A Bernoulli-Gamma hierarchical Bayesian model for daily rainfall forecasts

Abstract

We consider stochastic weather models originally developed for rainfall simulations to build a hierarchical Bayesian mixture model for daily rainfall forecasts using endogenous and external information. We model daily rainfall as a seasonal-varying mixture of a Bernoulli distribution for rainfall occurrence and a gamma distribution for the rainfall amount. The model scheme allows the inclusion of predictors to reduce the bias and variance of the forecasts, while the hierarchical Bayesian framework promotes a better understanding and reduction in parameter uncertainties, especially for gauges with short records, as well as supports the estimation of regional parameters that could be employed for forecasts at ungauged sites. The model was tested using 47 years (1973–2019) of daily rainfall data from 60 gauges in South Korea. Climate indices derived from the low-level wind over the region were analyzed using Principal Component Analysis (PCA) and embodied into the model to enhance its forecast skills. The model structure was based on a detailed exploratory data analysis, which included the application of Self-Organizing Maps (SOM) to examine the spatio-temporal patterns of rainfall. Cross-validated results reveal improved skills over reference models based on climatology and persistence up to a three days lead time. The average gains in metrics such as the Brier and Winkler skill scores vary from 5% to 50%, while the average correlation skill between predictions and observations reach values up to 0.55. The gains beyond a three days lead time are marginal, but the underlying structure of the proposed model still encourages its use over the reference models, being a step forward in improving real-time daily rainfall forecasts for the region. It has also a great potential to be combined with weather model forecasts and applied in other places across the world.