Rainfall variation analysis and optimization of gaging systems

Abstract

A general methodology is developed to compute the variance of mean rainfall using a covariance factor among rain gage stations. The relative variance, which can be reduced by increasing the density of the network, is presented as three cases; i.e., random sample method, stratified sample method without optimum allocation, and stratified sample method with optimum allocation. A special stratum‐weighted ratio is also developed for allocating the gages to the substratum. On the basis of two‐stage sampling theory, new methods are developed to decide the number of gages needed to estimate the mean rainfall with a given confidence level to achieve a specified accuracy. The stratified sample method required fewer stations to achieve the same level of statistical accuracy than the random sample method. In designing the rain gage network system, three steps are involved: (1) preliminary design, (2) allocation of the gages to substratum, and (3) improvement of the gage density according to the expected level of statistical accuracy. Three classes of low, medium, and high density of rain gage network design are recommended in accordance with the desired level of statistical accuracy. There is a nonlinear relationship between the increase in number of gages and the improvement in statistical accuracy.