Least‐Squares Parameter Estimation for Muskingum Flood Routing

Xie

et al. 2017

Water

This paper discusses the Muskingum model as a novel parameter estimation method. Sixty representative floods over the past four decades serve as research objects; a linear Muskingum model and Pigeon-inspired optimization (PIO) algorithm are used to obtain the parameters of each flood. The proposed "in-process type" dynamic parameter estimation (IP-DPE) method is used to establish the characteristic attributes set of 50 floods. The characteristic attributes set refers to a set of parameters that could describe the shape, magnitude, and duration of the flood before flood peak; they are the input, whereas parameters K and x of each flood are the output to establish a Neural Network model. Then we input flood characteristic attributes to obtain flood parameters when estimating flood parameters practically. Ten floods were used to test the parameter estimation and flood routing efficacy. The results show that the IP-DPE method can quickly identify parameters and facilitate accurate river flood forecasting.

“…min f = F + h(g 3 (c 0 , c 1 )) (6) where h(g 3 (c 0 , c 1 )) is the penalty term. When the constraint g 3 is satisfied, the value is 0; otherwise, the value is 10 6 .…”

Section: Establishing the Muskingum Parameter Optimization Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“In-Process Type” Dynamic Muskingum Model Parameter Estimation Method

Xie

et al. 2017

Water

Environmental Modelling & Software

“…Similarly to the case of the linear reservoir, the estimation of parameters A and B for the discretized Muskingum model is done by solving (2). This problem has been solved analytically in [24], then, both A and B can be computed in terms of the inflow, outflow, and stored volume by using the following expressions:…”

Section: Muskingum Modelmentioning

confidence: 99%

MatSWMM – An open-source toolbox for designing real-time control of urban drainage systems

Riaño-Briceño

Barreiro-Gómez

Ramirez-Jaime

et al. 2016

This manuscript describes the MatSWMM toolbox, an open-source Matlab, Python, and LabVIEW-based software package for the analysis and design of real-time control (RTC) strategies in urban drainage systems (UDS). MatSWMM includes control-oriented models of UDS, and the storm water management model (SWMM) of the US Environmental Protection Agency (EPA), as well as systematic-system edition functionalities. Furthermore, MatSWMM is also provided with a population-dynamics-based controller for UDS with three of the fundamental dynamics, i.e., the Smith, projection, and replicator dynamics. The simulation algorithm, and a detailed description of the features of MatSWMM are presented in this manuscript in order to illustrate the capabilities that the tool has for educational and research purposes.

Proceedings of the Institution of Civil Engineers - Water Manag

“…The routing equation of the linear model can be developed by combining Equations 1 and 2 of the original paper. Although several methods are available for determining the parameters of the linear model (Yoon and Padmanabhan, 1993), the least-squares method (LSM) of Aldama (1990) is used here.…”

Section: Selection Of Storage Equationmentioning

confidence: 99%

Discussion: Estimation of Muskingum parameter by meta-heuristic algorithms

Orouji¹,

Bozorg‐Haddad²,

Fallah-Mehdipour³

et al. 2014

Orouji et al. (2012) utilised simulated annealing (SA) and shuffled frog leaping algorithm (SFLA) algorithms to calibrate the parameters of the non-linear Muskingum model. The study is both appropriate and interesting, especially for the application of SFLA, but the discusser would like to draw attention to two points -flood routing model classification and storage equation selection. Orouji et al. (2012) indicated that there are two general procedures to route the hydrograph of flooding along river reaches -hydraulic (i.e. distributed) and hydrologic (i.e. lumped) routing procedures. However, not only one-dimensional (1D) and 2D distributed flood routing models (Akbari and Barati, 2012;Xia et al., 2012) and lumped flood routing models (Barati, 2011) can be used to route the hydrograph of the downstream section, but semi-distributed models such as Muskingum-Cunge procedures (Barati et al., 2013;Perumal and Sahoo, 2007) can also be used. et al. (2012) used the data of Karoon River as a real case study. However, the use of a non-linear model for this dataset is questionable. Selection of the storage equation is based on the relationship between weighted flow (i.e. Classification of flood routing models Selection of storage equationOrouji[XI t + (1 À X)O t ] where I t and O t are the inflow and outflow at time t, respectively, and X is the weighting factor) and storage volume (Yoon and Padmanabhan, 1993) by considering the features of catchments (e.g. area, shape, morphology, lithology and vegetation) and the features of flood and rainfall events (e.g. rainfall intensity and duration) that affect the relationship. Because the second case study of the original paper, unlike the first one, does not have a non-linear relationship (see Figure 9), use of a linear model might be more appropriate. The routing equation of the linear model can be developed by combining Equations 1 and 2 of the original paper. Although several methods are available for determining the parameters of the linear model (Yoon and Padmanabhan, 1993), the least-squares method (LSM) of Aldama (1990) is used here.In the original paper, the SFLA has better results than SA in terms of statistics. The best results of the SFLA, for the second case study, in ten runs were j sum of the square deviation of observed and computed outflows (SSQ) ¼ 130 928 . 6473, the absolute value of the deviations of the peak of computed and observed outflows (DPO) ¼ 12 . 9905 and the deviation of peak time of computed and observed outflows (DPOT) ¼ 0 j the sum of the absolute value of the deviations betweeen computed and observed outflows (SAD) ¼ 1835 .