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浙江大学学报(工学版)
Journal of ZheJiang University (Engineering Science)  2019, Vol. 53 Issue (2): 347-354    DOI: 10.3785/j.issn.1008-973X.2019.02.018
Water Resources and Ocean Engineering     
Sensitivity analysis of parameters of storm water management model with Sobol method
Yun-feng ZHOU1(),Yong-chao ZHOU1,Chun-hua ZHENG2,Xian-ming WENG2,Xiao-yu MA2,Jing-qing LIU1,*()
1. College of Civil Engineering and Architecture, Zhejiang University, Hangzhou 310058, China
2. Wenzhou Drainage Co. Ltd, Wenzhou 325000, China
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Abstract  

The Sobol method based on variance decomposition was used to calculate the sensitivity of parameters in the storm water management model (SWMM) to runoff, peak flow, and peak time under two different rainfall conditions, and the convergence of the results was briefly analyzed, in order to quantitatively explore the global sensitivity of hydro-hydraulic parameters in the typical urban SWMM. Results showed that the sensitive parameters and relative ranking of hydro-hydraulic modules in SWMM were different under different rainfall intensities. The impervious areas’ Manning roughness was the most sensitive parameter for all three kinds of output variables under the heavy rainfall intensity condition, and the total sensitivity values were all greater than 0.6. The Manning roughness coefficient of the concrete pipe section was much more sensitive to the peak time than to the other two types of output variables. Percent of impervious area with no depression storage was sensitive parameter, and the impervious ground surface store was the most sensitive parameter with the first-order sensitivity index of 0.396 in the small rainfall intensity condition. The calculated Sobol indexes fluctuated in the first 63 000 runs of the model and tended to converge after 84 000 runs.

Key words： sensitivity      Sobol method      storm water management model (SWMM)      model parameter      quantitative analysis     
Received: 08 January 2018      Published: 21 February 2019
CLC:  X 143  
Corresponding Authors: Jing-qing LIU     E-mail: zhouyunfeng1993@zju.edu.cn;liujingqing@zju.edu.cn
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Yun-feng ZHOU
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Xiao-yu MA
Jing-qing LIU
Cite this article:

Yun-feng ZHOU,Yong-chao ZHOU,Chun-hua ZHENG,Xian-ming WENG,Xiao-yu MA,Jing-qing LIU. Sensitivity analysis of parameters of storm water management model with Sobol method. Journal of ZheJiang University (Engineering Science), 2019, 53(2): 347-354.

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http://www.zjujournals.com/eng/10.3785/j.issn.1008-973X.2019.02.018     OR     http://www.zjujournals.com/eng/Y2019/V53/I2/347


采用Sobol方法的暴雨径流管理模型参数灵敏度分析

为了定量探究典型城市暴雨径流管理模型（SWMM）中水文水力参数的全局灵敏度，利用基于方差分解的Sobol方法，计算不同雨强下SWMM中各参数对径流量、峰值流量以及峰现时间的灵敏度，简要分析结果的收敛性. 研究结果表明，在不同雨强下，SWMM中水文水力模块的灵敏参数及相关排序有所差异. 在大雨强条件下，不渗透地区表面的曼宁糙率对3类输出变量都是最灵敏参数，总阶灵敏度均大于0.6；混凝土管段的曼宁糙率系数对峰现时间的灵敏度远大于对其他2类输出变量的灵敏度. 在小雨强条件下，无洼地蓄水不渗透性百分比为灵敏参数，不渗透性地面洼地储蓄为最灵敏参数，第1阶灵敏度指数为0.396. 在模型前63 000次运行中，计算得到的Sobol指数上下波动，在运行84 000次之后，Sobol指数逐渐趋于收敛.


关键词： 灵敏度,  Sobol方法,  暴雨径流管理模型(SWMM),  模型参数,  定量分析 
Fig.1 Storm water management drainage network model in study area
降雨
日期 		降雨历
时/min 		降雨
编号 		降雨记录
间隔/min 		降雨峰值强度/
（mm/5 min） 		降雨总
量/mm
2017-07-08 135 Rain1 5 7.40 43.30
2017-06-28 20 Rain2 1 1.32 3.26
Tab.2 Selected rainfall events for sensitivity analysis of storm water management model
分类类别 标签 地表属性 IL/% AL/hm2 PL/%
屋顶 A 混凝土，瓷砖 95 35.112 6 62.12
公用街道 B 沥青，水泥 95 1.845 3 3.27
绿化人行道 C 绿色植被，沥青 70 2.714 7 4.80
绿地 D 绿色植被 10 3.540 4 6.26
道路及旁
绿化带 		E 绿色植被，沥青，
水泥 		85 6.991 4 12.37
绿色屋顶 F 混凝土，瓷砖，
微小植被 		80 6.320 7 11.18
总计 ─ ─ 85.6 56.525 100.00
Tab.1 Land use situation in study area
参数名称 物理意义 单位 所属模块 最小值 最大值 初始估计值
si 不渗透性地面洼地储蓄 mm 水文径流模块 0.18 2.54 1.27
sp 渗透性地面洼地储蓄 mm 水文径流模块 2.54 5.08 3.78
Ni 不渗透地区表面曼宁粗糙系数 ? 水文径流模块 0.010 0.050 0.025
Np 渗透性地区表面曼宁粗糙系数 ? 水文径流模块 0.020 0.400 0.131
C1 混凝土管段曼宁糙率系数 ? 动态演算模块 0.011 0.017 0.015
C2 塑性管段曼宁糙率系数 ? 动态演算模块 0.011 0.015 0.013
C3 PVC管段曼宁糙率系数 ? 动态演算模块 0.008 0.012 0.010
Rmax 霍顿模型最大下渗系数 mm/h 水文下渗模块 50.8 101.6 76.2
Rmin 霍顿模型最小下渗系数 mm/h 水文下渗模块 7.6 15.2 12.7
Dc 霍顿模型衰减系数 h?1 水文下渗模块 2 7 4
Ks 子汇水区坡度系数 ? 水文径流模块 0.67 1.67 1.00
Kw 子汇水区特征宽度系数 ? 水文径流模块 0.6 1.2 0.8
PA 屋顶不渗透百分比 % 水文径流模块 90 100 95
PB 公用街道不渗透百分比 % 水文径流模块 90 100 95
PC 绿化人行道不渗透百分比 % 水文径流模块 65 85 70
PD 绿地不渗透百分 % 水文径流模块 0 15 10
PE 道路及旁绿化带不渗透百分比 % 水文径流模块 75 95 85
PF 绿色屋顶不渗透百分比 % 水文径流模块 75 90 80
PO 无洼地蓄水不渗透性百分比 % 水文径流模块 10 35 25
Tab.3 Ranges and initial estimates of major parameters in hydro-hydraulic modules of storm water management model
Fig.2 Comparison of parameters’ sensitivity indices in different rainfall intensities
径流量灵敏度
参数 Si 参数 $\scriptstyle{S_i^{\text{T}}}$
si 0.396 si 0.504
Ni 0.139 Ni 0.178
PO 0.067 PO 0.103
Kw 0.023 Kw 0.089
Ks 0.017 Ks 0.082
PA ?0.002 C1 0.079
C1 ?0.002 PA 0.073
PD ?0.003 PD 0.069
Rmax ?0.003 PE 0.061
$ \cdots $ $ \cdots $ $ \cdots $ $ \cdots $
PB ?0.005 Np 0.051
$ \cdots $ $ \cdots $ $ \cdots $ $ \cdots $
Dc ?0.012 PF 0.045
总计 0.560 总计 1.733
Tab.5 Sensitivity analysis of parameters of storm water management model in Rain2
径流量灵敏度 峰值流量灵敏度 峰现时间灵敏度
参数 Si $\scriptstyle{S_i^{\text{T}}}$ 参数 Si $\scriptstyle{S_i^{\text{T}}}$ 参数 Si $\scriptstyle{S_i^{\text{T}}}$
Ni 0.502 0.682 Ni 0.414 0.609 Ni 0.482 0.635
Kw 0.138 0.259 Kw 0.144 0.263 Kw 0.111 0.223
Ks 0.051 0.142 Ks 0.058 0.169 C1 0.102 0.233
C1 0.011 0.092 C1 0.037 0.140 Ks 0.047 0.132
si 0.010 0.081 Dc 0.012 0.069 si 0.011 0.077
PA ?0.006 0.056 si 0.010 0.062 Dc 0.007 0.081
PF ?0.007 0.056 PA ?0.001 0.072 PA 0.003 0.075
PD ?0.008 0.056 PD ?0.001 0.051 PO 0.002 0.073
Rmax ?0.008 0.056 PB ?0.002 0.052 PD ?0.002 0.072
$ \cdots $ $ \cdots $ $ \cdots $ $ \cdots $ $ \cdots $ $ \cdots $ $ \cdots $ $ \cdots $ $ \cdots $
PB ?0.009 0.056 sp ?0.006 0.055 PB ?0.006 0.065
$ \cdots $ $ \cdots $ $ \cdots $ $ \cdots $ $ \cdots $ $ \cdots $ $ \cdots $ $ \cdots $ $ \cdots $
Dc ?0.009 0.058 PF ?0.010 0.053 PE ?0.011 0.062
总计 0.594 2.051 总计 0.597 2.029 总计 0.686 2.266
Tab.4 Sensitivity analysis of parameters of storm water management model in Rain1
Fig.3 Convergence of parameters’ sensitivity indices calculated from runoff flow
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