On the Joint Calibration of Multivariate Seasonal Climate Forecasts from GCMs

Multivariate seasonal climate forecasts are increasingly required for quantitative modeling in support of natural resources management and agriculture. GCM forecasts typically require postprocessing to reduce biases and improve reliability; however, current seasonal postprocessing methods often ignore multivariate dependence. In low-dimensional settings, fully parametric methods may sufficiently model intervariable covariance. On the other hand, empirical ensemble reordering techniques can inject desired multivariate dependence in ensembles from template data after univariate postprocessing. To investigate the best approach for seasonal forecasting, this study develops and tests several strategies for calibrating seasonal GCM forecasts of rainfall, minimum temperature, and maximum temperature with intervariable dependence: 1) simultaneous calibration of multiple climate variables using the Bayesian joint probability modeling approach; 2) univariate BJP calibration coupled with an ensemble reordering method (the Schaake shuffle); and 3) transformation-based quantile mapping, which borrows intervariable dependence from the raw forecasts. Applied to Australian seasonal forecasts from the ECMWF System4 model, univariate calibration paired with empirical ensemble reordering performs best in terms of univariate and multivariate forecast verification metrics, including the energy and variogram scores. However, the performance of empirical ensemble reordering using the Schaake shuffle is influenced by the selection of historical data in constructing a dependence template. Direct multivariate calibration is the second-best method, with its far superior performance in in-sample testing vanishing in cross validation, likely because of insufficient data relative to the number of parameters. The continued development of multivariate forecast calibration methods will support the uptake of seasonal climate forecasts in complex application domains such as agriculture and hydrology.