Journal of Geodetic Science

• 1(2) • 2011 • 127-135 DOI: 10.2478/v10156-010-0015-2 •

Detecting and mitigating ocean tidal loading displacements in the Bay of Fundy using GPS Research Article

M. Rafiq, M.C. Santos

Department of Geodesy and Geomatics Engineering, University of New Brunswick, Fredericton, NB, Canada, E3B 5A3

Abstract: Tidal induced displacement is one of the systematic errors that contribute to the scatter in the geodetic measurements derived from the GPS system. This paper focuses on ascertaining and reducing tidal induced errors due to ocean tide loading (OTL) at two GPS sites, namely CGSJ (Coast Guard Saint John, New Brunswick) and DRHS (Digby High School, Nova Scotia), established under the Princess of Acadia project in Saint John, New Brunswick and in Digby, Nova Scotia, respectively. Baseline solutions were obtained by processing 3 and 24 hourly GPS data for the period of one month, using differential positioning software DIPOP and its client end GUI, FACE v2.0. The observed differential variations of GPS sites were compared to the OTL modeled differential variations along the baselines for statistical analysis. The predictive differential ocean tide loading induced variations of the baselines were modeled with global ocean tide model FES 95.2 (0.5 by 0.5 resolution) supplemented with a higher resolution regional tide model by Pagiatakis (0.25 by 0.25 resolution). After modeling for tidal effects the solutions for both the height component and baseline length show daily repeatability better than 1.5 mm for baselines ranging from 87.5 km to 170 km. The tidal model used in the investigation explains the observed motion considerably well, with correlation coefficients of greater than 0.70 between modeled and observed curves. Elimination of tidal effects has resulted in day-to-day rms reduction of height better than 80 percent.

Keywords: ocean tide loading • relative GPS positioning • site displacement © Versita Warsaw and Springer-Verlag Berlin Heidelberg.

Received 17 November 2010; accepted 16 February 2011

1. Introduction oceaniccrust. Oceantides, whenmoveabout, periodicallyloadand unload the Earth causing displacement, tilt and gravity changes in Our interest resided in assessing how much differential GPS data and around the region where the loading is occurring. This kind can be used to detect differential ocean tide loading (OTL) in the of loading is called tidal induced loading and the displacement Bay of Fundy, an area with the largest tidal range in the world, as experienced as a result of that loading is called as tidal induced well as how much the effect can be mitigated using a combined displacement. OTL model. For this purpose we used data collected by two The International Earth Rotation and Reference System Service baselines situated around the Bay of Fundy, in Atlantic Canada, (IERS) has recommended in its conventions, e.g., IERS (2003) and with length of 87.5 km and 170 km, over a period of 30 days.In IERS (2010), that space geodetic parameters must be corrected for this paper we used a combined OTL model composed of FES 95.2 vertical and horizontal tidal loading displacements. There has been (Le Provost et al., 1998) supplemented with a higher resolution a tremendous effort in the development and improvement of tidal regional ocean tide model (Lambert et al., 1998), as implemented models and the latest issue of the IERS Conventions (IERS, 2010) in program LODSDP (Pagiatakis, 1999a). presents a list of the leading global ocean tide models developed Tides occur due to the alternate rising and falling of an ocean since 1981. or water body (as gulfs and bays) connected with the ocean, or The accuracy of the ocean tide load modeling depends upon the they may also occur as periodic displacement on the continental or sophistication and completeness of the load response model for 128 Journal of Geodetic Science

Earth, i.e., Green's functions (Farrell, 1972), and accuracy of ocean tide model. Green's function incorporates the response of the Earth through load deformation coefficients or load Love numbers. The load deformation coefficients are computed through equations of deformation (partial differential equations). The investigation described in this paper used an improved Green's function devel- oped by Pagiatakis (1990) for a ``visco-elastic, anisotropic, rotating, self-gravitating and compressible Earth'', and implemented in Pagiatakis (1992). Pagiatakis, by incorporating anisotropic, visco- elastic and dissipative behavior of the Earth into his equations of deformation, enhanced the values of his calculated load. He developed Green functions for each displacement components, and then used the same to compute the OTL effects due to global ocean tides and local ocean tides. At each observation site, and for each constituent of the ocean tide, the displacement effect is cal- Figure 1. Atlantic Canadian coastal waters gridded with the finer size culated by convolving his complex Green's function, representing cells (adapted after Lambert et al. 1998). the response of the Earth to point mass load, with a set of mass loads representing the particular constituent of the ocean tide. In these calculations the load is assumed to act as a point mass load ing tidal corrections to GPS observations from epoch to epoch. The at the center of the mass of a cell. resulting time series was correlated with the predictive loading In this study we used program LOADSDP v5.03 (Pagiatakis, 1999a) curve for each station to ascertain the bias caused by loading to to generate the ocean loading corrections. LOADSDP v5.03 is the estimated positions. Additionally, efforts have also been made an upgraded version of LOADSDP v4.12 (Pagiatakis, 1998), for to retrieve different tidal constituents from the GPS time series

calculating the effects of global tides at a station, and LOADSDP such as M2. v3.4 (Pagiatakis, 1999b), for local or regional model. The global There are several studies found in the literature that indicate that modelisusedasareferencestandardintowhichmoredetailcoastal site displacements due to ocean tide loading can be measured by tide are integrated. LOADSDP has implemented the Grenoble space geodetic techniques and that ocean tide loading models can global model FES95.2 (with 0.5 by 0.5 resolution) supplemented be validated from GPS (Baker et al., 1995; Kirchener, 2001; Khan by a local model (with 0.25 by 0.25 resolution). According to and Sherneck, 2003; Allinson et al. 2004; Urschl at al., 2005; King Lambert et al. (1998), within 100 km of the Canadian coastlines, et al., 2005; Zahran et al., 2006; Thomas et al., 2007; Thomas et al., often 50% of the OTL effect is caused by the shallow coastal waters 2008; Melachroinos et al., 2009; Yuan et al., 2009). They involve which are not modeled accurately enough by the existing global different comparison techniques and invariably a period longer models. Even FES95.2 model is not complete and accurate enough than the 30 days used in this study. to represent tidal amplitude and phase data where coastline is irregular. Under these circumstances Pagiatakis (1998) envisaged 2. Design of Experiment a finer resolution grid for the calculation of displacement tides at stations around Canada, by creating a grid with fine resolution Under the Princess of Acadia Project, data from a network of four cells near the shore. This kind of scheme allowed him to substitute continuous GPS stations were used to carry out the investigation the near shore cells of the FES95.2 global ocean tide model with his in the current research work. Two stations are located in New own small size cells. This permitted an inclusion of coastal waters Brunswick and two in Nova Scotia. The location of the stations or water bodies too small to be included into the global model, as is shown in Figure2. The IGS (Dow et al., 2009) station HLFX illustrated by Figure1. is located directly on the open Atlantic coast. Station UNB1 It should be mentioned that there newer models, such FES2004 is located a little deeper inland, in the southern part of New (Letellier, 2004) and EOT08a (Savcenko and Bosch, 2008) that have Brunswick. Station UNB1 and HLFX, were selected as base stations a resolution of 0.125 by 0.125 . They were not used in this study for differentially correcting positioning observations of the remote since it relied on LOADSDP. They should be used in another study. stations CGSJ (Coast Guard Saint John, New Brunswick) and DRHS This paper evaluates the tidal response of the GPS stations estab- (Digby Regional High School, Nova Scotia). Data was collected lished under the Princess of Acadia Project (Santos et al., 2004) at for a period of over a year (between 2003 and 2004) but in this Coast Guard Headquarters, Saint John, New Brunswick and Digby investigation just one month was used, 4 weeks, from April 1, 2004 Regional High School, Nova Scotia, to tidal loading. Initially, po- to April 30, 2004. The data sets were collected with a sampling rate sition estimates of the stations were made without applying tidal of 1 Hz. corrections but later position estimates were computed by apply- An overview of the steps followed in experimentation are as follow: Journal of Geodetic Science 129 post-process data the GPS data set used in this investigation, forming baselines UNB1-CGSJ, 87.5 km and, HLFX-DRHS, about 170 km, using 3 h and 24 h sessions, with and without tide loading effects; compute the theoretical displacement at the user stations and rover stations due to global and local ocean tides using LOPADSDP; correlate the differential variation of rover stations with respect to reference stations using time series obtained from GPS and tidal models; decipher the tidal signal from both GPS derived time series ; if possible, extract major loading constituents from the GPS time series through harmonic analysis. The GPS data were processed with the Differential Positioning Package (DIPOP). DIPOP is baseline/network software developed at UNB (Vanícek et al., 1985) and used in subsequent years as a research platform (e.g., Santos, 1995; van der Wall, 1995; Komyathy, 1997; Santos et al., 2000). To better handle the data processing Rafiq (2005) developed a user-friendly graphical user interface (GUI), called FACE v2.0. The basic strategy in data processing is as follows:

· UNB1, HLFX were used as reference stations, while CGSJ Figure 2. GPS stations established under the Princess of Acadia and DRHS were the remote stations; project.

· Weekly final IGS GPS satellite orbits solutions were used; it was concluded that a 3 h estimation interval seemed a good Phase ambiguities were treated as float; · compromise in the present scientific investigation. Hence, the data · Residual tropospheric zenith delay parameter was esti- were processed using the following criteria: 3 h solutions with and mated for every hour of data processing using a priori without ocean loading corrections; 24 h solution with and without tropospheric information from Saastamoinen model and ocean loading corrections. Neil mapping function; 3. Observed and Predicted differential displacement of stations · Elevation cut-off angle was set at 10 degrees;

· Ionospheric delay-free observable was used; This section shows the comparison between the vertical crustal movements predicted by the model with the observed ones · Reference frame was selected as ITRF2000; estimated from the GPS observations. To decipher the OTL signal from continuous position GPS time series, the relative positioning A priori standard deviations of reference stations and re- · technique was applied. The predicted motion incorporates motion mote stations were 10−6 m and 100 m respectively. The a due to global tidal model augmented with regional tidal model. priori value for the remote stations was enough for letting Figure3 compares the predicted and observed vertical crustal the solution converge to their final value. movement at CGSJ with respect to the base station UNB1: (a) Predictive models support the existence of a dominant semidiurnal without taking OTL signal into account, and (b) taking OTL signal intoaccount. ThepredicteddifferentialmotionshowninFigure3(a) component in the project area, being that M2 is the most dominant tidal constituent observed at station CGSJ. Since stations CGSJ and and3(b) is less than the predicted absolute motion shown in DRHS lie in close proximity - the periphery of Bay of Fundy, the Figure4. tidal regime surrounding these stations is similar. Therefore, if a The fortnightly displacement peak is quite evident in Figure3(a), which indicates a spring tide (close to DOY 104 in Figure3(a), when semidiurnal component (e.g., M2) is expected in the given GPS time series, a 3 h estimation rate time series is an optimum compromise the Moon and the Sun are in direct alignment. Saddled parts of the between less than 3 h and a 6 h estimation rate. However, an curves, both predictive and observed indicate neap tides, when estimation rate less than 3 h is deemed as short and noisier, e.g., the Moon and Sun are not in direct alignment but 90 apart. This is a 1 h solution. As shorter intervals do tend to produce intrinsically the period when M2 and S2 are out of phase with each other. The noisiersolutions(Segaletal., 1997), andlongerestimationintervals, variation between successive highs and lows is also observable in e.g., 6 h in our investigation, would approach the Nyquist period Figure3(a). This variation is caused by variation in the declination of the dominant frequency. For example 6 h would be the Nyquist of the Moon and is termed as diurnal inequality (NOAA, 2003). period for semidiurnal components such as M2,S2. Therefore, As shown in Figure3 that the theoretical differential curve at the 130 Journal of Geodetic Science

Table 1. A comparative analysis of statistical data obtained from baselines UNB1-CGSJ and HLFX-DRHS (24 h mean).

techniques are used, such as averaging over 24 h period in case of GPS solutions. However, still if the tidal loading effect is not corrected on daily basis it will still be aliased in the GPS time series, with an increase in variance of height estimates over a fortnight Figure 3. Baseline: UNB1-CGSJ; (a) Circles indicating observed 3 h mean vertical differential GPS solution ; (b) Solid lines indi- period (Lambert et al., 1998). A statistical comparison of predicted cate predicted 3 h mean vertical differential displacement. and observed differential displacement (24 h mean) results has beensummarizedinTable1. However, iftheGPSpositionestimates are to be used for any derived geodetic quantities such as hourly water vapor content above the receiver, etc., then the tidal effect needs to be mitigated on hourly basis.

Figure 4. Predicted absolute vertical crustal motion at CGSJ due to tidal loading.

station is also based on 3 h mean to make it more comparable to 3 h mean GPS solution, and this factor further reduces its peak to peak amplitudes. Linear regression of the two time series showed in Figure3(a) yields a correlation coefficient of 0.78. The correlation analyses for Figure 5. Baseline: UNB1-CGSJ; (a) Triangles indicating observed the Figure3(b) yields a correlation coefficient of -0.07. This sharp 24 h mean vertical differential GPS solution; (b) Dashed decrease in correlation coefficient can be attributed to elimination lines indicate predicted 24 h mean vertical differential dis- of tidal component from the observed GPS solution. The standard placement. deviation has also decreased from 5.92 mm to 1.08 mm when OTL corrections are applied. Tidal loading also influences other geodetic parameters such as The applications of tidal loading corrections have an insignificant latitude and longitude estimates. But the impact on these quanti- effect on relative positioning based on 24 hour GPS solutions. This ties, in terms of amplitude, is approximately one-fourth the effect can be observed in Figure5(a) and5(b), in which the standard on differential vertical position estimates. This can be observed in deviation has decreased from 1.52 mm to 1.36 mm. This small Figures6 and7. The east-west differential variation influences the variation in standard deviation is expected since the principal longitude of a GPS station and north-south differential effects the latitude. The spring and neap tides effects are also observable but loading constituent in the Bay of Fundy area is M2, a semi-diurnal constituent, the effect of which tends to average close to zero with less intensity in Figures6 and7. over a period of 24 hours. It implies that tidal site displacements The effects of tidal loading on the position estimates of the baseline are considerably reduced and tidal variations aliased if averaging HLFX-DRHS are shown in Figure8,9 and 10. Spring and neap tides Journal of Geodetic Science 131

Figure 6. Baseline: UNB1-CGSJ; (a) Circles indicating observed 3 Figure 8. Baseline: HLFX-DRHS; (a) Circles indicating observed 3 h h mean east-west differential GPS solution; (b) Solid lines mean vertical differential GPS solution; (b) Solid lines indi- indicate predicted 3 h mean east-west differential displace- cate predicted 3 h mean vertical differential displacement. ment.

Figure 9. Baseline: HLFX-DRHS; (a) Circles indicating observed 3 hr mean east-west differential GPS solution; (b) Solid Figure 7. Baseline: UNB1-CGSJ; (a) Circles indicating observed 3 h lines indicate predicted 3 hr mean east-west differential dis- mean north-south differential GPS solution; (b) Solid lines placement. indicate predicted 3 h mean north-south differential dis- placement.

and observed differential east-west displacement, and between signature can be observed in Figure8, which shows the vertical north-south predicted and observed differential displacement (3 h differential displacement of station DRHS with respect to HLFX. But mean solutions) have been summarized in Table2. the standard deviation is higher in case of the observed differential It is evident from the statistics that tidal influence has been displacement of station DRHS as compared to CGSJ i.e. 8.5 mm eliminated from the observed GPS time series after the application for DRHS and 5.92 mm for the station CGSJ. Similarly theoretical of tidal corrections. However, it is also evident from Figure9(a) standard deviation for the vertical differential displacement is that the influence of spring and neap tides is difficult to observe in about 7.1 mm, which indicates a difference of 1 mm. both predictive and observed differential east-west variation of the The correlation coefficient is 0.8, which indicates that the two station DRHS. However, a spring and neap tides trend is observable curves are highly correlated and the predictive trend is observ- in Figure in Figure 10(a). Therefore it can be claimed that station able in observed GPS data. After applying tidal corrections, the DRHS is more responsive to tidal influence in north-south direction correlation coefficient becomes very small and negative, i.e. -0.06, than in the east-west direction. This may due to the fact that tides which indicates that almost 80% of the tidal signature has been in the Bay of Fundy area strong in the north-south direction (Godin, eliminated from the tidal data. A comparison between predicted 1968). 132 Journal of Geodetic Science

of the important objectives was to identify the time period over which a particular frequency or constituents have a higher power. The period in this case is just a function of frequency. To view the spectra of all displacement components on a uniform scale, the power spectra from both baselines was normalized. Figures 11 and 12 show the observed and predicted loading power spectra of 3 h mean values of the differential variations along the baselines UNB1-CGSJ and HLFX-DRHS, vertical displacement. The power spectrum has been normalized to unity to easily compare the spectral density graphs of different displacement components and baselines. It is very clear that all the spectra show higher peaks

at the M2 period. However, the peaks for the observed differential verticalvariation, forbothbaselinesaremorepronouncedattheM2 period. The normalized power spectral density number (NPSDN) for baseline UNB1-CGSJ (observed) is approximately equal to the

Figure 10. Baseline: HLFX-DRHS; (a) Circles indicating observed 3 NPSDN of HLFX-DRHS for the constituent M2. This may be due to hr mean north-south differential GPS solution; (b) Solid the fact that vertical variation of both the remote stations, CGSJ lines indicate predicted 3 hr mean north-south differential and DRHS, occur under the influence of M tide, which has similar displacement. 2 characteristics for both the remote stations. Almost similar peaks can be observed in plots for hourly predicted and observed peaks,

in Figures 13 and 14. Constituent S2 is not being observed with the Table 2. Table 2 A comparative analysis of statistical data obtained 3 hourly mean spectra. It is argued that S could be obtained in the from baselines UNB1-CGSJ and HLFX-DRHS (3 hr mean ). 2 power spectra with sampling frequency less than 3 hours, because of its smaller contribution towards site displacement. Figures 13 and 14, being sampled at 1 hour, show additional peaks for

constituents S2 and O1. As already mentioned these constituents could not be observed in 3 hourly predicted and observed data. Concerning the predicted and observed normalized power spectra of the differential east-west and north-south displacements along the baselines, they were less than 20% of those of the vertical displacements. The modeled and the observed peaks have about the same power. There are peaks at periods equal to K and P , A slight difference in peak to peak amplitude in the range of 2-5 mm 1 1 but the power of loading spectra is less for east-west differential is observable in Figure3(a) and8(a), between the differential GPS variation then the power of north-south differential variation. This solutions of UNB1-CGSJ and HLFX-DRHS. The absolute variations at may due to the fact that in the Bay of Fundy area the tides have the either ends of the baseline, i.e. at the stations HLFX and DRHS strong north-south circulation as reported by Godin (1968). are in phase and that is why the differential height variation of the station DRHS with respect to HLFX is higher as compared to the slightly out of phase variations at the stations UNB1 and CGSJ due 5. Conclusions and recommendations to slightly higher latitude difference between the stations UNB1 and CGSJ, i.e. approximately 0 40043.32''. This suggests the latitude This research focused on the utilization of GPS technology to dependence of these stations. A slight phase offset in the resultant monitor tidal effects via the analysis of data from two baselines differential variation of the two baselines may also be attributed UNB1-CGSJ and HLFX-DRHS established under the Princess of to the same reason. The higher differential height variation of Acadia Project. Most of the tidal loading in Bay of Fundy area the station DRHS with respect to HLFX as compared to baseline is due to the regional tidal conditions, which in turn are due UNB1-CGSJ may also be due to the fact that tidal conditions on to the special ocean tide regime in the area. The tidal induced either end of the baseline HLFX-DRHS are almost similar. displacements can be determined from analyses of continuous GPS data if the interval is 3 hours. Correcting for tidal loading 4. Power Spectral Analysis considerably reduced the standard deviation and variance of the estimates of positions for solution periods of few hours. Solutions In this research spectral analysis of the displacements was per- of daily positions are not strongly biased by the omission of formed using the functionalities provided in MATLABTM. It was ocean loading corrections because the most significant loading

considered more convenient to draw power versus period as one component is M2 (semi-diurnal) which average close to zero over Journal of Geodetic Science 133

Figure 11. Baseline: UNB1-CGSJ; (a) Power spectrum based on Figure 13. Baseline: UNB1-CGSJ; (a) Power spectrum based on 3 hourly predicted vertical differential tidal loading effect hourly predicted vertical differential tidal loading effect (b) (b) Power spectrum based on 3 hourly observed vertical Power spectrum based on hourly observed vertical differ- differential GPS solution. ential GPS solution.

Figure 12. Baseline: HLFX-DRHS; (a) Power spectrum based on Figure 14. Baseline: HLFX-DRHS; (a) Power spectrum based on 3 hourly predicted vertical differential tidal loading effect hourly predicted vertical differential tidal loading effect (b) (b) Power spectrum based on 3 hourly observed vertical Power spectrum based on hourly observed vertical differ- differential GPS solution. ential GPS solution.

a 24 hours period. The spring and neap tidal signal is clearly visible The tidal models used in the investigation explain the observed in all the differential variations of the stations, with the exception motion considerably well, with correlation coefficients of greater of east-west variations, where they are not so pronounced. The than 0.70 between modeled and observed curves. Elimination of test demonstrates, through spectral analysis, that M2 tidal loading tidal effects from the observed signal has resulted in reduction of wave for vertical and horizontal displacements is measurable by its rms better than 80 percent. It is suggested for future studies that differential GPS. For the Bay of Fundy area, M2 seems to have a very more recent models should be supplemented with the Pagiatakis strong spectrum. K1 and P1 are also observable in the differential model and investigations be made to notice any improvement in vertical component of the baseline. This also indicates that M2 tidal loading results. It is further suggested that a comparative is the main contributor to the differential vertical variation of the study of all the available ocean tidal models be carried out. The baselines and stations in the project area. The solutions for both the regional model must be updated to take into account any changes height component and baseline length show daily repeatability in the tidal characteristics of the area under investigation, which better than 1.5 mm for baselines ranging from 87.5 km to 170 km. might have occurred over the last few years. The combined global 134 Journal of Geodetic Science

and regional model must also take into account the effects of Godin G. (1968): The 1965 Survey of Bay of Fundy: a geocenter tide, if possible, as suggested by Scherneck and Webb new analysis of data and an interpretation of the results Deptt. (1998). It is intended to enlarge the time period from the 30 days to Energy, Mines, Resources., Mar. Sci. Branch, MS Rep. Ser. No. 8: 97p. 1 year, going beyond the 90 day stacking as suggested by Allinson et al. (2004). The Pagiatakis response function should be further IERS Conventions (2003): IERS Technical Note No. 32. IERS improved, to take into account any structural characteristics, major Conventions Center, pp 72-91. fault lines etc in the area under investigation. Improvements to the response functions are a continuous process. Since GPS has IERS Conventions (2010): IERS Technical Note 36. Gérard Petit and given some promising results in deciphering the tidal signal and Brian Luzum (eds.). Verlag des Bundesamts für Kartographie und

detecting M2 tidal constituent, it is strongly recommended that Geodäsie, 179 pp. a network of permanent GPS sites be established in the project area to carry out further investigations in this respect and recover Khan S.A. and Scherneck H.G. (2003): The M2 ocean tide loading long term tidal constituents and other tidal related data. Such wave in Alaska: vertical and horizontal displacements modeled stations could also be used for investigating atmospheric loading and observed. Journal of Geodesy, Vol. 77, No. 3-4, pp. 117-127. and meteorological parameters.

King M.A., Penna N.T. and Clarke P. J. (2005): Validation of Acknowledgments ocean tide models around Antarctice using onshore GPS and gravity data.Journal of Geophysical Research, Vol. 110, B08401, The funds for this investigation were provided by the Natural Sci- DOI:10.1029/2004JB003390. ences and Engineering Research Council of Canada via the second author's Discovery Grant and the Canadian International Devel- Kirchner M. (2001): Study of local site displacements due to ocean opment Agency (CIDA). Special thanks are also due to Dr. Spiros tide loading using a GPS Network in Island. Report 184, Onsala Pagiatakis, York University, for the use of his program and coeffi- Space Observatory, Onsala. cients. The data collection during the Princess of Acadia Project was funded by the Naval Oceanographic Office and the Office of Komjathy A. (1997): Global Ionospheric Total Electron Content Naval Research through a grant through the University of South- Mapping Using the Global Positioning System. Ph.D. dissertation, ern Mississippi. Data from station HLFX was obtained with Natural Department of Geodesy and Geomatics Engineering Technical Resources Canada. Report No. 188, University of New Brunswick, Fredericton, New Brunswick, Canada, 248 pp.

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