A seven-parameter Bernoulli-Gamma-Gaussian model to calibrate subseasonal to seasonal precipitation forecasts

Abstract

Subseasonal to seasonal (S2S) precipitation forecasts can fill the gap between weather and seasonal forecasts. While raw forecasts from S2S models are informative, calibration is necessary to correct systematic biases and quantify forecast uncertainty to facilitate applications of S2S forecasts. This paper develops a seven-parameter Bernoulli-Gamma-Gaussian model to calibrate S2S precipitation forecasts. The Bernoulli distribution characterizes the occurrence of zero versus non-zero values of precipitation, the Gamma distribution accounts for the distribution of non-zero precipitation amounts and the bivariate Gaussian distribution formulates the relationship between raw forecasts and observations. A case study of the East River catchment in South China is devised for the S2S forecasts provided by the European Centre for Medium-Range Weather Forecasts (ECWMF). The Bernoulli-Gamma-Gaussian model is used to calibrate raw forecasts at the daily time step and the Schaake Shuffle is used to instill the temporal patterns to form ensemble time series forecasts. The results show that raw S2S forecasts generally suffer from considerable forecast bias and unreliable ensemble spread and can exhibit negative forecast skill. Compared to the quantile mapping, the Bernoulli-Gamma-Gaussian model with the Schaake Shuffle is effective in correcting biases, improving reliability and yielding forecast skill for daily and accumulated precipitation. Furthermore, a sliding window of 15 days tends to be suitable to pool samples to deal with sampling variability and precipitation seasonality for the purpose of calibration of S2S forecasts. Overall, the Bernoulli-Gamma-Gaussian model can serve as an effective tool to calibrate S2S precipitation forecasts for hydrological modeling and water resources management.