Estimation of the Correlation Between Temperature and Precipitation in Bafra Plain Using Copula

Abstract

Temperature and precipitation are two critical climate parameters that influence agricultural productivity and various extreme hydrological and meteorological phenomena. Both temperature and precipitation have non-normal marginal distribution and have varying correlation over time. In many cases, while the marginal distributions of these two variables are known, their joint distributions remain unknown. Modelling the potential dependence under varying correlation and non-normal distribution can be achieved using Copula. In this study, we analysed the relationship between total precipitation and temperatures within the Bafra Plain using the Copula method considering maximum, minimum and average temperature, and total precipitation. First, the assumption of autocorrelation was tested using Ljung-Box unit root, Mann-Kendall trend, and Ollech-Webel seasonality tests. Then, the presence of autocorrelation was verified through autocorrelation functions (ACF). To mitigate autocorrelation, appropriate SARIMA and NNAR models were determined based on ACF. A multivariate analysis was conducted on residuals by examining the marginals distributions and copula dependency. Parameters of the marginal distributions and copula families were estimated by maximizing log-likelihood. The suitable copula families were determined based on Bayesian information criteria (BIC). Copula Kendall correlations (tau CK) together with Spearman (rho s) and Pearson correlation coefficient (rho p) calculated to show the effect of copula in revealing correct relationship. As a result, the Copula method demonstrated moderate negative correlation of minimum and maximum temperature with precipitation which is higher compared to low negative correlation of rho s and rho p. For average temperature and precipitation, all three methods showed similar low negative correlation. The outcomes contribute to establishing more robust foundations for implementing measures to preserve and strengthen the region's agricultural sustainability.