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Correlated Parameters Uncertainty Propagation in a Rainfall-Runoff Model, Considering 2-Copula; Case Study: Karoon III River Basin

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Abstract

Hydrological models are widely used to investigate practical issues of water resources. Parametric uncertainty is considered as one of the most important sources of uncertainty in environmental researches. Generally, it is assumed that the parameters are independent mutually, but correlation within the parameter space is an important factor having the potential to cause uncertainty. The objective and innovation of this study was to address the effects of parameters correlation on a continuous hydrological model uncertainty. HEC-HMS with soil moisture accounting (SMA) infiltration method was used to model daily flows and simulate certainty bounds for Karoon III basin, southwest of IRAN, in two scenarios, independent and correlated parameters using 2-copula. The parameters were represented by probability distributions, and the effect on prediction error were evaluated using Latin hypercube sampling (LHS) on Monte Carlo simulation (MCS). Saturated hydraulic conductivity (K), Clark storage-coefficient (R), and time of concentration (tc) were chosen for investigation, based on observed sensitivity analysis of simulated peak over threshold (POT). One hundred runs were randomly generated from 100 parameter sets captured from LHS of parameters distributions in each sub-basin. Using generated parameter sets, 100 continuous hydrographs were simulated and values of certainty bounds calculated. Results showed that when 2-copula correlated R and tc, with 0.656 Kendall’s Tau and 0.818 Spearman’s Rho coefficients, were propagated, decreasing of outputs’ sharpness was more than when considering K and R (K-R), with 0.166 and 0.262; therefore, incorporation of correlations in the MCS is important, especially when the correlation coefficients exceed 0.65. The model was evaluated at the outlet of the basin using daily stream flow data. Model reliability was better for above-normal flows than normal and below-normal. Reliability increases of simulated flow when considering correlated R-tc was more than K-R because of the correlation values. Incorporation of copula for K-tc not only did not improve the model reliability but also decreased it. Results showed improvement of model reliability, by decreasing predicted error of hydrologic modeling, when dealing with correlated parameters in the system.

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Notes

  1. Percent-error-in-peak=100 \( \left|\frac{q_{\mathrm{s}}\left(\mathrm{peak}\right)\hbox{-} {q}_{\mathrm{o}}\left(\mathrm{peak}\right)}{q_{\mathrm{o}}\left(\mathrm{peak}\right)}\right| \)

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Authors and Affiliations

  1. Department of Water Engineering, Marvdasht Branch, Islamic Azad University, Marvdasht, Iran

    Homa Razmkhah

  2. Department of Hydrology, College of Water Science and Engineering, Shahid Chamran University of Ahvaz, Ahvaz, Iran

    Ali-Mohammad AkhoundAli & Fereydoun Radmanesh

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  1. Homa Razmkhah
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Razmkhah, H., AkhoundAli, AM. & Radmanesh, F. Correlated Parameters Uncertainty Propagation in a Rainfall-Runoff Model, Considering 2-Copula; Case Study: Karoon III River Basin. Environ Model Assess 22, 503–521 (2017). https://doi.org/10.1007/s10666-017-9569-z

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