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Research on the nonlinear concentration model of scattering input and the method of real-time flood forecast with the shape restriction (State key laboratory of water resource and hydropower engineering science, Wuhan University, P.R. China) Wuhan University, P.R. China)

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Abstract The topography of the basin and the space-time changes of the rainfall have important effects on the basin concentration. So, based on the topic double pinnate drainage of the Bailianhe basin, the nonlinear concentration model of scattering input which establishes on the reservoirs mode of series-parallel connection are presented with the shape restriction. By means of the variable gain factor recursive least- square method, the forecasting model is real-timely corrected. Using them to forecast the floods of Bailianhe basin, it shows that the models and method are effective in practice, so it can be a feasible flood forecast method for the basin with special topography. The topography of the basin and the space-time changes of the rainfall have important effects on the basin concentration. So, based on the topic double pinnate drainage of the Bailianhe basin, the nonlinear concentration model of scattering input which establishes on the reservoirs mode of series-parallel connection are presented with the shape restriction. By means of the variable gain factor recursive least- square method, the forecasting model is real-timely corrected. Using them to forecast the floods of Bailianhe basin, it shows that the models and method are effective in practice, so it can be a feasible flood forecast method for the basin with special topography.

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Geographical characteristics, such as river system shape, the topography and river way character, and the distribution of precipitation have great effects on the concentration procedure of runoff in sub regions of a basin. Especially in the typical narrow and long of feather shape river system of basin like Bailianhe reservoir basin, the effect become more obviously. The nonlinear concentration model of scattering input in double pinnate basin system is based on the system theory, and it divides basin into different sub basin according the basin landform and river characteristic. The concentration procedure of every sub basin is calculated by the real-time intension of precipitation instantaneous unit lines which describes the nonlinear reservoir-adjusting model.

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白莲河水库流域简介 The basin of Bailianhe reservoir lies in the middle reach of Xishui river of Hubei Province eastern, it control 1797 square kilometers areas, its total capacity of reservoir is 1228 million cube kilometers. In the basin north and south is long, the west and east is narrow, and the average width is 15.7 kilometers. There are two rivers are gathered together in the basin, it is high in the Northeast, The southwest is low. It is distributed in double pinnate sharp. brief introduction about the basin of Bailianhe reservoir

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双羽形水系分散入流非线性汇流模型 The course of basin concentration is constituted by surface gathered and ground water concentration. The basin surface converge procedure are united between every sub basin course through the series or parallel connection. The ground water converge course simulates by the whole basin, and it simulates separately through linear reservoirs model. The basin converge model looks on the rain of every region calculated by the basin produce flow model as the input of concentrate system. According to the relationship between every region, under the shape restriction that must obeyed the flow course of exporting the place to of basin appears finally. The nonlinear concentration model of scattering input in double pinnate drainage

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双羽形水系分散入流非线性汇流模型双羽形水系分散入流非线性汇流模型 白莲河水库流域分块情况 According to the geographical sharp characteristic of the reservoir basin, the reservoir basin is divided into five partitions. and the topological relation between each region is shown as figure2. 分块 4 分块 2 分块 3 分块 5 分块 1 串连 并 连 串 连 The units in the basin of Bailianhe reservoir

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双羽形水系分散入流非线性汇流模型双羽形水系分散入流非线性汇流模型 形状约束条件下的流域分散 入流非线性汇流模型 流域分散入流非线性汇流模型 流域分散入流非线性汇流模型 形状约束条件 形状约束条件 The nonlinear concentration model of scattering input with the shape restriction

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流域分散入流非线性汇流模型 形状约束条件下的流域分散入流非线性汇流模型形状约束条件下的流域分散入流非线性汇流模型 The basins concentrate procedure is constituted by surface flow; subsurface flow and ground water. The concentration formula is ： Further more if we consider the basin geographical characteristic influence to the basin concentration, we can divide the whole basin into m pieces of sub basins with basin geographical characteristic. Each sub basin concentration is simulated by formula1. 壤中流和地下径流对洪水过程的贡献相对较小，采取全流域整体模拟，分别由线 性水库调蓄计算模型模拟。。 The total flow can be calculated by the following formula ： The nonlinear concentration model of scattering input

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形状约束条件下的流域分散入流非线性汇流模型形状约束条件下的流域分散入流非线性汇流模型形状约束条件 According to each sub area real geographical situation, the surface flow simulation adopt parallel connect, or series contact, or bunch mix connect, it consists the basin surface flow procedure. The changing units lines shape coefficient (n, c) in each sub basin can be controlled by restrain condition. When we calculate the concentrate model, the parameter (n, c) reflect the adjust function not only by its own precipitation but also the river between the sub basin export to the basin export. In order to guarantee that the parameter value of nuclear function in each sub basin, it is important to use sharp restrain. The sharp restrain reflect the relation among various nuclear functions. The sharp restrain condition is described by the following formula: 形状约束条件为： the shape restriction

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双羽形水系分散入流非线性汇流模型双羽形水系分散入流非线性汇流模型汇流模型参数的率定 目标函数及相应约束条件 目标函数及相应约束条件 模型参数优选结果 模型参数优选结果 洪水模拟效果 洪水模拟效果 To seek the optimal concentration model parameters

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汇流模型的目标函数及相应约束条件 When we use the concentration model to simulate the examination flood course to the reservoir, we will minimum the difference between the storage and simulation calculate flow by parameters, and between the storage and simulation flood peak, and the time they happened. The goal function is: For being in conformity with real situation of concentration, the rainfall from the upper reaches basin influence stronger than the down reaches. The sharp restrain condition is described by the following formula: 式中 c i 、 n i ( i=1,…,5) 分别为各分块的地面径流汇流参数。 汇流模型参数的率定汇流模型参数的率定 The goal function and. The corresponding restriction

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模型参数优选结果 The method for optimum seeking the model parameter adopts Rosenbrock method (rotates the law of coordinate axis). Considering the influence of the concentration parameter of size of flood, according to the coming water in Bailianhe reservoir basin, we classify the flood to three situations. It is major floods, medium floods and small floods. All kinds of flood non linear concentration model parameter is shown by table1: 汇流模型参数的率定汇流模型参数的率定 the non-linear concentration model parameter optimum seeking result

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汇流模型参数的率定汇流模型参数的率定 洪水模拟效果 From tale1 we can find out, the result of parameter through optimum seeking meet the restriction(5), It can reflect the rainfall from the upper reaches basin influence stronger than the down reaches, thus it makes the concentration simulation by the model accord further with the reality. Concentration prediction model estimate by the validity and the qualification rate, according to different flood style the flood simulation result is shown at table2: the flood simulation result

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洪水实时预报校正方法 The method of real-time flood forecast and correction 流域洪水实时预报校正模型 流域洪水实时预报校正模型 预报校正模型参数自适应识别 与实时校正技术 预报校正模型参数自适应识别 与实时校正技术

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洪水实时预报校正方法洪水实时预报校正方法 流域洪水实时预报校正模型 利用流域水文模型的计算流量序列 与实时观测的流量序列 的残差序列, 建立残差预报模型。 将预报的残差叠加到计算流量上, 从而有流域洪水实时预报校正模型： The basin model of real-time flood forecast and correction 其中： 式中 m 为模型的阶数； ai (t),(i=1,...,m) 为模型的参数。

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洪水实时预报校正方法洪水实时预报校正方法 预报校正模型参数自适应识别与实时校正技术 Self-tuning regulators of forecast and correction model parameters and real-time correcting technique The parameters of real time flood forecast and correction model are calculated by the Least square method with variable forgetting factors [3] and the recursion arithmetic is 参数估计： 增益因子： 协方差阵： 可变遗忘因子：

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实时校正以后各种类型的洪水的拟合结果 洪水实时预报校正方法洪水实时预报校正方法 The real-time flood forecast course corrects result Based on the nonlinear concentration model of scattering input, this paper uses the method of divisional variable instantaneous unit hydrograph to correct the forecast result in Bailianhe reservoir basin. It comes to the result be satisfied. It is shown in the following table: Table 3 the real time flood forecast course corrects result in Bailianhe reservoir basin 可以看到：在洪水过程的平均确定性系数和洪峰流量合格率的统计中， 实时校正预报方案高于流域汇流预报的计算结果。

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算例（ 1 ） Example 1 （ 1 ）白莲河水库 1999 年 6 月 25 日洪水计算结果

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算例（ 2 ） Example 2 （ 2 ）白莲河水库 1999 年 6 月 29 日洪水计算结果

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结语 Conclusion The hydrological procedure influenced by geographical basin characteristic and humans ’ activity is a “ focus" question at present [4]. At present it is still a kind of effective way through transformation to the already ripe lump model. This paper has developed the research of the flood prediction method of the double pinnate water system. For reflecting the influence to the basin concentrate procedure, this paper has set up the in series or parallel connection nonlinear concentration model of scattering input. Because it introduces the shape restriction, the model describes the basin concentrate characteristic excellently. At last we use the real time flood forecast. Not only flood course average efficient coefficient but also flood peak qualification rate the real time correct method is excelled to the ordinary way.

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