Wavelet analysis of high-resolution temperature data with applications to radio wave scattering

High-resolution balloon-borne temperature measurements have been made in the troposphere and stratosphere during late fall over the western plains of the United States. In one such experiment the data are of remarkable quality and quite suitable for investigating methods of separating organized and turbulent features from a geophysical data stream, exploring atmospheric dynamics, and estimating VHF radar backscatter. We are particularly interested in the mechanisms creating aspect sensitivity, i.e., a nonunity ratio of vertical to well off-vertical radar backscatter. We find that very steep positive vertical temperature gradients, as high as 40.0 K/km, can be supported. On the other hand, negative gradients are limited to values near the marginal stability boundary. The structures are thus anisotropic and similar to ramp cliff features found in other fluids. We use wavelet analysis to isolate the organized components of the signal and, after subtraction, the residual signal is investigated to determine its character. The Fourier transform of the residual is Kolmogorov in nature, unlike that of the original data stream, and yields C-n(2), the refractive index structure parameter, in good agreement with the higher-order structure function approach; this supports the success of our partition. We calculate the Fresnel reflection coefficient using the wavelet coefficients; the turbulent scatter is found using C-n(2). The ratio between the Fresnel scatter and the turbulent scatter, i.e., the aspect sensitivity, is similar to 10 decibels in the troposphere and over 20 decibels in the stratosphere, in agreement with published observations and supporting our assumption that the organized features have horizontal extent exceeding the Fresnel scale.