Spatial variances of wind fields: their sensitivity to sampling strategy and their relation to second-order structure functions and spectra

A statistical quantity called spatial variance is defined. It combines the advantages of spectral variance calculations and spatial statistics like second-order structure functions. In particular, spatial variances have a clear interpretation and are tolerant for missing data. They can be related in an exact manner to second-order structure functions, both for discrete and continuous data. The flexibility of spatial variances is used to study various sampling strategies, and to compare them with second-order structure functions and spectral variances. It is shown that spectral sampling is biased to calm conditions for scatterometer ocean surface winds, thus underestimating the variance by a factor of about 2. Moreover, variances calculated in the spectral domain over a finite interval can not be easily transformed to the spatial domain. Finally it is shown that one-fifth of the second-order structure function value is a good proxy for the cumulative variance.