The Probability Distribution of NSCAT Measurements

NSCAT makes only indirect measurements of wind. The direct measurement is of the backscattered radar power. The signal power is contaminated by radiometric noise so a separate measurement of the noise power is subtracted from the signal-plus-noise measurement to estimate the backscattered power. Using the radar equation, o is computed from the measured signal power. From multiple o measurements made at di erent azimuth angles, the wind is estimated. In wind retrieval, the NSCAT o measurements are assumed to have a Gaussian probability distribution with a variance which depends on the mean. Given this distribution model, the maximum-likelihood estimator is formed and optimized to estimate the wind. Because of the on-board signal processing used by NSCAT, the Gaussian distribution model for the measurements is only an approximation to the actual distribution. Working from rst principles and the design of the NSCAT signal processor we derive the distribution of the NSCAT measurements as a function of the surface , the signal to noise ratio and the cell number. The resulting distribution is skewed relative to the traditional Gaussian model. Simple compass simulations are used to compare the accuracy of winds estimated using the actual and Gaussian model distributions.