AN INTEGRAL EQUATION METHOD FOR DUAL-WAVELENGTH RADAR DATA USING A WEAK CONSTRAINT 5A.2

A set of integral equations for dual-wavelength radar data provides a means of estimating liquid water content and parameters of the particle size distribution (PSD) [Meneghini et al., 1997] and constitutes a potential algorithm for the proposed DPR (Dual-wavelength Precipitation Radar) on the Global Precipitation Mission (GPM) satellite [Iguchi et al., 2002]. One version of the method, the forward-recursion, starts at the storm top. Although this implementation requires no constraint, like the Hitschfeld-Bordan (1954) solution, it tends to be unstable when the path attenuation becomes significant. As such, the method can be applied with confidence only in regions of frozen hydrometeors or light rain. For moderate rain or mixed-phase precipitation, the backward recursion is preferable because it is more robust. The backward recursion, however, requires constraints of path-integrated attenuation (PIA) down to the surface at both wavelengths, estimates of which have typically come from the surface reference technique (SRT).