Scatterometer data interpretation: Estimation and validation of the transfer function CMOD4

TLDR

MLE methods must be applied cautiously with nonlinear relationships or measurement‑dependent errors, and prior work shows backscatter triplets form a coherent conical surface, with representativeness error explaining unexpected results. The study estimates the 18 coefficients of the CMOD4 σ0‑to‑wind transfer function via MLE to improve the prelaunch function and proposes a validation strategy that tests the function’s fit to the conical backscatter surface. The authors estimate the CMOD4 coefficients with a maximum‑likelihood approach, using wind components, logarithmic σ0, and well‑sampled data, and compute an objective measure of the transfer function’s average fit to the measured σ0 triplet distribution. CMOD4 fits the conical backscatter surface within ~0.2 dB (≈0.5 m s⁻¹ RMS error), yields scatterometer winds that outperform conventional surface data when compared to ECMWF model winds (≈3.0 m s⁻¹ RMS difference), and shows no significant spatial wind.

Abstract

In this paper we estimate the 18 coefficients of the CMOD4 σ 0 ‐to‐wind transfer function using a maximum likelihood estimation (MLE) method in order to improve the prelaunch function. We show that a MLE method has to be used with caution when dealing with a nonlinear relationship or with measurement errors that depend on the measured values. In the transfer function estimation it is crucial to use the components of the wind, rather than wind speed and direction, to use σ 0 in logarithmic units rather than physical ones, and to use well‐sampled input data. In Stoffelen and Anderson [1997a] we showed that the triplets of measured backscatter are very coherent and, when plotted in a three‐dimensional measurement space, they lie on a well‐defined conical surface. Here we propose a strategy for validation of a transfer function, the first step of which is to test the ability of a transfer function to fit this conical surface. We derive an objective measure to compute the average fit of the transfer function surface to the distribution of measured σ 0 triplets. The transfer function CMOD4, derived in the first part of this paper, is shown to fit the cone surface to within the observed scatter normal to the cone, i.e., within roughly 0.2 dB, equivalent to a root‐mean‐square wind vector error of ∼0.5 m s −1 The second step in the validation strategy is the verification of retrieved scatterometer winds at each position on the cone surface. Scatterometer winds computed from CMOD4 compare better to the European Centre for Medium‐Range Weather Forecasts model winds than real‐time conventional surface wind data (ship, buoy, or island reports) with the root‐mean‐square wind vector difference typically 3.0 m s −1 . This surprising result can be explained by the so‐called representativeness error. We further show that no significant spatial wind error correlation is present in scatterometer data and therefore conclude that the ERS 1 scatterometer provides winds useful for weather forecasting and climate studies.