Parameters Estimation for the New Four-Parameter Nonlinear Muskingum Model Using the Particle Swarm Optimization

The Muskingum model is a popular method for flood routing in river engineering. This model has several parameters, which should be estimated. Most of the techniques have applied to estimate these parameters to reduce the distance between observed flow and estimated flows. In this paper, for the first time, the parameters of a novel form of the nonlinear Muskingum model are estimated by the Particle Swarm Optimization (PSO) algorithm. The new Muskingum model, which have four parameters, is applied for three benchmark examples and one real case in Iran. The sum of the squared (SSQ) or absolute (SAD) deviations between the observed and estimated outflows was considered as objective functions. The results showed that although the new Muskingum model became more complex but this model by using PSO technique can improve the fit to observed flow especially in multiple-peak hydrographs.     

Application of New Hybrid Optimization Technique for Parameter Estimation of New Improved Version of Muskingum Model

The Muskingum method is one of the most utilized lumped flood routing model in which calibration of its parameters provides an active area of research in water resources engineering. Although various techniques and versions of Muskingum model have been presented to estimate the parameters of different versions of Muskingum model, more rigorous approaches and models are still required to improve the computational precision of calibration process. In this study, a new hybrid technique was proposed for Muskingum parameter estimation which combines the Modified Honey Bee Mating Optimization (MHBMO) and Generalized Reduced Gradient (GRG) algorithms. According to the conducted literature-review on the improvement of Muskingum flood routing models, a new six-parameter Muskingum model was proposed. The hybrid technique was successfully applied for parameter estimation of this new version of Muskingum model for three case studies selected from literature. The obtained results were compared with those of other methods using several common performance evaluation criteria. The new hybrid method with the new proposed Muskingum model perform the best among all the considered approaches based on most of utilized criteria. The new Muskingum model significantly reduces the SSQ value for the double-peak case study. Finally, the achieved results demonstrate that not only the hybrid MHBMO-GRG algorithm overcomes the shortcomings of both phenomenon-mimicking and mathematical optimization techniques, but also the presented Muskingum model is appeared to be the most reliable version of Muskingum model comparing with other considered models in this research.     

Parameter Identification of Nonlinear Muskingum Model with Backtracking Search Algorithm

Nonlinear Muskingum model is a popular approach widely used for flood routing in hydraulic engineering. An improved backtracking search algorithm (BSA) is proposed to estimate the parameters of nonlinear Muskingum model. The orthogonal designed initialization population strategy and chaotic sequences are introduced to improve the exploration and exploitation ability of BSA. At the same time, a selection strategy based individual feasibility violation is developed to ensure that the computed outflows are non-negative in the evolutionary process. Finally, three examples are employed to demonstrate the performance of the improved BSA. The comparison between the results of routing outflows and those of Wilcoxon signed ranks test shows that the improved BSA outperforms particle swarm optimization, genetic algorithm, differential evolution and other algorithms reported in the literature in terms of solution quality. Therefore, it is reasonable to draw the conclusion that the proposed BSA is a satisfactory and efficient choice for parameter estimation of nonlinear Muskingum model.     

差分进化算法在马斯京根模型参数优选中的应用

针对马斯京根模型参数最优估计中求解复杂、精度差等问题,结合绝对残差绝对值之和最小准则,提出应用差分进化算法（Differential Evolution Algorithm）直接优选模型参数。同其它算法相比,实例分析表明该算法具有较强的全局搜索能力和较高的计算精度。为更好地优选马斯京根模型参数提供了一种更为有效的新方法。     

多元优化算法在马斯京根模型参数优化中的应用

以2个实例为研究对象,利用一种新型群体智能算法——多元优化(MVO)算法优化马斯京根模型参数,并与相关文献中加速遗传算法等多种方法的优化结果进行对比。结果表明:MVO算法优化结果优于其他算法,利用MVO算法优化马斯京根模型参数,可以获得比相关文献更高的模拟精度,不但为精确估计马斯京根模型参数提供了有效方法,而且拓展了MVO算法在水文模型参数优化中的应用。     

A RIVER FLOW ROUTING MODEL BASED ON DIGITAL DRAINAGE NETWORK

On the basis of Digital Elevation Model （DEM） data, watershed delineation and spatial topological relationship were proposed by the Digital Elevation Drainage Network Model （DEDNM） for the area upstream of the Hanzhong Hydrological Station in the Hanjiang River in China. Then, the Muskingum-Cunge method considering lateral flow into the river was applied to flood routing on the platform of digital basin derived from DEDNM. Because of considering lateral flow into the river, the Muskingum-Cunge method performs better than the Muskingum method in terms of the Nash-Sutcliffe model efficiency coefficient and the relative error of flood discharge peak value. With a routing-after-superposition algorithm, the Muskingum-Cunge method performs better than the Muskingum method in terms of the Nash-Sutcliffe model efficiency coefficient and the relative error of flood discharge peak value. As a result, the digital basin coupled with the Muskingum-Cunge method provides a better platform for water resources management and flood control.     

河道洪水流量预测方法研究

及时准确地预报某区域内河道指定区段洪水流量及发生时间,对合理实施该区域的防洪预案、落实抗洪抢险措施、组织调度人员及防汛物资具有重要意义。目前河道洪水预报普遍采用马斯京根流量演算法及加里宁—米尔加科夫洪水演进法,两种方法的参数率定存在局限性,对应支流的河道分段处理也存在问题。本文依据最小二乘法,建立含有预测河段上游干流、支流水文站（或水位站）流量或水位预测模型,该模型不受其他水文参数的率定精度影响,直接利用以往洪水及当次洪水上游、下游站的观测资料建立回归预测模型,并通过递推方式完成当次洪水预测,表达形式简单直观、便于实际应用。利用该模型完成了嫩江干流齐齐哈尔水文站2013年洪水流量预测,经与实测成果比较,洪峰流量最大拟合误差小于5.2%,具有较好的计算精度。     

Rating Curve Development at Ungauged River Sites using Variable Parameter Muskingum Discharge Routing Method

A physically based simplified discharge routing method, namely, the variable parameter Muskingum discharge-hydrograph (VPMD) routing method, having the capability of estimating the stage hydrographs simultaneously in channels with floodplains is presented herein. The upstream discharge hydrograph is routed using this VPMD method in different two-stage symmetrical trapezoidal compound cross section channel reaches. The performance of the VPMD method is evaluated by numerical experiments using the benchmark MIKE11 hydrodynamic model and the field data of the Tiber River in central Italy. The proposed method is capable of accurately routing the discharge hydrographs, corresponding stage hydrographs and synthesizing the normal rating curves at any downstream ungauged river site which is not affected by any downstream effects. This study can be helpful for various planning and management of river water resources in both the diagnostic and prognostic modes.     

融冰洪水演进的马斯京根模型

为解决参数率定过程复杂的问题,将河段内的融冰产生的流量视为河段下断面出流的一部分,构建出适用于文开河融冰时期洪水演进的马斯京根模型,并将优化算法应用到模型参数率定的过程中。以黄河宁蒙河段为例,采用试错法、非线性规划法和智能算法中的遗传算法这3种方法对所构建的模型参数进行率定。模拟结果表明:3种方法所模拟的出流过程线均合格;整体上,非线性规划法模拟的精度最高,其洪水的确定性系数D_c为0.980,过程平均相对误差RE为4.840%;而试错法模拟的洪峰流量更为准确,且冰期模拟精度高于无冰期。本研究为融冰洪水演进的模拟提供了一种新方法。     

马斯京根模型改进新思路

马斯京根模型基于水量平衡原理和线性槽蓄假定而建立,模型自提出以来不断得到改进。归纳起来,模型改进思路主要体现在水量平衡微分方程、槽蓄方程以及参数取值三方面。在已有模型改进思路基础上,通过引入组合流量系数,尝试构建新的马斯京根演进模型。模型以同一断面历史多时刻流量线性组合代替槽蓄方程中当前单时刻流量,并采用微分进化算法进行模型参数率定。以滦河大黑汀水库以下至滦县河段为例,分别选取不同量级的10次代表性水流过程进行模拟。结果表明,模型模拟精度较未改进得到了提高。     

非线性马斯京根模型参数率定的新方法

本文在分析经典二进制遗传算法不足之处的基础上提出一种改进的混合遗传算法(MGA)，用于对非线性马斯京根模型参数的估计。同其它算法相比显示出求解精度高而且收敛速度快的特点。通过具体仿真计算验证了该方法的正确性，从而为准确估计非线性马斯京根模型参数提供了一种十分有效的方法。     

河道洪水演算模型评价探析

准确的洪水演算具有很强的理论及现实意义。研究了洪水演算的原理和数学模型，分析了圣维南演算模型与马斯京根演算模型的要点与难点，讨论了圣维南方程的定解条件并叙述了马斯京根演算理论，比较了两模型的优缺点及其适用情况。     

A Modified Muskingum Flow Routing Model for Flood Wave Propagation during River Ice Thawing-Breakup Period

During the period of river ice thawing and breakup process (termed as “ice cover thawing-breakup”), vast amount of water stored in ice-covered river reach will be released comparing to that under open flow condition. The flow routing process during river ice thawing-breakup period will be different from that under open flow condition, since water stored in and channel from ice thawing-breakup process and flow routing process are very complicated. If the flow routing process during river ice thawing-breakup period can be predicted, it will very important for flood protection in the downstream river reach. In present study, water released from ice cover thawing process is considered as the lateral inflow to the channel flow during propagation process of flood wave from upstream to downstream. A model for the flood routing process during river ice thawing-breakup period has been developed based on the Muskingum hydrologic method. Using the modified Muskingum model, the routed outflow hydrograph has been determined along the Baotou Reach of the Yellow River during river ice thawing-breakup period. Results showed that the simulated hydrographs using developed model agree well with those of field measurements.

     

基于长办汇流曲线的多模型联合洪水演算研究

传统长办汇流曲线采用试算法确定稳定流的河段传播时间K值时,计算过程繁琐且不一定能得到最优解。基于此,提出利用遗传算法求解马斯京根模型的河段传播时间,进而优化长办汇流曲线模型的参数K。该方法既充分利用了长办汇流曲线模型中的经验性汇流系数,又融入了改进马斯京根法,可以保证参数全局最优的特点,有效提高了河道洪水演算精度,为河道洪水演算研究提供了一种多模型联合求解的新思路。     

混沌粒子群优化算法在马斯京根模型参数优化中的应用

针对目前马斯京根模型参数率定中存在的求解复杂、精度不高等问题,本文将混沌搜索机制引入粒子群优化算法中,构建混沌粒子群优化算法对马斯京根模型参数进行率定。这种方法利用混沌运动的遍历性,改善了粒子群优化算法的全局寻优能力,避免算法陷入局部极值,使得粒子群体的进化速度加快,提高了算法的收敛速度和精度。通过实例应用表明,混沌粒子群优化算法可以有效地估算出马斯京根模型参数,优化效果明显优于粒子群优化算法及试错法,因此该算法具有很好的实用性。     

Study of the water budget of streets: experimentation and modelling.

The study of two stretches of street during 38 months has been performed to analyze the hydrological behavior of streets during rain events. The results show that runoff coefficients are very variable and runoff losses may be important. In order to better understand this behavior, a physically based model has been used. This model, BiL, combines a porous media flow module with a surface runoff module. The lateral runoff transfer in the lateral gutter is approximated by the Muskingum model. Evaporation is simulated by an adaptation of the Penman method. A sensitivity study shows that the model is mainly sensitive to saturated hydraulic conductivity of the asphalt pavement and to the storage capacity. The comparison of simulated and observed data gives good results for the runoff outflow at a 3 minutes time step. Nevertheless, the simulation results are less encouraging for the runoff coefficient. This study of the water budget of two street stretches during a time period of 38 months indicates that the infiltration and evaporation represent between 20 and 30% of rain.     

多智能体遗传算法用于马斯京根模型参数估计

将智能体对环境的感知和反作用的能力与遗传算法的搜索方式相结合提出了一种改进的多智能体遗传算法，用于马斯京根模型的参数估计。该方法中每个智能体代表一个候选解并固定在网格上，为了增加自身能量，它将与其邻域的智能体进行合作或竞争，也可以利用自身的知识进行自学习来增加能量，通过这些智能体与智能体间的相互作用来达到优化模型中参数的目的。应用实例表明，该算法同其他算法相比具有更好的优化性能，从而为准确估计马斯京根模型参数提供了一种更为有效的方法。     

Application of Muskingum routing method with variable parameters in ungauged basin

This paper describes a flood routing method applied in an ungauged basin, utilizing the Muskingum model with variable parameters of wave travel time K and weight coefficient of discharge x based on the physical characteristics of the river reach and flood, including the reach slope, length, width, and flood discharge. Three formulas for estimating parameters of wide rectangular, triangular, and parabolic cross sections are proposed. The influence of the flood on channel flow routing parameters is taken into account. The HEC-HMS hydrological model and the geospatial hydrologic analysis module HEC-GeoHMS were used to extract channel or watershed characteristics and to divide sub-basins. In addition, the initial and constant-rate method, user synthetic unit hydrograph method, and exponential recession method were used to estimate runoff volumes, the direct runoff hydrograph, and the baseflow hydrograph, respectively. The Muskingum model with variable parameters was then applied in the Louzigou Basin in Henan Province of China,and of the results, the percentages of flood events with a relative error of peak discharge less than 20% and runoff volume less than 10% are both 100%. They also show that the percentages of flood events with coefficients of determination greater than 0.8 are 83.33%, 91.67%, and 87.5%,respectively, for rectangular, triangular, and parabolic cross sections in 24 flood events. Therefore,this method is applicable to ungauged basins.     

淮河中游河段河道汇流参数的优化分析

利用1998~2005年的洪水资料对马斯京根模型参数进行优选,优选润河集、横排头、阜阳闸至正阳关最优的河道汇流参数,并对该优选参数值进行验证,预报洪水过程平均不确定性系数在0.85以上,预测洪峰流量误差控制在8%以内,达到较高预报作业精度。     

Methods to quantify and identify the sources of uncertainty for river basin water quality models.

Worldwide, the application of river basin water quality models is increasing, often imposed by law. It is, thus, important to know the degree of uncertainty associated with these models and their application to a specific watershed. These uncertainties lead to errors that are revealed when model outputs are compared to observations. Such uncertainty is typically described by calculating the residuals. However, residuals should not be seen as an estimate of total uncertainty, since through the calibration process, the residuals may be reduced by over-adjustment to the data, which is typically the case for over-parameterised models. Over-adjustment during a calibration period can also lead to highly biased results when the model is applied to other periods or environmental conditions. The total model uncertainties are, therefore, assessed by four components: the sum of the squares of the residuals (SSQ), parameter uncertainties (that can be ignored when their error is much smaller than SSQ), input data uncertainties, and an additional predictive uncertainty that is expressed when the model appears to be biased when it is applied for data other than the data used for calibration. The sources are ranked according to a quantification criterion (magnitude) as well as an identification criterion that depends on the number of observations that are covered by the confidence region. This approach is illustrated with SWAT2003 simulations for flow and sediment of Honey Creek, a tributary of the Sandusky River basin (Ohio). The results show the dominance of the model uncertainty. The input data uncertainty is less important.