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.

Effects of uncertainty in determining the parameters of the linear Muskingum method using the particle swarm optimization (PSO) algorithm

The Muskingum method is one the simplest and most applicable methods of flood routing. Optimizing the coefficients of linear Muskingum is of great importance to enhance accuracy of computations on an outflow hydrograph. In this study, considering the uncertainty of flood in the rivers and by application of the particle swarm optimization (PSO) algorithm, we used the data obtained from three floods simultaneously as basic flood to optimize parameters of linear Muskingum (X, K and Δt), rather than using inflow and outflow hydrographs of a single basic flood (observational flood), and optimized the outflow discharge at the beginning of flood (O1) as a percentage of inflow discharge at the beginning of flood (I1). The results suggest that the closer inflow discharge variation of basic flood to the inflow discharge variation of observational flood, the accuracy of outflow hydrograph computations will increase. Moreover, when the proposed approach is used to optimize parameters of X, K and Δt, the accuracy of outflow hydrograph computations will increase too. In other words, if rather than using a single basic flood, the proposed approach is applied, the average values of mean relative error (MRE) of total flood for the first, second, third and fourth flood will be improved as 31, 13, 39 and 33%, respectively.

Flood routing by linear Muskingum method using two basic floods data using particle swarm optimization (PSO) algorithm

The Muskingum method is one of hydrological approaches that has been used for flood routing for many years thanks to its simplicity and reasonable accuracy over other methods. In engineering works, the calculation of the Peak section of a flood hydrograph is crucially important. In the present study, using the particle swarm optimization (PSO) algorithm, instead of using a single basic flood, the parameters of the linear Muskingum method (X, K, Δt) are calculated by computed arithmetic and geometric means relevant to two basic floods in the form of eight different models for calculating the downstream hydrograph. The results indicate that if the numerical values of the calculated flood inflow are placed in the interval of the inflow and the basic flood which the parameters X, K, Δt are from, the computation accuracy in approximating the outflow flood related to the peak section of the inflow hydrograph increases for all the mentioned models. In other words, if the arithmetic mean of X, K and the geometric mean of Δt, relevant to the two basic floods, are used instead of using values of X, K, Δt of a single basic flood, the computational accuracy in estimating the flood peak section of the hydrograph in downstream has the highest increase among all the eight models. Thus, the Mean Relative Error (MRE) relevant to the peak section of the inflow hydrograph of the third flood (observational flood) obtained by the first and second basic floods was equal to 4.89% and 2.91%, respectively, while in case of using the arithmetic mean of X and K and the geometric mean of Δt, related to the first and second basic floods (the best models presented in this study), this value is equal to 1.66%.

The applicability of real-time flood forecasting correction techniques coupled with the Muskingum method

Improving flood forecasting performance is critical for flood management. Real-time flood forecasting correction techniques (e.g., proportional correction (PC) and Kalman filter (KF)) coupled with the Muskingum method improve the forecasting performance but have limitations (e.g., short lead times and inadequate performance, respectively). Here, particle filter (PF) and combination forecasting (CF) are coupled with the Muskingum method and then applied to 10 flood events along the Shaxi River, China. Two indexes (overall consistency and permissible range) are selected to compare the performances of PC, KF, PF and CF for 3 h lead time. The changes in overall consistency for different lead times (1–6 h) are used to evaluate the applicability of PC, KF, PF and CF. The main conclusions are as follows: (1) for 3 h lead time, the two indexes indicate that the PF performance is optimal, followed in order by KF and PC; CF performance is close to PF and better than KF. (2) The performance of PC decreases faster than that of KF and PF with increases in the lead time. PC and PF are applicable for short (1–2 h) and long lead times (3–6 h), respectively. CF is applicable for 1–6 h lead times; however, it has no advantage over PC and PF for short and long lead times, respectively, which may be due to insufficient training and increase in cumulative errors.

Variable Parameter Multilinear Muskingum Method: Case Study on the Danube River

The Muskingum method is based on a linear relationship between a channel’s storage and inflow and outflow discharges. The applicability of using travel-time discharge relationships to model the variability of the K parameter in a Muskingum routing model was tested. The new parameter estimation method is based on the relationships between the traveltime parameter (K) and the input discharge for the reach of the Danube River between Devín-Bratislava and Medveďov, which includes the Gabčíkovo hydropower scheme. The variable parametrisation method was compared with the classical approach. The parameter X was taken as the average of its values from a small set of flood waves, K was estimated as a function of the travel-time parameter and discharge, which was optimized for one flood wave. The results were validated using the Nash-Sutcliffe coefficient on 5 floods. The results obtained by these methods were satisfactory and, with their use, one could reduce the amount of data required for calibration in practical applications.

Studi Penelusuran Aliran Pada Sungai Krueng Meureubo Kecamatan Meurebo Kabupaten Aceh Barat

Flood routing can be called a procedure for estimating / predicting the time and magnitude of the flood that will occur at a point based on known data. The purpose of this research is to know the flow of river flow in Krueng Meureubo watershed and to know characteristic of hydrograph in the upstream and downstream by using Muskingum method. The data used in this research is secondary data that is daily rainfall data and topographic map. The highest intensity of rainfall occurred in the 10th return period and the lowest occurred in the second return period. Coefficient value (k) 3400 s and value x 0.462. The results of this study indicate that the peak inflow discharge at 36,543 m3 / s, while the peak discharge outflow 35.934 m3 / s. The flow hydrograph with the Muskingum method shows that the difference in the initial value of the outflow input does not have a large effect on the resulting discharge, the resulting debit value is almost equal to the end of the hydrograph. From the results of this study is expected to be a reference for related parties to take preventive action or reduce the impact of flood disaster, and build an early warning system so that people can have a preparedness system. Keywords—Flood, Flow Routing, Krueng Meureubo River, Muskingum