Principal Modes of Variation of Rain-Rate Probability Distributions

Abstract

Radar or satellite observations of an area generate sequences of rain-rate maps. From a gridded map a histogram of rain rates can be obtained representing the relative areas occupied by rain rates of various strengths. The histograms vary with time as precipitating systems in the area evolve and decay and amounts of convective and stratiform rain in the area change. A method of decomposing the histograms into linear combinations of a few empirical distributions with time-dependent coefficients is developed, using principal component analysis as a starting point. When applied to a tropical Atlantic dataset (GATE), two distributions emerge naturally from the analysis, resembling stratiform and convective rain-rate distributions in that they peak at low and high rain rates, respectively. The two ?modes? have different timescales and only the high-rain-rate mode has a statistically significant diurnal cycle. The ability of just two modes to describe rain variability over an area can explain why methods of estimating area-averaged rain rate from the area covered by rain rates above a certain threshold are so successful.