Absolute Calibration of Radar Altimeters: Consistency with Electromagnetic Modeling

Abstract

Empirical Ku-band altimeter model functions of near-nadir normalized radar cross-sectional σ° are compared to electromagnetic two-scale quasi-specular theory in the context of a standard sea wave spectral model. Three empirical model functions are tested: (i) the modified Chelton and Wentz model (WCM) using data from Geosat, (ii) the Callahan et al. model using data from TOPEX, and (iii) the Freilich and Vanhoff model using data from the Tropical Rainfall Measuring Mission (TRMM) precipitation radar (PR). These three models are basically very similar, except that they differ in terms of the level of absolute calibration. The difference between the absolute calibrations of the two extreme models (MCW and Freilich and Vanhoff) is as high as 1.9 dB. Assuming a sea wave spectrum similar to that used by Elfouhaily et al., the two-scale quasi-specular electromagnetic model is run, with a wave separation wavenumber kd adjusted so as to minimize the rms difference between the theoretical σ°(?) function and the empirical near-nadir model function. The quality of the best-fit solution is not perfect, however, because the shape and absolute level of the function σ°(?) cannot usually be adjusted simultaneously by the electromagnetic model. Taking the model function used by Freilich and Vanhoff as a reference, an offset is then introduced to the empirical model function, and the residual error is computed as a function of the offset. The overall quality of the fit is shown to be best when a ?1.1 dB offset is introduced into the Freilich and Vanhoff model function. To within 0.1 dB, this corresponds to the offset that would be required to match Callahan et al.?s model function. This result is obtained in a context where the effect of the peakedness of the sea surface was assumed negligible. When this effect is introduced, with a peakedness parameter ? assumed to be independent of wind speed and taken tentatively as ? = 0.23, as suggested by Chapron et al., the optimal offset is then found to be ?0.2 dB, thus indicating that for this example the best consistency with electromagnetic modeling is closer to Freilich and Vanhoff?s calibration. A more refined assessment would require accurate measurements of the parameter ? involving both magnitude and variability with wind speed. Such accurate measurements are, unfortunately, not available at this time.