The Schaake shuffle: A method for reconstructing space-time variability in forecasted precipitation and temperature fields

A number of statistical methods that are used to provide local-scale ensemble forecasts of precipitation and temperature do not contain realistic spatial covariability between neighboring stations or realistic temporal persistence for subsequent forecast lead times. To demonstrate this point, output from a global-scale numerical weather prediction model is used in a stepwise multiple linear regression approach to downscale precipitation and temperature to individual stations located in and around four study basins in the United States. Output from the forecast model is downscaled for lead times up to 14 days. Residuals in the regression equation are modeled stochastically to provide 100 ensemble forecasts. The precipitation and temperature ensembles from this approach have a poor representation of the spatial variability and temporal persistence. The spatial correlations for downscaled output are considerably lower than observed spatial correlations at short forecast lead times (e.g., less than 5 days) when there is high accuracy in the forecasts. At longer forecast lead times, the downscaled spatial correlations are close to zero. Similarly, the observed temporal persistence is only partly present at short forecast lead times. A method is presented for reordering the ensemble output in order to recover the space-time variability in precipitation and temperature fields. In this approach, the ensemble members for a given forecast day are ranked and matched with the rank of precipitation and temperature data from days randomly selected from similar dates in the historical record. The ensembles are then reordered to correspond to the original order of the selection of historical data. Using this approach, the observed intersite correlations, intervariable correlations, and the observed temporal persistence are almost entirely recovered. This reordering methodology also has applications for recovering the space-time variability in modeled streamflow.