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On the application of Satellite Altimetry as a new source of information for Sea Geoid computation


A. A. Ardalan
Department of Surveying and Geomatics Eng.,
Center of Excellence in Geomatics Eng. And Disaster Management,
University of Tehran
[email protected]


G. Joodaki
Department of Surveying and Geomatics Eng.,
Center of Excellence in Geomatics Eng. And Disaster Management,
University of Tehran


V. Nafisi
Department of Surveying and Geomatics Eng.,
Center of Excellence in Geomatics Eng. And Disaster Management,
University of Tehran


M. Jafari
Department of Surveying and Geomatics Eng.,
Center of Excellence in Geomatics Eng. And Disaster Management,
University of Tehran

 

Abstract
Satellite altimetry has proven its Potentiality in the observations of sea level variations in the global sense. The sea level variations observed by the satellite altimetry missions can be processed in order to derive the tidal constituents and the static sea level known as Mean Sea Level (MSL) in geodesy. In this paper, satellite altimetry derived MSL is taken as input data and using a Geopotential model, gravity potential values at the MSL points are computed. Knowing geoid’s potential value (W0), the difference between gravity potential values at the MSL points is computed. These potential differences which can be interpreted as the Sea Surface Topographic height (SST) in terms of potential unit can be readily converted to height difference by using suitable transformation function between potential and geometry spaces. Having computed SST, the geoid can be derived point-wise as the MSL minus SST. Aforementioned procedure is tested numerically at the Persian Gulf and Oman Sea. The computed geoid is tested against other available geoid solutions of the same region to verify the obtained accuracy.

Introduction
At coastal areas tidal information can be obtained by tide gauge observations, however, in the offshore and open seas there is no such possibility. Of course, there are also submerged tide gauges, which could be mounted under water, but considering the size of oceans and water areas of the Earth that amount to 2/3 of the whole Earth’s surface, such type of point-wise observations could not ever provide a uniform coverage of the sea areas. On the other hand altimetry satellites are capable of providing sea level variations at a global scale and therefore they can be used as a fair substitute of tide gauge observations at the offshore and open seas.

Modern altimetry satellites are equipped with range-measuring instruments, which can measure the distance between satellites to the sea surface with up to few centimeters accuracy. For example, the altimeter of TOPEX/Poseidon satellite is reported to be accurate to to (Benada 1997). Besides altimetry satellites are equipped with variety of positioning systems which could provide the geocentric position of the altimetry satellites to a very high degree of precision, e.g. TOPEX/Poseidon could be positioned in its orbit up to to accuracy level (Benada 1997).

One of the mostly demanding products of the satellite altimetry observations is Sea Surface Topography (SST), or in oceanographic terminology, Statistic SST. This surface is the deviation between Mean Sea Level (MSL), which is also known as static sea surface, and the geoid. In fact if the sea surface were affected only by gravitational forces should have be formed as an equipotential surface, called geoid. In reality due to various numbers of non-gravitational forces, as well as the tidal force, we have a dynamic sea surface. The tidal part of the dynamic sea surface can be modeled and having removed these time varying effect one arrives at the MSL, which is static but still not an equipotential surface of the Earth due to non-gravitational affects such as winds, currents, salinity and temperature variations, for example. Therefore tide gauge observations could only provide us with tidal constituents and MSL; however connection of individual coastal tide gauge observations requires that the zero point of the tide gauges be connected to each other. This might be accomplished via precise leveling along the coast for the tide gauges which are close to each other. However distant tide gauges and especially those which are separated by water, like tide gauges at the different continents could not be connected that way. An alternative approach to the connection of the zero points of the tide gauge stations is via a reference surface, to which the MSL’s could be compared. This reference surface could be considered as the one nowadays used as the height datum, i.e. the geoid. Therefore if we would like to connect the zero points of the world-wide tide gauges to each other via geoid, we would need to now SST at individual tide gauge stations.

In this paper based on the algorithm shown in Flowchart 1 we have computed SST at the test area, Persian Gulf and Oman Sea and having computed SST marine geoid at the test area has been computed by subtracting SST from MSL. As Flowchart 1 shows the procedure towards computation of a marine geoid from satellite altimetry observations can be summarized as follows:

  1. From the satellite altimetry observations using one of the standard tidal analysis techniques temporal sea level variations observed by satellite altimetry can be decomposed into tidal constituents and a constant (time invariant) part. The time invariant part is called Mean Sea Level (MSL).
  2. Using one of the current geopotential models, gravity potential values at the MSL points can be computed. For this one may resort to one of the current best geopotential models.
  3. Knowing the geoid’s potential value, as one of the fundamental geodesy parameters, the difference between geoid’s potential and the potential value at the MSL level can be computed. This difference corresponds to the separation between geoid and MSL and as such could be considered as the Sea Surface Topography (SST) in potential units or “SST in potential space”.
  4. Using a transformation formula SST value in potential space can be transferred into geometry space, in order to have SST as a height difference.
  5. Having computed SST and MSL the marine geoid can be readily computed by subtracting SST from MSL in point-wise manner.


Flowchart 1: Algorithmic procedure towards marine geoid from satellite altimetry observations.

This is a continuation of the work on the marine geoid computations, which has been developed during the past years within the Department of Surveying and Geomatics Eng. of the University of Tehran and the Geodetic Institute of the Stuttgart University, to which we refer via following major contributions: Ardalan (2002), Ardalan and Hashemi (2004), Ardalan and Grafarend (2002), Ardalan and Grafarend (2000), Ardalan et al. (2003), Ardalan et al. (2002), Grafarend and Ardalan (2000), Safari and Ardalan (2005).

With this introduction we proceed into our case study results at our test area “Persian Gulf and Oman Sea”.

Numerical Computations
In this section we present our numerical results derived by application of the algorithm explained in the Introduction, which is dedicated to our test area “Persian Gulf and Oman Sea”. Figure 1 shows our 720 computational points long track of TOPEX/Poseidon satellite over the test region.


Fig 1: 12 tracks and 720 computational points along track of TOPEX/Poseidon satellite over Persian Gulf and Oman Sea (our test area).

Figure 2 shows gravity potential of MSL at the 720 computational points, computed based on the ellipsoidal geopotential model SEGEN computed by Ardalan and Grafarend (1999) ).


Fig 2: Gravity potential of MSL at 720 computational points, computed based on the ellipsoidal geopotential model SEGEN.

Knowing the geoid’s potential value Wo and the computed gravity potential values at the MSL level, one can compute the difference between these two potential values point-wise. In this way we arrived at point-wise estimation of Sea Surface Topography (SST) in terms of potential units, or as we call it, “SST in potential space”. Having computed SST in potential space, Bruns type formulas, or transformations, can be used to convert the computed potential difference into height differences. Figure 3 shows the SST values at our test region once transformed from the potential space into the geometry space as was mentioned. This transformation needed for such transformation reads as follows:

Where, WMSL is the computed gravity potential value at the MSL level point-wise, Wo is the Geoid’s potential value, and gradW corresponds to the gradient of gravity potential at the differential distance between the geoid and MSL. In our computations we used SEGEN 1999 ellipsoidal geopotential model for both computation of WMSL and gradW.


Fig 3: Contour map presentations of SST values at 720 computational points in geometry space.

Finally, having available SST and the MSL, both in geometry space, a point-wise marine geoid estimation can be derived readily by subtraction of SST from MSL. Figure 4 shows such a marine Geoid computed at our test area.


Fig 4: The marine Geoid computed at our test area, as SST minus MSL..

Conclusions
In this paper we presented an algorithm for computation of the marine geoid, using satellite altimetry observations and geopotential model. Our approach is characterized by transformation of the MSL from geometry space into gravity potential space, where in gravity potential space the geoid can be presented by its potential value alone. This transformation enabled us to derive SST in potential space as the difference between MSL potential value and geoid’s potential value. Next using a Bruns like transformation relation the computed SST in potential space is transformed into geometry space in order to have SST as the geometrical deviation between geoid and MSL. Having SST and MSL in geometry space the marine geoid has been computed as the difference between these two heights. The next step in this computation procedure is verification and validation of the computed geoid values from other approaches, which we have left to a separate work.

References

  • Ardalan AA (2002), Special ellipsoidal gravity earth normal (SEGEN) program. Case studies: Ellipsoidal harmonic gravity disturbances, regional, continental, global maps of the vertical derivative of the incremental gravity potential. NCC scientific seminars. Tehran, Iran September 2002.
  • Ardalan AA and Hashemi H (2004) A new estimate for gravity potential value of geoid W0, SST, and global geoid based on 11 years of Topex/Poseidon satellite altimetry data. Geophysical Research Abstracts 6: 00663. European Geosciences Union 2004.
  • Ardalan AA and Grafarend EW (2002) From free-air and Bouguer anomalies to EGM / SEGEN gravity anomalies: Test computations of ellipsoidal harmonic gravity disturbances. Geophysical Research Abstracts 4. 27th General assembly of the European Geophysical Society. Nice, France 2002.
  • Ardalan AA and Grafarend EW (2000) Global geoid computation as a solution of the implicit function theorem: the spheroidal Bruns formula. Geophysical Research Abstracts Volume 2, G3.02, The Earth gravity field (joint EGS/AGU Nice/France 25-29 April 2000): Geoid use in engineering, geophysical and oceanographic applications, page 115.
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