PPP, Fourier Transform and Spectrum Width Estimates from Scanning Radar Measurements

This study will show that the existing analytical expression of the effective beam power pattern for a scanning radar is applicable only to the reflectivity measurement; For the measurements of the higher moments the analytical expression of the power pattern is different. However, the difference is trivial and usually negligible. The effective beam pattern results from the combination of antenna rotation and signal processing. It is well-known that the effective beam width is the function of radar antenna rotation rate, but here we show that it is also the function of the antenna elevation angle. Doppler spectrum width, a parameter of great importance for retrieving microphysical and turbulence properties, can be estimated from the Doppler spectrum that is obtained by Fourier transformation (FT) of the normalized autocorrelation function of the radar signals. It can also be estimated from lagged one, i.e. Pulse-Pair-Processing (PPP), or from lagged one and lagged two correlation functions of the radar signals. It will be shown that the spectrum width equation depends on the signal processing method. The one for the estimate obtained using the FT method is different from that for the estimate obtained using pulse-pair processing method. Recognizing and paying attention to this difference is very important when using radar measured spectrum width to investigate microphysical and turbulence properties in clouds and storms. The data collected by an Atmospheric Radiation Measurement program scanning radar of the Department of Energy is used to investigate the spectrum width estimate errors associated with the misusing of the formulas in the signal processing.