Rain estimation from partially filled scattering volumes

Atmospheric parameters retrieved by remote sensing techniques often represent averages over considerable space or time intervals. Unresolved variability of corresponding primary physical values is a problem as soon as non-linear relations between the primary physical value and the retrieved parameter come into play, as for example the R(Z)relation between radar reflectivity Z and rain rate R. While this is recognized to be a crucial issue for many space based techniques (particularly for cloud and rainfall retrievals) due to the large sensor footprints (Durden et al. 1998, Heymsfield et al. 2000), ground based radar measurements of rainfall are sometimes considered as a reference having sufficient resolution with negligible unresolved variability. On the other hand precipitation is known to show strong variability even on very small scales. There is in fact evidence that no scale exists for spatial hydrometeor distributions, where Poisson statistics would be an adequate description analogue to molecules of a gas in thermodynamic equilibrium (Jameson, 2005). Radar calibration using distrometerdata is therefore faced with the problem of non-matched spatial resolution of distrometerand radar-data respectively. If radar rain fall is adjusted with rain gauge networks, one may argue, that such effects are included already in the adjustment. But this argument would hold only, if the pertinent spatial distribution parameters would be universal for all rain events. In addition, the spatial resolution of radar data (at least of raw data) is range dependent.