Stochastic Analysis of Annual Rainfall Affected by Urbanization

Abstract

Several investigators have pointed out the changes in microclimate brought about by large urban areas. In particular, the precipitation and precipitation-related activity have been shown to be larger in and around urban areas than in the surrounding countryside. The seasonality of the increased precipitation is another question which has been investigated. The present paper deals with testing the significance of observed changes in the mean and in the trends of annual precipitation series in and around urban areas. The results of analysis of data from St. Louis, Missouri and LaPorte, Indiana and other stations in the vicinity of these stations are reported. The annual precipitation data may not be assumed to be independent random variables because they may be correlated. For example, the annual rainfall series at LaPorte and St. Louis were found to be correlated. Consequently, the traditional univariate and multivariate tests which are based on the assumption that the variates are independent random variables may not be applicable to testing changes in the characteristics of annual precipitation data. As a result, Integrated Moving Average (IMA) models of the annual precipitation data are used in the present study. The posterior distributions of the parameters of the IMA models have been obtained by assuming locally uniform and independent prior distributions of the parameters. Significance tests based on these posterior distributions are used to determine the statistical significance of the observed changes in precipitation which are attributed to the effects of urbanization. Simpler tests based on the standard errors of the parameter estimates are also discussed. The importance of model validation tests and their relationship to the inference are demonstrated by considering the IMA models of different orders. The statistical significance of the observed changes in the urban precipitation data are discussed and a set of conclusions are presented.