Bayesian Joint Probability Approach for Post‐Processing Monthly Precipitation Prediction in Northwest Iran

Abstract The probabilistic prediction of monthly precipitation events, specifically more‐than‐normal (MN), normal (N), and less‐than‐normal (LN) events, holds significant importance in the field of water resource management. In this paper, we employ the Bayesian Joint Probability (BJP) modeling approach to generate monthly probabilistic forecasts for LN, N, and MN events in Northwest Iran. To model the joint distribution of observed precipitation and model precipitation, we propose the utilization of a log‐sinh transformed multivariate normal distribution. The prior distribution for the parameters of this multivariate normal distribution is established as the normal‐inverse‐Wishart, which is known to be the conjugate of the multivariate normal distribution. Bayesian inference of model parameters and associated uncertainties is conducted using STAN Markov Chain Monte Carlo (MCMC) sampling. The methodology is applied to the outputs of four North American Multi‐Model Ensemble (NMME) models, namely CanCM4i, CCSM4, NEMO, and NASA, spanning the period from 1982 to 2017 for a 4‐month forecast horizon. The accuracy of predictions is assessed through various statistical measures and graphical methods using a 12‐fold cross‐validation strategy. The results demonstrate that (a) BJP probabilistic predictions of precipitation consistently outperform raw predictions across all models, months, lead times. (b) The BJP‐NASA model exhibits superior discrimination and reliability compared to other models. (c) May and November show the least amount of discrimination. This observation may be attributed to the fact that these months serve as transitional periods in Iran. (d) Fall forecasts are the most reliable, while summer forecasts are the least reliable.