基于集合卡尔曼滤波法的二维土壤水流状态变量和参数联合估计
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摘要
集合卡尔曼滤波方法(EnKF)显式地考虑了模型输入、输出以及模型结构等因素的不确定性,近年来被广泛应用于水文模型参数估计研究中。本文基于EnKF方法开展二维土壤水流运动模型状态变量和参数联合估计研究,设计数值实验探究了在线源入渗条件下EnKF方法对粉壤土、壤土和砂壤土的饱和导水率和进气值参数的估计以及压力水头的同化效果,分析了观测点布置方式和观测点数量对同化效果的影响。研究结果表明,粉壤土条件下观测点垂向布置方式更好;壤土和砂壤土条件下,在0～30cm深土壤中水平向布置观测点可以得到较好的参数估计值。观测点水平向布置时应尽量靠近地表,同化系统可以有效地利用观测信息更新状态向量,参数更快地收敛于真值,但压力水头的同化效果仅限于一定深度的土壤。增加观测点数量可以有效地减小参数估计偏差,进而提高土壤剖面压力水头的预测精度。
The Ensemble Kalman Filter method(EnKF) explicitly considers the uncertainties such as input,output and model structure,and has been widely used in the parameter estimation problem in hydrology. The objective of this study was to extend the use of EnKF to state and parameters estimation of two-dimensional soil water flow model. Numerical experiments were conducted to assess the performance of EnKF on soil hydraulic parameters estimation and pressure head assimilation under the condition of line source infiltration for silt loam,loam and sandy loam. The influence of the arrangement of observation points and the number of observation points on assimilation results was further analyzed. The results show that the vertical arrangement of observation points can obtain better parameter estimation in comparison with that of horizontal arrangement for silt loam. The saturated hydraulic conductivity and shape parameter can be well estimated when the observation points are arranged horizontally in 0-30 cm deep soil for loam and sandy loam.The observation points should be arranged as close as possible to the soil surface,so that the assimilation system can update the state as soon as possible and the parameters converge to the true value more quickly. However the assimilation effect on the pressure head is limited to a certain depth of soil. The prediction errors of soil pressure head in the areas with observation points are smaller than that of areas without observation points. Increasing the number of observation points can improve the prediction of soil pressure head and the estimation of soil hydraulic parameters. The result of this study indicates that the EnKF is an effective method for parameter estimation in two-dimensional soil water flow model.
The Ensemble Kalman Filter method(EnKF) explicitly considers the uncertainties such as input,output and model structure,and has been widely used in the parameter estimation problem in hydrology. The objective of this study was to extend the use of EnKF to state and parameters estimation of two-dimensional soil water flow model. Numerical experiments were conducted to assess the performance of EnKF on soil hydraulic parameters estimation and pressure head assimilation under the condition of line source infiltration for silt loam,loam and sandy loam. The influence of the arrangement of observation points and the number of observation points on assimilation results was further analyzed. The results show that the vertical arrangement of observation points can obtain better parameter estimation in comparison with that of horizontal arrangement for silt loam. The saturated hydraulic conductivity and shape parameter can be well estimated when the observation points are arranged horizontally in 0-30 cm deep soil for loam and sandy loam.The observation points should be arranged as close as possible to the soil surface,so that the assimilation system can update the state as soon as possible and the parameters converge to the true value more quickly. However the assimilation effect on the pressure head is limited to a certain depth of soil. The prediction errors of soil pressure head in the areas with observation points are smaller than that of areas without observation points. Increasing the number of observation points can improve the prediction of soil pressure head and the estimation of soil hydraulic parameters. The result of this study indicates that the EnKF is an effective method for parameter estimation in two-dimensional soil water flow model.
引文
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[11]张秋汝,史良胜,宋雪航,等.非饱和土壤水的集合卡尔曼滤波I:状态向量与非饱和流算法的选择[J].水利学报,2015,46(10):1189-1198.
[12]李超,惠建忠,唐千红,等. EnKF优化土壤湿度方程中参数的性能研究[J].自然资源学报,2015,30(12):2131-2140.
[13] MUALEM Y. A new model for predicting the hydraulic conductivity of unsaturated porous media[J]. Water Re?sources Research,1976,12(3):513-522.
[14] van GENUCHTEN M T. A closed-form equation for predicting the hydraulic conductivity of unsaturated soils 1[J]. Soil Science Society of America Journal,1980,44(5):892-898.
[15]?IM?NEK J,van GENUCHTEN M T,?EJNA M. Development and applications of the HYDRUS and STANMOD software packages and related codes[J]. Vadose Zone Journal,2008,7(2):587-600.
[16] EVENSEN G. The Ensemble Kalman Filter:Theoretical formulation and practical implementation[J]. Ocean Dy?namics,2003,53(4):343-367.
[17] CARSEL R F,PARRISH R S. Developing joint probability distributions of soil water retention characteristics[J]. Water Resources Research,1988,24(5):755-769.
[18] MONTZKA C,MORADKHANI H,WEIHERMüLLER L,et al. Hydraulic parameter estimation by remotelysensed top soil moisture observations with the particle filter[J]. Journal of Hydrology,2011,399(3/4):410-421.
[19] MONTALDO N,ALBERTSON J D,MANCINI M,et al. Robust simulation of root zone soil moisture with assimi?lation of surface soil moisture data[J]. Water Resources Research,2001,37(12):2889-2900.
[20]兰天,康学远,施小清,等.基于EnKF综合水头和浓度观测数据推估地下水流模型参数[J].水文地质工程地质,2017,44(5):6-13.
[2] DUAN J,HOLMES P,TITI E S. Global existence theory for a generalized Ginzburg-Landau equation[J]. Non?linearity,1992,5(6):1303-1314.
[3] EVENSEN G. Sequential data assimilation with a nonlinear quasi-geostrophic model using Monte Carlo methods to forecast error statistics[J]. Journal of Geophysical Research:Oceans,1994,99(C5):10143-10162.
[4] ERDAL D,CIRPKA O A. Joint inference of groundwater-recharge and hydraulic-conductivity fields from head data using the ensemble Kalman filter[J]. Hydrology and Earth System Sciences,2016,20(1):555-569.
[5] HUANG C,HU B X,LI X,et al. Using data assimilation method to calibrate a heterogeneous conductivity field and improve solute transport prediction with an unknown contamination source[J]. Stochastic Environmental Re?search and Risk Assessment,2009,23(8):1155-1167.
[6] MORADKHANI H,HSU K L,GUPTA H,et al. Uncertainty assessment of hydrologic model states and parame?ters:Sequential data assimilation using the particle filter[J]. Water Resources Research,2005,41(5):W05012.
[7] BRANDHORST N,ERDAL D,NEUWEILER I. Soil moisture prediction with the ensemble Kalman filter:Han?dling uncertainty of soil hydraulic parameters[J]. Advances in Water Resources,2017,110:360-370.
[8] LI C,REN L. Estimation of unsaturated soil hydraulic parameters using the ensemble Kalman filter[J]. Vadose Zone Journal,2011,10(4):1205-1227.
[9] SONG X,SHI L,YE M,et al. Numerical comparison of iterative ensemble Kalman filters for unsaturated flow in?verse modeling[J]. Vadose Zone Journal,2014,13(2):1-12.
[10]王文,刘永伟,寇小华,等.基于集合卡尔曼滤波和HYDRUS-1D模型的土壤剖面含水量同化试验[J].水利学报,2012,43(11):1302-1311.
[11]张秋汝,史良胜,宋雪航,等.非饱和土壤水的集合卡尔曼滤波I:状态向量与非饱和流算法的选择[J].水利学报,2015,46(10):1189-1198.
[12]李超,惠建忠,唐千红,等. EnKF优化土壤湿度方程中参数的性能研究[J].自然资源学报,2015,30(12):2131-2140.
[13] MUALEM Y. A new model for predicting the hydraulic conductivity of unsaturated porous media[J]. Water Re?sources Research,1976,12(3):513-522.
[14] van GENUCHTEN M T. A closed-form equation for predicting the hydraulic conductivity of unsaturated soils 1[J]. Soil Science Society of America Journal,1980,44(5):892-898.
[15]?IM?NEK J,van GENUCHTEN M T,?EJNA M. Development and applications of the HYDRUS and STANMOD software packages and related codes[J]. Vadose Zone Journal,2008,7(2):587-600.
[16] EVENSEN G. The Ensemble Kalman Filter:Theoretical formulation and practical implementation[J]. Ocean Dy?namics,2003,53(4):343-367.
[17] CARSEL R F,PARRISH R S. Developing joint probability distributions of soil water retention characteristics[J]. Water Resources Research,1988,24(5):755-769.
[18] MONTZKA C,MORADKHANI H,WEIHERMüLLER L,et al. Hydraulic parameter estimation by remotelysensed top soil moisture observations with the particle filter[J]. Journal of Hydrology,2011,399(3/4):410-421.
[19] MONTALDO N,ALBERTSON J D,MANCINI M,et al. Robust simulation of root zone soil moisture with assimi?lation of surface soil moisture data[J]. Water Resources Research,2001,37(12):2889-2900.
[20]兰天,康学远,施小清,等.基于EnKF综合水头和浓度观测数据推估地下水流模型参数[J].水文地质工程地质,2017,44(5):6-13.
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