Joint modeling of rainfall and temperature in Bahir Dar, Ethiopia: Application of copula

Abstract

ObjectiveClimate change has effects on the economy development of any country. This paper aimed to fit the best marginal and joint distribution models of rainfall with minimum and maximum temperatures.MethodsThe average values of minimum and maximum monthly temperature, and rainfall were used in this study. For the marginal model, five probability distributions and five families of copula models were employed to show the interdependence between the maximum and minimum average annual temperature with rainfall. The Kendall's tau (τ) correlation coefficient was used to find out the correlations between rainfall with minimum and maximum temperature. Both the Akaki Information Criteria (AIC) and Bayesian information criteria (BIC) were used to select the best marginal and copula.ResultsThe result revealed that there is a significant negative relationship between the maximum temperature and rainfall. The maximum average rainfall was obtained from June to August and the maximum temperature is almost consistent in all months. Based on AIC/BIC, the Weibull distribution for rainfall, the Beta for minimum, and the Gaussian for maximum temperature were identified as the best marginal distributions. The Clayton copula distribution was identified as the best copula for rainfall and minimum temperature (with parameter of θ =1. 21, tau correlation = −0.41, p < 0.001), and Frank copula was identified for rainfall and maximum temperature (with unique Frank parameter of θ = −3.94, correlation = −0.38, p < 0.001).ConclusionThe result showed that there is a significant positive relationship between the average annual minimum temperature and rainfall; whereas a negative relationship occurred between the maximum temperature and rainfall. The Clayton and Frank copula were found to be the most appropriate to the model of a bivariate distribution of mean annual rainfall with minimum/maximum temperature respectively.