Bayesian Model Averaging with Stratified Sampling for Probabilistic Quantitative Precipitation Forecasting in Northern China during Summer 2010

To study the impact of training sample heterogeneity on the performance of Bayesian model averaging (BMA), two BMA experiments were performed on probabilistic quantitative precipitation forecasts (PQPFs) in the northern China region in July and August of 2010 generated from an 11-member short-range ensemble forecasting system. One experiment, as in many conventional BMA studies, used an overall training sample that consisted of all available cases in the training period, while the second experiment used stratified sampling BMA by first dividing all available training cases into subsamples according to their ensemble spread, and then performing BMA on each subsample. The results showed that ensemble spread is a good criterion to divide ensemble precipitation cases into subsamples, and that the subsamples have different statistical properties. Pooling the subsamples together forms a heterogeneous overall sample. Conventional BMA is incapable of interpreting heterogeneous samples, and produces unreliable PQPF. It underestimates the forecast probability at high-threshold PQPF and local rainfall maxima in BMA percentile forecasts. BMA with stratified sampling according to ensemble spread overcomes the problem reasonably well, producing sharper predictive probability density functions and BMA percentile forecasts, and more reliable PQPF than the conventional BMA approach. The continuous ranked probability scores, Brier skill scores, and reliability diagrams of the two BMA experiments were examined for all available forecast days, along with a logistic regression experiment. Stratified sampling BMA outperformed the raw ensemble and conventional BMA in all verifications, and also showed better skill than logistic regression in low-threshold forecasts.