Abstract
River flood routing is an important issue in current water resources management. As a popular hydrological flood routing method, Muskingum model has always been the dominant method of flood routing. This paper reviews the development of Muskingum model and the research status of its parameter estimation. The characteristics and relationships of different types of Muskingum models are compared, and it is found that the combination of mathematical techniques and evolutionary algorithms has shown good results in parameter estimation in recent years. In addition, this paper also gives a brief overview of six accuracy evaluation criteria and nine research case data sets commonly used in the literature. It also introduces some challenges of the Muskingum model and new trends in future research, which should interest researchers and engineers.
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Abbreviations
- LMM:
-
Linear Muskingum model
- NLM:
-
Nonlinear Muskingum model
- NLM-VEP:
-
Nonlinear Muskingum model with variable exponent parameter
- LMM-LF:
-
Linear Muskingum model with lateral flow
- NLM-LF:
-
Nonlinear Muskingum model with lateral flow
- NLM-VEP-LF:
-
Nonlinear Muskingum model with variable exponent parameter and lateral flow
- NLM-LF-GS:
-
Nonlinear Muskingum model with variable exponential parameters and transverse flow in the presence of stable GW-SW interaction process
- NLM-GS:
-
Nonlinear Muskingum model considering the nonlinear relationship between lateral and channel inflow
- HJ:
-
Hooke Jeeves pattern search
- LR:
-
Linear Regression
- CG:
-
Conjugate Gradient method
- DFP:
-
Davidon-Fletcher-Powell
- HJ + DFP:
-
HJ pattern search in conjunction with Davidon-Fletcher-Powell
- NONLR:
-
Nonlinear Multivariate Parameter estimation technique
- GA:
-
Genetic Algorithm
- HS:
-
Harmony Search Algorithm
- PSO:
-
Particle Swarm Optimization Algorithm
- ICSA:
-
Immune Clonal Selection Algorithm
- DE:
-
Differential Evolution Algorithm
- SFLA:
-
Shuffled Frog Leaping Algorithm
- MHBMOA:
-
Modified Honey Bee Mating Optimization Algorithm
- CSA:
-
Cuckoo Search Algorithm
- IGSA:
-
Improved Gravitational Search Algorithm
- NMS:
-
Nelder-Mead simplex Algorithm
- GRG:
-
Generalized Reduced Gradient Algorithm
- BFGS:
-
Broyden–Fletcher–Goldfarb–Shanno
- GA-NMS:
-
Hybrid GA and Nelder-Mead simplex Algorithm
- GA-GRG:
-
Hybrid GA and GRG
- HS-BFGS:
-
Hybrid HS and BFGS
- SFLA-GRG:
-
Hybrid SFLA and GRG
- BA:
-
Bat Algorithm
- GGA:
-
Gray-encoded Genetic Algorithm
- BGA:
-
Binary-encoded Genetic Algorithm
- HCGA:
-
Hybrid Chaotic Genetic Algorithm
- SAA:
-
Simulated Annealing Algorithm
- SAVCA:
-
Self-Adaptive Vision Correction Algorithm
- CSS :
-
Charged System Search
- LM:
-
Leven Berg-Marquardt Algorithm
- PRP:
-
Polak–Ribière–Polyak method
- SA :
-
Shark Algorithm
- SSD:
-
Sum of squared deviations
- SAD:
-
Sum of absolute value of deviations,
- DPO:
-
Absolute value deviations between peaks of observed and routed flows
- DPOT:
-
Absolute value of deviations of peak times of observed and routed flows
- MARE:
-
Mean absolute relative error
- NSC:
-
Nash-Sutcliffe criterion
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Special project for collaborative innovation of science and technology in 2021 (No: 202121206), Henan province university scientific and technological innovation team (No: 18IRTSTHN009).
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Wen-chuan Wang: Conceptualization, Methodology, Writing-original draft. Wei-can Tian: Investigation, Writing-original draft preparation. Dong-mei Xu: Formal analysis and data collection. Kwok-wing Chau: Writing and editing-original draft. Qiang Ma: Investigation. Chang-jun Liu: Formal analysis.
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Wang, Wc., Tian, Wc., Xu, Dm. et al. Muskingum Models’ Development and their Parameter Estimation: A State-of-the-art Review. Water Resour Manage 37, 3129–3150 (2023). https://doi.org/10.1007/s11269-023-03493-1
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DOI: https://doi.org/10.1007/s11269-023-03493-1