Abstract
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 runoff, 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 flow 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-fitted distributions on rainfall, river flow, 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 flow (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 runoff 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 runoff 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 flow at different probability levels. The results showed that using the rotated copulas can describe the correlation in all directions, and therefore provide more reliable results.
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Availability of data and material
The data used in this research will be available (by the corresponding author), upon reasonable request.
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The codes written and used in this research will be available (by the corresponding author), upon reasonable request.
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Acknowledgements
The authors are thankful to the Iran Water Resources Management Company for providing the data needed in this research.
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The participation of A. Khashei-Siuki, M. Nazeri Tahroudi, and A. M. Jafari includes the data collection, running the model, and writing the original draft, and the participation of M. J. Vahidi and Rasoul Mirabbasi includes running the model, analyzing the results, and writing - editing the revised article.
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Vahidi, M.J., Mirabbasi, R., Khashei-Siuki, A. et al. Modeling of daily suspended sediment load by trivariate probabilistic model (case study, Allah River Basin, Iran). J Soils Sediments 24, 473–484 (2024). https://doi.org/10.1007/s11368-023-03629-1
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DOI: https://doi.org/10.1007/s11368-023-03629-1