Numerical analysis of the sea state bias for satellite altimetry

Abstract

Theoretical understanding of the dependence of sea state bias (SSB) on wind wave conditions has been achieved only for the case of a unidirectional wind‐driven sea [Jackson, 1979; Rodriguez et al., 1992; Glazman and Srokosz, 1991]. Recent analysis of Geosat and TOPEX altimeter data showed that additional factors, such as swell, ocean currents, and complex directional properties of realistic wave fields, may influence SSB behavior. Here we investigate effects of two‐dimensional multimodal wave spectra using a numerical model of radar reflection from a random, non‐Gaussian surface. A recently proposed ocean wave spectrum is employed to describe sea surface statistics. The following findings appear to be of particular interest: (1) Sea swell has an appreciable effect in reducing the SSB coefficient compared with the pure wind sea case but has less effect on the actual SSB, owing to the corresponding increase in significant wave height. (2) Hidden multimodal structure (the two‐dimensional wavenumber spectrum contains separate peaks, for swell and wind seas, while the frequency spectrum looks unimodal) results in an appreciable change of SSB. (3) For unimodal, purely wind‐driven seas, the influence of the angular spectral width is relatively unimportant; that is, a unidirectional sea provides a good qualitative model for SSB if the swell is absent. (4) The pseudo wave age is generally much better for parametrizing the SSB coefficient than the actual wave age (which is ill‐defined for a multimodal sea) or wind speed. (5) SSB can be as high as 5% of the significant wave height, which is significantly greater than predicted by present empirical model functions tuned on global data sets. (6) Parameterization of SSB in terms of wind speed is likely to lead to errors due to the dependence on the (in practice, unknown) fetch.

An investigation of altimeter sea state bias theories

“…Here, we examine the dependence of the SSB on environmental parameters using the theoretical SSB calculated for the wave spectra obtained for the idealized WAM runs. As indicated earlier, a number of previous papers have investigated the behavior of the SSB with swell, varying wind and fetch conditions [ Glazman et al , 1994, 1996] and we will not rehearse their findings here. Instead, we make use of the unusually wide range of wind/wave/current conditions generated by WAM to examine the dependence of the theoretical SSB coefficient with wind speed, SWH and wave slope for these conditions.…”

“…The available data sets enable a number of issues to be examined: First, the use of WAM wave spectra allows us to compute the theoretical SSB for a wide range of wind/wave/currents conditions unlikely to occur in any time‐limited location‐specific experiment. Since the dependence of SSB on wind speed, sea state and the presence/absence of swell was already investigated extensively in previous studies [ Glazman et al , 1996; Glazman et al , 1994], we will not rehearse these here. The wide range of wind/wave/currents conditions generated within WAM does however provide the opportunity to examine the relative robustness of the relationships between the theoretical SSB and wind speed, wave height and wave slope over a wide range of conditions.…”

Numerical Computation of the Electromagnetic Bias in GNSS-R Altimetry

“…The impact of long waves is a modulation of the radar crosssection density (σ 0 ) by the waves' slopes, which is actually correlated to the surface's elevation, because of the non-linear processes caused by the wave-wave interactions. The coupling effect between long and short waves is also accounted for in the EM bias computation [8,10,15,16,24].…”

“…The estimation of the EM bias for a two-dimensional surface using the WNL theory was proposed in [15,16], although it is applicable only for long waves. To overcome the previous limitations, in [8] a modified WNL theory was proposed to estimate the EM bias applying a unified directional sea surface spectrum that was able to account for long and short waves [17].…”

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

“…Later, it was estimated using the Weakly Non Linear (WNL) theory in a one-dimensional scenario [6]. The estimation of the EM bias for two-dimensional surfaces was first performed in [7,8], and then using the WNL theory [9]. The Modulation Transfer Function (MTF) was used to estimate the EM bias taking into account the statistics of the local short-waves over the long ones [10].…”