Multi-model ensemble prediction of pan evaporation based on the Copula Bayesian Model Averaging approach

Abstract

Pan evaporation (Ep) is an efficient and practical tool for planning and managing water resources, understanding the water balance in hydrological processes, and developing irrigation systems, particularly in regions with limited water resources. Accurate prediction of Ep using easy-to-measure meteorological variables is beneficial for any region. The current study aimed to explore the applicability of Copula-based Bayesian Model Averaging (CBMA) for improving probabilistic Ep predictions in different climates of Iran. To this end, the parameters of the Adaptive Neuro-Fuzzy Interface System (ANFIS) were optimized using four meta-heuristic algorithms of Seagull Optimization Algorithm (SOA), Crow search Algorithm (CA), Firefly Algorithm (FFA), and Particle Swarm Optimization (PSO) for finding global solutions. The ANFIS-SOA, ANFIS-CA, ANFIS-FFA, ANFIS-PSO, and ANFIS models were implemented as inputs for employing ensemble CBMA and Bayesian Model Averaging (BMA) methods. Daily meteorological variables of average air temperature (Ta), sunshine hours (SH), relative humidity (RH), wind speed (WS), and Ep from six stations from 2000 to 2003 were applied. Evaluation of five Posterior Distribution Functions (PDFs) and three copula functions showed that Gumbel marginal distribution and Gumbel–Hougaard copula function provide the smallest Kolmogorov–Smirnov statistic indicator at the 5% significance level for all predictive models. The results established that the ensemble CBMA approach exhibited the highest prediction accuracy in all climates, followed by the BMA model, superior to the other individual models. The average root mean square error (RMSE) of the ensemble CBMA model was lower than BMA, ANFIS-SOA, ANFIS-CA, ANFIS-PSO, ANFIS-FFA, ANFIS, by 20.35%, 43.19%, 51.28%, 56.74%, 61.15%, and 64.36%, respectively. Furthermore, the uncertainty analysis indicated the Ep predictions were more confident after applying CBMA. In conclusion, we highly recommend applying the ensemble CBMA model to improve Ep’s prediction performance by standalone and hybrid machine learning models. The combination of Ta-SH was suggested to be used for robust predicting daily Ep in the regions of hot desert, cold desert, and cold semi-arid and Ta-RH in the humid subtropical area regarding the convenience of data acquisition.