A new method for dividing flood period in the variable-parameter Muskingum models

The Muskingum routing model is favored by water engineers owing to its simplicity and accuracy. A large amount of research is done to improve the accuracy of the model. One way to do so is to consider variable hydrological parameters during the flood routing period. In this study, the random selection (RS) method was proposed to divide the flood period of the nonlinear Muskingum model into three sub-periods. The proposed method was based on RS of members in each sub-region. It was applied to rout three flood hydrographs, and the objective function was the sum of squared errors. Comparing the results from the three variable-parameter nonlinear Muskingum model with those from the variable-parameter nonlinear Muskingum models in previous studies, the proposed model optimized the objective function in these hydrographs up to 61%. The uncertainty analysis of Muskingum parameters for Wilson's hydrograph was performed by the fuzzy alpha cut method, and it was found that the uncertainty of the parameter x is greater than the uncertainty of the parameters k and m.

Optimization of the Nonlinear Muskingum Model Parameters for the River Routing, Tigris River a Case Study

Flood forecasting and management are one of the most important strategies necessary for water resource and decision planners in combating flood problems. The Muskingum model is one of the most popular and widely used applications for the purpose of predicting flood routing. The particle swarm optimization (PSO) methodology was used to estimate the coefficients of the nonlinear Muskingum model in this study, comparing the results with the methods of genetic algorithm (GA), harmony search (HS), least-squares method (LSM), and Hook-Jeeves (HJ). The average monthly inflow for the Tigris River upstream at the Al-Mosul dam was selected as a case study for estimating the Muskingum model's parameters. The analytical and statistical results showed that the PSO method is the best application and corresponds to the results of the Muskingum model, followed by the genetic algorithm method, according to the following general descending sequence: PSO, GA, LSM, HJ, HS. The PSO method is characterized by its accurate results and does not require many assumptions and conditions for its application, which facilitates its use a lot in the subject of hydrology. Therefore, it is better to recommend further research in the use of this method in the implementation of future studies and applications.

Network Flow and Flood Routing Model for Water Resources Optimization

Real-time management of hydraulic systems composed of multi-reservoir involves conflicting objectives. Its representation requires complex variables to consider all the systems dynamics. Interfacing simulation model with optimization algorithm permits to integrate flow routing into reservoir operation decisions and consists in solving separately hydraulic and operational constraints, but it requires that the water resource management model is based on an evolutionary algorithm. Considering channel routing in optimization algorithm can be done using conceptual models such as the Muskingum model. However, the structure of algorithms based on a network flow approach, inhibits the integration of the Muskingum model in the approach formulation. In this work, a flood routing model, corresponding to a singular form of the Muskingum model, constructed as a network flow is proposed, so that it can be easily integrated into the water management problem. A genetic algorithm is involved for the calibration of the model. The proposed flood routing model was applied on the standard Wilson test and on a 40 km reach of the Arrats river (southwest of France). The results were compared with the results of the Muskingum model. Finally, operational results for a water resource management system including this model are illustrated on a rainfall event.

Developing a novel parameter-free optimization framework for flood routing

The Muskingum model is a popular hydrologic flood routing technique; however, the accurate estimation of model parameters challenges the effective, precise, and rapid-response operation of flood routing. Evolutionary and metaheuristic optimization algorithms (EMOAs) are well suited for parameter estimation task associated with a wide range of complex models including the nonlinear Muskingum model. However, more proficient frameworks requiring less computational effort are substantially advantageous. Among the EMOAs teaching–learning-based optimization (TLBO) is a relatively new, parameter-free, and efficient metaheuristic optimization algorithm, inspired by the teacher-student interactions in a classroom to upgrade the overall knowledge of a topic through a teaching–learning procedure. The novelty of this study originates from (1) coupling TLBO and the nonlinear Muskingum routing model to estimate the Muskingum parameters by outflow predictability enhancement, and (2) evaluating a parameter-free algorithm’s functionality and accuracy involving complex Muskingum model’s parameter determination. TLBO, unlike previous EMOAs linked to the Muskingum model, is free of algorithmic parameters which makes it ideal for prediction without optimizing EMOAs parameters. The hypothesis herein entertained is that TLBO is effective in estimating the nonlinear Muskingum parameters efficiently and accurately. This hypothesis is evaluated with two popular benchmark examples, the Wilson and Wye River case studies. The results show the excellent performance of the “TLBO-Muskingum” for estimating accurately the Muskingum parameters based on the Nash–Sutcliffe Efficiency (NSE) to evaluate the TLBO’s predictive skill using benchmark problems. The NSE index is calculated 0.99 and 0.94 for the Wilson and Wye River benchmarks, respectively.

Estimation of Fuzzy Parameters in the Linear Muskingum Model with the Aid of Particle Swarm Optimization

The Muskingum method is one of the widely used methods for lumped flood routing in natural rivers. Calibration of its parameters remains an active challenge for the researchers. The task has been mostly addressed by using crisp numbers, but fuzzy seems a reasonable alternative to account for parameter uncertainty. In this work, a fuzzy Muskingum model is proposed where the assessment of the outflow as a fuzzy quantity is based on the crisp linear Muskingum method but with fuzzy parameters as inputs. This calculation can be achieved based on the extension principle of the fuzzy sets and logic. The critical point is the calibration of the proposed fuzzy extension of the Muskingum method. Due to complexity of the model, the particle swarm optimization (PSO) method is used to enable the use of a simulation process for each possible solution that composes the swarm. A weighted sum of several performance criteria is used as the fitness function of the PSO. The function accounts for the inclusive constraints (the property that the data must be included within the produced fuzzy band) and for the magnitude of the fuzzy band, since large uncertainty may render the model non-functional. Four case studies from the references are used to benchmark the proposed method, including smooth, double, and non-smooth data and a complex, real case study that shows the advantages of the approach. The use of fuzzy parameters is closer to the uncertain nature of the problem. The new methodology increases the reliability of the prediction. Furthermore, the produced fuzzy band can include, to a significant degree, the observed data and the output of the existent crisp methodologies even if they include more complex assumptions.

Estimation of Nonlinear Parameters of Type 6 Hydrological Method in Flood Routing With the Spotted Hyena Optimizer Algorithm (SHO)

In this study, The Spotted hyena optimizer Algorithm (SHO) is used to optimize the parameters of the Non-linear type 6 Muskingum model for flood routing. To evaluate the performance of the SHO in the Non-linear Muskingum models, The Wilson River and the Wye River are applied by many researchers for validation. Moreover, in these studies, the Non-linear Muskingum parameters were estimated by the SHO Algorithm. The SSQ and DPO were considered as objective functions between computed and observed data. According to the results of Wilson river flood, the values of these objective functions for the NL3 model are 128.781, and 0.92 m3/s, and for the NL6 model, are 3.20 and 0.027, respectively. The results of the Wye River flood with the SHO showed that the SSQ and DPO for the NL3 model are 34789.39 and 90.05, and for the NL6 model are 30812.07 and 72.35, respectively. The results show that the proposed algorithm can be applied confidently to estimate the parameter optimal values of the nonlinear Muskingum model. Moreover, this algorithm may be applicable to any continuous engineering optimization problems.

Developing a Novel Parameter-free Optimization Algorithm for Flood Routing

The Muskingum model is a popular hydrologic flood routing method; however, the accurate estimation of Muskingum model parameters is a critical task in the successful and precise implementation of flood routing. Evolutionary and metaheuristic optimization algorithms (EMOAs) are well suited for parameter estimation associated with various complex models including the nonlinear Muskingum model. Among EMOAs, teaching-learning-based optimization (TLBO) is a relatively new parameterless metaheuristic optimization algorithm, inspired by the relationship between teacher and students in a classroom to improve the overall knowledge of a topic in a class. This paper presents an application of TLBO to estimate Muskingum model parameters by minimizing the prediction error of outflow measurements. Several examples evaluate and confirm the successful performance of TLBO for the estimation of Muskingum-routing parameters precisely. The results show TLBO-Muskingum’s high accuracy for estimating accurately Muskingum’s parameters based on the Nash-Sutcliffe Efficiency (NSE) to evaluate the TLBO’s predictive skill with benchmark problems.

Convergence Analysis of an Improved BFGS Method and Its Application in the Muskingum Model

The BFGS method is one of the most effective quasi-Newton algorithms for minimization-optimization problems. In this paper, an improved BFGS method with a modified weak Wolfe–Powell line search technique is used to solve convex minimization problems and its convergence analysis is established. Seventy-four academic test problems and the Muskingum model are implemented in the numerical experiment. The numerical results show that our algorithm is comparable to the usual BFGS algorithm in terms of the number of iterations and the time consumed, which indicates our algorithm is effective and reliable.