Statistical distribution of daily rainfall and its association with the coefficient of variation of rainfall series

Abstract

The paper deals with the statistical analysis of the daily rainfall series (monthly, seasonal, and annual) of 15 Indian stations representing a wide variety of rainfall regimes, utilizing the data for the period 1901-1980. The study focuses attention on the normalized rainfall curve (NRC) depicting the association between cumulated percentage rain amount (x) and cumulated percentage number of rain days (y) of the rainfall series. It is shown that the NRC is uniquely determined by the coefficient of variation (CV) of the rainfall series. There is no universal NRC that can represent all rainfall regimes.The equation x = y exp[ -b(100 - y)c], where b and c are two empirical constants, gives a good analytical representation of the NRCs over a wide range of CV values of the rainfall series. This analytical equation is able to account for the occurrence of high rainfall intensities towards the upper extremity of the NRC for rainfall series with high values of CV. The rain intensity corresponding to any point on the NRC is inversely proportional to the slope of the tangent at that point. The point where the slope is 45° corresponds to the mean rain amount per rain day (r) of the rainfall series. It is shown that days with rain amount greater than r (considered as days of significant rainfall) constitute about 30 per cent of the rain days and contribute 75-80 per cent of the total rain amount, with some local and seasonal variations.