Chapter 3 - Monthly rainfall forecasting with Markov Chain Monte Carlo simulations integrated with statistical bivariate copulas

Abstract

Probabilistic models used for forecasting rainfall can help stakeholders in improving crop productivity through better utilization and preplanning of water resources, as it is the crucial element of major decisions because of the dynamic nature of climate phenomena. In this chapter, Markov Chain Monte Carlo simulation technique was integrated with statistical bivariate copulas to develop rainfall forecasting models by incorporating antecedent rainfall significant lag (t-1) as a predictor to forecast rainfall of the preceding month in Peshawar, Pakistan. Twenty-five copula models were developed using some well-know copula families (Gaussian, t, Clayton, Gumble Frank and Fischer-Hinzmann etc.) to sort out the optimal model using Akaike information criterion (AIC), Bayesian information criterion (BIC), and maximum likelihood (MaxL) as base criteria for each region. The Markov Chain Monte Carlo (MCMC)-bivariate Farlie-Gumbel-Morgenstern copula attained the highest values of AIC≈-4167.1, Bayesian Information Criterion≈-4163.1, and MaxL≈ 2084.5.