GiST: A Stochastic Model for Generating Spatially and Temporally Correlated Daily Rainfall Data

Abstract

Weather generators are tools that create synthetic daily weather data over long periods of time. These tools have also been used for downscaling monthly to seasonal climate forecasts, from global and regional circulation models to daily values for use as inputs for crop and other environmental models. One main limitation of most weather generators is that they do not take into account the spatial structure of weather. Spatial correlation of daily rainfall is important when one aggregates, for example, simulated crop yields or hydrology in a watershed or region. A method was developed to generate realizations of daily rainfall for multiple sites in an area while preserving the spatial and temporal correlations among sites. A two-step method generates rainfall events at multiple sites followed by rainfall amounts at sites where generated rainfall events occur. The generation of rainfall events was based on a new orthogonal Markov chain for discrete distributions. For generating rainfall amounts, a vector of random numbers (from a uniform distribution), of order equal to the number of locations with rainfall events that were generated to occur in a day, was matrix-multiplied by the corresponding factorized correlation matrix to create spatially correlated random numbers. Elements from the resulting vector were transformed to a gamma distribution using cumulative probability functions for each location and rescaled to rainfall amounts. One study area was located in north-central Florida, where correlated rainfall data were generated for seven weather stations to evaluate its performance versus a widely used single-site weather generator. A second area was in North Carolina, where rainfall was generated for 25 weather stations to evaluate the effects of a larger number of stations in other regions. One thousand yearlong replications of daily rainfall data were generated for each area. Monthly spatial correlations of generated daily rainfall events and amounts among all pairs of weather stations closely matched their observed counterparts. For daily rainfall amounts the correlation coefficients between the observed pairwise correlation coefficients and the ones estimated from synthetic data among weather stations were 0.977 for Florida and 0.964 for North Carolina. The performance of the geospatial?temporal (GiST) weather generator was also analyzed by comparing the distributions of lengths of dry and wet spells, joint probabilities, Markov transitional probabilities, distance decay of correlation functions, and regionwide days without rainfall at any station. Multiannual mean and standard deviation of the number of rainy days per month and mean monthly rainfall were also calculated. All comparisons between observed and generated rainfall events and amounts using the GiST weather generator were highly correlated. The root-mean-square errors of pairwise correlation values ranged from 0.05 to 0.11 for rainfall events and from 0.03 to 0.06 for amounts.