基于Morris和Sobol的水文模型参数敏感性分析
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摘要
敏感性分析有助于识别模型相对敏感的重要参数,降低参数维度,为模型参数优化与不确定性分析提供支撑。该文以三水源新安江模型为研究模型,汉江上游高滩流域为研究对象,选用Nash-Sutcliffe效率系数DC和水量平衡系数WB及其线性组合作为目标函数,联合运用Morris筛选法与Sobol方法分析了新安江模型所选13个参数的敏感性。结果表明:流域蒸散发折算系数KC、自由水蓄水容量SM、壤中流出流系数KI/地下水出流系数KG、壤中流消退系数CI、地下水消退系数CG和地表径流消退系数CS属于敏感参数,其中KC为高敏感参数;不同目标函数下模型参数的敏感性分析结果有所差异,水量平衡系数对于KC更加敏感,Nash-Sutcliffe效率系数对于SM、KI/KG、CI、CG、CS更加敏感;部分模型参数(如SM)的交互效应超过其自身敏感度,主要以两两参数组合的二阶敏感性为主,证明参数之间的相关性也是造成参数敏感性的重要原因。Morris筛选法减少敏感性分析的参数数量,Sobol方法准确刻画了模型参数的敏感性特征,两者结合提高了新安江模型参数敏感性分析的可靠性与准确性。
The emerging and popularity of distributed hydrological models promote the development of hydrology sciences meanwhile massive model parameters are introduced, emphasizing the necessity of screening out sensitive parameters. Sensitivity analysis(SA) helps recognize sensitive parameters, reduce the number of model parameters to be analyzed and facilitates parametric optimization and uncertainty estimation. In this study the Xin'anjiang model was applied to Gaotan catchment located in the upstream of Han River basin and Nash-Sutcliffe efficiency(DC), water balance coefficient(WB) and their combination served as objective functions to evaluate the accuracy of daily streamflow simulation. A qualitative SA approach, Morris method was first used to screen out sensitive parameters and reduce the dimensionality of model parameters. The Sobol method was then adopted to quantify degrees of sensitivity of sensitive parameters quantitatively. Both methods are implemented for three different objective functions. The result showed that among 13 selected model parameters, runoff generation parameter KC, runoff separation parameters SM and KI/KG, runoff routing parameters CI,CG and CS are identified as sensitive parameters, among which KC is most sensitive. Furthermore, the selection of objective functions to be evaluated has significant impact on the determination of sensitive parameters: water balance coefficient is most sensitive to KC while Nash-Sutcliffe efficiency more sensitive to other sensitive parameters, especially CS. Further investigation into sensitive parameters revealed that some parameters like SM have higher interaction sensitivities compared to first-order sensitivities, indicating that the interactions between model parameters should be regarded as an unnegligible factor of parameters sensitivity. The Morris method facilitates the reduction of dimensionalities of model parameters while the Sobol method precisely characterizes the features of parametric sensitivities and provides more information on the sensitivities. The integration of both methods is demonstrated to enhance the reliability and accuracy of sensitivity analysis.
The emerging and popularity of distributed hydrological models promote the development of hydrology sciences meanwhile massive model parameters are introduced, emphasizing the necessity of screening out sensitive parameters. Sensitivity analysis(SA) helps recognize sensitive parameters, reduce the number of model parameters to be analyzed and facilitates parametric optimization and uncertainty estimation. In this study the Xin'anjiang model was applied to Gaotan catchment located in the upstream of Han River basin and Nash-Sutcliffe efficiency(DC), water balance coefficient(WB) and their combination served as objective functions to evaluate the accuracy of daily streamflow simulation. A qualitative SA approach, Morris method was first used to screen out sensitive parameters and reduce the dimensionality of model parameters. The Sobol method was then adopted to quantify degrees of sensitivity of sensitive parameters quantitatively. Both methods are implemented for three different objective functions. The result showed that among 13 selected model parameters, runoff generation parameter KC, runoff separation parameters SM and KI/KG, runoff routing parameters CI,CG and CS are identified as sensitive parameters, among which KC is most sensitive. Furthermore, the selection of objective functions to be evaluated has significant impact on the determination of sensitive parameters: water balance coefficient is most sensitive to KC while Nash-Sutcliffe efficiency more sensitive to other sensitive parameters, especially CS. Further investigation into sensitive parameters revealed that some parameters like SM have higher interaction sensitivities compared to first-order sensitivities, indicating that the interactions between model parameters should be regarded as an unnegligible factor of parameters sensitivity. The Morris method facilitates the reduction of dimensionalities of model parameters while the Sobol method precisely characterizes the features of parametric sensitivities and provides more information on the sensitivities. The integration of both methods is demonstrated to enhance the reliability and accuracy of sensitivity analysis.
引文
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[11] 段明印,李传奇,韩典乘,等.SWMM模型参数全局敏感性分析[J].中国农村水利水电,2018(1):101-106.DUAN M Y,LI C Q,HAN D C,et al.Parameter global sensitivity analysis for storm water management model [J].China Rural Water and Hydropower,2018(1):101-106.
[12] 张少钦,吴珊,李俊.全局敏感性分析在LID措施选择中的应用研究[J].中国给水排水,2017,33(19):125-129.ZHANG S Q,WU S,LI J.Application of global sensitivity analysis in selection of LID measures [J].China Water & Wastewater,2017,33(19):125-129.
[13] 舒畅,刘苏峡,莫兴国,等.新安江模型参数的不确定性分析[J].地理研究,2008,27(2):343-352.SHU C,LIU S X,MO X G,et al.Uncertainty analysis of Xin’anjiang model parameter [J].Geographical Research,2008,27(2):343-352.
[14] 廖征红,陈洋波,徐会军,等.基于E-FAST的流溪河模型参数敏感性分析[J].热带地理,2012,32(6):606-612.LIAO Z G,CHEN Y B,XU H J,et al.Parameter sensitivity analysis of the Liuxihe model based on E-FAST algorithm [J].Tropical Geography,2012,32(6):606-612.
[15] STAHN P,BUSCH S,SALZMANN T,et al.Combining global sensitivity analysis and multiobjective optimisation to estimate soil hydraulic properties and representations of various sole and mixed crops for the agro-hydrological SWAP model[J].Environmental Earth Sciences,2017,76(10).
[16] XU X,SUN C,HUANG G,et al.Global sensitivity analysis and calibration of parameters for a physically-based agro-hydrological model[J].Environmental Modelling & Software,2016,83:88-102.
[17] 李剑铎,段青云,戴永久,等.CoLM模拟土壤温度和湿度最敏感参数的研究[J].大气科学,2013,37(4):841-851.LI J D,DUAN Q Y,DAI Y J,et al.A study of the most sensitive parameters for simulating soil temperature and moisture of CoLM [J].Chinese Journal of Atmospheric Science,2013,37(4):841-851.
[18] 宋明丹,冯浩,李正鹏,等.基于Morris和EFAST的CERES-Wheat模型敏感性分析[J].农业机械学报,2014,45(10):124-131.SONG M D,FENG H,LI Z P,et al.Global sensitivity analyses of DSSAT-CERES-Wheat model using Morris and EFAST methods [J].Transactions of the Chinese Society for Agricultural Machinery,2014,45(10):124-131.
[19] GAN Y,DUAN Q,GONG W,et al.A comprehensive evaluation of various sensitivity analysis methods:A case study with a hydrological model[J].Environmental Modelling & Software,2014,51:269-285.
[20] 袁作新.流域水文模型[M].北京:水利电力出版社,1990:113-117.YUAN Z X.Catchment hydrological model [M].Beijing:Water Resources and Electric Power Press,1990:113-117.
[21] MORRIS M D.Factorial sampling plans for preliminary computational experiments[J].Technometrics,1991,33(2):161-174.
[22] CAMPOLONGO F,CARIBONI J,SALTELLI A.An effective screening design for sensitivity analysis of large models[J].Environmental Modelling & Software,2007,22(10):1509-1518.
[23] SOBOL I M.Sensitivity analysis for non-linear mathematical models[J].Mathematical Modeling & Computational Experiment,1993,1:407-414.
[24] CUKIER R I,FORTUIN C M,SHULER K E,et al.Study of the sensitivity of coupled reaction systems to uncertainties in rate coefficients.I Theory[J].The Journal of Chemical Physics,1973,59(8):3873-3878.
[25] SCHAIBLY J H,SHULER K E.Study of the sensitivity of coupled reaction systems to uncertainties in rate coefficients.II Applications[J].The Journal of Chemical Physics,1973,59(8):3879-3888.
[26] CUKIER R I,SCHAIBLY J H,SHULER K E.Study of the sensitivity of coupled reaction systems to uncertainties in rate coefficients.III.Analysis of the approximations[J].The Journal of Chemical Physics,1975,63(3):1140-1149.
[27] SALTELLI A,TARANTOLA S,CHAN K P S.A quantitative model-independent method for global sensitivity analysis of model output[J].Technometrics,1999,41(1):39-56.
[28] SALTELLI A,ANNONI P,AZZINI I,et al.Variance based sensitivity analysis of model output:Design and estimator for the total sensitivity index[J].Computer Physics Communications,2010,181(2):259-270.
[2] GUPTA H V,SOROOSHIAN S,YAPO P O.Toward improved calibration of hydrologic models:Multiple and noncommensurable measures of information [J].Water Resources Research,1998,34(4):751-763.
[3] TIAN F,HU H,LEI Z,et al.Extension of the representative elementary watershed approach for cold regions via explicit treatment of energy related processes [J].Hydrology and Earth System Sciences,2006,10(5):619-644.
[4] DENG C,LIU P,LIU Y,et al.Integrated hydrologic and reservoir routing model for real-time water level forecasts [J].Journal of Hydrologic Engineering,2015,20(9):5014032.
[5] 孙飞飞,许钦,任立良,等.水文模型参数敏感性分析概述[J].中国农村水利水电,2014(3):92-95.SUN F F,XU Q,REN L L,et al.An analysis of the parameter sensitivity of hydrological models [J].China Rural Water and Hydropower,2014(3):92-95.
[6] 宋晓猛,张建云,占车生,等.水文模型参数敏感性分析方法评述[J].水利水电科技进展,2015,35(6):105-112.SONG X M,ZHANG J Y,ZHAN C S,et al.Review of methods of parameter sensitivity analysis in hydrologic modeling [J].Advances in Science and Technology of Water Resources,2015,35(6):105-112.
[7] RICHARD H M.The role of sensitivity analysis in hydrologic modeling[J].Journal of Hydrology,1973,18(1):37-53.
[8] BEVEN K,BINLEY A.The future of distributed models:model calibration and uncertainty prediction[J].Hydrological Processes,1992(6):279-298.
[9] 宋晓猛,孔凡哲,占车生,等.基于统计理论方法的水文模型参数敏感性分析[J].水科学进展,2012,23(5):642-649.SONG X M,KONG F Z,ZHAN C S,et al.Sensitivity analysis of hydrological model parameters using a statistical approach [J].Advances in Water Science,2012,23(5):642-649.
[10] 宋晓猛.基于响应曲面方法的分布式时变增益水文模型不确定性量化研究[D].徐州:中国矿业大学,2012.SONG X M.Uncertainty quantification for distributed time-variant gain hydrological model based on response surface methodology [D].Xuzhou:China University of Mining and Technology,2012.
[11] 段明印,李传奇,韩典乘,等.SWMM模型参数全局敏感性分析[J].中国农村水利水电,2018(1):101-106.DUAN M Y,LI C Q,HAN D C,et al.Parameter global sensitivity analysis for storm water management model [J].China Rural Water and Hydropower,2018(1):101-106.
[12] 张少钦,吴珊,李俊.全局敏感性分析在LID措施选择中的应用研究[J].中国给水排水,2017,33(19):125-129.ZHANG S Q,WU S,LI J.Application of global sensitivity analysis in selection of LID measures [J].China Water & Wastewater,2017,33(19):125-129.
[13] 舒畅,刘苏峡,莫兴国,等.新安江模型参数的不确定性分析[J].地理研究,2008,27(2):343-352.SHU C,LIU S X,MO X G,et al.Uncertainty analysis of Xin’anjiang model parameter [J].Geographical Research,2008,27(2):343-352.
[14] 廖征红,陈洋波,徐会军,等.基于E-FAST的流溪河模型参数敏感性分析[J].热带地理,2012,32(6):606-612.LIAO Z G,CHEN Y B,XU H J,et al.Parameter sensitivity analysis of the Liuxihe model based on E-FAST algorithm [J].Tropical Geography,2012,32(6):606-612.
[15] STAHN P,BUSCH S,SALZMANN T,et al.Combining global sensitivity analysis and multiobjective optimisation to estimate soil hydraulic properties and representations of various sole and mixed crops for the agro-hydrological SWAP model[J].Environmental Earth Sciences,2017,76(10).
[16] XU X,SUN C,HUANG G,et al.Global sensitivity analysis and calibration of parameters for a physically-based agro-hydrological model[J].Environmental Modelling & Software,2016,83:88-102.
[17] 李剑铎,段青云,戴永久,等.CoLM模拟土壤温度和湿度最敏感参数的研究[J].大气科学,2013,37(4):841-851.LI J D,DUAN Q Y,DAI Y J,et al.A study of the most sensitive parameters for simulating soil temperature and moisture of CoLM [J].Chinese Journal of Atmospheric Science,2013,37(4):841-851.
[18] 宋明丹,冯浩,李正鹏,等.基于Morris和EFAST的CERES-Wheat模型敏感性分析[J].农业机械学报,2014,45(10):124-131.SONG M D,FENG H,LI Z P,et al.Global sensitivity analyses of DSSAT-CERES-Wheat model using Morris and EFAST methods [J].Transactions of the Chinese Society for Agricultural Machinery,2014,45(10):124-131.
[19] GAN Y,DUAN Q,GONG W,et al.A comprehensive evaluation of various sensitivity analysis methods:A case study with a hydrological model[J].Environmental Modelling & Software,2014,51:269-285.
[20] 袁作新.流域水文模型[M].北京:水利电力出版社,1990:113-117.YUAN Z X.Catchment hydrological model [M].Beijing:Water Resources and Electric Power Press,1990:113-117.
[21] MORRIS M D.Factorial sampling plans for preliminary computational experiments[J].Technometrics,1991,33(2):161-174.
[22] CAMPOLONGO F,CARIBONI J,SALTELLI A.An effective screening design for sensitivity analysis of large models[J].Environmental Modelling & Software,2007,22(10):1509-1518.
[23] SOBOL I M.Sensitivity analysis for non-linear mathematical models[J].Mathematical Modeling & Computational Experiment,1993,1:407-414.
[24] CUKIER R I,FORTUIN C M,SHULER K E,et al.Study of the sensitivity of coupled reaction systems to uncertainties in rate coefficients.I Theory[J].The Journal of Chemical Physics,1973,59(8):3873-3878.
[25] SCHAIBLY J H,SHULER K E.Study of the sensitivity of coupled reaction systems to uncertainties in rate coefficients.II Applications[J].The Journal of Chemical Physics,1973,59(8):3879-3888.
[26] CUKIER R I,SCHAIBLY J H,SHULER K E.Study of the sensitivity of coupled reaction systems to uncertainties in rate coefficients.III.Analysis of the approximations[J].The Journal of Chemical Physics,1975,63(3):1140-1149.
[27] SALTELLI A,TARANTOLA S,CHAN K P S.A quantitative model-independent method for global sensitivity analysis of model output[J].Technometrics,1999,41(1):39-56.
[28] SALTELLI A,ANNONI P,AZZINI I,et al.Variance based sensitivity analysis of model output:Design and estimator for the total sensitivity index[J].Computer Physics Communications,2010,181(2):259-270.
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