Ismael Foroughi

Determining the Gravitational Gradient Tensor Using Satellite-Altimetry Observations over the Persian Gulf

With the advent of satellite altimetry in 1973, new scientific applications became available in oceanography, climatology, and marine geosciences. Moreover, satellite altimetry provides a significant source of information facilitated in the geoid determination with a high accuracy and spatial resolution. The information from this approach is a sufficient alternate for marine gravity data in the high-frequency modeling of the marine gravity field quantities. The gravity gradient tensor, consisting of the second-order partial derivatives of the gravity potential, provides more localized information than gravity measurements. Marine gravity observations always carry a high noise level due to environmental effects. Moreover, it is not possible to model the high frequencies of the Earths gravity field in a global scale using these observations. In this article, we introduce a novel approach for a determination of the gravity gradient tensor at sea level using satellite altimetry. Two numerical techniques are applied and compared for this purpose. In particular, we facilitate the radial basis functions (RBFs) and the harmonic splines. As a case study, the gravitational gradient tensor is determined and results presented in the Persian Gulf. Validation of results reveals that the solution of the harmonic spline approach has a better agreement with a theoretical zero-value of the trace of the Marussi gravitational gradient tensor. However, the data-adaptive technique in the RBF approach allows more efficient selection of the parameters and 3-D configuration of RBFs compared to a fixed parameterization by the harmonic splines.

Does Poisson’s downward continuation give physically meaningful results?

The downward continuation (DWC) of the gravity anomalies from the Earth’s surface to the geoid is still probably the most problematic step in the precise geoid determination. It is this step that motivates the quasi-geoid users to opt for Molodenskij’s rather than Stokes’s theory. The reason for this is that the DWC is perceived as suffering from two major flaws: first, a physically meaningful DWC technique requires the knowledge of the irregular topographical density; second, the Poisson DWC, which is the only physically meaningful technique we know, presents itself mathematically in the form of Fredholm integral equation of the 1st kind. As Fredholm integral equations are often numerically ill-conditioned, this makes some people believe that the DWC problem is physically ill-posed. According to a revered French mathematician Hadamard, the DWC problem is physically well-posed and as such gives always a finite and unique solution. The necessity of knowing the topographical density is, of course, a real problem but one that is being solved with an ever increasing accuracy; so sooner or later it will allow us to determine the geoid with the centimetre accuracy.

Local evaluation of Earth Gravitational Models, case study: Iran

Global gravity models are being developed according to new data sets available from satellite gravity missions and terrestrial/marine gravity data which are provided by different countries. Some countries do not provide all their available data and the global gravity models have many vague computational methods. Therefore, the models need to be evaluated locally before using. It is generally understood that the accuracy of global gravity models is enough for local (civil, mining, construction, etc.) projects, however, our results in Iran show that the differences between synthesized values and observation data reach up to ∼300 mGal for gravity anomalies and ∼2 m for geoid heights. Even by applying the residual topographical correction to synthetized gravity anomalies, the differences are still notable. The accuracy of global gravity models for predicting marine gravity anomalies is also investigated in Persian Gulf and the results show differences of ∼140 mGal in coastal areas. The results of evaluating selected global gravity models in Iran indicate that the EIGEN-6C4 achieves the lowest RMS for estimating the geoid heights. EGM08 predicts the closest results to terrestrial gravity anomalies. DIR-R5 GOCE satellite-only model estimates the low-frequency part of gravity field more accurately. The best prediction of marine gravity anomalies is also achieved by EGM08.

Effect of the Mean Dynamic Topography on the Geoid-to-Quasigeoid Separation Offshore

ABSTRACT It is commonly acknowledged that offshore the quasigeoid very closely coincides with the geoid. Nevertheless, the numerical assessment supporting this assumption has not yet been provided. Moreover, the rigorous definition of the quasigeoid surface and consequently the geoid-to-quasigeoid separation offshore is not given in geodetic literature. To address these issues, we define in this study the quasigeoid surface offshore in the context of the mean sea level. We then derive the spectral expressions for computing the geoid-to-quasigeoid separation offshore and apply these expressions estimate the vertical separation between the geoid and the quasigeoid over the worlds oceans and marginal seas using the global dataset of the DTU15 mean dynamic topography. By taking the analogy of defining the geoid-to-quasigeoid separation inland by means of the disturbing potential differences of values evaluated on the geoid and at the topographic surface, the computation offshore is practically realized from values of the disturbing potential on the geoid and at the mean sea surface. Our result shows that the geoid-to-quasigeoid separation offshore is completely negligible, with most of the values within the interval ±0.3 mm.

Spatiotemporal monitoring of upwelled water motions using optical flow method in the Eastern Coasts of Caspian Sea

Abstract. Upwelling is an oceanographic process that transfers cool and nutrient-rich waters toward the sea surface. Due to the relation between low sea surface temperature (SST) and high nutrient-rich water, the upwelling regions can be easily recognized in satellite imagery. An optical flow (OF) method, Horn–Schunck, is used to discover the upwelled water motion (UWM) and its pattern using sequential (pair) SST imageries. The SST imageries of Aqua and Terra satellites between 2004 and 2012 are processed to extract the properties of upwelling in the Shevchenko area (Caspian Sea). Results show that the upwelling is periodic (with an ∼24  h period) and it matches with a Fourier model. In addition, the UWM has a specific direction from morning to night. It is also shown that the OF cannot extract correct UWM if the SST imageries are selected on different cycles. Level of chlorophyll_a in the same area is used to independently validate the existence of the upwelling.

Optimal Combination of Satellite and Terrestrial Gravity Data for Regional Geoid Determination Using Stokes-Helmert’s Method, the Auvergne Test Case

The precise regional geoid modelling requires combination of terrestrial gravity data with satellite-only Earth Gravitational Models (EGMs). In determining the geoid using the Stokes-Helmert approach, the relative contribution of terrestrial and satellite data to the computed geoid can be specified by the Stokes integration cap size defined by the spherical distance ψ0 and the maximum degree l0 of the EGM-based reference spheroid. Larger values of l0 decrease the role of terrestrial gravity data and increase the contribution of satellite data and vice versa for larger values of ψ0. The determination of the optimal combination of the parameters l0 and ψ0 is numerically investigated in this paper. A numerical procedure is proposed to find the best geoid solution by comparing derived gravimetric geoidal heights with those at GNSS/levelling points. The proposed method is tested over the Auvergne geoid computation area. The results show that despite the availability of recent satellite-only EGMs with the maximum degree/order 300, the combination of l0 = 160 and ψ0 = 45 arc-min yields the best fitting geoid in terms of the standard deviation and the range of the differences between the estimated gravimetric and GNSS/levelling geoidal heights. Depending on the accuracy of available ground gravity data and reference geoidal heights at GNSS/levelling points, the optimal combination of these two parameters may be different in other regions.

The Effect of Noise on Geoid Height in Stokes-Helmert Method

Noises are an inevitable part of gravity observations and they can affect the accuracy of the height datum if they are not treated properly in geoid determination. To provide data for geodetic boundary value problems, surface gravity observations must be transferred harmonically down to the geoid, which is called Downward Continuation (DC). Fredholm integral of the first kind is one of the physically meaningful ways of DC, where the Poisson kernel is used to evaluate the data on the geoid. DC behaves inherently as a high pass filter so it magnifies existing noise in Helmert gravity anomalies on geoid (free air anomalies after applying the Helmert’s second condensation method); although the results on the geoid will be later smoothed by evaluating the Stokes’s integral so the noise is less pronounced in the final geoid heights. The effect of noise in Stokes-Helmert geoid determination approach is numerically investigated in this study. The territory of Iran, limited to 44–62° longitude and 24–40° latitude, is considered as the area of interest in this study. The global gravity model EGM2008, up to degree/order 2160, is used to synthesize the free air gravity anomalies on a regular grid on topography and are then transferred to Helmert space using available Digital Elevation Models (DEMs). Different levels of noise are added to the data and the effects of noise are investigated using the SHGeo software package, developed at the University of New Brunswick (UNB). Results show that if the downward continuation of 5*5 arc-min surface points is required, the standard deviation of differences between “noisy” and “clean” data on the geoid will increase by 15% with respect to the corresponding standard deviation on topography. These differences will increase for denser grid resolutions. For example, the noise of ∆g on geoid will increase up to 100% if 1*1 arc-min points are used. The results of evaluating the Stokes integral show smoother results in terms of noise in the data. For example, 2 mGal noise in the gravity anomalies on a 5*5 arc-min grid can cause 1.5 cm of error in the geoid heights. This value is smaller when denser grids are used. Despite increasing noise in downward continuation steps, the results show smaller error in geoid heights if gravity anomalies are located on a denser grid.

Rigorous Evaluation of Gravity Field Functionals from Satellite-Only Gravitational Models Within Topography

Currently, extensive work is being done in the field of geodesy on producing better gravitational models using purely space-based techniques. With the large datasets spanning a long timeframe, thanks to the GOCE and GRACE missions, it is now possible to compute high quality global gravitational models and publish them in a convenient form: spherical harmonics. For regional geoid modeling, this is advantageous as these models provide a useful reference which can be improved with terrestrial observations. In order for these global models to be usable below the topographical surface, certain considerations are required; topographical masses cause the function that describes the gravity potential to be non-harmonic in the space between the topographical surface and the geoid. This violates the mathematical assumptions behind solid spherical harmonics.

Computation of precise geoid model of Auvergne using current UNB Stokes-Helmert’s approach

Abstract The aim of this paper is to show a present state-of-the-art precise gravimetric geoid determination using the UNB Stokes-Helmert’s technique in a simple schematic way. A detailed description of a practical application of this technique in the Auvergne test area is also provided. In this paper, we discuss the most problematic parts of the solution: correct application of topographic and atmospheric effects including the lateral topographical density variations, downward continuation of gravity anomalies from the Earth surface to the geoid, and the optimal incorporation of the global gravity field into the final geoid model. The final model is tested on 75 GNSS/levelling points supplied with normal Molodenskij heights, which for this investigation are transformed to rigorous orthometric heights. The standard deviation of the computed geoid model is 3.3 cm without applying any artificial improvement which is the same as that of the most accurate quasigeoid.