Spatial Variances of Wind Fields and Their Relation to Second-Order Structure Functions and Spectra

Abstract:

Kinetic energy variance as a function of spatial scale for wind fields is commonly estimated either using second-order structure functions (in the spatial domain) or by spectral analysis (in the frequency domain). It will be demonstrated that neither spectra nor second-order structure functions offer a good representation of the variance as a function of scale. These difficulties can be circumvented by using a statistical quantity called spatial variance. It combines the advantages of spectral analysis and spatial statistics. In particular, when applied to observations, spatial variances have a clear interpretation and are tolerant for missing data. They can be related to second-order structure functions, both for discrete and continuous data. For data sets without missing points the relation is statistically exact. Spatial variances can also be Fourier transformed to yield a relation with spectra. 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 the spectral sampling strategy is not seriously biased to calm conditions for scatterometer ocean surface vector winds, and that one-fifth of the second-order structure function value is a good proxy for the cumulative variance.