Multistation, multiyear synthesis of hydrologic time series by disaggregation

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Abstract
A model is presented which is designed for multivariate (multistation, multiyear) data syntheses such as the simulation of several rainfall series over a region, of tributaries and mainstream runoff series, and of rainfall and concurrent runoff series in watersheds. The model is an application of the disaggregation scheme proposed by Valencia and Schaake. If a time series of higher‐level (e.g., annual) events for each station has been generated by some scheme which preserves the long‐term properties, then the disaggregation model can be used to generate parallel time series of lower‐level (e.g., monthly, weekly) events for each corresponding station. The aggregation of the generated lower‐level sequences can preserve the long‐term properties of the original higher‐level series. The seasonal variations, the means, the variances, the autocovariances, and the cross‐covariances, properties of the original lower‐level time series, are also conserved. The lower‐level generated series also preserves the correlations between stations. The generation of multivariate normal random numbers makes use of either the Crout factorization or the principal component analysis depending on whether the covariance matrix of the lower‐level series is positive definite or positive semidefinite, respectively. A technique for modeling nonnormal residual components is discussed. The model has been applied to 36 rainfall, runoff, and rainfall‐runoff sequences in the lower Ohio and upper Mississippi River basins located in Indiana, Illinois, Ohio, and Kentucky. The properties of the generated data series show excellent agreement with those of the historical observed data series.

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