Application of Copula Functions for Rainfall Interception Modelling

Abstract

Rainfall interception is an important process of the water cycle that can have significant influence on surface runoff and groundwater storage. Since rainfall interception measurements are rare and time consuming, rainfall interception estimation can be made indirectly using different meteorological variables. Experimental data of rainfall interception for birch and pine trees was measured at an experimental plot located in an urban area of Ljubljana, Slovenia in this study. A copula model was applied to predict the rainfall interception using meteorological variables, namely air temperature and vapour pressure deficit data. The copula model performance was compared to some other models such as decision trees, multiple linear regressions, and exponential functions. Using random sampling, we found that the copula model where Khoudraji-Liebscher copula functions were used yielded slightly smaller root mean square error (RMSE) and mean absolute error (MAE) values than other tested methods (i.e., RMSE and MAE results for birch trees were 24.2% and 18.2%, respectively and RMSE and MAE results for pine trees were 25.0% and 19.6%, respectively). The results demonstrate that the copula-based proposed method and other tested models could be used for the prediction of rainfall interception at the considered plot and in the wider surroundings. Furthermore, these models could also be applied for the prediction of rainfall interception for these two tree species in other locations under similar vegetation and meteorological conditions.