IEEE Transactions on Geoscience and Remote Sensing, 2021
Coastal sea level variation as an indicator of climate change is extremely important due to its l... more Coastal sea level variation as an indicator of climate change is extremely important due to its large socioeconomic and environmental impact. The ground-based Global Navigation Satellite System (GNSS) reflectometry (GNSS-R) is becoming a reliable alternative for sea surface altimetry. We investigate the impact of antenna polarization and orientation on GNSS-R altimetric performance at different carrier frequencies. A one-year dataset of ground-based observations at Onsala Space Observatory using a dedicated reflectometry receiver is used. Interferometric patterns produced by the superposition of direct and reflected signals are analyzed using the Least-Squares Harmonic Estimation (LS-HE) method to retrieve sea surface height. The results suggest that the observations from GPS L1 and L2 frequencies provide similar levels of accuracy. However, the overall performance of the height products from the GPS L1 show slightly better performance owing to more observations. The combination of L1 and L2 observations (L12) improves the accuracy up to 25% and 40% compared to the L1 and L2 heights. The impacts of antenna orientation and polarization are also evaluated. A sea-looking Left-Handed Circular Polarization (LHCP) antenna shows the best performance compared to both zenith-and sea-looking Right-Handed Circular Polarization (RHCP) antennas. The results are presented using different averaging windows ranging from 15-minute to 6-hour. Based on a 6-hour window, the yearly Root Mean Square Error (RMSE) between GNSS-R L12 sea surface heights with collocated tide gauge observations are 2.4, 3.1, and 4.1 cm with the correlation of 0.990, 0.982, and 0.969 for LHCP sea-looking, RHCP sealooking, and RHCP up-looking antennas, respectively.
2021 IEEE International Geoscience and Remote Sensing Symposium IGARSS, 2021
Monitoring coastal sea level has gained a large socioeconomic and environmental significance. Gro... more Monitoring coastal sea level has gained a large socioeconomic and environmental significance. Ground-based Global Navigation Satellite System Reflectometry (GNSS-R) offers various geophysical parameters including sea surface height. We investigate a one-year dataset from January to December 2016 to evaluate the performance of GNSS-R coastal sea levels during different sea states. Our experiment setup uses three types of antenna in terms of polarization and orientation. A zenith-looking antenna tracks Right-Handed Circular Polarization (RHCP) signals and two sea-looking antennas capture both Left-Handed Circular Polarization (LHCP) and RHCP reflections. The Singular Spectrum Analysis (SSA) is used for extracting interferometric frequency from the data and calculating the heights. The results indicate that the height estimates from the sea-looking antennas have better accuracy compared to the zenith-looking orientation. The LHCP antenna delivers the best performance. The yearly Root Mean Square Errors (RMSE) of 5-min GNSS-R L1 water levels compared to the nearest tide gauge are 2.8 and 3.9 cm for the sea-looking antennas and 4.7 cm for the zenith-looking antenna with correlations of 97.63, 95.02, 95.35 percent, respectively. Our analysis shows that the roughness can both affect the GNSS-R retrieval accuracy and introduce a bias to the measurements.
The regional gravimetric geoid solved using boundary-value problems of the potential theory is us... more The regional gravimetric geoid solved using boundary-value problems of the potential theory is usually determined in two computational steps: (1) downward continuing ground gravity data onto the geoid using inverse Poisson's integral equation in a mass-free space and (2) evaluating geoidal heights by applying Stokes integral to downward continued gravity. In this contribution, the two integration steps are combined in one step and the so-called one-step integration method in spherical approximation is implemented to compute the regional gravimetric geoid model. Advantages of using the one-step integration method instead of the two integration steps include less computational cost, more stable numerical computation and better utilization of input ground gravity data (reduced in each integration step to avoid edge effects). A discrete form of the onestep integral equation is used to convert mean values of ground gravity anomalies into mean values of geoidal heights. To evaluate mean values of the integral kernel in the vicinity of the computation point, a fast and numerically accurate analytical formula is proposed using planar approximation. The proposed formula is tested to determine the regional gravimetric geoid of the Auvergne test area, France. Results show a good agreement of the estimated geoid with geoidal heights estimated at GNSS-levelling reference points, with the standard deviation for the difference of 3.3 cm. Considering the uncertainty of geoidal heights derived at the GNSS/levelling reference points, one can conclude the geoid models computed by the one-step and two-step integration methods have negligible differences. Thus, the one-step method can be recommended for regional geoid modelling with its methodological and numerical advantages.
The uncertainties of the geoidal heights estimated from ground gravity data caused by their spati... more The uncertainties of the geoidal heights estimated from ground gravity data caused by their spatial distribution and noise are investigated in this study. To test these effects, the geoidal heights are estimated from synthetic ground gravity data using the Stokes-Helmert approach. Five different magnitudes of the random noise in ground gravity data and three types of their spatial distribution are considered in the study, namely grid, semigrid and random. The noise propagation is estimated for the two major computational steps of the Stokes-Helmert approach, i.e., the downward continuation of ground gravity and Stokes's integration. Numerical results show that in order to achieve the 1-cm geoid, the ground gravity data should be distributed on the grid or semi-grid with the average angular distance less than 2. If they are randomly distributed (scattered gravity points), the 1-cm geoid cannot be estimated if the average angular distance between scattered gravity points is larger than 1. Besides, the noise of the gravity data for the tree types of their spatial distribution should be below 1 mGal to estimate the 1-cm geoid. The advantage of interpolating scattered gravity points onto the regular grid, rather than using them directly, is also investigated in this study. Numerical test shows that it is always worth interpolating the scattered points to the regular grid except if the scattered gravity points are sparser than 5.
This paper represents a milestone in the UNB effort to formulate an accurate and self-consistent ... more This paper represents a milestone in the UNB effort to formulate an accurate and self-consistent theory for regional geoid determination. To get the geoid to a sub-centimetre accuracy, we had to formulate the theory in a spherical rather than linear approximation, advance the modelling of the effect of topographic mass density, formulate the solid spherical Bouguer anomaly, develop the probabilistic downward continuation approach, incorporate improved satellite determined global gravitational models and introduce a whole host of smaller improvements. Having adopted Auvergne, an area in France as our testing ground, where the mean standard deviation of observed gravity values is 0.5 mGal, according to the Institute Geographique Nationale (Duquenne in Proceedings of the 1st international symposium of the international gravity field service “gravity field of the earth”, International gravity field service meeting, Istanbul, Turkey, 2006), we obtained the standard deviation of the gravity anomalies continued downward to the geoid, as estimated by minimizing the L2 norm of their residuals, to be in average 3 times larger than those on the surface with large spikes underneath the highest topographic points. The standard deviations of resulting geoidal heights range from a few millimetres to just over 6 cm for the highest topographic points in the Alpine region (just short of 2000 m). The mean standard deviations of the geoidal heights for the whole region are only 0.6 cm, which should be considered quite reasonable even if one acknowledges that the area of Auvergne is mostly flat. As one should expect, the main contributing factors to these uncertainties are the Poisson probabilistic downward continuation process, with the maximum standard deviation just short of 6 cm (the average value of 2.5 mm) and the topographic density uncertainties, with the maximum value of 5.6 cm (the average value of 3.0 mm). The comparison of our geoidal heights with the testing geoidal heights, obtained for a set of 75 control points (regularly spaced throughout the region), shows the mean shift of 13 cm which is believed to reflect the displacement of the French vertical datum from the geoid due to sea surface topography. The mean root square error of the misfit is 3.3 cm. This misfit, when we consider the estimated accuracy of our geoid, indicates that the mean standard deviation of the “test geoid” is about 3 cm, which makes it about 5 times less accurate than the Stokes–Helmert computed geoid.
Planar, spherical and ellipsoidal approximations of Poisson's integral in near zonePlanar, sp... more Planar, spherical and ellipsoidal approximations of Poisson's integral in near zonePlanar, spherical, and ellipsoidal approximations of Poisson's integral for downward continuation (DWC) of gravity anomalies are discussed in this study. The planar approximation of Poisson integral is assessed versus the spherical and ellipsoidal approximations by examining the outcomes of DWC and finally the geoidal heights. We present the analytical solution of Poisson's kernel in the point-mean discretization model that speed up computation time 500 times faster than spherical Poisson kernel while preserving a good numerical accuracy. The new formulas are very simple and stable even for regions with very low height. It is shown that the maximum differences between spherical and planar DWC as well as planar and ellipsoidal DWC are about 6 mm and 18 mm respectively in the geoidal heights for a rough mountainous area such as Iran.
Summary Generally, gravity anomaly is the difference between the observed acceleration of Earth&#... more Summary Generally, gravity anomaly is the difference between the observed acceleration of Earth's gravity and a normal value. Topography (all masses above geoid) plays a main role in definition of the gravity anomaly. Based on modeling of the effect of topography, there are different models of gravity anomaly such as free-air and Bouguer anomaly. The main goal of the Bouguer anomaly is removing of gravitational effect of all masses above the geoid (topography and atmosphere). This anomaly is widely used in exploration geophysics. In geodetic applications, in the absence of topography, Bouguer gravity anomaly is smooth and thus more suitable for interpolation and even stable downward continuation. In the other hand, gravity anomaly is the difference between real gravity at a point and normal gravity in corresponding point where the real and normal potentials in both points are the same. In geodesy, the gravity disturbance is defined as the difference between the real gravity obse...
The numerical results of downward continuation (DWC) of point and mean gravity anomalies by the P... more The numerical results of downward continuation (DWC) of point and mean gravity anomalies by the Poisson integral using point, single mean, and doubly averaged kernel are examined. Correct evaluation of the integral in its innermost zone is a challenging task. To avoid instabilities, an analytical planar approximation is used in the innermost integration zone. In addition it is shown that the single mean mode has the minimum discretization error. Downward continuation of point and mean anomalies by singly and doubly averaged kernel are the same mean anomalies on the geoid.
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Papers by Mehdi Goli