Anticipating the frequency distribution of precipitation if climate change alters its mean

Abstract

The relationship between the shape and dispersion of the frequency distributions of precipitation amounts and their means among present climates gives a clue as to how the probabilities of extremes will change if the mean changes. The distribution is limited at zero and, as the means decrease, the standard deviations decrease and the distributions become more skewed. The gamma distribution function fits these distributions from the nearly normal of annual amounts in humid climates to the skewed of monthly in arid ones. Its mean, M, is BG and variance, V, is B 2 G, where B is the scale and G the shape parameter. Among 660 cases of 12 monthly distributions at 55 diverse stations, the variance increased as M 1.3 ( r 2=0.90), which specifies relationships between the mean and B and G. Thus, probabilities are specified by the mean and among 660 cases, 572 specified probabilities of amounts less than half the mean were not significantly different from observed. For precipitation more than three halves the mean, 653 were not significantly different from observed. The relationships among parameters specify a dimensionless elasticity or relative increase in the probability of extremes with a relative decrease in the mean. For amounts below a threshold, the elasticity is greater for lower thresholds and higher means, and it is often >1, signifying a relatively greater rise in the probability of extremes than a fall in the mean.