DOCSLIB.ORG

What Type of Geoid Is Needed for Oceanic Applications and What Can Geodesy Deliver?

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
What Type of Geoid Is Needed for Oceanic Applications and What Can Geodesy Deliver? 1 What type of geoid is needed for oceanic applications and what can geodesy deliver? by E. Groten, Darmstadt e-mail: [email protected] Abstract: Interdisciplinary application of geoids as reference surfaces for geophysical and oceanographic purposes is affected by a variety of imprecise definitions and conse- quent uncertainties. This is still all the more true in connection with time variable geoids as soon as secular changes of mean sea level (MSL) as well as long-period and long-term variations play a role. From a mathematical as well as from a physical viewpoint the combination of gravimetric, satellite (GRACE, GOCE as well as GPS and GLONASS), levelling, tide gauge, altimetric and solid earth tide data poses sev- eral unresolved problems. This is also true for shipborne and airborne gravimetry on sea. One principal problem arises due to the fact that in geodesy mainly relative ob- servations (not absolute data) are available. Absolute gravimetry is one of the few exeptions. On the other hand, ocean circulation models are dominated by gradient computation so that relative data (up to an unknown constant) are sufficient in many cases. With GRACE and GOCE data, which will soon be available, the situation im- proves substantially. Nevertheless, an identification of oceanographic needs and clearer and unique definitions of geodetic quantities and parameters may now be helpful. Mainly global definitions and practical implementations of the geoid are still far apart from uniqueness and from desired accuracy, respectively; this affects also the quasigeoid which coincides with the geoid on the ocean. The main impact of better gravity data at sea will be due to the possibility to better separate stationary from transient ocean circulation as well as its small scale from larger scales phe- nomena. 1. Introduction Using assimilation techniques C. Wunsch and M. Gaposchkin were among the first to interre- late ocean circulation and geoid in least-squares approaches where a set of parameters is op- timized and the associated residuals and the errors, which can now be checked and verified by satellite altimetry, are presently being used to stepwise evaluate improved models and also take into account temporal variations of geoids and circulation models at the same time. So this parameter estimation process quite well elucidates the interrelations between dynamic topography and geoid or geopotential. As Topex-Poseidon (T/P) and similar altimetry data deliver averages of SST (= sea surface topography) over 10 days or so, GRACE could give additional information in the future on regional short-term variability, typically in the Antarc- tic and arctic area. Until now mostly the EGM 96 geoid model served as the base for such investigations. Dealiasing plays a specific role where short-term variability with time is con- sidered. Here focus is on geodetic aspects of geoid computation. Particularly with respect to GRACE it is important to note that it is possible to determine now temporal changes of the geoid, at least for low and medium degree harmonic expansion, more precisely than the geoid itself. So transient and stationary geoids should be clearly distin- guished. Recently, the geoid became more popular as a reference surface for a variety of geophysical and mathematical or physical considerations. As a level surface it fulfills a series of require- 2 ments related to level surfaces of the geopotential. As a particular level surface quite close to mean sea level (MSL) it is easily evaluated, at least in spherical approximation, from gravity anomalies, ∆g, and related quantities in terms of a perturbation equation. The convolution type Stokes’ integral can be expressed in terms of a low-pass filter (n-1)-1 applied to a spheri- cal harmonics expansion ∆g = ∑ ∆gn . For higher approximation, however, the evaluation n becomes more “intricate”, as ellipsoidal and terrain corrections have to be taken into account. Based on the well known Runge Theorem related integral equation or similar solutions were designed by Molodensky, Bjerhammar, Moritz, Arnold etc. The differences between quasige- oid and geoid need no further explanation if we confine ourselves to the ocean because both surfaces are basically identical there. However, as the aforementioned filter function tends to infinity for n = 1 most evaluations ignore the terms for n < 2 which leads to a constant term No which is basically the difference between absolute and relative geoids. If, besides ∆g, also altimetric data are used at sea, they may either be used to evaluate the difference between the sea surface, and after appropriate reduction, between mean sea level (MSL) and the geoid. Or we ignore that difference (of the order of d < 1.5 m) and solve an “improperly posed problem” (in Hadamard’s sense) and determine ∆gn from altimetric observations using the inverse (high-pass) filter function (n-1). With GPS-data at hand we may also replace the aforemen- tioned “free boundary value problem” by a fixed boundary value problem where (n-1) is re- placed by (n+1) whenever GPS positioning is accurate enough. In coastal areas where sea surface noise becomes relevant we may combine tide gauge data together with GPS- positioning in order to bridge oceanic and continental sections of the geoid. The situation be- comes more intricate whenever similar variations are taken into account because Stokes’ the- ory is based on potential theory where explicit time dependence is not compatible with har- monic or even conservative fields of force so that tidal reductions and similar operations need to be applied to eliminate such dependences. On the other hand, such problems can be avoided by step-wise constant functions so that time dependent ∆g and geoids can be consid- ered in detail. Whenever oceanic circulation models are derived from gradient observations and related par- tial differential equations, such relative geoids, as mentioned before, will be sufficient. Details of the earth’s gravity field on ocean circulation modeling are found in (Dombrowsky et al., 1999). However, problems may come up, if the aforementioned step-functions are not compatible with the applied tidal corrections and vice versa. In principle, this is a matter of convention but such conventions must be applied to make the data compatible with each other. For long tide gauge records simple averaging techniques may be sufficient but for short tidal records and for altimetric observations careful considerations may be appropriate. If, for instance, secular mean sea level variations of the order of a few millimeters are considered for the latter type of observations, systematic deviations could arise. For details see (Fenoglio-Marc and Groten, 2002). 2. Absolute geoid In some cases the actual location of the geoid and the associated numerical value of the geo- potential, W°, are needed. In that case also the aforementioned terms for n = 0 and n = 1 have to be considered. But in geocentric reference systems all terms for n = 1 disappear so that only the zero degree term is of interest. Depending on the selection of the appropriate (for linear approximation) approximation figure (sphere, ellipsoid etc.) correction terms need to be taken 3 4 5 6 into account which make things intricate. Also in view of long-periodic variations of MSL (such as El Nino) more sophisticated mathematics and detailed considerations of physical effects are necessary (Marcus et al., 2001). In Fig. 1 those types of observations are summarized which are usually being applied to Ver- tical Datum and geoid evaluation. It is important to realize that, depending on the type of ob- servation and data processing, the observations are transformed from “observation space” (i.e. reality) to stationary “model spaces”. As far as tidal corrections are concerned, three different model spaces are to be distinguished. a) zero tide, b) mean tide and c) tide-free, as mentioned before. The reason for using 3 models is due to the fact that, even after eliminat- ing time-dependent tides, permanent tides can only be handled in those different models if (1) we want to stay as close as possible to reality and (2) take all non-harmonic parts of tidal po- tential out, in order to be able to apply potential theory in terms of harmonic functions. For non-experts the transition from one to the other models is not always easily understood. But comparison and compatibility are only possible within one model space. Also non-tidal time dependences have to be considered in an analogous way. One good example is time-varying ocean bottom pressure variations as considered in detail by Wuensch et al. (2001). Another aspect of data reductions is due to the fact that national height systems are basically independent of each other. Thus the evaluation of gravity anomalies is reduced to different “zero-levels” which leads to systematic offsets in geoid computation ∆g → N where N is the geoid height, i.e. the separation of the ellipsoid from the geoid. All what is true for one spe- cific epoch holds, of course, also for repeat observations. Optimal data treatment is possible whenever data are related to the same reference frame, as, e.g., in case of the TIGA project. This is illustrated in Fig. 2. The transition from one national height system to any other or to a common continental system is illustrated in Fig. 3 (courtesy BKG, Dr. Ihde) for the European System. The pioneer attempt to evaluate a global unified height system based on the joint use of altimetric, gravimetric, levelling and positioning (GPS, GLONASS etc.) data is illustrated in (Bursa et al., 2002). In the absence of strong currents and dominant circulation, mean sea level reflects to a large extent the underlying ocean-bottom topography and gravitational fields so that its variations are close to those of the associated geoid.
Load more

Recommended publications
  • Preliminary Estimation and Validation of Polar Motion Excitation from Different Types of the GRACE and GRACE Follow-On Missions Data
    remote sensing Article Preliminary Estimation and Validation of Polar Motion Excitation from Different Types of the GRACE and GRACE Follow-On Missions Data Justyna Sliwi´ ´nska 1,* , Małgorzata Wi ´nska 2 and Jolanta Nastula 1 1 Space Research Centre, Polish Academy of Sciences, 00-716 Warsaw, Poland; [email protected] 2 Faculty of Civil Engineering, Warsaw University of Technology, 00-637 Warsaw, Poland; [email protected] * Correspondence: [email protected] Received: 18 September 2020; Accepted: 22 October 2020; Published: 23 October 2020 Abstract: The Gravity Recovery and Climate Experiment (GRACE) mission has provided global observations of temporal variations in the gravity field resulting from mass redistribution at the surface and within the Earth for the period 2002–2017. Although GRACE satellites are not able to realistically detect the second zonal parameter (DC20) of geopotential associated with the flattening of the Earth, they can accurately determine variations in degree-2 order-1 (DC21, DS21) coefficients that are proportional to variations in polar motion. Therefore, GRACE measurements are commonly exploited to interpret polar motion changes due to variations in the global mass redistribution, especially in the continental hydrosphere and cryosphere. Such impacts are usually examined by computing the so-called hydrological polar motion excitation (HAM) and cryospheric polar motion excitation (CAM), often analyzed together as HAM/CAM. The great success of the GRACE mission and the scientific robustness of its data contributed to the launch of its successor, GRACE Follow-On (GRACE-FO), which began in May 2018 and continues to the present. This study presents the first estimates of HAM/CAM computed from GRACE-FO data provided by three data centers: Center for Space Research (CSR), Jet Propulsion Laboratory (JPL), and GeoForschungsZentrum (GFZ).
    [Show full text]
  • THE EARTH's GRAVITY OUTLINE the Earth's Gravitational Field
    GEOPHYSICS (08/430/0012) THE EARTH'S GRAVITY OUTLINE The Earth's gravitational field 2 Newton's law of gravitation: Fgrav = GMm=r ; Gravitational field = gravitational acceleration g; gravitational potential, equipotential surfaces. g for a non–rotating spherically symmetric Earth; Effects of rotation and ellipticity – variation with latitude, the reference ellipsoid and International Gravity Formula; Effects of elevation and topography, intervening rock, density inhomogeneities, tides. The geoid: equipotential mean–sea–level surface on which g = IGF value. Gravity surveys Measurement: gravity units, gravimeters, survey procedures; the geoid; satellite altimetry. Gravity corrections – latitude, elevation, Bouguer, terrain, drift; Interpretation of gravity anomalies: regional–residual separation; regional variations and deep (crust, mantle) structure; local variations and shallow density anomalies; Examples of Bouguer gravity anomalies. Isostasy Mechanism: level of compensation; Pratt and Airy models; mountain roots; Isostasy and free–air gravity, examples of isostatic balance and isostatic anomalies. Background reading: Fowler §5.1–5.6; Lowrie §2.2–2.6; Kearey & Vine §2.11. GEOPHYSICS (08/430/0012) THE EARTH'S GRAVITY FIELD Newton's law of gravitation is: ¯ GMm F = r2 11 2 2 1 3 2 where the Gravitational Constant G = 6:673 10− Nm kg− (kg− m s− ). ¢ The field strength of the Earth's gravitational field is defined as the gravitational force acting on unit mass. From Newton's third¯ law of mechanics, F = ma, it follows that gravitational force per unit mass = gravitational acceleration g. g is approximately 9:8m/s2 at the surface of the Earth. A related concept is gravitational potential: the gravitational potential V at a point P is the work done against gravity in ¯ P bringing unit mass from infinity to P.
    [Show full text]
  • The Global Positioning System the Global Positioning System
    The Global Positioning System The Global Positioning System 1. System Overview 2. Biases and Errors 3. Signal Structure and Observables 4. Absolute v. Relative Positioning 5. GPS Field Procedures 6. Ellipsoids, Datums and Coordinate Systems 7. Mission Planning I. System Overview ! GPS is a passive navigation and positioning system available worldwide 24 hours a day in all weather conditions developed and maintained by the Department of Defense ! The Global Positioning System consists of three segments: ! Space Segment ! Control Segment ! User Segment Space Segment Space Segment ! The current GPS constellation consists of 29 Block II/IIA/IIR/IIR-M satellites. The first Block II satellite was launched in February 1989. Control Segment User Segment How it Works II. Biases and Errors Biases GPS Error Sources • Satellite Dependent ? – Orbit representation ? Satellite Orbit Error Satellite Clock Error including 12 biases ? 9 3 Selective Availability 6 – Satellite clock model biases Ionospheric refraction • Station Dependent L2 L1 – Receiver clock biases – Station Coordinates Tropospheric Delay • Observation Multi- pathing Dependent – Ionospheric delay 12 9 3 – Tropospheric delay Receiver Clock Error 6 1000 – Carrier phase ambiguity Satellite Biases ! The satellite is not where the GPS broadcast message says it is. ! The satellite clocks are not perfectly synchronized with GPS time. Station Biases ! Receiver clock time differs from satellite clock time. ! Uncertainties in the coordinates of the station. ! Time transfer and orbital tracking. Observation Dependent Biases ! Those associated with signal propagation Errors ! Residual Biases ! Cycle Slips ! Multipath ! Antenna Phase Center Movement ! Random Observation Error Errors ! In addition to biases factors effecting position and/or time determined by GPS is dependant upon: ! The geometric strength of the satellite configuration being observed (DOP).
    [Show full text]
  • Detection of Caves by Gravimetry
    Detection of Caves by Gravimetry By HAnlUi'DO J. Cmco1) lVi/h plates 18 (1)-21 (4) Illtroduction A growing interest in locating caves - largely among non-speleolo- gists - has developed within the last decade, arising from industrial or military needs, such as: (1) analyzing subsUl'face characteristics for building sites or highway projects in karst areas; (2) locating shallow caves under airport runways constructed on karst terrain covered by a thin residual soil; and (3) finding strategic shelters of tactical significance. As a result, geologists and geophysicists have been experimenting with the possibility of applying standard geophysical methods toward void detection at shallow depths. Pioneering work along this line was accomplishecl by the U.S. Geological Survey illilitary Geology teams dUl'ing World War II on Okinawan airfields. Nicol (1951) reported that the residual soil covel' of these runways frequently indicated subsi- dence due to the collapse of the rooves of caves in an underlying coralline-limestone formation (partially detected by seismic methods). In spite of the wide application of geophysics to exploration, not much has been published regarding subsUl'face interpretation of ground conditions within the upper 50 feet of the earth's surface. Recently, however, Homberg (1962) and Colley (1962) did report some encoUl'ag- ing data using the gravity technique for void detection. This led to the present field study into the practical means of how this complex method can be simplified, and to a use-and-limitations appraisal of gravimetric techniques for speleologic research. Principles all(1 Correctiolls The fundamentals of gravimetry are based on the fact that natUl'al 01' artificial voids within the earth's sUl'face - which are filled with ail' 3 (negligible density) 01' water (density about 1 gmjcm ) - have a remark- able density contrast with the sUl'roun<ling rocks (density 2.0 to 1) 4609 Keswick Hoad, Baltimore 10, Maryland, U.S.A.
    [Show full text]
  • Airborne Geoid Determination
    LETTER Earth Planets Space, 52, 863–866, 2000 Airborne geoid determination R. Forsberg1, A. Olesen1, L. Bastos2, A. Gidskehaug3,U.Meyer4∗, and L. Timmen5 1KMS, Geodynamics Department, Rentemestervej 8, 2400 Copenhagen NV, Denmark 2Astronomical Observatory, University of Porto, Portugal 3Institute of Solid Earth Physics, University of Bergen, Norway 4Alfred Wegener Institute, Bremerhaven, Germany 5Geo Forschungs Zentrum, Potsdam, Germany (Received January 17, 2000; Revised August 18, 2000; Accepted August 18, 2000) Airborne geoid mapping techniques may provide the opportunity to improve the geoid over vast areas of the Earth, such as polar areas, tropical jungles and mountainous areas, and provide an accurate “seam-less” geoid model across most coastal regions. Determination of the geoid by airborne methods relies on the development of airborne gravimetry, which in turn is dependent on developments in kinematic GPS. Routine accuracy of airborne gravimetry are now at the 2 mGal level, which may translate into 5–10 cm geoid accuracy on regional scales. The error behaviour of airborne gravimetry is well-suited for geoid determination, with high-frequency survey and downward continuation noise being offset by the low-pass gravity to geoid filtering operation. In the paper the basic principles of airborne geoid determination are outlined, and examples of results of recent airborne gravity and geoid surveys in the North Sea and Greenland are given. 1. Introduction the sea-surface (H) by airborne altimetry. This allows— Precise geoid determination has in recent years been facil- in principle—the determination of the dynamic sea-surface itated through the progress in airborne gravimetry. The first topography (ζ) through the equation large-scale aerogravity experiment was the airborne gravity survey of Greenland 1991–92 (Brozena, 1991).
    [Show full text]
  • A Hierarchy of Models, from Planetary to Mesoscale, Within a Single
    A hierarchy of models, from planetary to mesoscale, within a single switchable numerical framework Nigel Wood, Andy White and Andrew Staniforth Dynamics Research, Met Office © Crown copyright Met Office Outline of the talk • Overview of Met Office’s Unified Model • Spherical Geopotential Approximation • Relaxing that approximation • A method of implementation • Alternative view of Shallow-Atmosphere Approximation • Application to departure points © Crown copyright Met Office Met Office’s Unified Model Unified Model (UM) in that single model for: Operational forecasts at ¾Mesoscale (resolution approx. 12km → 4km → 1km) ¾Global scale (resolution approx. 25km) Global and regional climate predictions (resolution approx. 100km, run for 10-100 years) + Research mode (1km - 10m) and single column model 20 years old this year © Crown copyright Met Office Timescales & applications © Crown copyright Met Office © Crown copyright Met Office UKV Domain 4x4 1.5x4 4x4 4x1.5 1.5x1.5 4x1.5 4x4 1.5x4 4x4 Variable 744(622) x 928( 810) points zone © Crown copyright Met Office The ‘Morpeth Flood’, 06/09/2008 1.5 km L70 Prototype UKV From 15 UTC 05/09 12 km 0600 UTC © Crown copyright Met Office 2009: Clark et al, Morpeth Flood UKV 4-20hr forecast 1.5km gridlength UK radar network convection permitting model © Crown copyright Met Office © Crown copyright Met Office © Crown copyright Met Office The underlying equations... c Crown Copyright Met Office © Crown copyright Met Office Traditional Spherically Based Equations Dru uv tan φ cpdθv ∂Π uw u − − (2Ω sin
    [Show full text]
  • Geophysical Journal International
    Geophysical Journal International Geophys. J. Int. (2015) 203, 1773–1786 doi: 10.1093/gji/ggv392 GJI Gravity, geodesy and tides GRACE time-variable gravity field recovery using an improved energy balance approach Kun Shang,1 Junyi Guo,1 C.K. Shum,1,2 Chunli Dai1 and Jia Luo3 1Division of Geodetic Science, School of Earth Sciences, The Ohio State University, 125 S. Oval Mall, Columbus, OH 43210, USA. E-mail: [email protected] 2Institute of Geodesy & Geophysics, Chinese Academy of Sciences, Wuhan, China 3School of Geodesy and Geomatics, Wuhan University, 129 Luoyu Road, Wuhan 430079, China Accepted 2015 September 14. Received 2015 September 12; in original form 2015 March 19 Downloaded from SUMMARY A new approach based on energy conservation principle for satellite gravimetry mission has been developed and yields more accurate estimation of in situ geopotential difference observ- ables using K-band ranging (KBR) measurements from the Gravity Recovery and Climate Experiment (GRACE) twin-satellite mission. This new approach preserves more gravity in- http://gji.oxfordjournals.org/ formation sensed by KBR range-rate measurements and reduces orbit error as compared to previous energy balance methods. Results from analysis of 11 yr of GRACE data indicated that the resulting geopotential difference estimates agree well with predicted values from of- ficial Level 2 solutions: with much higher correlation at 0.9, as compared to 0.5–0.8 reported by previous published energy balance studies. We demonstrate that our approach produced a comparable time-variable gravity solution with the Level 2 solutions. The regional GRACE temporal gravity solutions over Greenland reveals that a substantially higher temporal resolu- at Ohio State University Libraries on December 20, 2016 tion is achievable at 10-d sampling as compared to the official monthly solutions, but without the compromise of spatial resolution, nor the need to use regularization or post-processing.
    [Show full text]
  • Resolving Geophysical Signals by Terrestrial Gravimetry: a Time Domain Assessment of the Correction-Induced Uncertainty
    Originally published as: Mikolaj, M., Reich, M., Güntner, A. (2019): Resolving Geophysical Signals by Terrestrial Gravimetry: A Time Domain Assessment of the Correction-Induced Uncertainty. - Journal of Geophysical Research, 124, 2, pp. 2153—2165. DOI: http://doi.org/10.1029/2018JB016682 RESEARCH ARTICLE Resolving Geophysical Signals by Terrestrial Gravimetry: 10.1029/2018JB016682 A Time Domain Assessment of the Correction-Induced Key Points: Uncertainty • Global-scale uncertainty assessment of tidal, oceanic, large-scale 1 1 1,2 hydrological, and atmospheric M. Mikolaj , M. Reich , and A. Güntner corrections for terrestrial gravimetry • Resolving subtle gravity signals in the 1Section Hydrology, GFZ German Research Centre for Geosciences, Potsdam, Germany, 2Institute of Environmental order of few nanometers per square Science and Geography, University of Potsdam, Potsdam, Germany second is challenged by the statistical uncertainty of correction models • Uncertainty computed for selected periods varies significantly Abstract Terrestrial gravimetry is increasingly used to monitor mass transport processes in with latitude and altitude of the geophysics boosted by the ongoing technological development of instruments. Resolving a particular gravimeter phenomenon of interest, however, requires a set of gravity corrections of which the uncertainties have not been addressed up to now. In this study, we quantify the time domain uncertainty of tide, global Supporting Information: atmospheric, large-scale hydrological, and nontidal ocean loading corrections. The uncertainty is • Supporting Information S1 assessed by comparing the majority of available global models for a suite of sites worldwide. The average uncertainty expressed as root-mean-square error equals 5.1 nm/s2, discounting local hydrology or air Correspondence to: pressure. The correction-induced uncertainty of gravity changes over various time periods of interest M.
    [Show full text]
  • The Global Positioning System II Field Experiments
    The Global Positioning System II Field Experiments Geo327G/386G: GIS & GPS Applications in Earth Sciences Jackson School of Geosciences, University of Texas at Austin 10/8/2020 5-1 Mexico DGPS Field Campaign Cenotes in Tamaulipas, MX, near Aldama Geo327G/386G: GIS & GPS Applications in Earth Sciences 10/8/2020 Jackson School of Geosciences, University of Texas at Austin 5-2 Are Cenote Water Levels Related? Geo327G/386G: GIS & GPS Applications in Earth Sciences 10/8/2020 Jackson School of Geosciences, University of Texas at Austin 5-3 DGPS Static Survey of Cenote Water Levels Geo327G/386G: GIS & GPS Applications in Earth Sciences 10/8/2020 Jackson School of Geosciences, University of Texas at Austin 5-4 Determining Orthometric Heights ❑Ortho. Height = H.A.E. – Geoid Height Height above MSL (Orthometric height) H.A.E. Geoid height Earth Surface = H.A.E. Geoid Ellipsoid Geoid Height Geo327G/386G: GIS & GPS Applications in Earth Sciences 10/8/2020 Jackson School of Geosciences, University of Texas at Austin 5-5 Determining Orthometric Heights ❑Ortho. Height = (H.A.E. – Geoid Height) Need: 1) Ellipsoid model – GRS80 – NAVD88 ❑reference stations: HARN (+ 2 cm), CORS (+ ~2 cm) 2) Geoid model – GEOID99 ( + 5 cm for US) Procedure: Base receiver at reference station, rover at point of interest a) measure HAE, apply DGS corrections b) subtract local Geoid Height Geo327G/386G: GIS & GPS Applications in Earth Sciences 10/8/2020 Jackson School of Geosciences, University of Texas at Austin 5-6 Sources of Error ❑Geoid error – model less well constrained in areas of few gravity measurement ❑NAVD88 error – benchmark stability, measurement errors ❑GPS errors – need precise ephemeri, tropospheric delay model, equipment (antennae should be same for base and rover) Geo327G/386G: GIS & GPS Applications in Earth Sciences 10/8/2020 Jackson School of Geosciences, University of Texas at Austin 5-7 Static Carrier-phase solutions obtained by: ❑Commercial post-processing software ❑e.g.
    [Show full text]
  • Gravity, Geoid and Earth Observation IAG Commission 2: Gravity Field, Chania, Crete, Greece, 23-27 June 2008
    S.P. Mertikas (Ed.) Gravity, Geoid and Earth Observation IAG Commission 2: Gravity Field, Chania, Crete, Greece, 23-27 June 2008 Series: International Association of Geodesy Symposia, Vol. 135 ▶ State of the art scientific achievements of gravity field research prospects These Proceedings include the written version of papers presented at the IAG International Symposium on "Gravity, Geoid and Earth Observation 2008". The Symposium was held in Chania, Crete, Greece, 23-27 June 2008 and organized by the Laboratory of Geodesy and Geomatics Engineering, Technical University of Crete, Greece. The meeting was arranged by the International Association of Geodesy and in particular by the IAG Commission 2: Gravity Field. The symposium aimed at bringing together geodesists and geophysicists working in the 2010, XXXIV, 702 p. 340 illus. general areas of gravity, geoid, geodynamics and Earth observation. Besides covering the traditional research areas, special attention was paid to the use of geodetic methods for: Earth observation, environmental monitoring, Global Geodetic Observing System (GGOS), Printed book Earth Gravity Models (e.g., EGM08), geodynamics studies, dedicated gravity satellite Hardcover missions (i.e., GOCE), airborne gravity surveys, Geodesy and geodynamics in polar regions, and the integration of geodetic and geophysical information. ▶ 299,99 € | £249.99 | $379.99 ▶ *320,99 € (D) | 329,99 € (A) | CHF 354.00 eBook Available from your bookstore or ▶ springer.com/shop MyCopy Printed eBook for just ▶ € | $ 24.99 ▶ springer.com/mycopy Order online at springer.com ▶ or for the Americas call (toll free) 1-800-SPRINGER ▶ or email us at: [email protected]. ▶ For outside the Americas call +49 (0) 6221-345-4301 ▶ or email us at: [email protected].
    [Show full text]
  • Vertical Structure
    ESCI 341 – Atmospheric Thermodynamics Lesson 7 – Vertical Structure References: An Introduction to Dynamic Meteorology, Holton Introduction to Theoretical Meteorology, Hess Synoptic-dynamic Meteorology in Midlatitudes, Vol. 1, Bluestein ‘An example of uncertainty in sea level pressure reduction’, P.M. Pauley, Mon. Wea. Rev., 13, 1998, pp. 833-850 GEOPOTENTIAL l The acceleration due to gravity is not constant. It varies from place to place, with the largest variation due to latitude. o What we call gravity is the combination of the gravitational acceleration and the centrifugal acceleration from the Earth’s rotation. o Gravity at the North Pole is approximately 9.83 m/s2, while at the Equator it is about 9.78 m/s2. l Though small, the variation in gravity must be accounted for. We do this via the concept of geopotential. l Geopotential is essentially the potential energy per unit mass. l A surface of constant geopotential represents a surface along which all objects of the same mass have the same potential energy. l If gravity were constant, a geopotential surface would lie at a constant altitude. Since gravity is not constant, a geopotential surface will have varying altitude. l Geopotential is defined as z F º ò gdz, (1) 0 or in differential form as dF = gdz. l Geopotential height is defined as F 1 Z Zº=ò gdZ (2) gg000 2 where g0 is a constant called standard gravity, and has a value of 9.80665 m/s . o Geopotential height is expressed in geopotential meters, abbreviated as gpm. l If the change in gravity with height is ignored, geopotential height and geometric height are related via g Z = z.
    [Show full text]
  • The History of Geodesy Told Through Maps
    The History of Geodesy Told through Maps Prof. Dr. Rahmi Nurhan Çelik & Prof. Dr. Erol KÖKTÜRK 16 th May 2015 Sofia Missionaries in 5000 years With all due respect... 3rd FIG Young Surveyors European Meeting 1 SUMMARIZED CHRONOLOGY 3000 BC : While settling, people were needed who understand geometries for building villages and dividing lands into parts. It is known that Egyptian, Assyrian, Babylonian were realized such surveying techniques. 1700 BC : After floating of Nile river, land surveying were realized to set back to lost fields’ boundaries. (32 cm wide and 5.36 m long first text book “Papyrus Rhind” explain the geometric shapes like circle, triangle, trapezoids, etc. 550+ BC : Thereafter Greeks took important role in surveying. Names in that period are well known by almost everybody in the world. Pythagoras (570–495 BC), Plato (428– 348 BC), Aristotle (384-322 BC), Eratosthenes (275–194 BC), Ptolemy (83–161 BC) 500 BC : Pythagoras thought and proposed that earth is not like a disk, it is round as a sphere 450 BC : Herodotus (484-425 BC), make a World map 350 BC : Aristotle prove Pythagoras’s thesis. 230 BC : Eratosthenes, made a survey in Egypt using sun’s angle of elevation in Alexandria and Syene (now Aswan) in order to calculate Earth circumferences. As a result of that survey he calculated the Earth circumferences about 46.000 km Moreover he also make the map of known World, c. 194 BC. 3rd FIG Young Surveyors European Meeting 2 150 : Ptolemy (AD 90-168) argued that the earth was the center of the universe.
    [Show full text]