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

Fig.1. Lines of constant radial velocity at a fixed height H.This function can be accurately calculated, and this was done by Hocking (1983) for onespecific set of polar diagrams. However, the integration is not trivial, requiring (a) anaccurate polar diagram determination, (b) a good representation of the transmitted pulse, (c) aconvolution and (d) integration over (θ,φ) space along the contours shown in fig. 1. Thecomputation can be very time-intensive, and many authors have avoided performing the fullintegration for real-time applications. This has in turn led to occasional poor representationsof the beam-broadened spectral width.However, it is a relatively simple (although lengthy) task to utilize this equation in its mostcomplete form for real-time applications, and the purpose of this paper is to demonstrate thatnot only is this feasible, but in fact it has already been done. Examples are discussed.The Procedure.Fig. 2 shows a typical (non-linear) wind profile, which has been divided into thin layers. Inany realistic situation, the wind is sampled only at discrete range-intervals. Often the wind issampled at a resolution equal to the pulse length, but it is advantageous to sample at higherresolution. In any case, a good estimate of the true wind profile can be obtained byinterpolation using a linear spline in both the north-south and east-west components.Although the optimum interpolation method can be the subject of debate, any reasonablefitting procedure will generally be far superior to assuming a constant wind speed, or usinglinear interpolation. We use a cubic spline. Sample spectra are shown in fig. 2 for layers Aand B. (As a warning, it should be noted that the spectral width does not just depend on thewind speed in the direction of tilt, but rather the total magnitude of the wind speed. Hencealthough the spectrum for layer B has been drawn as a narrow one, in reality it could be aswide as that for A if the wind perpendicular to the page in layer B were large.)In order to accurately determine the spectrum, the key spectral parameters are parameterizedas functions of various variables. We only need to do this for a thin representative sub-layer,like the one labeled as A in fig. 2. For thin layers, the spectrum can be accurately representedas a Gaussian with spectral offset (f off ), peak power (P 0 ) and spectral width (f 1/2 ). In realitywe do not determine the frequency spectrum directly, but determine the spectrum of thenormalized radial velocity V = v r /V mag , where v r is the radial velocity seen by the radar andV mag is the speed of the horizontal wind in the layer. Choice of this variable avoids the need215