Spatial variances of wind fields and their relation to second‐order structure functions and spectra

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). Both techniques give an order‐of‐magnitude estimate. More accurate estimates are given by a statistic called spatial variance. 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. 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. When the second‐order structure function behaves like , its ratio with the spatial variance equals . Ocean surface winds in the tropics have between 2/3 and 1, so one‐sixth to one‐fifth of the second‐order structure function value is a good proxy for the cumulative variance.