Stochastic Models to Generate Geospatial-, Temporal-, and Cross-Correlated Daily Maximum and Minimum Temperatures

Abstract

Weather generators are tools used to downscale monthly to seasonal climate forecasts, from numerical climate models to daily values for use as inputs for crop and other environmental models. One main limitation of most of weather generators is that they do not incorporate neither the spatial/temporal correlations between/within sites nor the cross-correlations between variables, characteristics specially important when aggregating, for example, simulated crop yields, freeze events, or heat waves in a watershed or region. Three models were developed to generate realization of daily maximum and minimum temperatures for multiple sites. The first model incorporates only spatial correlation, whereas temporal correlation using a 1-day lag and cross-correlation between variables were added to model one, respectively, by the other two models. Vectors of correlated random numbers were rescaled to temperature values by multiplying each element with the standard deviation and adding the mean of the corresponding weather station. An extension of Crout's algorithm was developed to enable the factorization of nonpositive definite matrices. Monthly spatial correlations of generated daily maximum and minimum temperatures between all pairs of weather stations closely matched their observed counterparts. Performance was analyzed by comparing the root mean squared error, temporal semivariograms, correlation/cross-correlation matrices, multiannual monthly means, and standard deviations.