Data assimilation in groundwater modelling: ensemble Kalman filter versus ensemble smoothers

Groundwater modelling calls for an effective and robust data integrating method to fill the gap between the model and observation data. The ensemble Kalman filter (EnKF), a real‐time data assimilation method, has been increasingly applied in multiple disciplines such as petroleum engineering and hydrogeology. In this approach, a groundwater model is updated sequentially with measured data such as hydraulic head and concentration. As an alternative to the EnKF, the ensemble smoother (ES) has been proposed for updating groundwater models using all the data together, with much less computational cost. To further improve the performance of the ES, an iterative ES has been proposed for continuously updating the model by assimilating measurements together. In this work, we compare the performance of the EnKF, the ES, and the iterative ES using a synthetic example in groundwater modelling. Hydraulic head data modelled on the basis of the reference conductivity field are used to inversely estimate conductivities at unsampled locations. Results are evaluated in terms of the characterization of conductivity and groundwater flow predictions. It is concluded that (a) the iterative ES works better than the standard ES because of its continuous updating and (b) the iterative ES could achieve results comparable with those of the EnKF, with less computational cost. These findings show that the iterative ES should be paid much more attention for data assimilation in groundwater modelling.     

A discretization and multigrid solver for a Darcy–Stokes system of three dimensional vuggy porous media

We develop a finite element discretization and multigrid solver for a Darcy–Stokes system of three-dimensional vuggy porous media, i.e., porous media with cavities. The finite element method uses low-order mixed finite elements in the Darcy and Stokes domains and special transition elements near the Darcy–Stokes interface to allow for tangential discontinuities implied by the Beavers–Joseph boundary condition. We design a multigrid method to solve the resulting saddle point linear system. The intertwining of the Darcy and Stokes subdomains makes the resulting matrix highly ill-conditioned. The velocity field is very irregular, and its discontinuous tangential component at the Darcy–Stokes interface makes it difficult to define intergrid transfer operators. Our definition is based on mass conservation and the analysis of the orders of magnitude of the solution. The coarser grid equations are defined using the Galerkin method. A new smoother of Uzawa type is developed based on taking an optimal step in a good search direction. Our algorithm has a measured convergence factor independent of the size of the system, at least when there are no disconnected vugs. We study the macroscopic effective permeability of a vuggy medium, showing that the influence of vug orientation; shape; and, most importantly, interconnectivity determine the macroscopic flow properties of the medium. This work was supported by the U.S. National Science Foundation under grants DMS-0074310 and DMS-0417431.     

LOESS用于GNSS垂向坐标时间序列噪声识别与提取

针对GNSS垂向坐标时间序列噪声复杂、精度较差等特点,采用局部加权回归模型(locally weighted regression, LOESS)对中国大陆构造环境监测网络中289个GNSS站的垂向坐标时间序列进行降噪分析。首先利用LOESS方法对预处理后的时间序列进行降噪处理,得到降噪后的时间序列及噪声序列;然后采用Durbin-Watson(DW)检验对降噪后的噪声序列进行自相关性检验,同时采用Wilcoxon秩和检验方法对降噪前后序列的标准差、噪声项、速度不确定度等指标进行显著性检验;最后采用降噪前后序列的信噪比及前3个指标来定量评价降噪效果。结果表明,各测站降噪后的噪声序列不存在自相关性,采用LOESS方法降噪处理后各评价指标均有显著改正,表明LOESS方法能够有效减少GNSS垂向坐标时间序列中的噪声,进一步提高GNSS垂向坐标时间序列的精度。     

Multi-level arc combination with stochastic parameters

 The method of square root information filtering and smoothing (SRIF/S) is reviewed and has been implemented in the combined square root information filter and smoother (CSRIFS) program. CSRIFS is a part of the GEOSAT space geodesy software developed at Forsvarets forskningsinstitutt (FFI, The Norwegian Defence Research Establishment). The state vectors and complete variance–covariance matrices from the analyses of a number of independent arcs of space geodesy data can be combined using CSRIFS. Four parameter levels are available and any parameter can, at each level, be represented as either a constant or a stochastic parameter (white noise, colored noise, or random walk). The batch length (i.e. the time interval between the addition of noise to the SRIF array) can be made time and parameter dependent. CSRIFS was applied in the combination of 623 very long baseline interferometry (VLBI) observing sessions. The purpose of this test was to validate the computer implementation of the SRIF/S method and to give an example of how this method can be used in the analysis of a large number of space geodetic observations. The results show that the implementation is very satisfactory. Received: 28 May 1999 / Accepted: 15 June 2000     

Palaeolimnological evidence for recent climatic change in lakes from the northern Urals, arctic Russia

The recent sediments from two deep arctic lakes, Mitrofanovskoe and Vanuk-ty, situated in the permafrost belt within the Bolshezemelskaya Tundra in the northern Ural region, were studied for diatoms, chironomids, spheroidal carbonaceous particles and stable lead isotopes. The magnitudes and rates-of-change in diatom and chironomid assemblages were numerically estimated. Instrumental climate records were used to assess statistically the amount of variance in diatom and chironomid data explained by temperature. August and September air temperatures have a statistically significant effect on diatom composition at both lakes. At Mitrofanovskoe Lake, major compositional changes in diatom and chironomid assemblages occurred at the turn of the 20th century and might be related to the regional increase in temperature. Chironomid-inferred air temperature also increased by approximately 1 °C since the early 1900s. At both lakes diatom compositional changes, coincident with the increase in June and September temperatures, also occurred in the late 1960s. These compositional changes are correlated with the increase in diatom production, sediment organic content and diatom species richness, and are likely to be a diatom response to the lengthening of the growing season. These changes are also correlated with the circum-Arctic temperature increase from the 1960s. A chironomid response to the late 1960s temperature increase was less pronounced at both lakes. Pollution levels are relatively low and pollution history is unrelated to ecological changes. Both lead isotopes and spheroidal carbonaceous particles show a clear atmospheric pollution signal, peaking in the 1980s.     

四维LOESS插值法在台湾海峡及其邻近海域温盐场研究中的应用

将四维LOESS(locally weighted regression)插值法应用至台湾海峡及其邻近海域,在考虑了研究海域海底地形和岸界对分析结果影响的基础上,通过引入空间和时间拟合函数,有效地解决了调查资料在时间和空间上的不均匀性.通过与气候态WOD01数据及卫星遥感资料的对比分析,可以发现,四维LOESS插值法不仅能够较好地再现研究海域的水文要素整体分布特征,而且对于台湾海峡及其邻近海域的中尺度现象(如夏季浅滩附近的局地低温、东山外海上升流等)也有较好的分辨能力.总的来说,四维LOESS插值法在台湾海峡及其邻近海域的应用是可行、可靠的.     

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。     

The representer method, the ensemble Kalman filter and the ensemble Kalman smoother: A comparison study using a nonlinear reduced gravity ocean model

This paper compares contending advanced data assimilation algorithms using the same dynamical model and measurements. Assimilation experiments use the ensemble Kalman filter (EnKF), the ensemble Kalman smoother (EnKS) and the representer method involving a nonlinear model and synthetic measurements of a mesoscale eddy. Twin model experiments provide the “truth” and assimilated state. The difference between truth and assimilation state is a mispositioning of an eddy in the initial state affected by a temporal shift. The systems are constructed to represent the dynamics, error covariances and data density as similarly as possible, though because of the differing assumptions in the system derivations subtle differences do occur. The results reflect some of these differences in the tangent linear assumption made in the representer adjoint and the temporal covariance of the EnKF, which does not correct initial condition errors. These differences are assessed through the accuracy of each method as a function of measurement density. Results indicate that these methods are comparably accurate for sufficiently dense measurement networks; and each is able to correct the position of a purposefully misplaced mesoscale eddy. As measurement density is decreased, the EnKS and the representer method retain accuracy longer than the EnKF. While the representer method is more accurate than the sequential methods within the time period covered by the observations (particularly during the first part of the assimilation time), the representer method is less accurate during later times and during the forecast time period for sparse networks as the tangent linear assumption becomes less accurate. Furthermore, the representer method proves to be significantly more costly (2–4 times) than the EnKS and EnKF even with only a few outer iterations of the iterated indirect representer method.     

基于交互多模算法的Kalman平滑器在滑坡监测中的应用

将滑坡的监测视为机动目标的跟踪问题,基于传统机动目标跟踪算法的不足,首次引入交互多模算法对滑坡监测数据进行处理。最后在此基础上给出了一种卡尔曼滤波平滑算法,实例仿真结果说明了其有效性。     

卫星导航定位卡尔曼滤波时延平滑方法研究

为进一步提高卫星导航定位精度和性能,介绍和讨论了卡尔曼滤波延时平滑方法,并建立了一种卡尔曼滤波延时平滑定位模型与算法。与经典卡尔曼滤波类似,该算法同样具有状态系统与测量系统两类方程,能够根据后续历元测量值及定位结果向前进行逆向预测与更新,从而达到对整体定位过程再次平滑的目的,更大程度地获得定位结果跟随性与平滑性之间的平衡。通过多种不同情况下的GPS实测试验,对方法的正确性和可行性进行了分析与验证。结果表明,卡尔曼滤波延时平滑定位方法能够适用于多种静态、动态导航应用领域,使输出结果更为平滑和准确,在有效提高定位精度的同时具有更强的抗多径和抗干扰性。