title: A spatial rainfall simulator for crop production modeling in Southern Africa
abstract: This paper describes a methodology for simulating rainfall in dekads across a set of spatial units in areas where long-term meteorological records are available for a small number of sites only. The work forms part of a larger simulation model of the food system in a district of Zimbabwe, which includes a crop production component for yields of maize, small grains and groundnuts. Only a limited number of meteorological stations are available within or surrounding the district that have long time series of rainfall records. Preliminary analysis of rainfall data for these stations suggested that intra-seasonal temporal correlation was negligible, but that rainfall at any given station was correlated with rainfall at neighbouring stations. This spatial correlation structure can be modeled using a multivariate normal distribution consisting of 30 related variables, representing dekadly rainfall in each of the 30 wards. For each ward, log-transformed rainfall for each of the 36 dekads in the year was characterized by a mean and standard deviation, which were interpolated from surrounding meteorological stations. A covariance matrix derived from a distance measure was then used to represent the spatial correlation between wards. Sets of random numbers were then drawn from this distribution to simulate rainfall across the wards in any given dekad. Cross-validation of estimated rainfall parameters against observed parameters for the one meteorological station within the district suggests that the interpolation process works well. The methodology developed is useful in situations where long-term climatic records are scarce and where rainfall shows pronounced spatial correlation, but negligible temporal correlation
keyphrases: crop production modeling Southern Africa simulating rainfall Zimbabwe rainfall records rainfall data spatial correlation multivariate normal distribution covariance matrix parameter estimation