非饱和土壤水的集合卡尔曼滤波Ⅱ:不一致性问题解决方法比较  

Ensemble Kalman filter for unsaturated soil water flowⅡ:Comparison of methods to deal with inconsistency

作　　者：张秋汝[1] 史良胜[1] 林琳[1] 杨楚慧 

机构地区：[1]武汉大学水资源与水电工程科学国家重点实验室

出　　处：《水利学报》2015年第12期1470-1478,1486,共10页Journal of Hydraulic Engineering

基　　金：国家自然科学基金项目(51179132;51279141)

摘　　要：集合卡尔曼滤波(En KF)能够便捷地根据观测信息改进土壤水的预测精度,但在非线性问题中存在不一致性问题:当同时更新变量(水头或含水率)和非饱和水力参数时,En KF会导致参数和变量之间不再服从Richards方程关系。本文以Borden试验场的饱和渗透系数数据为基础,构造土柱试验,研究了不一致性对土壤水数据同化带来的破坏以及相应的迭代型解决方案。研究结果表明:在非均匀土壤中,En KF可能会引发强烈的不一致性,对含水率预测和参数估计的精度造成破坏;不一致性的峰值位置与水流锋面保持一致,且受边界条件影响;对于同类型的观测与待求参数,不一致性一般是随着观测点数量与待求参数数量的比例的增大而减小;当观测与水头或含水率之间具有强烈的非线性时(如强烈的干湿交替),推荐采用能在保证计算效率的前提下有效降低不一致性影响的CEn KF或MREn KF方法;当观测信息相对充足,不一致性可忽略时,En KF方法更具优势。Ensemble Kalman filter （EnKF） can easily improve the soil water prediction by incorporating measurement information, but it may cause inconsistency in non-linear problems. In this paper, inconsisten- cy is defined as that parameters and pressure head are no longer subject to Richards＂ equation when they are updated simultaneously. Based on the hydraulic conductivity data in Borden experimental site, a synthet- ic soil column experiment is constructed to investigate the potential damage from inconsistency and the itera- tive approaches to eliminate or alleviate inconsistency. The results show that in heterogeneous soil, EnKF may cause strong inconsistency, which damages the accuracy of soil water prediction and parameter estima- tion. The peak of inconsistency is consistent with the flow front and influenced by the boundary condition. In general, when using the same type of observations to estimate the same type of parameters, the greater the proportion of observation number to parameter number, the less the inconsistency. When the relation- ship between pressure head, soil moisture and the observations is strongly nonlinear, we propose CEnKF or MREnKF algorithm which can effectively reduce the influence of inconsistency with low cost. When the observation information is relatively abundant ,then the negative effects of inconsistency can be ignored, En- KF is advantageous.

关 键 词：非饱和流 集合卡尔曼滤波 不一致性 迭代型方法 

分 类 号：S152.7[农业科学—土壤学]