湖泊科学   2020, Vol. 32 Issue (2): 528-538.  DOI: 10.18307/2020.0221. 0

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BAO Weimin, GU Yuwei, SI Wei, HOU Lu, LU Jinli, LUO Quanfu. Application of rainfall dynamic system response curve method for streamflow and sediment simulation in loess region. Journal of Lake Sciences, 2020, 32(2): 528-538. DOI: 10.18307/2020.0221.
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2019-09-11 收稿
2019-09-18 收修改稿

### 码上扫一扫

(1: 河海大学水文水资源学院, 南京 210098)
(2: 台州市水文站, 台州 318001)
(3: 青山水库管理处, 杭州 311305)

Application of rainfall dynamic system response curve method for streamflow and sediment simulation in loess region
BAO Weimin1 , GU Yuwei1 , SI Wei1 , HOU Lu1 , LU Jinli2 , LUO Quanfu3
(1: College of Hydrology and Water Resources, Hohai University, Nanjing 210098, P. R. China)
(2: Taizhou Hydrological Station, Taizhou 318001, P. R. China)
(3: Qingshan Reservoir Management Office, Hangzhou 311305, P. R. China)
Abstract: It is an effective way to use the conceptual model of water and sediment to calculate the water-sediment process in loess region to analyze the current soil erosion and water-sediment reduction problems. There are errors in the rainfall data due to the temporal homogenization, missing measurements and mismeasurements, which influence the accuracy of the important input variable and dynamic factor of the model-rainfall, and then affect the accuracy of flow and sediment process simulation. Therefore, this study combines the rainfall dynamic system response curve method with the conceptual model of water and sediment to improve the accuracy of water and sediment process simulation. This method takes the water simulation part of the model as a response system to update the important input variable-mean area rainfall. Then the runoff, sediment yield and concentration is recalculated using the updated rainfall series to improve the accuracy of flow and sediment process simulation. After validating the feasibility of this method by the ideal case, an actual case is occurred in Caoping Basin in loess region. The results show that the method can both significantly improve the accuracy of the water and sediment simulation, and the average increases are 17.56% and 15.86% respectively.
Keywords: Conceptual model of water and sediment simulation    rainfall error correction    dynamic system response    Caoping Basin

1 水沙模拟概念模型介绍

 图 1 水沙模拟概念模型结构图 Fig.1 Structural chart of conceptual model of water and sediment simulation

2 降雨动态系统响应方法介绍

 图 2 水沙模型概化系统 Fig.2 Generalization system of conceptual model of water and sediment simulation
 $Q(t) = f[X(t),\theta ,t]$ (1)

 $Q(P) = f(P)$ (2)

 $Q(P) \approx QC\left( {{P_0}} \right) + U\Delta P + W$ (3)

U矩阵如下：

 $U = \left[ {\begin{array}{*{20}{c}} {\frac{{\partial {Q_1}(P)}}{{\partial {P_1}}}}& \cdots &{\frac{{\partial {Q_1}(P)}}{{\partial {P_m}}}}\\ {\frac{{\partial {Q_2}(P)}}{{\partial {P_1}}}}& \cdots &{\frac{{\partial {Q_2}(P)}}{{\partial {P_m}}}}\\ \cdots & \cdots & \cdots \\ {\frac{{\partial {Q_n}(P)}}{{\partial {P_1}}}}& \cdots &{\frac{{\partial {Q_n}(P)}}{{\partial {P_m}}}} \end{array}} \right]$ (4)

(1) 假设流域有降雨系列PO，实测流量为QOPO输入模型计算得到流域原始计算流量系列为QC.

(2) 流域各站点降雨系列PO中第i个时段Pi，在其余时段各站点降雨均不变的情况下，增加一个单位值，得到新的降雨系列PCi.

(3) 将新的降雨系列PCi输入模型进行计算，得到新的计算流量过程QCi.

(4) 将新的流量过程QCi与原始计算流量QC相减，其差值为Pi的系统响应曲线，属于U矩阵中的第i列.

(5) 依次计算U矩阵中的每一列，最终建立降雨系列PO的动态系统响应曲线.运用最小二乘法，计算得到降雨的修正误差值：

 $\Delta P = {\left( {{U^{\rm{T}}}U} \right)^{ - 1}}{U^{\rm{T}}}\left( {{Q_{\rm{O}}} - {Q_{\rm{C}}}} \right)$ (5)

(6) 修正后的降雨系列:

 ${P_{\rm{U}}} = {P_{\rm{O}}} + \Delta P$ (6)

3 应用检验

(1) 径流深相对误差ΔR，本文取误差绝对值：

 $\Delta R = \left| {\frac{{{R_{\rm{C}}} - {R_{\rm{O}}}}}{{{R_{\rm{O}}}}} \times 100\% } \right|$ (7)

(2) 产沙量相对误差ΔS，本文取误差绝对值：

 $\Delta S = \left| {\frac{{{S_{\rm{C}}} - {S_{\rm{O}}}}}{{{S_{\rm{O}}}}} \times 100\% } \right|$ (8)

(3) 纳什效率系数NS

 $NS = 1 - \frac{{\sum\limits_i^n {{{\left[ {{y_{{\rm{C}}i}} - {y_{{\rm{O}}i}}} \right]}^2}} }}{{\sum\limits_i^n {{{\left[ {{y_{{\rm{O}}i}} - \overline {{y_{\rm{O}}}} } \right]}^2}} }}$ (9)

(4) 纳什效率系数提高幅度INS：

 $INS = \frac{{N{S_{\rm{U}}} - N{S_{\rm{O}}}}}{{N{S_{\rm{O}}}}} \times 100\%$ (10)

3.1 理想案例检验

 ${P_{\rm{C}}} = {P_{\rm{O}}} + \Delta P$ (11)

PC系列降雨进行动态系统响应修正，修正得到降雨误差值为-ΔP′，修正的降雨系列为:

 ${P_{\rm{U}}} = {P_{\rm{C}}} - \Delta {P^\prime } = {P_{\rm{O}}} + \Delta P - \Delta {P^\prime }$ (12)

PU输入模型计算得到修正后流量QU和输沙率SU.分别将修正降雨误差值-ΔP′与给定降雨误差值ΔP进行对比，比较两者相关性，检验该方法是否能够精确反演降雨误差；分别将修正后流量、输沙率和计算流量、输沙率与实测流量、输沙率进行对比分析，检验修正后的模型模拟精度是否得到提高.

 图 3 理想案例给定雨量误差ΔP及修正雨量误差ΔP′值(图中1个时刻为模型计算时间尺度0.5 h) Fig.3 Given rainfall error ΔP and corrected rainfall error ΔP′ of ideal case
 图 4 理想案例修正前后降雨值(图中1个时刻为模型计算时间尺度0.5 h) Fig.4 Rainfall values before and after revision of ideal case
 图 5 理想案例修正效果(图中1个时刻为模型计算时间尺度0.5 h) Fig.5 Correction effect of ideal case

3.2 实际流域应用

 图 6 曹坪流域水系及站网布设 Fig.6 Layout of water system and station network in Caoping Basin

 图 7 曹坪流域13场洪水纳什效率系数修正前后对比 Fig.7 Contrast of NS coefficient before and after correction of 13 floods in Caoping Basin
 图 8 第8场次洪水修正效果(图中1个时刻为模型计算时间尺度0.5 h) Fig.8 Correction effect of flood 8

4 结论

5 参考文献