɝɨ section of the densification network (West-Estonia ɧɢɜɟɥɢɪɨɜɚɧɢɹ. Ɉɫɨɛɟɧɧɨɫɬɢ ɜɵɫɨɤɨɬɨɱɧɨɝɨ islands). Report of GPS measurements. Volume 1. ɧɢɜɟɥɢɪɨɜɚɧɢɹ ɧɚ ɝɟɨɞɢɧɚɦɢɱɟɫɤɢɯ ɩɨɥɢɝɨɧɚɯ. Tallinn, 2001 (in Estonia). Ɍɚɥɥɢɧ, 1988, p. 52-61. 7. Jürgenson, H. Determination of Estonian Precision 4. Jevrejeva, S., Rüdja, A., Mäkinen, J. Postglacial Geoid. Tartu, 2003. 157 p. (in Estonia). rebound in Fennoscandia: new results from Estonian

200 IV Liibusk, A., Kõuts, T., Ellmann, A. 2012 TRANSFER OF HEIGHTS TO ISLANDS IN WEST-ESTONIAN ARCHIPELAGO USING HYDRODYNAMIC LEVELLING

Reprinted from: IEEE/OES Baltic 2012 International Symposium: IEEE Conference Proceedings. 8 pp.

Transfer of heights to islands in West-Estonian Archipelago using hydrodynamic levelling

Aive Liibusk1, Tarmo Kõuts2, Artu Ellmann3 1Department of Geomatics, Estonian University of Life Sciences, Tartu, Estonia; [email protected] 2Marine Systems Institute, Tallinn University of Technology, Tallinn, Estonia; [email protected] 3Faculty of Civil Engineering, Tallinn University of Technology, Tallinn, Estonia; [email protected]

Abstract - During the last decade sea level sea level series were used in [2] and [3], respectively. Note measurements by means of pressure sensors have become that sea level observations from SGs were taken either two or wide-spread, since they are compact, can withstand icy four times a day. In other words, such data series are blind to conditions, are easy to integrate with data loggers and sudden water level changes in between the readings. Note also communication systems. This study uses two years (2010- possible stability problems of staff gauges and inconsistencies 2011) long sea level series collected by pressure gauges for and uncertainties in the sea level series, e.g. due to staff hydrodynamic levelling. As a result, the accuracy of replacements. Most staff gauge stations in the given study area hydrodynamic levelling was estimated to be ±1.5 cm in ceased to be operational decade(s) ago. Besides, the locations West-Estonian Archipelago. Therefore the height of historic sea level stations were not optimal for establishing differences calculated from sea level series of a reliable across-water connection between the Estonian contemporary pressure gauges were used as reference for mainland the island Saaremaa and between the islands historic staff gauge readings with data sampling 12h and Saaremaa and Hiiumaa. Therefore, a constellation of six for some days sea level observations in calm weather and pressure gauges (PG) was installed into coasts of straits to be ice covered sea conditions. The comparisons indicated that bridged by the sea level observations in West–Estonian the height transfer accuracy ±1.5 cm with different Archipelago. All the PGs have been operational two years observation periods and data samplings is guaranteed only (2010-2011). This study applies the same hydrodynamic up to 20 km distances. Over longer distances the frequent levelling methodology developed in [4] for 2 years long data data sampling and at least one year sea level observations series (rather than annual data used in [4]). An advantage of must be carried out for geodetic applications. PG is that data sampling interval can be easily changed, note that typically 5 or 10 minutes is used for maritime purposes. Key words: pressure gauges, staff gauges, Different aspects of data sampling were investigated more hydrodynamic levelling, sea level series thoroughly in this study. The data sampling interval 5 minutes was used to validate sea level series with 12 hours data

sampling interval, i.e. similarly as it was adopted for the I. INTRODUCTION historic SG sea level series. The results may be useful for Implementation of a common national height system may estimating the reliability of the historic data. Also an require transferring of heights to adjacent islands. Accordingly, additional historic dataset was incorporated to verify the this study applies principles of hydrodynamic levelling for results of the hydrodynamic levelling. connecting levellings on the islands of Saaremaa and Hiiumaa The outline of the paper is as follows. First, the principles in West-Estonian Archipelago with the national levelling of hydrodynamic levelling are reviewed. Section III tackles network in the Estonian mainland. Recall that hydrodynamic locations of historic and contemporary sea level gauges in levelling utilizes sea level observations for determining height West-Estonian Archipelago. Next, the main characteristic of (potential) differences between coastal points or over oceanic the pressure sensors in contemporary sea level gauges are regions (e.g. [1], Section 5.5.3). described. The adopted data processing principles are Long-term (from several years up to decades) sea level explained in Section V. The results of hydrodynamic observations using staff gauges (SG) have traditionally been levellings were verified by using different alternative considered for this task. Although several SG were erected measurements. The discrepancies between the height and observed in West-Estonian Archipelago from 1950-ies, differences obtained from different levellings are presented in there are only a couple of experimental attempts to use them Section VI. A brief summary concludes the paper. for hydrodynamic levelling. For instance, 13 and 4 years long

203

II. PRINCIPLES OF HYDRODYNAMIC LEVELLING study area the influence due to mean SST can be neglected. The height of the mean sea level (MSL) at a tide gauge Then the corresponding height difference (ǻH) between CP (TG) can be determined by sea level observations. Also the pairs is computed as (cf. Fig. 1): tide gauge needs to be connected to the levelling network using tide gauge zero (TGZ), contact point (CP) and tide ο ൌ ୆ െ ୅ (2) gauge benchmark (TGBM), cf. Fig. 1. III. LOCATIONS OF HISTORIC AND CONTEMPORARY SEA LEVEL GAUGES IN THE STUDY AREA Within the frame of the renovation of Estonian high- precision levelling network also levellings on the islands Saaremaa and Hiiumaa need to be connected rigorously to the Estonian height system. In the study area altogether 7 staff gauges (cf. Fig. 2) were erected and observed within the period of 1894-2008. Most of them were operational only a few decades and had longer or shorter gaps in sea level series. More details about SGs and related problems can be found in Figure 1. Principles of hydrodynamic levelling. The height difference (ο ሻ is [5]. Only three of them (Virtsu, Rohuküla and Heltermaa) determined between paired contact points (CP). Readings of the MSL values have continuous sea level series more than 50 years. Rohuküla (୅ǡ୆) are obtained by averaging. Other values are either calculated and Heltermaa form a pair for hydrodynamic levelling (heights: ଵ, ଶ, HA, HB) or assigned (tide gauge zeros: TGZA and TGZB). between the mainland and Hiiumaa. No other SG pairs can be formed due to unsuitable location. The sea level readings from TGZ is a pre-determined point that is determined at each the Rohuküla and Heltermaa SGs were taken during period TG independently from other TGs. The sea level fluctuations 1954-2006. Due to data gaps and uncertainties only 43 years are measured with respect of TGZ. In principle, TGZ is synchronous data (monthly mean values of staff readings) selected arbitrarily. For instance, such a point could be in the were available for our study. middle of the staff (a zero-reading, thus the sea level readings are either positive or negative) or at the bottom of the staff (in this case the readings are one-signed). In order to connect the TGZ with the national height datum, the vertical distance between the TGZ and the CP is determined. CP is a benchmark-type reference mark on the top of staff gauge, which is in turn connected to a nearby TGBM by spirit levelling, cf. Fig. 1. The readings at each TG are taken with respect to some arbitrary local initial value (i.e. TGZ), which generally is not coinciding with the level surface of the TGZ on the opposite side of the strait. At an island TG the CPB height (HB) needs to be determined with respect to HA by using mean annual sea

level values ( ଵǡ ଶ) (cf. Fig. 1). The CPB height (HB) across- water is calculated as follows (cf. [4, Section 2]):

୅ ୆ ୆ ൌ ሺ ୅ െ୅ሻ ൅୆ െ൫୘ୋ୞ െ୅൯൅൫୘ୋ୞ െ୆൯ (1) Figure 2. Locations of pressure and staff gauges around the Väinameri Basin in an eastern part of the Baltic Sea. Inset – location of the study area within the Baltic Sea region. where TA and TB are the lengths between CP and TGZ (cf. Fig. ୅ ୆ 1). The readings ୘ୋ୞ and ୘ୋ୞ correspond to the TGZ of Contemporary automatic sea level gauges equipped with Station A and B, respectively. The averaged readings ୅ and pressure sensors (PG) have been operational in Estonia since ୆ correspond to the annual MSL ( ଵǡ ଶ) at Station A and B, 1993. This positive experience allowed us to consider them for respectively. In general, the observations have to be reduced achieving the goals of this study. In 2009–2010 six PGs were due to the sea surface topography (SST), which is a deviation installed in selected locations: two on mainland Estonia from the MSL from an equipotential surface (e.g. geoid). (Rohuküla, Virtsu) and two on both islands, Saaremaa However, Liibusk et al [4] demonstrate that in the selected (Kuivastu, Triigi) and Hiiumaa (Sõru, Heltermaa) (cf. Fig. 2).

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All six PGs are located on opposite coasts of three straits in period and battery voltage) were calculated from raw data and sheltered ferry harbours. The station-to-station distances recorded as well. All the observation data were transmitted in within the PG pairs vary from 7 km (across-water Virtsu and real time into the central database using GPRS (General Kuivastu) up to 65 km (land-connected Rohuküla and Virtsu), Packet Radio Service) communication protocol and stored see the connections in Fig. 2. Within the mainland and both also on the SD (Secure Digital) memory card at the station as islands the PGs were connected with each other by using back-up. national high-precision levellings, see bold lines in Fig. 2. Thus, three across-water and three land-connected sections TABLE I form a 253 km long levelling loop around the Väinameri. Also CHARACTERISTICS OF THE KELLER 36XW AND 46X PRESSURE the historic Rohuküla-Heltermaa sea level series could have SENSORS been connected with nearby PGs by combining results of Pressure sensor Keller 36XW Keller 46X historic and new spirit levellings. Type Piezoresistive Capacitive Length (cm) 12.1 4.5 Diameter (cm) 2.2 3.8 IV. PRESSURE GAUGES Full scale (FS) pressure 1000 300 range (mbar) In our study the PGs were equipped with piezoresistive Accuracy ±0.1% FS ±0.1% FS Keller 36XW and capacitive Keller 46X sensors. These are the (in units of length) (±1.0 cm) (±0.3 cm) force collector type pressure sensors, which measure the pressure force changes caused by the stress of column of water above the sensor. The accuracy of the water column height is ±0.1% of the full scale pressure range (cf. Table I). In units of length these correspond to ±1.0 cm and ±0.3 cm for Keller 36XW and Keller 46X, respectively. It is quite difficult to connect the diaphragm of the pressure sensor to the CP precisely with direct length measurements. This problem can be overcome by collocating the PG with a staff gauge, see Fig. 3. The used sensors were mounted on the backside of 3 m long staff gauge (at the bottom). The staff gauges were securely fastened to a pier in such a way that the average water level would correspond to the reading ~1.5 m. The Virtsu, Rohuküla and Heltermaa stations were equipped with the Keller 36XW sensors and the Kuivastu, Triigi and Sõru stations were equipped with the Keller 46X sensors. Note that at the three latter stations the Figure 3. Contemporary (A) and historic (B) staff gauges. Recess at the sensors were duplicated. The duplicate sensor was mounted at bottom (circled) of the 3 m long staff gauge holds the pressure sensor. At the height of ~50 cm from the bottom of the staff gauge (cf. selected stations a duplicate pressure sensor was installed ~50 cm above the Fig. 3). These concurrent sensors were used as back-up to main sensor. ensure that the PG continues collect sea level values in the occasion of malfunctioning of the main sensor. V. DATA PROCESSING After installation the PG initial reading of the sea level was taken visually from the staff gauge and entered into the Recall, theoretically 288 sea level readings daily were data handling system (into server). Note that only with ideal collected in every PG. In practice, however, some data gaps and very calm weather conditions the accuracy ±0.5 cm for and erratic values (e.g. due to technical problems) occurred in the staff gauge reading can be achieved. datasets. Furthermore, pressure sensors are affected by time- Furthermore, all PGs were equipped with a separate dependent drift, which influences the accuracy of sea level installation box, which is containing data-logger, modem and values. The drift corrections can be determined by the control power supply. Also a solar panel was mounted at each PG readings from staff gauge. The control reading is compared ensuring the recharging of the battery. with the reading of the pressure sensor at the same time In all stations the sea level was determined every 5 moment. The drift corrections are added to the raw sea level minutes (5´) from raw pressure data during 30 second time values. Thereafter the sea level values are filtered. The applied span. 12 and 288 sea level readings were stored hourly and principles and data processing stages are explained below. daily, respectively. Additionally, some basic parameters (water temperature, maximum and mean wave height, wave

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A. Estimating corrections due to the pressure sensor drift identify possible reasons for such trend behavior. One reason Drift of pressure sensors are affected by many factors. could be biofouling, which appears during summer season. One of them is temperature changes. A polynomial The unusual behaviour of the Kuivastu and Heltermaa PGs compensation is used by the in-built microprocessor of sensor remains unclear and needs further studies. Nevertheless the to compensate this effect. This uses a mathematical model to involved data series are corrected by the detected drift values. derive the pressure value from the signals measured by All in all, it is very important to determine the drift pressure and temperature sensors [6]. The sensors are corrections precisely and periodically to detect changes in drift individually calibrated by the manufactory and the calibration trend caused by different factors (cf. Fig. 4 and 5). In this data matrix is stored into the EEPROM (Electrically Erasable study the annual linear drift trends were used in future data Programmable Read-Only Memory) of the microprocessor. processing in all six stations. Therefore, drift caused by temperature can be easily determined in laboratory calibration. For example, good stability due to temperature changes for the Keller 46X prototype was revealed in tests carried out by California Polytechnic State University [7]. Also other factors could cause sensor drifts. For example, during long-term measurements the pressure sensors could barnacled which may cause stability issues. All the mentioned factors add up in time and the drift values could increase up to several cm per year. Figure 4. Detected drift trends of the main sensors at six PG-s during 2010 In this study, the control readings for detecting drift and 2011 (left and right hand sides of the vertical line, respectively). Triigi* values at six PGs were taken at variable intervals – mostly denotes the drift trend of the duplicate sensor. once a month or less frequently. The control readings from staff gauge revealed linearity of the drift trends in most stations, which allowed interpolating the drift values for each observation day. The drift trends at six PGs are shown in Fig. 4. Note that different PGs reveal differences in the trend magnitude and direction (cf. Fig. 4). The drift trends of the piesoresistive Keller 36XW appear to be negative, whereas the capacitive Keller 46X exhibited positive drift trends during first year (2010) of operations. Note also that there are two drift trends for Triigi station in Fig. 4. The 2010 trend values are given for the main (lower) pressure sensor, which ceased Figure 5. Drift corrections of the Keller 36XW pressure gauge in Heltermaa. to be operational in July 2011. This yielded usage of the Seasonality of the trend values (expressed by the 4th degree polynomial) can readings of the duplicate sensor (Triigi*), which has been used be detected. for the hydrodynamic levelling computations for 2011.

Some aspects and anomalies were detected in drift trends. B. Filtering of sea level series Two PGs (Heltermaa and Sõru) were more or less stable in Raw sea level series from PGs include gaps and the 2010, whereas the drift values for the rest may reach up to 5–6 occasional data jumps caused by external (e.g. ferry traffic) cm per year. The trend of Rohuküla, Virtsu and Sõru sensors and internal factors. Algorithms and critical thresholds used were stabile through 2 years (cf. Fig. 4). In some stations were for data filtering are explained in [4, Section 5.2]. observed also changes in the drift trends, cf. Kuivastu and For the sake of experiment three data series were Heltermaa. The drift of Kuivastu sensor was markedly slowed compiled for each PG pair: (i) year 2010 separately, (ii) year down during the measurements. It should be noted though, 2011 separately, (iii) conjointly 2010 and 2011. After filtering that the Kuivastu station was piled up with 2 m thick ice of sea level series up to 30% of the observation days were ridges and snow in February 2011. eliminated, cf. Tables II and III. The largest number of A polynomial-like (rather than linear) trend was detected eliminations was associated with the Rohuküla-Virtsu and in Heltermaa PG, cf. Fig. 5. The 4th degree polynomial shows Kuivastu-Triigi pairs, both some 60+ km apart from each strong seasonal signal in time series (Fig. 5), thus this could be other. Apparently, the filtering thresholds are more likely to due to variations in the sea water temperature. In summer occur for longer hydrodynamic levelling sections. Recall, that the reliability of the 12h data sampling (adopted in the historic months the values of drift corrections are prevailingly positive, h whereas during the winter months negative. Such seasonality SG readings) interval was tested. The 12 data was obtained was not observed in other stations [cf. 9, Fig. 6]. It is difficult by picking the 6 am and 6 pm readings of the original 5´ data.

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The daily height differences ǻH for the PG pairs (cf. Eqs. 1 days is larger than that for the 12h data days. The and 2) were obtained by averaging 288 readings of the original corresponding solutions are presented in Tables II and III. It 5´data and 2 readings of the 12h data. Thereafter the follows thus, that the filtering threshold cannot be exceeded so occurrence of the filtering thresholds [cf. 4, Section 5.2] was easily by using the frequent data sampling interval, i.e such checked. Such threshold-exceeding data-days were removed data-series are less affected by anomalous events in the sea from the corresponding yearly solution, denoted by ͷԢഥ and ͳʹതതതതത level series. respectively. Note that after filtering the number of 5´ data-

TABLE II HEIGHT DIFFERENCES AND THEIR STANDARD DEVIATION BETWEEN THE ACROSS-WATER PRESSURE GAUGE PAIRS OBTAINED BY HYDRODYNAMIC AND HYDROSTATIC LEVELLING. UNIT IS CM Historic Short- Short- Conjoint solution Across-water Direct Hydro- staff term term 2010+2011 Solution 2010 Solution 2011 pressure distance static gauge measu- measu- gauge pair (km) levelling readings1 rements rements Averaged Averaged Averaged Averaged Averaged Averaged 12h 2011 2012 ͷԢഥ ͳʹതതതതത ͷԢഥ ͳʹതതതതത ͷԢഥ തͳʹതതതത Virtsu- 7 -0.2 - 0.6 0.7 1.5±1.1 1.5±1.2 1.4±1.0 1.4±1.2 1.2±0.8 1.2±0.9 Kuivastu (6)2 (4) (653) (620) (338) (314) (315) (306) Triigi-Sõru 16 63.1 - 65.0 65.0 65.0±1.4 65.1±2.6 65.0±1.5 65.2±3.3 64.8±1.3 65.0±1.7 (6) (4) (566) (532) (254) (236) (312) (296) Heltermaa- 22 - -4.0±1.3 -2.4 -3.1 -3.4±1.6 -3.6±1.7 -4.0±1.8 -4.3±2.0 -2.9±1.4 -3.1±1.5 Rohuküla (6) (4) (538) (483) (265) (245) (273) (238) 1 Monthly mean sea level values in period 1954-2006. 2 Digits in italics denote number of data-days after filtering.

TABLE III HEIGHT DIFFERENCES AND THEIR STANDARD DEVIATION BETWEEN THE LAND-CONNECTED PRESSURE GAUGE PAIRS OBTAINED BY HYDRODYNAMIC, HYDROSTATIC AND SPIRIT LEVELLING. UNIT IS CM Land-connected Along- Spirit Short-term Short-term Conjoint solution pressure gauge coast levelling measurements measurements 2010+2011 Solution 2010 Solution 2011 pair distance 2011 2012 Averaged Averaged Averaged Averaged Averaged Averaged (km) ͷԢഥ ͳʹതതതതത ͷԢഥ ͳʹതതതതത ͷԢഥ തͳʹതതതത Rohuküla-Virtsu 65 19.8 19.4 21.8 19.6±1.5 19.5±2.1 20.1±1.3 20.0±2.0 19.1±1.6 18.9±2.3 (6)1 (4) (469) (437) (241) (235) (228) (202) Kuivastu-Triigi 65 -69.3 -69.2 -71.7 -68.5±2.6 -68.3±3.4 -68.3±1.8 -68.1±3.8 -68.5±2.6 -68.3±3.5 (6) (4) (449) (431) (181) (172) (268) (259) Sõru-Heltermaa 45 -12.8 -13.4 -12.8 -14.2±1.9 -14.2±2.3 -14.1±2.1 -14.3±2.6 -14.2±1.9 -14.3±2.3 (6) (4) (538) (507) (285) (271) (253) (236) 1 Digits in italics denote number of data-days after filtering.

The daily height differences between across-water pairs VI. VERIFICATIONS OF THE HYDRODYNAMIC LEVELLING RESULTS WITH ALTERNATIVE are presented in Fig. 7. The results indicate that the largest ǻH DATA-SETS scattering is occuring for the data sampling interval ͳʹതതതതത in the Triigi-Sõru PG pair, ±3.3 cm. Note that Sõru station could be A. Differences between ͷԢഥ and ͳʹ݄തതതതത solutions affected by the open sea winds more than the Triigi station, The averaged ͷԢഥ hydrodynamic results in the 2010, 2011 which is located in the enclosed Väinameri. and 2010+2011 solutions appeared to be almost the same (cf. All in all, the results of ͳʹതതതതത coincide well with the results ഥ Tables II, III and Fig. 6). The maximum discrepancy (±0.6 cm) of ͷԢ but where possible, the frequent data sampling intervals occurred for the longest sections (the Heltermaa-Rohuküla and and longer observation periods should be used. Therefore the Rohuküla-Virtsu PG pairs). In other pairs the discrepancies results of two years (2010+2011) hydrodynamic levelling ഥ remained within ±0.3 cm. Note also that ͳʹതതതതത hydrodynamic based on data sampling interval ͷԢ were used in further results agree reasonably with the ͷԢഥ solution, although the verifications (cf. Fig. 6) as well. number of ͳʹതതതതത data-days after filtering were considerably less. The discrepancies between different ǻH solutions remained within ±0.1 cm (cf. Tables II and III).

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B. Verifications with historic and alternative data-sets The hydrodynamic levelling results in different sections can be verified with results of: (i) historic hydrostatic levellings, (ii) recent precise spirit levellings, (iii) series of historic staff gauge readings, and (iv) short term measurements in winter. (i) The hydrostatic levelling was used for height connection between the island Saaremaa and the mainland (in 1968) and between islands Saaremaa and Hiiumaa (in 1976 and 1977) in Estonia [8]. The discussion in [4] concluded that

the accuracy of these historic levellings could be at 1.0 cm Figure 6. Discrepancies between height differences of different solutions level. Therefore it is good opportunity to verify the accuracy and methods. The zero line denotes the results of the two years (2010+2011) of hydrodynamic levellings. The benchmarks used in hydrodynamic levelling as the reference. The vertical error bars denote the individual standard deviation values of the hydrodynamic levelling results hydrostatic levellings were connected with contemporary PGs (cf. Tables II and III). by using precise levellings. The ǻHs are presented in [4, Table 6] and Table II, column 3. (ii) All land-connected PGs are connected in 2005-2010 by using high precision spirit levellings with the average random and systematic root mean square errors, Ș = 0.18 Ȁξ and ı = 0.03 Ȁ, respectively (Estonian Land Board, www.maaamet.ee). The ǻHs of high precision levellings are presented in Table III, column 3. (iii) Based on the historic, 43 years long series of the monthly MSL readings, the across-water ǻH between the Rohuküla and Heltermaa staff gauges was computed, cf. Table II, column 4. (iv) In the past some short-term (with duration of a few days) sea level observations were made in case of ice cover and calm weather in West-Estonian Archipelago [3]. Such measurements was repeated by us as well. Two expeditions were carried out in February 20-25, 2011 and March 4-7, 2012. The Väinameri was covered by the 50 cm thick fast ice and the weather was stabile and calm during these periods. Thus it can be expected water tilts between the paired PGs to be minimal. Importantly, in such conditions the control readings from staff gauge can be taken with an accuracy of ±0.3 cm. The drift corrections values were added to the sea level readings and the results were filtered as discussed in previous Section. The MSL of 6 and 4 days were calculated, the corresponding across-water and land-connected ǻHs are presented in Tables II and III. More details about sea level observations in ice cover conditions can be found in [4]. Discrepancies 1.9 cm between the historic hydrostatic levellings and the 2010+2011 hydrodynamic solutions were detected, cf. Table II. Better agreement was achieved between the hydrodynamic and spirit levellings of the land-connected PG pairs, cf. Table III, columns 3 and 6. The maximum discrepancy between Sõru and Heltermaa was 1.4 cm. Note that the distances between land-connected PGs were three

times longer than in the across-water sections. In conclusion, Figure 7. Height differences (ǻH) between pressure gauge pairs. Black and based on the results of verifications (i) and (ii) and on the white dots based on ͷԢഥ and ͳʹതതതതത data sampling, respectively. Linear trend is standard deviations of H (2010+2011), cf. Fig. 6, the denoted by ͷԢഥ data sampling. The data-gap in the Triigi-Sõru pair is due to the ǻ Triigi sensor malfunctioning in July-August 2010. hydrodynamic levelling accuracy could be estimated to be

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±1.5 cm in West-Estonian Archipelago. Therefore the results Note that the misclosures of the levelling loop increased of hydrodynamic levelling can be used to compare the ǻHs with time, cf. Fig. 8. The trend is up to 1.2 cm during 2 years. based on historic staff gauge series (iii) and short term sea This could be related to the time-dependent drift of pressure level observations (iv). The detected discrepancy between the sensors. As discussed in Section V, the control readings from results of contemporary and 43 years long historic staff gauge need to be taken at least once a month to detect hydrodynamic levellings (iii) was only 0.6 cm between sensors drift. This enables to increase the accuracy of Heltermaa-Rohuküla, cf. Table II and Fig. 6. This result hydrodynamic levelling as well. In this study the linear trend helped to check the reliability of historic staff gauge readings of sensors was taken into account as first approach and the and confirmed historic data suitability for hydrodynamic results are reasonably good, cf. Fig. 6. levellings as well. The results of short term sea level observations (iv) displayed larger discrepancies from the two years (2010+2011) sea level observations, cf. Tables II and III, Fig. 6. Larger disagreements occurred between the land-connected pairs for distances up to 65 km, cf. Fig. 6. It indicates that some residual water tilt could still be present between the pressure gauges even in calm weather and ice covered sea conditions. Therefore, it is very critical to use short term sea level observations for hydrodynamic levelling, especially over long distances (over 20 km).

C. Combining the hydrodynamic and spirit levelling results into a closed loop Figure 8. Daily misclosures of the 253 km levelling loop around Väinameri. Black and white dots based on ͷԢഥ (414 data-days) and ͳʹതതതതത (363 data-days) Note that the comparisons with (i) and (ii) include errors data sampling, respectively. Continuous lines denote the corresponding linear of alternative height determination methods as well. Therefore and 4th degree polynomial trend of misclosures. an adequate accuracy estimation for hydrodynamic levelling could be based on the misclosures of closed levelling loop. This all-around Väinameri loop (total length 253 km) comprises 3 across-water and 3 land-connected sections, see VII. SUMMARY Fig. 2. For the combinations of spirit and hydrodynamic This study explained methodology of hydrodynamic levellings the misclosure values of the around Väinameri levelling using pressure sensor data. Two years (2010+2011) levelling loop remain under 1.0 cm, cf. Table IV. sea level series from PGs were used for estimating height differences between the pressure gauges installed in the TABLE IV Estonian mainland and adjacent islands in West-Estonian MISCLOSURES OF THE 253 KM LEVELLING LOOP AROUND Archipelago. To detect the time-dependent drift of used VÄINAMERI. UNIT IS CM pressure sensors, the control readings from staff gauges were Solution Solution Solution taken during two years period in all six stations. In some Con- Pressure 2010+2011 2010 2011 nec- gauge pair Ave- Ave- Ave- Ave- Ave- Ave- stations the drift corrections indicated nonlinear trend, which tion raged raged raged raged raged raged could be caused by water temperature changes and/or ͷԢഥ ͳʹതതതതത ͷԢഥ ͳʹതതതതത ͷԢഥ ͳʹതതതതത barnacles and algae. This issue was unresolved in this study Virtsu- and linear drift corrections were added to sea level values Kuivastu 1.5 1.5 1.4 1.4 1.2 1.2 before time series filtering. Triigi-Sõru 65.0 65.1 65.0 65.2 64.8 65.0 The hydrodynamic across-water and land-connected

levelling) Heltermaa- height differences were verified with historic hydrostatic and Across-water (hydrodynamic Rohuküla -3.4 -3.6 -4.0 -4.3 -2.9 -3.1 spirit levellings, respectively. As a result, the ±1.5 cm Rohuküla- Virtsu 19.8 accuracy was estimated for the hydrodynamic levelling results. Kuivastu- This was checked with misclosure values of the 253 km long Triigi -69.3 closed levelling loop, which did not exceed 0.8 cm for any Sõru- combination of measurements. These results indicated that Land-connected (spirit levelling) levelling) (spirit Heltermaa -12.8 Misclosure: 0.8 0.7 0.1 0.0 0.8 0.8 hydrodynamic levelling based on the sea level series of PGs with linear drift corrections is acceptable for geodetic applications. Also the height differences calculated from sea level series of contemporary PGs are good reference for

209 historic staff gauge readings with data sampling 12h from Ɉɛɳɟɝɨɫɭɞɚɪɫɬɜɟɧɧɨɣ ɧɢɜɟɥɢɪɧɨɣ ɫɟɬɢ ɦɟɬɨɞɨɦ period 1954-2006. The discrepancy between the two height ɜɨɞɧɨɣ ɧɢɜɟɥɢɪɨɜɤɢ). ɋɛ. ɪɚɛɨɬ Ɍɚɥɥɢɧɫɤɨɣ ȽɆɈ differences was only 0.6 cm. Finally, the results of two short ɜɵɩ. 1. 1964. (in Russian). term hydrodynamic levelling experiments of the winter 2011 [3] A. Tamm. “Levelling between the islands and and 2012 were evaluated. The sea level readings were mainland“ (Loodimised saarte ja mandri vahel). Geodeet acquired during short term periods with calm weather and ice 2(26), pp. 13-15, 1992. (in Estonian). covered sea. The assumption was that under these conditions [4] A. Liibusk, A. Ellmann, T. Kõuts, H. Jürgenson. “Precise the water tilts between PGs are not-existing or minimal. The hydrodynamic levelling by using pressure gauges” (in drift corrections were determined with an accuracy ±0.3 cm in review). all six stations and added to PG series before data processing. [5] S. Jevrejeva, A. Rüdja, and J. Mäkinen. “Postglacial The results indicated that short term sea level observations in rebound in Fennoscandia: new results from Estonian tide calm weather conditions are usable for hydrodynamic gauges”. Proceedings of IAG Symposia 123: 193-198. levellings only in short distances (up to 20 km). Therefore, at Canada, July 31 – August 4, 2001. least one year long sea level observations with frequent data [6] B. Vetterli. When precision is required. Digitally sampling can be used for rigorous determination of height compensated pressure transmitters show the limits of differences. what is possible. [http://www.kellerdruck.com/picts/pdf/engl/fachbeitrag_33x_e.pdf]. ACKNOWLEDGMENTS 30.03.12. This study is supported by the Estonian Science [7] S. Styles, S. Herman, M. Yasutake, C. Keezer. Water Foundation grant ETF 8749: Determination of height level sensor testing. ITRC Report No. 04-005. California reference frame on the Estonian coastal sea using water lever Polytechnic State University, 2003. monitoring and laser scanning data. The installation and [8] L. Tamme. Experience of using hydrostatic levelling for operation of pressure gauges and their connection to the precise height connection over wide water obstacles. national levelling network were financed by the Estonian Land (Ɉɩɵɬ ɩɪɢɦɟɧɟɧɢɹ ɝɢɞɪɨɫɬɚɬɢɱɟɫɤɨɝɨ ɧɢɜɟɥɢɪɨɜɚɧɢɹ Board. ɞɥɹ ɜɵɫɨɤɨɬɨɱɧɨɣ ɩɟɪɟɞɚɱɢ ɜɵɫɨɬ ɱɟɪɟɡ ɡɧɚɱɢɬɟɥɶɧɵɟ ɜɨɞɧɵɟ ɩɪɟɝɪɚɞɵ). Ⱦɢɫɫɟɪɬɚɰɢɹ, ɂɧɫɬɢɬɭɬɟ Ɏɢɫɢɤɢ ɢ Aɫɬɪɨɧɨɦɢ Ⱥɇ ɗCCɊ. 1969. (in REFERENCES Russian). [1] W. Torge. Geodesy. 3rd Edition. Berlin-New York: Walter [9] A. Liibusk, A. Ellmann, T. Kõuts. “Use of high de Gruyter. 2001. resolution sea level measurements for height transfer in [2] Ɍ. Eipre. Height connection between islands Vormsi and West-Estonian Archipelago” 8th International Hiiumaa and national levelling network by using water Conference on Environmental Engineering. Vilnius, pp. levelling. (ɉɪɢɜɹɷɤɚ ɨɫɬɪɨɜɨɜ ȼɨɪɦɫɢ ɢ ɏɢɭɦɚ ɤ 1374-1381. 2011.

210 V Liibusk, A., Jürgenson, H. 2008. DETECTING THE BALTIC SEA LEVEL SURFACE WITH GPS-MEASUREMENTS AND COMPARING IT WITH THE LOCAL GEOID MODEL

Reprinted from: Observing our Changing Earth. International Association of Geodesy Symposia, Proceedings of the 2007 IAG General Assembly Perugia: Springer-Verlag Heidelberg Proceedings 133:125–134. Detecting the Baltic Sea Level Surface with GPS-Measurements and Comparing it with the Local Geoid Model

Aive Liibusk and Harli Jurgenson¨

Abstract Gravimetric geoid NKG04 (Forsberg et al., separation is restored. In addition, we analyzed all the NKG Geoid Meeting, Copenhagen) is derived by KMS Estonian and Swedish profiles, also using GPS data using all available gravimetric data from the region. from Swedish base stations. Some areas, also close to the Estonia are not com- We also performed the same kind of measure- pletely covered by gravity measurements, example the ments on ferries running the regular line Tallinn- eastern part of the Gulf of Finland. Baltic Sea is mea- St. Petersburg-Helsinki-Tallinn. Those measurements sured by airborn gravimetry with accuracy probably were of particular interest as there was no gravimetric 2 mGal. Our idea was to compare the geoid on the data available for the eastern part of the Gulf of sea areas against the independent method like GPS- Finland. levelling on the mainland. Main problem have been of As a third track, measurements were performed on course how to remove water tilt during the campaign. liners running between Sillamae¨ and Kotka. The existent GPS device on board a ship stores data The results show that the 150-km geoid NKG04 every second and determines the heights with an accu- profile close to Hiiumaa did not differ any more than racy of a few centimetres (using the kinematic method 15 cm from the GPS-measured level surface. The influ- with post-processing, several base stations close to the ence of the water tilt was more or less eliminated us- ferry line). As a result, it is possible to observe the ing the available tide gauge data. The profile between present relative water level profile in reference to the el- Tallinn and St. Petersburg manifested similar differ- lipsoid. If we take into account the tilt of the water level ence. Most of the measurements were repeated several at the moment of measurement, we can observe the rel- times on the same profile. ative change of the geoid using independent methodology, which serves as a comparison to the gravimetric geoid solution. With this method we explored some areas on the 1 Introduction Baltic Sea covered with regular ferry lines where the geoid profile changes faster. One such area lies about The gravimetric geoid NKG04 was derived by KMS 30 km north of the island of Hiiumaa, where the geoid using all the gravimetric data available from the region. has a “lump”: the separation of the geoid from the Unfortunately, the data set does not originate from one ellipsoid changes by 1 m over a 70-km distance start- and the same time period, the coverage is not homo- ing from Paldiski; further towards Sweden the original geneous, and the quality varies from region to region. Some areas, including those close to Estonia, such as Aive Liibusk the eastern part of the Gulf of Finland, are almost Department of Geomatics, Estonian University of Life Sciences, uncovered by gravity measurements. The Baltic Sea Kreutzwaldi 5, Tartu 51014, Estonia, was measured by airborne gravimetry with the accu- e-mail: [email protected] racy of probably 2 mGal. Our idea was to compare the Harli Jurgenson¨ Department of Geomatics, Estonian University of Life Sciences, geoid for the sea areas with an independent method. We Kreutzwaldi 5, Tartu 51014, Estonia used GPS-measurements and ferries on regular lines to

M.G. Sideris (ed.), Observing our Changing Earth, International Association of Geodesy Symposia 133, 125 c Springer-Verlag Berlin Heidelberg 2009

213 126 A. Liibusk and H. Jurgenson¨

Fig. 1 Tracks measured by GPS on ferry. Background is Geoid Model NKG04; contour interval is 0.2 m (500,000 m responses to longitude 24◦) cover areas on the Baltic Sea. The good coverage of the for water tilt estimation. After processing the GPS GPS permanent base stations made the measurements data, the water tilt correction was added. The wave ef- easier. How to eliminate water tilt during the campaign fect was eliminated using the trend line of real stored was the main hurdle to negotiate. points. Estonian tide gauges provide a water level relative to the Baltic height system (BK77) and Finnish ones relative to the mean sea level. The mean sea level values of tide gauges were recalculated into the N60 2 Method height system to eliminate the land uplift effect. The formula presented by The Finnish Institute of Marine A GPS receiver was placed on a ferry, using kinematic Research (http://www.ﬁmr.ﬁ) was used. technology (or real-time kinematic). The GPS receiver The Finnish N60 height system differs from stores the position and the height every second. Post- the BK77 system by about 3 cm (Jurgenson¨ and processing was performed using several base stations Kall, 2004). Furthermore, the Estonian height system located close to the measured line. The GPS receiver has been affected by relative land uplift – about 6 cm was placed on the open deck of the ferry (Fig. 2) and during the 30 years. However, the Estonian tide gauges was static during the measuring period. GPS receivers used in the campaign are situated often in the region Trimble 5700 and 5800 were used. We only wanted to with similar land uplift. Hence, all the water level determine the relative change of the level surface; the heights were computed to the Baltic height system absolute height from the sea level was not important. In BK77 before they were used. some instances, two GPS receivers were used simulta- The mean sea topography was small in the tested neously on the ferry (Sillamae¨ – Kotka ferry line). regions, about 4 cm between Tallinn and St. Peters- During the measurements, the present water level burg, (Ekman and Makinen,¨ 1996) and probably heights were obtained from the closest tide gauges 10 cm between Paldiski and Stockholm (Putanen and

214 Detecting the Baltic Sea Level Surface 127

Kakkuri, 1999) (Fig. 3). The measuring lines were mostly shorter, as a result of which the inﬂuence was smaller and was not taken into account here. The accuracy of the GPS measurements is a few cm depending on the actual atmosphere, the number of satellites and the PDOP as well as the vector length (for example 1 ppm makes 4 cm per 40 km). The number of satellites in particular may become a problem due to long distances from base stations. Planning the timing of the measurement is difﬁcult because we are depending on the ferry schedule. Taking into account also the water tilt elimination problems, the level surface accuracy is 5–15 cm according to our estimation. Yet this method is estimation to the geoid, and actual geoid changes are usually 10 times bigger along the measuring route. This is of special interest in the case of areas for which gravimetric data is missing or has serious quality problems.

3 Test Measurements

The ﬁrst test measurements took place in 2004 between Fig. 2 GPS Trimble 5700 on board Paldiski and Kapellskare.¨ The method was tested in

Fig. 3 The mean sea surface topography on the Baltic Sea (Poutanen, Kakkuri 1999 a)

215 128 A. Liibusk and H. Jurgenson¨

Fig. 4 GPS measurement on ferry to determine relative geoid change. Background is the gravimetric geoid NKG04 with a contour line interval of 0.2 m areas of faster geoid changes. One of the areas lies (less than 3 cm). However, that day’s water level about 30 km to the north of the island of Hiiumaa at the tide gauges of Ristna and Dirhami (Fig. 4) (North-West Estonia). The area is especially interest- differed from the mean sea level by +3 and +17 cm ing because the geoid surface is placed a little higher respectively. This indicated that water was tilted by compared to the surrounding area (Fig. 4). Continuous 14 cm between the tide gauges (over 80 km in the RTK measurements were performed on board ferries East–West direction). The Paldiski tide gauge provided running the regular line between Paldiski, Estonia, and a reading similar to that of Dirhami. Unfortunately, Kapellskare,¨ Sweden. Two base stations were used for there were no more tide gauges available in the region. RTK (in Dirhami and in the north of Hiiumaa) in or- From the results, a smooth trend line was generated der to ensure that the baseline length does not exceed to eliminate local sea level change caused by wind 34 km. A GSM connection was used for transmission effect. of corrections. Ship speed was 30 km/h, thus the half The gravimetric geoid difference from Paldiski to distance (70 km) was measured during 3 h. The west- the maximum point was 92 cm (Figs. 4 and 5) while ernmost part of the line was measured using the kine- the RTK GPS measurements showed a relative change matic method with post-processing from the Hiiumaa of 77 cm (Fig. 5, the value was obtained from the trend base station. The storing interval of the GPS measure- line) along the same line. ments was 1 and 2 s. Trimble 5700 GPS devices were If we take into account the tilt of the water level used. The RTK ﬁxed solution was obtained during the (about 7 cm per 70 km, Table 1), the results agree with measurements. Wind speed was generally less than about 8-cm accuracy: 92–7 = 85 cm, 85–77 = 8cm. 6 km/h. The ferry’s up-and-down movement was nor- So, a comparison of the relative change using the gravi- mally less than 20 cm (Fig. 5, scale of the ﬁgures is a metric solution with the ship GPS solution showed that little distorted, while only east or north component is the preliminary results agreed within an 8-cm accuracy used). range for the eastern part of the test line. The mid- The tide gauge data did not show any remarkable dle part (measured from the Tahku base station using changes in water level during the measurements RTK, 410–430 km in the East–West direction) was a bit

216 Detecting the Baltic Sea Level Surface 129

Fig. 5 Water level relative heights by kinematic GPS between 370 and 502 km along the East coordinate (500 km responses to longitude 24◦)

Table 1 Tide gauges at Ristna, Dirhami and Paldiski tance from Paldiski to Sweden was measured using Station/time Water level kinematic GPS. Only the kinematic method with post- BK77 (cm) processing was used. A base station was established in 29.06.2004 the north of Hiiumaa (Lehtma, Fig. 1). Additionally, Ristna 08.00 +4 data from a second base station at Hanko was used. Ristna 14.00 +1 Ristna 20.00 +3 Figure 6 shows the same distance as Fig. 5. Unfor- Paldiski 08.00 +17 tunately, that time the west part of the distance was Paldsiki 20.00 +12 measured under a stronger wind. The water level was Dirhami 08.00 +17 even more stable than the first time; the western part of Dirhami 20.00 +14 30.06.2004 the profile was about 10 cm lower; consequently, the Ristna 08.00 +3 tilt was 10 cm per 130 km (Table 2). Ristna 14.00 +5 The results are about the same as those obtained in Paldiski 08.00 +16 the first round. From Paldiski to the maximum point of Paldiski 20.00 +26 Ristna 20.00 +5 the gravimetric geoid the height increased by 84 cm, Dirhami 08.00 +17 tilt-corrected water level 94 cm (correction applied Dirhami 20.00 +23 +4 cm) (Table 2). As well, the western part coincided within the range of 14 cm. biased (ca 15 cm, Fig. 5). The last 30 km of the western part of the line were measured using kinematic measurement with post-processing. 3.1 Measurements between In the western part, the water difference measured Estonia and Sweden on with GPS was 1.08 m. If we subtract the water tilt correction 8 cm, the water profile difference is 1 m. Simi- 6 and 7 November 2004 larly, the west part shows a clearly negative trend until East coordinate 370 km, as does the gravimetric geoid: Figure 1 presents the measured lines between Paldiski by 1.1 m respectively (Figs. 5 and 6). We can see that and Kapellskare.¨ The aim was to measure a geoid low the tilt-corrected water (sea) level change agrees with situated south of Marinehamn. Again, a ferry running the NKG04 model in the region within the range of the regular line was used; the results are presented in 10 cm. Figs. 7 and 8. To improve reliability the measurements were Additionally, data from base stations Godby and repeated on 28 and 29 June, 2004. The entire dis- Stavsnas was used for post-processing. The stations are

217 130 A. Liibusk and H. Jurgenson¨

Fig. 6 Water level relative heights by kinematic GPS over 132 km, 6 November 2004 (500 km responses to longitude 24◦)

Table 2 Tide gauge data from some stations in Estonia and a part of the RTK network in Finland and Sweden re- Sweden (6 and 7 November 2004) spectively. As well, tide gauge data from Stockholm Station/time Water level BK77 (cm) and Marviken was used (Table 2). All the tide gauge 06.11.2004 data were converted to the Baltic height system. As Ristna 08.00 −1 the water was almost untilted during the measurements Ristna 14.00 −1 Ristna 20.00 +2 (Table 2) we did not apply any water tilt correction. Lehtma 08.00 +7 The changes in the geoid and the measured water pro- Lehtma 14.00 0 ﬁle coincide with each other within the range of 10 cm Lehtma 20.00 +5 (Figs. 7 and 8) (Morozova, 2005). Dirhami 08.00 +7 Dirhami 20.00 +4 Paldiski 08.00 +12 Paldiski 20.00 +4 Stockholm 14.00 0 Stockholm 18.00 +3 Stockholm 20.00 +2 3.2 Measurements between Estonia Stockholm 23.00 −1 and St. Petersburg on 13 and 14 Marviken 14.00 −5 Marviken 18.00 −3 December 2004 Marviken 20.00 0 Marviken 23.00 −4 07.11.2004 Figure 1 presents the measured lines between Tallinn- Ristna 08.00 −1 St. Petersburg-Helsinki. The regular ferry was used. Lehtma 01.00 0 The results are presented in Fig. 9. Lehtma 07.00 +7 Dirhami 08.00 +5 The base stations at Pedassaare and Virolahti were Paldiski 08.00 +5 used for post-processing. The Virolahti base is a part Stockholm 00.00 −5 of the Finnish RTK network. A dual-frequency GPS Stockholm 01.00 −3 receiver Geotracer 3220 was stationed in Pedassaare Stockholm 03.00 −8 Stockholm 05.00 −7 (Estonian coast). Stockholm 07.00 −7 Tide gauge data from Hamina, St. Petersburg, Toila, Stockholm 08.00 −7 Kunda, Loksa and Narva-Joesuu˜ was used (Table 3). Marviken 00.00 −6 The tide gauge data was converted to the Baltic height Marviken 01.00 −6 Marviken 03.00 −10 system. The proﬁles coincide within the accuracy Marviken 05.00 −7 of a few cm-s between Tallinn and St. Petersburg Marviken 07.00 −4 (Fig. 9) and about 10 cm between St. Petersburg and Marviken 08.00 −5 Helsinki.

218 Detecting the Baltic Sea Level Surface 131

Fig. 7 Water level relative heights by kinematic GPS, 6 November 2004 (300 km responses to longitude ∼ 20.5◦)

Fig. 8 Water level relative heights by kinematic GPS, 7 November 2004 (300 km responses to longitude ∼ 20.5◦)

3.3 Measurements Between Estonia situated in Toila, Estonia, were used in post-processing. and Finland on 16 and 18 May 2006 Southern part of the route is post-processed from Toila and North part of the route from Pernaja base station (Fig. 10). The measurement track between Estonia and Finland Tide gauge data were collected from Hamina and is presented in Fig. 1. Two dual-frequency GPS- Helsinki in Finland and from Toila, Narva-Joesuu˜ receivers set up on board a ferry were used for the and Kunda in Estonia. As the tide gauge data var- measurements (Trimble R8 and Trimble 5800). The ied very little, by a maximum of 5 cm, during the receivers were placed on the right and left boards of the measurements, no water tilt corrections were added to ferry. The use of two receivers simultaneously allowed the GPS measurement results. the comparison and estimation of the measurement Figure 10 presents the chart of the Kotka-Sillamae¨ results. track. To improve the readability of the chart, 17 m was Data from the Pernaja GPS base station, a part of subtracted from the heights measured by the Trimble the Finnish network of GPS permanent base stations, 5800 receiver and 17.5 m from those measured by the and from the dual-frequency Geotracer 3220 receiver

219 132 A. Liibusk and H. Jurgenson¨

Fig. 9 Water level relative heights by kinematic GPS between Tallinn and St. Petersburg, 13 December 2004. (700 km responses to longitude ∼ 27.5◦)

Table 3 Tide gauge data from some Estonian, Finnish and Rus- theless, it follows the same trend as in all the earlier sia stations (13 and 14 December 2004) measurements. The lack of data in Fig. 10 is due to Station/time Water level the kinematic data processing software ambiguity BK77 (cm) solutions yielding no solution in the middle of the Gulf 12of Finland. 13.12.2004 The data (heights) from the two GPS receivers used Loksa 20.00 +17 on the ferry show identical sharp protrusions, which Kunda 20.00 +19 Toila 20.00 +22 invite a conclusion that they have to do with sea surface Narva-Joesuu˜ 20.00 +21 peculiarities or external disturbances in these particular St. Peterburg 20.00 +35 areas rather than with GPS measurement errors. The Hamina 20.00 – protrusions were observed in exactly the same places Helsinki 20.00 – Hanko 20.00 – irrespective of whether the ferry was bound for Estonia 14.12.2004 or Finland. The sharp changes in height (10–40 cm) oc- Loksa 08.00 +21 curred over short distances (1–6 km). Kunda 08.00 +21 Toila 08.00 +24 Narva-Joesuu˜ 08.00 +24 Narva-Joesuu˜ 20.00 +24 St. Peterburg 08.00 +44 3.4 The Accuracy of the GPS St. Peterburg 19.00 +42 Measurements St. Peterburg 20.00 +45 St. Peterburg 21.00 +47 St. Peterburg 22.00 +48 We calculated some proﬁles from different base sta- St. Peterburg 00.00 +55 tions. An example is given in Fig. 11. Between Estonia and Sweden, the different GPS stations yielded results that were close, with the vertical R8 receiver. As for the most part the Sillamae–Kotka¨ component remaining within the range of 10 cm. The ferry line runs parallel to geoid NKG04 contours distance between the base stations was in some cases (Fig. 1), the height change is not so drastic; never- more than 80 km.

220 Detecting the Baltic Sea Level Surface 133

Fig. 10 Water level relative heights by kinematic GPS between Sillamae¨ and Kotka, 18 May 2006. (6655 km responses to latitude ∼ 60◦). (Scale is slightly distorted, while only north component is used)

Fig. 11 Water proﬁles calculated from different GPS base stations (Hanko, Godby, Stavsnas,¨ Lehtma) (Liibusk, 2005)

4 Conclusion of 15 cm. Consequently, we did not discover any big or remarkable differences between the measured Using GPS kinematic measurements, some water level surface and the NKG04, even in areas for level profiles were measured on the sea. The water which the gravity data was of low quality or missing tilt effect was eliminated inasmuch as possible using altogether. different tide gauge data. The GPS measurements yielded results with the accuracy of about 6 cm; the regional water tilt effect could not be completely Acknowledgments We are thankful to the companies Geotrim OY in Finland and SWEPOS in Sweden, who supplied us with removed. However, the results showed a profile similar GPS base stations data, and to the Estonian Science Foundation, to that of Geoid Model NKG04 within the bounds who financed the research under Grant 5731.

221 134 A. Liibusk and H. Jurgenson¨

References Liibusk, A. (2005): Detecting the Baltic Sea level surface with GPS-measurements and Comparing it with the Nordic Geoid Model NKG04. Poster. Metobs 140 Geophysics Meeting, Ekman, M., Makinen¨ J. (1996): Mean sea surface topography in Tartu. the Baltic Sea and its transition area to the Northern Sea: a Morozova, N. (2005): Comparison of the gravimetric geoid geodetic solution and comparisons with oceanographic mod- NKG04 against the geoid surface tracked by GPS on some els. J. Geoph. Res. 101, C5, pp 11993–11999. areas of the Baltic Sea. MSc thesis. Estonian Agricultural Forsberg, R., Strykowski, G., Bilker, M. (2004): NKG-2004 University, pp 94. Geoid Model – most recent model. NKG Geoid Meeting, Poutanen, M., Kakkuri, J. (1999 a): Final Results of the Baltic Copenhagen. Sea Level 1997 GPS Campaign. Research works ot the SSC Jurgenson,¨ H. (2003): Determination of Estonian Precision 8.1 of the International Association of Geodecy. Kirkkon- Geoid. PhD thesis. Estonian Agricultural University, Tartu. ummi, pp 192. Jurgenson,¨ H., Kall, T. (2004): The difference between the N60 and BK77 height systems. Nord J Surv Real Estate Res, Volume1, Number 1, pp 72–85.

222 CURRICULUM VITAE

Personal data Name Aive Liibusk Citizenship Estonian Date of birth October 11, 1979

Contact information Address Estonian University of Life Sciences Department of Geomatics Fr. R. Kreutzwaldi 5, 51014 Tartu, Estonia E-mail [email protected]

Education 1986–1997 Elva Gymnasium 1997–2001 Estonian Agricultural University, BSc, geodesy 2001–2004 Estonian Agricultural University, MSc, geodesy 2005–2013 Estonian University of Life Sciences, PhD, geodesy

Additional training 11.2008–01.2009 Mobility stay at the Ohio State University, USA. Satellite altimetry related research.

Professional employment 2005–2009 Estonian University of Life Sciences, Institute of Forestry and Rural Engineering, Department of Geomatics, Assistant Since 2009 Estonian University of Life Sciences, Institute of Forestry and Rural Engineering, Department of Geomatics, Lector

Research-administrative experience 2004–2011 Journal Geodeet, Editor Since 2006 Association of Estonian Surveyors, Member 2006–2010 Association of Estonian Surveyors, Member of board Since 2008 American Geophysical Union, Student membership

223 Field of research Natural Sciences and Engineering, Geosciences (sea level, levelling, geoid, GNSS)

Projects 2004–2007 Grant ETF5731: Influence of the Gravimetric Anomalies on the Geoid of the Gulfs of Riga and Finland. Senior personnel. (Principal investigator: Harli Jürgenson) 2011–2012 Grant ETF8749: Determination of height reference frame on the Estonian coastal sea using water lever monitoring and laser scanning data. Senior personnel. (Principal investigator: Harli Jürgenson) 2006–2007 National research project: Overview of land uplift in Estonia. Principal investigator 2008 National research project: Research about the use of GPS in the forest. Principal investigator 2009 National research project: Validation of GPS receivers in the forest. Principal investigator

Awards 2008 Scholarship of the Estonian World Council

Dissertations supervised The total number of supervised dissertations (Master’s degree) – 5

Publications The total number of publications – 11

224 ELULOOKIRJELDUS

Isikuandmed Nimi Aive Liibusk Kodakondsus Eesti Sünniaeg 11. oktoober 1979

Kontaktandmed Aadress Eesti Maaülikool, metsandus- ja maaehitusinstituut, geomaatika osakond Fr. R. Kreutzwaldi 5, 51014 Tartu, Eesti E-post [email protected]

Haridustee 1986–1997 Elva Gümnaasium 1997–2001 Eesti Põllumajandusülikool, bakalaureuseõpe geodeesia erialal 2001–2004 Eesti Põllumajandusülikool, magistriõpe geodeesia erialal 2005–2013 Eesti Maaülikool, doktoriõpe geodeesia erialal

Täiendõpe 11.2008–01.2009 Satelliitaltimeetria-alane uurimustöö, Ohio State University, USA

Teenistuskäik 2005–2009 Eesti Maaülikool, metsandus- ja maaehitusinstituut, geomaatika osakond, assistent Alates 2009 Eesti Maaülikool, metsandus- ja maaehitusinstituut, geomaatika osakond, lektor

Teadusorganisatsiooniline ja -administratiivne tegevus 2004–2011 Erialaajakiri Geodeet, toimetaja Alates 2006 Eesti Geodeetide Ühing, liige 2006–2010 Eesti Geodeetide Ühing, juhatuse liige Alates 2008 Ameerika geofüüsikaliit (AGU), tudengi liikmestaatus

Teadustöö põhisuunad Loodusteadused ja tehnika, Maateadused (merevee tase, loodimine, geoid, GNSS)

225 Projektid 2004–2007 Grant ETF5731: Gravimeetriliste anomaaliate mõju geoidile Riia- ja Soome lahel. Põhitäitja. (Vastutav täitja: Harli Jürgenson) 2011–2012 Grant ETF8749: Eesti rannikumere kõrgusraamistiku määramine veetaseme monitooringu ja laserskanneerimise andmetest. Põhitäitja. (Vastutav täitja: Harli Jürgenson) 2006–2007 Siseriiklik leping: Ülevaade Eesti mandriala vertikaalliikumistest. Vastutav täitja. 2008 Siseriiklik leping: Uuring GPS tehnoloogia kasutamise kohta metsas. Vastutav täitja 2009 Siseriiklik leping: GPS seadmete valideerimine metsas. Vastutav täitja

Tunnustused 2008 Ülemaailmse Eesti Kesknõukogu stipendium

Juhendatud väitekirjad Juhendatud väitekirjade (magistrikraad) üldarv – 5

Publikatsioonid Teaduslike publikatsioonide üldarv – 11

226

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