Modeling of daily suspended sediment load by trivariate probabilistic model (case study, Allah River Basin, Iran)

چکیده مقاله

Purpose Estimating the joint probability of occurrence and joint return period of suspended sediment load (SSL) is necessary for the design and operation of hydraulic structures. The amount of SSL is closely related to the amount of runof, which is highly dependent on the amount of rainfall. Therefore, the purpose of this study is to estimate the joint probability of occurrence and the joint return period of SSL values given rainfall and river discharge values. Methods The vine copula family was used in this study to trivariate frequency analyses of SSL associated with rainfall and stream fow in Allah Basin, Iran. We used daily data of 140 events recorded at Jokanak station during 1975–2020. To create the probabilistic model, the structures of D-vine, C-vine, and R-vine copula functions, as well as rotational, Gaussian, and independent modes, were examined based on log-likelihood, AIC, and BIC criteria. Results The results of examining the marginal distributions showed that the generalized Pareto (RMSE=3.91, NSE=0.98, MAPE=3.91), log-normal (RMSE=2.69, NSE=0.99, MAPE=7.69), and GEV (RMSE=2.16, NSE=0.99, MAPE=5.43) are the best-ftted distributions on rainfall, river fow, and SSL data, respectively. By examining the various vine structures, the D-vine was chosen as a suitable copula (AIC=−727.8, BIC=−714.3, and log-likelihood=366.9) for modeling the dependency structure among rainfall (R), river fow (Q), and SSL. Examining the tree structure of considered copulas revealed that the D-vine copula maintains the dependency of the pairs of variables by selecting the best edges until the last tree. Frank and Clayton’s 180-degree copulas were chosen as the best internal copula functions. The conditional return period of suspended sediment load in the study area was calculated and presented as contour curves based on rainfall and corresponding discharge. The return period provided is given by the occurrence of runof and rainfall values. Compared to the univariate method, the presented return period includes a range of data. For example, in the 2-year return period, changes in SSL values provide a range of 0.46 to 1,395,579 tons per day, given the corresponding rainfall and runof values with probabilities of 0.0031 to 0.50. Conclusions Using this model, SSL values can be estimated by having the amounts of rainfall and river fow at diferent probability levels. The results showed that using the rotated copulas can describe the correlation in all directions, and therefore provide more reliable results.