Application and Evaluation of the Ability of Copulas in Estimating Daily Precipitation in the East of Lake Urmia Basin

Abstract

The use of accurate and continuous data series is a necessary condition for most statistical and hydrological studies. Due to the importance of precipitation as one of the most important climatic and hydrological variables, in the present study, in order to predict the daily precipitation of Tabriz, Copula functions were used and the results were compared with intelligent methods and classical statistics. To predict precipitation in Tabriz station, precipitation data of Sarab, Sahand, and Maragheh stations were also used as auxiliary stations. Based on the obtained results, among all the methods studied, the M5 method with RMSE values of 3.14 mm, and the MAD method with 2.13 mm and the RF method with RMSE values of 5.18 mm and MAD 3.04 mm have the highest and lowest accuracy in estimating precipitation events, respectively. Among Archimedean copulas, the RMSE and MAD values for the Gambel function are 3.89 and 2.51 mm, respectively. Despite the range of estimation data is still very close to other methods, considering the capabilities of Copula functions, including the ability to apply multiple conditions and its probabilistic nature, which considers the behavior of the phenomenon, it can be acknowledged that in similar circumstances, the ability of Copula functions to estimate the missing data of phenomena such as rainfall is acceptable.

Keywords

• probabilistic analysis
• missing data
• forecasting
• archimedean copulas