Cramer-Rao bound for wind estimation from scatterometer measurements

A wind scatterometer makes measurements of the normalized radar backscatter coefficient, σ⁰, of the surface. To retrieve the wind, a Geophysical Model Function (GMF), which relates σ⁰ to the near-surface wind, is used. The wind vector is estimated using maximum likelihood techniques from the σ⁰ measurements. The probability density of the measured σ⁰ is assumed to be Gaussian with a variance that depends on the true σ⁰ and therefore the wind through the GMF. The measurements from different azimuth angles are assumed independent in estimating the wind. Given this model for wind estimation, the Cramer-Rao bound is derived for wind estimation, and its implications for wind retrieval are discussed. As part of this discussion, the role of geophysical modeling error is considered and shown to play a significant role in the performance of near surface wind estimates