基于伴随同化法的一维河流水质模型参数反演
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摘要
本文利用伴随同化法研究了一维河流水质模型中污染源源强与纵向离散系数的反演问题.伴随同化法通过使模型计算值尽可能接近实测值即模型计算值和实测值的距离(目标函数)最小来反演最优模型参数,利用拉格朗日算子法将以模型方程作为约束条件的反演问题转化为无约束最优化问题,并利用最速下降法求解.在污染源源强反演算例中,利用河道一维瞬时污染源的解析解作为约束条件,开展了4个污染源源强反演的数值实验,采用不同组合源强初值进行反演计算均能取得较好的演算效果,验证了该方法对多参数的适用性以及对初始值的鲁棒性.纵向离散系数反演算例中,以河道上下游相邻断面的浓度关系为模型约束方程,采用Guymer(1998)示踪实验中得到的观测数据反演河道纵向离散系数,得到的纵向离散系数值比传统的演算法得到的结果更加准确.
The adjoint data assimilation method minimized the objective function which defined as the difference value between simulation value and observation value to find the optimal parameters.Transform the inverse problem with constraint equation into unconstrained control variables optimization problem by the Lagrange operator method. Used the steepest descent method solve the control variables optimization problem. In the pollution source intension inversing case,the analytical solution of instantaneous source was treated as the model constraint equation to inverse four pollution sources intension with different initial emission intensities. The results indicates that the adjoint data assimilation method can find multi-variables successfully,with great robustness and applicability. In the longitudinal dispersion coefficient inversing case,the adjoint assimilation method was applied to predict the longitudinal dispersion coefficient based on the measured data of pollutants concentration by Guymer. The results of the adjoint data assimilation method agree better with the observed values compared with the results of the artificial trial method which Guymer used.
The adjoint data assimilation method minimized the objective function which defined as the difference value between simulation value and observation value to find the optimal parameters.Transform the inverse problem with constraint equation into unconstrained control variables optimization problem by the Lagrange operator method. Used the steepest descent method solve the control variables optimization problem. In the pollution source intension inversing case,the analytical solution of instantaneous source was treated as the model constraint equation to inverse four pollution sources intension with different initial emission intensities. The results indicates that the adjoint data assimilation method can find multi-variables successfully,with great robustness and applicability. In the longitudinal dispersion coefficient inversing case,the adjoint assimilation method was applied to predict the longitudinal dispersion coefficient based on the measured data of pollutants concentration by Guymer. The results of the adjoint data assimilation method agree better with the observed values compared with the results of the artificial trial method which Guymer used.
引文
[1]王建平.环境模型参数识别方法研究综述[J].水科学进展,2006,17(4):574-580Wang Jianping.Advances in study on parameter identification methods for environmental models[J].Advances in Water Science,2006,17(4):574-580
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[13]吕咸青,刘文剑.数据同化中的伴随方法及其有关问题的研究[J].海洋科学,2001,25(3):44-50LüXianqing,Liu Wenjian.Study on the adjoint method in data assimilation and the related problems[J].Marine Sciences,2001,25(3):44-50
[14]吕咸青,田纪伟,吴自库.渤、黄海的底摩擦系数[J].力学学报,2003,35(4):465-468LüXianqing,Tian Jiwei,Wu Ziku.The bottom friction coefficients of the Bohai Sea and the Huanghai Sea[J].Acta Mechanica Sinica,2003,35(4):465-468
[15]吕咸青,方国洪.渤海开边界潮汐的伴随反演[J].海洋与湖沼,2002,33(2):113-120LüXianqing,Fang Guohong.Inversion of the tides on the open boundary of the Bohai Sea by adjoint method[J].Oceanologica et Limnologia Sinica,2002,33(2):113-120
[16]何伯荣,马继瑞,韩桂军,等.海水温度垂直分布预报数据同化的离散伴随算子法[J].计算物理,2000,17(5):553-559He Borong,Ma Jirui,Han Guijun,et al.A method of discrete adjoint operator in data assimilation for the prediction of the vertical distribution of sea temperature[J].Chinese Journal of Computational Physics,2000,17(5):553-559
[17]徐青,刘玉光,程永存,等.海洋生态模型中的伴随同化方法[J].海洋通报,2005,24(6):58-64Xu Qing,Liu Yuguang,Chen Yongcun,et al.Adjoint method in marine ecosystem models[J].Marine Science Bulletin,2005,24(6):58-64
[18]武周虎.倾斜岸坡深度平均浓度分布及污染混合区解析计算[J].水利学报,2015,46(10):1172-1180Wu Zhouhu.Analytical calculation of the depth-averaged concentration distribution and pollutant mixing zone for sloped bank[J].Journal of Hydraulic Engineering,2015,46(10):1172-1180
[19]金文龙,彭辉,高俊杰,等.中小河道突发事故污染源强非稳态过程反问题[J].水资源保护,2013,29(2):18-21Jin Wenlong,Peng Hui,Gao Junjie,et al.Inverse problem of unsteady source intensity change process in sudden pollution accidents in medium-and small-sized rivers[J].Water Resources Protection,2013,29(2):18-21
[20]Guymer I.Longitudinal dispersion in sinuous channel with changes in shape[J].Hydraulic Engineering,1998,124(1):33-40
[21]Ding Y,Wang S S Y.Optimal control of open-channel flow using adjoint sensitivity analysis[J].Journal of Hydraulic Engineering,2006,132(11):1215-1228
[22]Yoshida K,Maeno S.Inverse estimation of distributed roughness coefficients in vegetated flooded rivers[J].Journal of Hydraulic Research,2014,52(6):811-823
[2]刘晓东,姚琪,薛红琴,等.环境水力学反问题研究进展[J].水科学进展,2009,20(6):885-893Liu Xiaodong,Yao Qi,Xue Hongqin,et al.Advance in inverse problems of environmental hydraulics[J].Advances in Water Science,2009,20(6):885-893
[3]顾莉,华祖林,何伟,等.河流污染物纵向离散系数确定的演算优化法[J].水利学报,2007,38(12):1421-1425Gu Li,Hua Zulin,He Wei,et al.Routing-optimization method for determination of longitudinal dispersion coefficient in river[J].Journal of Hydraulic Engineering,2007,38(12):1421-1425
[4]李兰.水质反问题模型的时域频域算法[J].水科学进展,1998,9(3):218-223Li Lan.Two numerical inverse methods for water quality model in both time frequency domain[J].Advances in Water Science,1998,9(3):218-223
[5]李兰.河流水质纵向弥散系数的频域反演[J].水利学报,1999,(8):67-71Li Lan.A frequency yield inverse algorithms for diffuse distribution coefficient for water quality model[J].Journal of Hydraulic Engineering,1999,(8):67-71
[6]闵涛,周孝德.河流水质纵向弥散系数反问题的迭代算法[J].水动力学研究与进展:A辑,2003,18(5):547-552Min Tao,Zhou Xiaode.An iterature method of the inverse problem for the dispersion coefficient in water quality model[J].Journal of Hydrodynamics:Ser A,2003,18(5):547-552
[7]刘晓东,陈立强,华祖林,等.河道一维污染源识别反问题[J].水力发电学报,2014,33(6):132-135Liu Xiaodong,Chen Liqiang,Hua Zulin,et al.Inverse problem on pollutant source identification in 1D channel[J].Journal of Hydroelectric Engineering,2014,33(6):132-135
[8]金忠青,陈夕庆.用脉冲谱-优化法求解对流-扩散方程源项控制反问题[J].河海大学学报,1992,20(2):1-8Jin Zhongqing,Chen Xiqing.Numerical solution to an inverse problem of source control for convection-diffusion equations by PST-Optimization[J].Journal of Hohai University,1992,20(2):1-8
[9]金忠青,陈金杭.二维对流-扩散方程反问题的求解[J].河海大学学报,1993,21(5):1-10Jin Zhongqing,Chen Jinhang.Numerical solution to the inverse problem of 2-Dimensional convection-diffusion equation[J].Journal of Hohai University,1993,21(5):1-10
[10]高秀敏,魏泽勋,吕咸青,等.伴随同化方法在中国近海海洋数值模拟中的应用[J].海洋科学进展,2010,28(4):545-553Gao Xiumin,Wei Zexun,LüXianqing,et al.Applications of adjoint data-assimilation method to ocean numerical simulation for China adjacent seas[J].Advances in Marine Science,2010,28(4):545-553
[11]刘峰,胡非,王锷一.用伴随方程研究空气污染的优化控制[J].环境科学学报,2003,23(4):472-475Liu Feng,Hu Fei,Wang Eyi.Study on optimal control of air pollution using adjoint equation[J].Acta Scientiae Circumstantiae,2003,23(4):472-475
[12]王东晓,朱江.伴随同化方法在海洋数值模式中的应用[J].地球物理学进展,1997,12(1):98-107Wang Dongxiao,Zhu Jiang.Applications of the adjoint method to oceanic numerical models[J].Progress in Geophysics,1997,12(1):98-107
[13]吕咸青,刘文剑.数据同化中的伴随方法及其有关问题的研究[J].海洋科学,2001,25(3):44-50LüXianqing,Liu Wenjian.Study on the adjoint method in data assimilation and the related problems[J].Marine Sciences,2001,25(3):44-50
[14]吕咸青,田纪伟,吴自库.渤、黄海的底摩擦系数[J].力学学报,2003,35(4):465-468LüXianqing,Tian Jiwei,Wu Ziku.The bottom friction coefficients of the Bohai Sea and the Huanghai Sea[J].Acta Mechanica Sinica,2003,35(4):465-468
[15]吕咸青,方国洪.渤海开边界潮汐的伴随反演[J].海洋与湖沼,2002,33(2):113-120LüXianqing,Fang Guohong.Inversion of the tides on the open boundary of the Bohai Sea by adjoint method[J].Oceanologica et Limnologia Sinica,2002,33(2):113-120
[16]何伯荣,马继瑞,韩桂军,等.海水温度垂直分布预报数据同化的离散伴随算子法[J].计算物理,2000,17(5):553-559He Borong,Ma Jirui,Han Guijun,et al.A method of discrete adjoint operator in data assimilation for the prediction of the vertical distribution of sea temperature[J].Chinese Journal of Computational Physics,2000,17(5):553-559
[17]徐青,刘玉光,程永存,等.海洋生态模型中的伴随同化方法[J].海洋通报,2005,24(6):58-64Xu Qing,Liu Yuguang,Chen Yongcun,et al.Adjoint method in marine ecosystem models[J].Marine Science Bulletin,2005,24(6):58-64
[18]武周虎.倾斜岸坡深度平均浓度分布及污染混合区解析计算[J].水利学报,2015,46(10):1172-1180Wu Zhouhu.Analytical calculation of the depth-averaged concentration distribution and pollutant mixing zone for sloped bank[J].Journal of Hydraulic Engineering,2015,46(10):1172-1180
[19]金文龙,彭辉,高俊杰,等.中小河道突发事故污染源强非稳态过程反问题[J].水资源保护,2013,29(2):18-21Jin Wenlong,Peng Hui,Gao Junjie,et al.Inverse problem of unsteady source intensity change process in sudden pollution accidents in medium-and small-sized rivers[J].Water Resources Protection,2013,29(2):18-21
[20]Guymer I.Longitudinal dispersion in sinuous channel with changes in shape[J].Hydraulic Engineering,1998,124(1):33-40
[21]Ding Y,Wang S S Y.Optimal control of open-channel flow using adjoint sensitivity analysis[J].Journal of Hydraulic Engineering,2006,132(11):1215-1228
[22]Yoshida K,Maeno S.Inverse estimation of distributed roughness coefficients in vegetated flooded rivers[J].Journal of Hydraulic Research,2014,52(6):811-823