Proceedings with Extended Abstracts (single PDF file) - Radio ...

to perform simulations for a wide variety of V mag values. We actually produce parameters V off(offset), P V0 (peak power) and V 1/2 (half-width). Then it is necessary to perform the integralshown above for a wide variety of different wind speed directions, layer ranges (R), rangeoffsets from the pulse-peak (R-R 0 ), radar pulse lengths, and polar diagram parameters, andproduce empirically fitted functions for each of these dependencies. Often polynomial fits,Gaussians and exponentials are suitable fitting-functions. As an example, sample graphs ofthe dependence of the frequency offset and spectral width as a function of (R-R 0 ) were shownin the insets of figs. 8 and 9 of Hocking (1983). Due to lack of space, we cannot specify thedependencies determined in detail, but all of the variables V off , P V0 and V 1/2 depend on θ t (theradar zenithal tilt angle), V perp /V mag and V par /V mag (normalized components of the windparallel and perpendicular to the azimuthal direction of beam tilt), R, R-R 0 , θ 1/2 (the radarbeam half-power half-width), the sub-layer depth, and θ s .Fig. 2. Diagram showing the dependencies of the spectra produced from thin layers as afunction of various atmospheric and radar parameters.The key parameters V off , V 1/2 and P V0 should be parameterized, and stored as computersubroutines. Sometimes such computer subroutines are called “look-up tables”. Then, forany realistic wind profile, the scattering region can be considered to be composed of manysub-layers, each with different wind speeds, as shown in fig. 2. For a VHF radar, a sub-layerdepth of 50 m (less than the normal buoyancy scales for turbulence) might be typical. The“look-up tables” described above can be used to determine appropriate values for V off , V 1/2and P V0 for each sub-layer, and then these can be converted to matching parameters f off , P 0and f 1/2 . Care is required to ensure that an appropriate Jacobian is used in the conversion. Theconversion will be different for each sub-layer, depending on the value of V mag within eachsub-layer. The parameters f off , P 0 and f 1/2 now describe the spectrum as a function of trueDoppler frequency for each sub-layer. Once the parameters P 0 , f off and f 1/2 have been deducedfor each sub-layer, the spectrum can be explicitly calculated as a function of frequency.Then the spectral values from each sub-layer are added together at user-specified frequenciesvarying from some reasonable minimum to a reasonable maximum value, to produce thefinal spectrum. It is quite possible that the resultant spectrum is asymmetric, and largenumbers of numerical experiments have demonstrated that this procedure quite closelyproduces the true spectrum determined from the full integral. Spectral half-power half-widthvalues may now be found by simple search algorithms applied to the final spectrum. Theprocedure properly considers pulse-length dependencies, and anisotropic scatter – factors216