Characterization of rainfall rate distribution for satellite networks

Rain rate, conditional on actual occurrence of rain and averaged over a region, is well modelled as lognormal distribution. The lognormal parameters {μ, σ} with changing space-/time-scales have been confirmed confines to exponential distribution. A numerical model that yields accurate fit to the measurements has been proposed while the model parameters are calculated using the Least Squares (LSQ) regression fit plot. The novelty of this paper is that it first proposes a numerical model that can accurately give the prediction of the lognormal distribution parameters at finer space and/or time scales. We showed that the exponential formula is good format of the model and fits the observed scale dependence {μ, σ} values throughout the whole range of integration length. The model performance has been validated from two aspects, which are: (1) comparsion of the the model predictions with measurements achieved from radar esitmation with better resolution, and (2) comparison of the rain rate exceedance distribution achieved from radar data and predicted and measured lognormal parameters. The results show that the proposed model can accurately estimate the measurement throughout the whole range of integration length both in space and time domains and can give reasonable prediction at finer scales.