Monthly Simulation of Pan Evaporation Using Copula-Based Models Considering the Effect of Heteroscedasticity

Abstract

This study presents a simulation-based investigation of time series models in high-dimensional settings, focusing on improving the simulation of pan evaporation values using contemporaneous time series models enhanced by a proposed approach based on vine copulas. The research utilizes monthly pan evaporation data (in millimeters) from 1992 to 2020, collected from stations located in provincial centers across Iran. Additional meteorological variables, including wind speed, dew point temperature, average temperature, average wet-bulb temperature, sunshine duration, relative humidity, precipitation, and cloudiness, were also incorporated into the analysis. The study begins by examining data dependencies and conducting an eight-variable simulation using the contemporaneous autoregressive moving average (CARMA) model during both the training and testing phases, based on 1000 simulations. Subsequently, the residual series from the CARMA model were extracted and fitted with conditional variance models, leading to the development of a hybrid CARMA-generalized autoregressive conditional heteroscedasticity (GARCH) model for simulating pan evaporation. In the final step, a novel approach was introduced to simulate the residual series of the CARMA model. This approach employed the conditional density of vine copulas and their tree sequence, which demonstrated strong performance in simulating the residual series, as evidenced by their distributional characteristics. The findings revealed that incorporating variance heterogeneity into the CARMA models significantly reduced error rates in simulating pan evaporation values. Specifically, the hybrid CARMA-GARCH model improved error rates by an average of 25% in the training phase and 24% in the testing phase compared to the standard CARMA model. Furthermore, the proposed CARMA-Copula approach demonstrated substantial improvements, reducing simulation errors by 50% in both the training and testing phases. The Nash–Sutcliffe efficiency (NSE) statistic, exceeding 94%, underscores the high efficacy of the proposed approach in simulating pan evaporation values. The results indicate that the proposed CARMA-Copula approach, leveraging the marginal distribution of the residual series, conditional density, and an optimized tree sequence, serves as a robust alternative to both CARMA and CARMA-GARCH models. Compared to the CARMA-GARCH model, the CARMA-Copula approach achieved error rate improvements of approximately 36%, 39%, and 35% in the minimum, maximum, and average cases, respectively. These outcomes highlight the potential of the proposed methodology to enhance the accuracy and reliability of pan evaporation simulations in high-dimensional settings.