Stochastic Multisite Generation of Daily Precipitation Data Using Spatial Autocorrelation

Abstract

There are a number of stochastic models that simulate weather data required for various water resources applications in hydrology, agriculture, ecosystem, and climate change studies. However, many of them ignore the dependence between station locations exhibited by the observed meteorological time series. This paper proposes a multisite generation approach of daily precipitation data based on the concept of spatial autocorrelation. This theory refers to spatial dependence between observations with respect to their geographical adjacency. In hydrometeorology, spatial autocorrelation can be computed to describe daily dependence between the weather stations through the use of a spatial weight matrix, which defines the degree of significance of the weather stations surrounding each observation. The methodology is based on the use of the spatial moving average process to generate spatially autocorrelated random numbers that will be used in a stochastic weather generator. The resulting precipitation processes satisfy the daily spatial autocorrelations computed using the observed data. Monthly relationships between the spatial moving average coefficients and daily spatial autocorrelations of the precipitation processes have been developed to find the spatial moving average coefficients that reproduce the observed daily spatial autocorrelations in the synthetic precipitation processes. To assess the effectiveness of the proposed methodology, seven stations in the Peribonca River basin in the Canadian province of Quebec were used. The daily spatial autocorrelations of both precipitation occurrences and amounts were adequately reproduced, as well as the total monthly precipitations, the number of rainy days per month, and the daily precipitation variance. Using appropriate weight matrices, the proposed multisite approach permits one not only to reproduce the spatial autocorrelation of precipitation between the set of stations, but also the interstation correlation of precipitation between each pair of stations.