A five-parameter Gamma-Gaussian model to calibrate monthly and seasonal GCM precipitation forecasts

Abstract

Calibration is necessary for improving raw forecasts generated by global climate models (GCMs) to fully utilize potential benefits of the forecasts in practical applications. Based on quantile mapping (QM), this paper proposes a five-parameter Gamma-Gaussian model to calibrate monthly and seasonal GCM precipitation forecasts. While QM directly maps forecasts to observations without accounting for the dependency relationship, the Gamma-Gaussian model employs the Gamma distribution to normalize precipitation forecasts and observations using normal quantile transform (NQT) and then formulates a bivariate Gaussian distribution to characterize the dependency relationship. A case study is devised to calibrate global precipitation forecasts generated by the Climate Forecast System version 2 (CFSv2) using both QM and Gamma-Gaussian models. The results show that both QM and Gamma-Gaussian models can effectively correct biases. While QM can improve forecast reliability to some degree by reducing biases, reliability is not always satisfactory. The Gamma-Gaussian model outperforms QM because it can ensure forecast reliability and coherence. To facilitate the selection of marginal distributions for the purpose of calibrating GCM precipitation forecasts, six alternative distributions, i.e., Gamma, lognormal, generalized extreme value, generalized logistic, Pearson type III and Kappa distributions, are employed to characterize the marginal distribution of forecasts (observations) in NQT. It is observed that the Gamma distribution is overall the most suitable and that the alternative distributions tend to fit sample-specific noises and get penalized under cross validation. Overall, the Gamma-Gaussian model can serve as an effective tool to calibrate raw GCM forecasts for hydrological modeling and water resources management.