Spatiotemporal Stochastic Simulation of Monthly Rainfall Patterns in the United Kingdom (1980–87)

Abstract

With few exceptions, spatial estimation of rainfall typically relies on information in the spatial domain only. In this paper, a method that utilizes information in time and space and provides an assessment of estimate uncertainty is used to create a gridded monthly rainfall dataset for the United Kingdom over the period 1980–87. Observed rainfall profiles within the region were regarded as the sum of a deterministic temporal trend and a stochastic residual component. The parameters of the temporal trend components established at the rain gauges were interpolated in space, accounting for their auto- and cross correlation, and for relationships with ancillary spatial variables. Stochastic Gaussian simulation was then employed to generate alternative realizations of the spatiotemporal residual component, which were added to the estimated trend component to yield realizations of rainfall (after distributional corrections). In total, 40 realizations of rainfall were generated for each month of the 8-yr period. The methodology resulted in reasonably accurate estimates of rainfall but underestimated in northwest and north Scotland and northwest England. The cause for the underestimation was identified as a weak relationship between local rainfall and the spatial area average rainfall, used to estimate the temporal trend model in these regions, and suggestions were made for improvement. The strengths of this method are the utilization of information from the time and space domain, and the assessment of spatial uncertainty in the estimated rainfall values