Improved River Flood Routing with Spatially Variable Exponent Muskingum Model and Sine Cosine Optimization Algorithm

Due to advancements in optimization technology, numerous variable-parameter Muskingum models have been proposed in recent decades, aiming at enhancing the effectiveness of the Muskingum model. However, a knowledge gap exists in understanding the implications of incorporating spatial variations and l...

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Published in:	Environmental processes Vol. 10; no. 3; p. 42
Main Authors:	Atashi, Vida, Barati, Reza, Lim, Yeo Howe
Format:	Journal Article
Language:	English
Published:	Cham Springer International Publishing 01.09.2023 Springer Nature B.V
Subjects:	Algorithms Case studies Earth and Environmental Science Earth Sciences Environmental Management Environmental Science and Engineering Errors Flood routing Floods Inflow Mathematical models Optimization Outflow Parameter estimation Parameter modification Rivers Spatial variations Temporal variations Trigonometric functions Waste Management/Waste Technology Water Quality/Water Pollution Variable Exponent Parameter Sine Cosine Algorithm (SCA) Nonlinear Muskingum Model Spatial Variation Lateral inflow
ISSN:	2198-7491, 2198-7505
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Abstract	Due to advancements in optimization technology, numerous variable-parameter Muskingum models have been proposed in recent decades, aiming at enhancing the effectiveness of the Muskingum model. However, a knowledge gap exists in understanding the implications of incorporating spatial variations and lateral inflow considerations into the Muskingum model, as well as the performance and applicability of different sub-reach configurations, calling for further research in river flood routing. This study proposed a novel approach to river flood routing using a spatial variable exponent parameter nonlinear Muskingum model with lateral inflow considerations. Unlike previous studies that focused on modifying exponent parameters based on variable inflow levels (i.e., temporal variations), the proposed model considered spatial variations. The proposed Muskingum parameters were estimated using an improved Sine Cosine algorithm (SCA), applied to fit six previously reported case datasets. The proposed method minimized the sum of square errors (SSE) between observed and routed outflows. Results show that the proposed model outperforms others in the Wilson flood case study with an SSE of 6.072 for Number of Sub-reaches (NR)=2, representing an 82.89% reduction compared to NR=1 and constant exponent parameter. Additionally, both the Viessman and Lewis case study and the Dinavar case study demonstrate that NR=3 achieves the best performance and fit to observed data. NR=3 yields the best fit achieving SSE of 9.81 and 2466.62 in the Viessman and Lewis case and the Dinavar case, respectively. The Lawler flood case suggests that a traditional nonlinear model with an SSE of 0.36 for NR=1, 2, or 3 may suffice. Highlights The nonlinear Muskingum model is an extension of the standard Muskingum method. Nonlinear Muskingum Model with Variable Exponent Parameter improves flood routing. The proposed method minimized the sum of square errors (SSE) between observed and routed outflows. The Wilson flood case study demonstrates SSE of 6.072 for NR=2.
AbstractList	Due to advancements in optimization technology, numerous variable-parameter Muskingum models have been proposed in recent decades, aiming at enhancing the effectiveness of the Muskingum model. However, a knowledge gap exists in understanding the implications of incorporating spatial variations and lateral inflow considerations into the Muskingum model, as well as the performance and applicability of different sub-reach configurations, calling for further research in river flood routing. This study proposed a novel approach to river flood routing using a spatial variable exponent parameter nonlinear Muskingum model with lateral inflow considerations. Unlike previous studies that focused on modifying exponent parameters based on variable inflow levels (i.e., temporal variations), the proposed model considered spatial variations. The proposed Muskingum parameters were estimated using an improved Sine Cosine algorithm (SCA), applied to fit six previously reported case datasets. The proposed method minimized the sum of square errors (SSE) between observed and routed outflows. Results show that the proposed model outperforms others in the Wilson flood case study with an SSE of 6.072 for Number of Sub-reaches (NR)=2, representing an 82.89% reduction compared to NR=1 and constant exponent parameter. Additionally, both the Viessman and Lewis case study and the Dinavar case study demonstrate that NR=3 achieves the best performance and fit to observed data. NR=3 yields the best fit achieving SSE of 9.81 and 2466.62 in the Viessman and Lewis case and the Dinavar case, respectively. The Lawler flood case suggests that a traditional nonlinear model with an SSE of 0.36 for NR=1, 2, or 3 may suffice. Highlights The nonlinear Muskingum model is an extension of the standard Muskingum method. Nonlinear Muskingum Model with Variable Exponent Parameter improves flood routing. The proposed method minimized the sum of square errors (SSE) between observed and routed outflows. The Wilson flood case study demonstrates SSE of 6.072 for NR=2. Due to advancements in optimization technology, numerous variable-parameter Muskingum models have been proposed in recent decades, aiming at enhancing the effectiveness of the Muskingum model. However, a knowledge gap exists in understanding the implications of incorporating spatial variations and lateral inflow considerations into the Muskingum model, as well as the performance and applicability of different sub-reach configurations, calling for further research in river flood routing. This study proposed a novel approach to river flood routing using a spatial variable exponent parameter nonlinear Muskingum model with lateral inflow considerations. Unlike previous studies that focused on modifying exponent parameters based on variable inflow levels (i.e., temporal variations), the proposed model considered spatial variations. The proposed Muskingum parameters were estimated using an improved Sine Cosine algorithm (SCA), applied to fit six previously reported case datasets. The proposed method minimized the sum of square errors (SSE) between observed and routed outflows. Results show that the proposed model outperforms others in the Wilson flood case study with an SSE of 6.072 for Number of Sub-reaches (NR)=2, representing an 82.89% reduction compared to NR=1 and constant exponent parameter. Additionally, both the Viessman and Lewis case study and the Dinavar case study demonstrate that NR=3 achieves the best performance and fit to observed data. NR=3 yields the best fit achieving SSE of 9.81 and 2466.62 in the Viessman and Lewis case and the Dinavar case, respectively. The Lawler flood case suggests that a traditional nonlinear model with an SSE of 0.36 for NR=1, 2, or 3 may suffice.HighlightsThe nonlinear Muskingum model is an extension of the standard Muskingum method.Nonlinear Muskingum Model with Variable Exponent Parameter improves flood routing.The proposed method minimized the sum of square errors (SSE) between observed and routed outflows.The Wilson flood case study demonstrates SSE of 6.072 for NR=2.
ArticleNumber	42
Author	Atashi, Vida Barati, Reza Lim, Yeo Howe
Author_xml	– sequence: 1 givenname: Vida surname: Atashi fullname: Atashi, Vida email: Vida.atashi@und.edu organization: Department of Civil Engineering, University of North Dakota – sequence: 2 givenname: Reza surname: Barati fullname: Barati, Reza organization: Department of Civil Engineering, Tarbiat Modares University – sequence: 3 givenname: Yeo Howe surname: Lim fullname: Lim, Yeo Howe organization: Department of Civil Engineering, University of North Dakota
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SubjectTerms	Algorithms Case studies Earth and Environmental Science Earth Sciences Environmental Management Environmental Science and Engineering Errors Flood routing Floods Inflow Mathematical models Optimization Outflow Parameter estimation Parameter modification Rivers Spatial variations Temporal variations Trigonometric functions Waste Management/Waste Technology Water Quality/Water Pollution
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Title	Improved River Flood Routing with Spatially Variable Exponent Muskingum Model and Sine Cosine Optimization Algorithm
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