Evaluating the efficiency and accuracy of the copula-based rainfall-runoff model

Various methods have been proposed for runoff simulation and forecasting, with one of the latest being the copula-based simulation based on marginal distribution and tree sequence. The objective of this research is to establish a connection to predict runoff alongside rainfall, utilizing the tree sequence and analyzing their abundance in the Qale Shahrokh sub-basin of the Zayandeh Rood basin in Iran. The study aims to assess the precision and effectiveness of the suggested approach in simulating and predicting rainfall-runoff through field measurements across various river sections. By analyzing the consecutive delays in precipitation data, lag 1 was identified as the delay showing a strong correlation. The optimal tree sequence was selected from the vine copulas using AIC and BIC criteria for simulating the river flow in the examined sub-basin. This simulation was conducted considering the rainfall at the upstream stations, resulting in an error rate of 18.48 cubic meters per second and a model efficiency of 0.88 based on RMSE and NSE respectively. By examining the joint frequency in the three-variable mode, the predictive link between river flow values at the researched station and rainfall values at the upstream stations was depicted within confidence intervals of 90-95% and 95-99%. The validity of these equations, as derived from field measurements, was verified. Calculations based on these equations indicated that, with 95-99% certainty, the predicted river flow for 78 mm of rainfall is 117.59 cubic meters per second, and for 98 mm of rainfall, it is 153.19 cubic meters per second. These estimates are approximately 1.7% lower and 7% higher than the actual values (measured values), respectively. The approach introduced in this research regarding rainfall-runoff modeling has no limitations in implementation due to the use of marginal distribution of data and tree sequence. This approach can be effective in hydrological planning and according to the amount of rainfall in the upstream stations, it can be effective for flood risk management in the downstream.