GiST, A model for generating spatial-temporal daily rainfall data

Weather generators are tools developed to create synthetic daily weather data over long periods of time. These tools have also been used for downscaling monthly to seasonal forecasts, produced by global and regional circulation models, to daily values in order to provide inputs for crop and other environmental models. One main limitation of weather generators is that they do not take into account the spatial structure of weather and climate in a given region or watershed. This spatial correlation is important when one spatially aggregates, for example, simulated crop yields or water resources 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 correlation among sites. A two-step method generates rainfall events followed by rainfall amounts at sites where a generated rainfall event occurs. Generation of rainfall events was based on a newly-developed two-state orthogonal Markov chain. 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 specific day was matrix-multiplied by the corresponding factorized correlation matrix to create correlated random numbers. To generate the final rainfall amounts, elements from the resulting vector of spatially-correlated random numbers were transformed to a gamma distribution using cumulative probability functions calculated individually for each location. Values were next rescaled to rainfall amounts. Seven and 73 weather stations were selected for North-Central Florida and North Carolina respectively. A thousand and a hundred realizations of daily rainfall data were generated respectively for North-Central Florida and North Carolina. Rainfall events and amounts from the new method were compared to those from the WGEN point-based weather generator. The correlations in generated daily rainfall events and amounts closely matched the observed monthly spatial Pearson's correlations among all pairs of weather stations and other monthly rainfall statistics for each weather station. Correlation coefficient between observed and generated (ro-g) joint probabilities that station pairs are both with rainfall was 0.996 and for both without rainfall was 0.991. The ro-g correlations among weather stations was 0.983 for rainfall amounts significant at the 0.01 probability level. The root mean square errors of correlation values ranged from 0.04 to 0.08 for rainfall events and from 0.01 to 0.09 for amounts.