集合卡尔曼滤波估计水文地质参数的局域化修正

集合卡尔曼滤波(Ensemble Kalman Filter,EnKF)作为一种有效的数据同化方法,在众多数值实验中体现优势的同时,也暴露了它使用小集合估计协方差情况下精度较低的缺陷。为了降低取样噪声对协方差估计的干扰并提高滤波精度,应用局域化函数对小集合估计的协方差进行修正,即在协方差矩阵中以舒尔积的形式增加空间距离权重以限制远距离相关。在一个二维理想孔隙承压含水层模型中的运行结果表明,局域化对集合卡尔曼滤波估计地下水参数的修正十分有效,局域化可以很好地过滤小集合估计中噪声的影响,节省计算量的同时又可以防止滤波发散。相关长度较小的水文地质参数(如对数渗透系数)更容易受到噪声的干扰,更有必要进行局域化修正。     

基于局域化EnKF同时同化地下水水流和溶质运移数据的渗透系数场识别研究

局域化改进集合卡尔曼滤波（EnKF）可以克服EnKF方法在使用小集合时,对参数识别精度较低的缺陷,其能同化 地下水位观测数据有效识别渗透系数场。实际工作中,溶质运移数据也较容易获得。崔凯鹏（2013）尝试增加溶质运移 数据以改进只同化水流数据对渗透系数的估计结果,但是精度提高有限。本文在其基础上修改模型,进一步增加溶质注 入井,探究同时同化水头和溶质运移数据,对渗透系数场识别效果,之后对比了局域化EnKF与非局域化EnKF参数识别结 果,并分析了溶质影响范围与参数识别的关系。结果表明：同时同化溶质运移和水头资料,比同化单一种类观测数据识别 的渗透系数精度更高;相同实现数目下,局域化EnKF比EnKF对渗透系数场的估计结果与真实场更为接近;仅考虑溶质影 响范围内的渗透系数,同化水头数据在最后时刻参数识别结果好于同化溶质运移数据参数识别结果,但差别不大。     

基于集合卡尔曼平滑算法的土壤水分同化

为研究观测资料稀少情况下土壤质地及有机质对土壤水分同化的影响,发展了集合卡尔曼平滑(Ensemble Kalman Smooth, EnKS)的土壤水分同化方案。利用黑河上游阿柔冻融观测站2008年6月1日至10月29日的观测数据,使用EnKS算法将表层土壤水分观测数据同化到简单生物圈模型(Simple Biosphere Model 2, SiB2)中,分析不同方案对土壤水分估计的影响,并与集合卡尔曼滤波算法(EnKF)的结果进行比较。研究结果表明,土壤质地和有机质对表层土壤水分模拟结果影响最大而对深层的影响相对较小;利用EnKF和EnKS算法同化表层土壤水分观测数据,均能够显著提高表层和根区土壤水分估计的精度,EnKS算法的精度略高于EnKF且所受土壤质地和有机质的影响小于EnKF;当观测数据稀少时,EnKS算法仍然可以得到较高精度的土壤水分估计。     

基于EnKF融合地球物理数据刻画含水层非均质性

含水层非均质性的刻画是模拟地下水中污染物运移的关键。以渗透系数为研究对象,构建了综合集合卡尔曼滤波方法、有效电阻率模型与地下水运移模型的同化框架,通过融合地球物理观测数据与污染物浓度观测数据来推估渗透系数的空间分布。基于理想算例,验证了该同化框架刻画含水层非均质渗透系数场的有效性,并针对不同初始参数信息与观测类型对比了耦合与非耦合水文地球物理方法的适用性。研究结果表明:基于集合卡尔曼滤波方法同化多种类型的观测数据,可有效地推估非均质参数空间分布。当初始信息较准确时,耦合方法的参数推估精度更高;初始信息存在偏差时,非耦合方法有更好的同化效果。由于非耦合方法计算成本较低且对初始信息缺失时适用性更强,在实际应用中可先基于非耦合方法初步估计参数,再利用耦合方法进一步提高参数推估精度。融合多种类型观测数据可有效提高参数推估效果。     

土壤水分同化系统的敏感性试验研究

利用1998年7月6日至8月9日青藏高原GAME-Tibet试验区MS3608站点的4cm、20cm和100cm的土壤水分观测数据同化SiB2模型输出的表层、根区和深层土壤水分,探讨了一个基于集合卡尔曼滤波和简单生物圈模型的单点土壤水分同化方案。分析和评价了集合大小、同化周期、模型误差、背景场误差以及观测误差对同化系统性能的影响。结果表明:①增加集合数目可以减小土壤水分同化系统的误差,但同时又降低了运行效率;②对于集合卡尔曼滤波,初始场的估计是否准确对同化系统性能影响不大;③模型误差和观测误差的准确估计可以提高土壤水分的估计精度;④利用数据同化的方法对土壤水分的估计有显著提高。     

不同滤波算法在土壤湿度同化中的应用

为研究不同滤波算法在土壤湿度同化中的有效性,以及土壤湿度模拟结果对模型参数的敏感性,结合简单生物圈模型SiB2,设置敏感性实验,探求土壤饱和水力传导度对土壤湿度模拟结果的影响;并在此基础上,采用集合卡尔曼滤波（EnKF）、无迹卡尔曼滤波（UKF）和无迹粒子滤波（UPF）开展土壤湿度实时同化实验。结果表明：土壤饱和水力传导度能显著影响土壤湿度模拟精度;利用EnKF、UKF、UPF同化站点观测数据,均能改善土壤湿度模拟结果;3种同化方法在不同土壤层的同化效果不同,在土壤表层,EnKF的有效性优于UKF和UPF,在根域层和土壤深层,3种滤波方法有效性在降雨前后相差较大。因此,针对性地选择同化方法,是提高土壤湿度模拟精度的有效手段。     

基于集合卡尔曼滤波的多相流模型参数估计——以室内二维砂箱中重质非水相污染物入渗为例

重质非水相有机污染物(DNAPL)泄漏到地下后,其运移与分布特征受渗透率非均质性影响显著。为刻画DNAPL污染源区结构特征,需进行参数估计以描述水文地质参数的非均质性。本研究构建了基于集合卡尔曼滤波方法(EnKF)与多相流运移模型的同化方案,通过融合DNAPL饱和度观测数据推估非均质介质渗透率空间分布。通过二维砂箱实际与理想算例,验证了同化方法的推估效果,并探讨了不同因素对同化的影响。研究结果表明:基于EnKF方法同化饱和度观测资料可有效地推估非均质渗透率场;参数推估精度随观测时空密度的增大而提高;观测点位置分布对同化效果有所影响,布置在污染集中区域的观测数据对于参数估计具有较高的数据价值。     

地下水位预测:集合卡尔曼滤波（EnKF）应用概述

以地下水数值模型为例,分析了集合卡尔曼滤波在进行数据融合时的基本原理和步骤。根据集合卡尔曼滤波的实际功能,并结合中国地下水监测的实际状况,分析了集合卡尔曼滤波在地下水位预测中的应用前景:认为在未来地下水位预报预警工作中,利用集合卡尔曼滤波技术提高地下水位预测的准确性,具有良好的应用前景。     

地下水位预测:集合卡尔曼滤波（EnKF）应用概述

以地下水数值模型为例,分析了集合卡尔曼滤波在进行数据融合时的基本原理和步骤。根据集合卡尔曼滤波的实际功能,并结合中国地下水监测的实际状况,分析了集合卡尔曼滤波在地下水位预测中的应用前景:认为在未来地下水位预报预警工作中,利用集合卡尔曼滤波技术提高地下水位预测的准确性,具有良好的应用前景。     

基于EnKF综合水头和浓度观测数据推估地下水流模型参数

地下水反应运移模型具有参数个数众多,观测数据类型多样的特点。为了探究不同类型观测数据在反应运移模拟数据同化中的数据价值,构建了三氯乙烯降解反应运移模型的理想算例,基于水头和浓度两种类型观测数据,采用集合卡尔曼滤波方法推估渗透系数和贮水系数的非均质空间分布,讨论了影响同化结果的因素。结果表明:与仅同化水头数据的结果相比,联合同化水头和浓度观测数据推估渗透系数场和贮水系数场时具有更高的精度,在观测数据拟合和模型预测方面也有更好的表现。与目前溶质运移模型、非饱和流模型等地下水模型中的研究结果相似,数据同化结果受样本数量,观测井的数量和位置的影响,合理优化布置监测井和选择样本数量可有效改善数据同化效果并提高计算效率。     

土壤湿度观测、模拟和估算研究

总结土壤湿度的观测手段和土壤湿度数据集建立的现状,详细阐述与土壤湿度模拟有关的方程离散化求解、物理和生化过程、陆面过程模式比较和陆面模式参数优化等方面的研究进展;综述估算土壤湿度廓线的数据同化方法,仔细比较集合卡曼滤波(EnKF)和四维变分(4-D Var)2类目前流行的同化算法,并对估算土壤湿度廓线的研究工作进行全面评估;最后,对土壤湿度观测、模拟和同化中需继续努力的方向进行了思索和展望。     

Localization Analysis of Data Assimilation Methods Coupled with Fuzzy Control Algorithms

Due to the fake correlation between distance-observations and assimilation-states during data assimilation, more attention has been paid to the localization method. Meanwhile, in the case of assimilation with a small number of sets, the observation data is difficult to be used effectively, which makes the assimilation effect not good enough. Therefore, a new fuzzy control was proposed to analyze the local method. The fuzzy control algorithm was used to judge the distance between the observation point and the status update point and to construct the fuzzy weight of the observation position. The study aimed to make use of the nonlinear Lorenz-96 model to compare the Fuzzy control combine Local Analysis algorithm (FLETKF) and Fuzzy control combine Ensemble Transform Kalman Filter method (FETKF), local Ensemble Transform Kalman Fliter (LETKF) and Ensemble Transform Kalman Filter algorithm (ETKF) when the nonlinear forced parameter changed. In addition, the strengths and weaknesses of four algorithms were discussed by different intensities. The results show that the new method can obtain more effective observation weights, avoiding the false correlation between long-distance observations and state variables, reducing the errors caused by the observation data which is difficult to be used effectively. Under different assimilation strength, FLETKF can maintain good robustness. However, in terms of assimilation time, the construction of the equivalent weight of the observation position requires additional time because the localization assimilation method of fuzzy control determines the distance between the observation point and the status update point. Parallel computing performance needs further study.     

评估集合卡曼滤波反演土壤湿度廓线的性能

集合卡曼滤波由于易于使用而被广泛地应用到陆面数据同化研究中,它是建立在模型为线性、误差为正态分布的假设上,而实际土壤湿度方程是高度非线性的,并且当土壤过干或过湿时会发生样本偏斜.为了全面评估它在同化表层土壤湿度观测来反演土壤湿度廓线的性能,特引入不需要上述假设的采样重要性重采样粒子滤波,比较非线性和偏斜性对同化算法的影响.结果显示:不管是小样本还是大样本,集合卡曼滤波都能快速、准确地逼近样本均值,而粒子滤波只有在大样本时才能缓慢地趋近;此外,集合卡曼滤波的粒子边缘概率密度及其偏度和峰度与粒子滤波完全不同,前者粒子虽不完全满足正态分布,但始终为单峰状态,而后者粒子随同化推进经历了单峰到双峰再到单峰的变化.     

数据同化算法在青藏高原高寒生态系统能量—水分平衡分析中的应用

位于青藏高原腹地的多年冻土地带,其冻融过程中的土壤含水量和土壤冻结深度的变化对气候强烈响应并产生显著的陆面能—水平衡变化,进而又对全球气候产生较大的反馈作用。为了能准确模拟这种变化,选取青藏高原多年冻土分布区的风火山左冒孔流域（长江源）进行了相关的野外数据采集和试验,以考虑土壤冻融影响的水—热耦合陆面过程模型——SHAW为动力学约束框架,验证集合卡尔曼滤波算法在改进模型对土壤冻融过程中土壤水分和冻土深度的计算效果。基于试验点的数据同化计算结果表明：数据同化方法可以融合观测信息显著提高水—热耦合模型对土壤冻融过程中状态变量（土壤水分和冻深）的模拟,并进而改善模型对其它相关能量—水分变量的计算,为在高寒冻土地区利用多源信息进行融合监测提供了理论依据。     

Fast linearized forecasts for subsurface flow data assimilation with ensemble Kalman filter

Ensemble methods present a practical framework for parameter estimation, performance prediction, and uncertainty quantification in subsurface flow and transport modeling. In particular, the ensemble Kalman filter (EnKF) has received significant attention for its promising performance in calibrating heterogeneous subsurface flow models. Since an ensemble of model realizations is used to compute the statistical moments needed to perform the EnKF updates, large ensemble sizes are needed to provide accurate updates and uncertainty assessment. However, for realistic problems that involve large-scale models with computationally demanding flow simulation runs, the EnKF implementation is limited to small-sized ensembles. As a result, spurious numerical correlations can develop and lead to inaccurate EnKF updates, which tend to underestimate or even eliminate the ensemble spread. Ad hoc practical remedies, such as localization, local analysis, and covariance inflation schemes, have been developed and applied to reduce the effect of sampling errors due to small ensemble sizes. In this paper, a fast linear approximate forecast method is proposed as an alternative approach to enable the use of large ensemble sizes in operational settings to obtain more improved sample statistics and EnKF updates. The proposed method first clusters a large number of initial geologic model realizations into a small number of groups. A representative member from each group is used to run a full forward flow simulation. The flow predictions for the remaining realizations in each group are approximated by a linearization around the full simulation results of the representative model (centroid) of the respective cluster. The linearization can be performed using either adjoint-based or ensemble-based gradients. Results from several numerical experiments with two-phase and three-phase flow systems in this paper suggest that the proposed method can be applied to improve the EnKF performance in large-scale problems where the number of full simulation is constrained.     

Improved initial ensemble generation coupled with ensemble square root filters and inflation to estimate uncertainty

The performance of the Ensemble Kalman Filter method (EnKF) depends on the sample size compared to the dimension of the parameters space. In real applications insufficient sampling may result in spurious correlations which reduce the accuracy of the filter with a strong underestimation of the uncertainty. Covariance localization and inflation are common solutions to these problems. The Ensemble Square Root Filters (ESRF) is also better to estimate uncertainty with respect to the EnKF. In this work we propose a method that limits the consequences of sampling errors by means of a convenient generation of the initial ensemble. This regeneration is based on a Stationary Orthogonal-Base Representation (SOBR) obtained via a singular value decomposition of a stationary covariance matrix estimated from the ensemble. The technique is tested on a 2D single phase reservoir and compared with the other common techniques. The evaluation is based on a reference solution obtained with a very large ensemble (one million members) which remove the spurious correlations. The example gives evidence that the SOBR technique is a valid alternative to reduce the effect of sampling error. In addition, when the SOBR method is applied in combination with the ESRF and inflation, it gives the best performance in terms of uncertainty estimation and oil production forecast.     

An efficient matrix-free algorithm for the ensemble Kalman filter

In this work, we present an efficient matrix-free ensemble Kalman filter (EnKF) algorithm for the assimilation of large data sets. The EnKF has increasingly become an essential tool for data assimilation of numerical models. It is an attractive assimilation method because it can evolve the model covariance matrix for a non-linear model, through the use of an ensemble of model states, and it is easy to implement for any numerical model. Nevertheless, the computational cost of the EnKF can increase significantly for cases involving the assimilation of large data sets. As more data become available for assimilation, a potential bottleneck in most EnKF algorithms involves the operation of the Kalman gain matrix. To reduce the complexity and cost of assimilating large data sets, a matrix-free EnKF algorithm is proposed. The algorithm uses an efficient matrix-free linear solver, based on the Sherman–Morrison formulas, to solve the implicit linear system within the Kalman gain matrix and compute the analysis. Numerical experiments with a two-dimensional shallow water model on the sphere are presented, where results show the matrix-free implementation outperforming an singular value decomposition-based implementation in computational time.