Modelling and Estimation of Characteristics of the Rainfall Distribution

Rainfall varies in space and time in a highly irregular manner and is described naturally in terms of a stochastic process. A characteristic of rainfall statistics is that they depend strongly on the space-time scales over which rain data are averaged. A spectral model of precipitation has been developed based on a stochastic differential equation of fractional order, which allows concise description of the second moment statistics over any space-time averaging scale. The model is thus capable of providing a unified description of both radar and rain gauge data. We test the model with radar and gauge data collected contemporaneously at the NASA TRMM ground validation sites located near Melbourne, Florida. Understanding precipitation is an essential component of climate modeling. Part of the calibration process for the recently launched GPM satellite involves comparison with radar observations. Ensuring that the radars are well calibrated is an import part of this process. We have used the developed stochastic model to explore sampling error for gauge and radar derived estimates of rain rates. This allows us to detect the presence and estimate the magnitude of any retrieval errors for the radar or gauge. We also formulated a standard linear regression analysis approach to the intercomparison of radar and gauge rain rate estimates in terms of the appropriate observed and model-derived quantities