Numerical Computation of the Electromagnetic Bias in GNSS-R Altimetry

Abstract

In radar altimetry the electromagnetic (EM) bias is originated by the smaller reflectivity of wave crests than troughs, thus the average sea surface height is under-estimated. Bias uncertainty is currently the largest factor in altimetry error budgets. The EM bias in a bistatic forward-scattering configuration at L-band, such as in Global Navigation Satellite SystemsReflectometry (GNSS-R) altimetry, remains one of the major sources of uncertainty in the altimetry error budget. In this work the EM bias is computed using numerical simulations.To do so, a time-dependent synthetic non-Gaussian sea surface is created using the PiersonMoskowitz and Elfouhaily sea surface height spectra and spreading function. The sea surface is then discretized in facets and "illuminated" using a Right Hand Circular Polarization data at C-and Ku-bands. Then, the numerical model is applied at L-band, for bistatic configurations, including different azimuth angles, and different wind speeds. It is found that the EM bias is almost insensitive to the sea surface spectra selected and increases with increasing wind speed and incidence/scattering angle (up to ~20 cm at θi,s = 45° and U10 = 12 m/s), and it also exhibits a non-negligible azimuthal dependence, that must be accounted for in the error budgets of upcoming GNSS-R altimetry missions.

A Conceptually Simple Modeling Approach for Jason-1 Sea State Bias Correction Based on 3 Parameters Exclusively Derived from Altimetric Information

“…An electromagnetic bias (EM) evidenced by the signal-surface interactions, where ocean wave troughs are better radar reflectors than wave crests, thus overestimating the measured satellite-to-surface range. The EM bias perturbs all microwave frequencies with wavelengths of a few centimeters, affecting not only the Ka-, C-, and Ku-bands regularly used for satellite altimetry [1,2], but also the L-band frequency usually adopted for Global Navigation Satellite Systems Reflectometry (GNSS-R) altimetry [3]. In addition to EM bias, the SSB is also characterized by a skewness bias linked to the effect of a non-Gaussian surface height distribution, inducing an error due to the difference between the determined median sea surface and the true mean sea surface (MSS), and finally, a tracker bias which can occur due to both instrumental and retracking effects.…”

Time-domain Statistics of the Electromagnetic Bias in GNSS-Reflectometry

“…Nowadays, one of the promising applications of GNSS-R is mesoscale altimetry, originally proposed in 1993 [2] using the Global Positioning System (GPS) signals. As in conventional nadir-looking radar altimetry, in order to achieve the centimetric accuracy [3] required to track the mean sea level and its spatio-temporal variations, related to large-scale circulation, ocean currents and eddies, or El Niño events, one of the challenging errors to be corrected for is the EM bias, which in GNSS-R it also exhibits a dependence with the elevation and azimuth angles [4]. The EM bias has been a matter of research during the past decades in conventional radar altimetry, but very few studies exist for GNSS-R.…”

“…Recently, the EM bias was numerically computed for bistatic GNSS-R altimeters using the Geometric Optics (GO) method [15] in a two-dimensional scenario, and then improved using the Physical Optics (PO) method [4] under the Kirchhoff Approximation (KA). In [4], this model was validated against the combined model [13,14], and then extended to L-band.…”

“…In [4], this model was validated against the combined model [13,14], and then extended to L-band. An angular dependence not only with the incidence/scattering angle, but with the azimuth angle was found as well, in addition to the wind speed dependence.…”

“…In this study, the sea surface is generated using Elfouhaily's spectrum and spreading function [16], because of its capability to generate the full wave spectra (long and short waves), and an ocean surface height with a non-Gaussian probability density function (as confirmed in [4] following the procedure described in [17]). …”