Validation of Vector Magnitude Datasets: Effects of Random Component Errors

A statistically consistent and physically realistic approach for validating vector magnitude measurements is developed, based on a model for random measurement noise that explicitly satisfies a nonnegativity constraint for all ‘‘noisy’’ vector magnitude measurements. Numerical and analytic approximations are used to quantify the nonlinear functional dependence of sample conditional means on true values and component noise magnitudes. In particular, it is shown analytically that random component errors will result in overall vector magnitude biases. A simple nonlinear regression of measured sample conditional mean vector magnitudes (calculated from traditional collocated data) against Monte Carlo simulation results is proposed for determining both deterministic trends and random errors in the data to be validated. The approach is demonstrated using Seasat and ERS-1 scatterometer measurements and collocated buoy data. The approach accounts well for the observed qualitative features of the collocated datasets and yields realistic values of random component error magnitudes and deterministic gain and offset for each dataset. An apparent systematic insensitivity of scatterometers at low wind speeds is shown to be a consequence of random component speed errors if it is assumed that the comparison buoy measurements are error free.