An explicit four-dimensional variational data assimilation method based on the proper orthogonal decomposition: Theoretics and evaluation

The proper orthogonal decomposition (POD) method is used to construct a set of basis functions for spanning the ensemble of data in a certain least squares optimal sense. Compared with the singular value decomposition (SVD), the POD basis functions can capture more energy in the forecast ensemble space and can represent its spatial structure and temporal evolution more effectively. After the analysis variables are expressed by a truncated expansion of the POD basis vectors in the ensemble space, the control variables appear explicitly in the cost function, so that the adjoint model, which is used to derive the gradient of the cost function with respect to the control variables, is no longer needed. The application of this new technique significantly simplifies the data assimilation process. Several assimilation experiments show that this POD-based explicit four-dimensional variational data assimilation method performs much better than the usual ensemble Kalman filter method on both enhancing the assimilation precision and reducing the computation cost. It is also better than the SVD-based explicit four-dimensional assimilation method, especially when the forecast model is not perfect and the forecast error comes from both the noise of the initial filed and the uncertainty of the forecast model. Supported by the National Natural Science Foundation of China (Grant No. 40705035), National High Technology Research and Development Program of China (Grant No. 2007AA12Z144), Knowledge Innovation Project of Chinese Academy of Sciences (Grant Nos. KZCX2-YW-217 and KZCX2-YW-126-2), and National Basic Research Program of China (Grant No. 2005CB321704)     

Estimating the 4DVAR analysis error of GODAE products

We explore the ocean circulation estimates obtained by assimilating observational products made available by the Global Ocean Data Assimilation Experiment (GODAE) and other sources in an incremental, four-dimensional variational data assimilation system for the Intra-Americas Sea. Estimates of the analysis error (formally, the inverse Hessian matrix) are computed during the assimilation procedure. Comparing the impact of differing sea surface height and sea surface temperature products on both the final analysis error and difference between the model state estimates, we find that assimilating GODAE and non-GODAE products yields differences between the model and observations that are comparable to the differences between the observation products themselves. While the resulting analysis error estimates depend on the configuration of the assimilation system, the basic spatial structures of the standard deviations of the ocean circulation estimates are fairly robust and reveal that the assimilation procedure is capable of reducing the circulation uncertainty when only surface data are assimilated.     

Evaluation of Global Ocean Data Assimilation Experiment products on South Florida nested simulations with the Hybrid Coordinate Ocean Model

The South Florida Hybrid Coordinate Ocean Model (SoFLA-HYCOM) encompasses a variety of coastal regions (the broad Southwest Florida shelf, the narrow Atlantic Keys shelf, the shallow Florida Bay, and Biscayne Bay) and deep regions (the Straits of Florida), including Marine Protected Areas (the Florida Keys Marine Sanctuary and the Dry Tortugas Ecological Reserve). The presence of the strong Loop Current/Florida Current system and associated eddies connects the local and basin-wide dynamics. A multi-nested approach has been developed to ensure resolution of coastal-scale processes and proper interaction with the large scale flows. The simulations are free running and effects of data assimilation are introduced through boundary conditions derived from Global Ocean Data Assimilation Experiment products. The study evaluates the effects of boundary conditions on the successful hindcasting of circulation patterns by a nested model, applied on a dynamically and topographically complex shelf area. Independent (not assimilated) observations are employed for a quantitative validation of the numerical results. The discussion of the prevailing dynamics that are revealed in both modeled and observed patterns suggests the importance of topography resolution and local forcing on the inner shelf to middle shelf areas, while large scale processes are found to dominate the outer shelf flows. The results indicate that the successful hindcasting of circulation patterns in a coastal area that is characterized by complex topography and proximity to a large scale current system requires a dynamical downscaling approach, with simulations that are nested in a hierarchy of data assimilative outer models.     

基于集合卡尔曼滤波的土壤水分同化变权实验研究

将集合预报成员不等权重思想与集合卡尔曼滤波(EnKF)同化方法相结合,利用集合成员的离散度作为权重因子,对EnKF算法优化后的集合成员采用不等权重取平均值,作为同化后的预报值。首先检验了集合离散度和预报误差的相关性,证明将集合离散度作为权重因子的可靠性;利用一个水文过程模型(DHSVM)和实测数据进行了土壤水分的同化变权实验,对EnKF分析和更新后产生的土壤水分集合,分别采用算术平均和变权平均的方法,计算土壤水分预报结果并进行比较。实验表明,集合变权平均法可以进一步提高同化的预报效果。     

Sequential assimilation of a year-long time-series of SeaWiFS chlorophyll data into a 3D biogeochemical model on the French Mediterranean coast

The objective of this paper was to explore the potentialities of sequential statistical estimation methods to assimilate ocean color observations in a primary production model coupled to a 3D hydrodynamic model. The study site was the gulf of Fos—Rhone delta region on the French Mediterranean coast. The high rate of primary production generally observed in this area is mainly due to strong nutrient inputs of the Rhone River. The assimilation method is derived from the singular evolutive extended Kalman filter (SEEK), which uses an error subspace represented by multivariate empirical orthogonal functions (EOF). SeaWiFS chlorophyll data were assimilated by the ecosystem model during a simulation performed under realistic meteorological conditions for the year 2001. An ‘adaptive’ computing method of the EOF was applied in order to lower the instabilities of the filter. Data assimilation system permitted to reduce the mean absolute error between model and data from 1.51 to 0.77 mg m⁻³ thanks to the SEEK filter, showing a substantial 49% gain. Efficiency of the SEEK filter was then investigated considering several areas of interest inside the modelled domain. Finally, impact of the assimilation scheme on non-observed variables was illustrated and discussed. Throughout this experimentation the data assimilation system showed its potential regarding operational systems.     

Flow relevant covariance localization during dynamic data assimilation using EnKF

Multiphase dynamic data integration into high resolution subsurface models is an integral aspect of reservoir and groundwater management strategies and uncertainty assessment. Over the past two decades, advances in computing and the development and implementation of robust algorithms for automatic history matching have considerably reduced the time and effort associated with subsurface characterization and reduced the subjectivity associated with manual model calibration. However, reliable and accurate subsurface characterization continues to be challenging due to the large number of model unknowns to be estimated using a relatively smaller set of measurements. For ensemble-based methods in particular, the difficulties are compounded by the need for a large number of model replicates to estimate sample-based statistical measures, specifically the covariances and cross-covariances that directly impact the spread of information from the measurement locations to the model parameters. Statistical noise resulting from modest ensemble sizes can overwhelm and degrade the model updates leading to geologically inconsistent subsurface models. In this work we propose to address the difficulties in the implementation of the ensemble Kalman filter (EnKF) for operational data integration problems. The methods described here use streamline-derived information to identify regions within the reservoir that will have a maximum impact on the dynamic response. This is achieved through spatial localization of the sample-based cross-covariance estimates between the measurements and the model unknowns using streamline trajectories. We illustrate the approach with a synthetic example and a large field-study that demonstrate the difficulties with the traditional EnKF implementation. In both the numerical experiments, it is shown that these challenges are addressed using flow relevant conditioning of the cross-covariance matrix. By mitigating sampling error in the cross-covariance estimates, the proposed approach provides significant computational savings through the use of modest ensemble sizes, and consequently offers the opportunity for use with large field-scale groundwater and reservoir characterization studies.     

Assimilation of TOPEX/POSEIDON Altimeter Data with a Reduced Gravity Model of the Japan Sea

Sea level data measured by TOPEX/POSEIDON over the Japan Sea from 1993 to 1994 is analyzed by assimilation using an approximate Kalman filter with a 1.5 layer (reduced-gravity) shallow water model. The study aims to extract signals associated with the first baroclinic mode and to determine the extent of its significance. The assimilation dramatically improves the model south of the Polar Front where as much as 20 cm² of the observed sea level variance can be accounted for. In comparison, little variability in the northern cold water region is found consistent with the model dynamics, possibly due to significant differences in stratification.     

国家气候中心全球海洋资料四维同化系统在热带太平洋的结果初步分析

介绍了国家气候中心(NCC)“全球海洋资料四维同化系统”(简称NCC-GODAS).该系统包含观测资料预处理系统、插值分析系统和所应用的动力模式.插值分析系统采用四维同化技术方案,在时间上设置一个4周的窗口,将此窗口之内的观测资料以一定的权重插入插值分析系统,在空间上采用三维变分方案.海洋动力模式为“九五”期间LASG研制的L30T63OGCM 1 0版本.文中考察了该系统从1982年到2003年3月在热带太平洋的部分同化分析结果,并与NCEP的再分析资料和EMC/NCEP的太平洋区域海洋资料同化系统的结果进行了对比分析.结果显示,该系统的同化结果(如SST,SSTA,Nino指数,次表层海温变化等)与NCEP的同期同化结果具有很好的一致性.同时,该系统得出的海洋同化资料气候场与海洋模式气候场相比,有显著的改进.表明该系统具有较好的同化能力,其同化结果可为海-气耦合模式进行季节和跨季节的气候预测业务提供可信的海洋初始场资料,同时还可以为相关研究提供海洋分析场.     

循环同化相控阵雷达数据模拟对流触发同化方案研究

利用WRF-EnKF同化系统,以2020年7月5日北京大兴发生的一次强对流天气背景下对流触发过程为个例,研究同化C波段相控阵雷达数据时更优的同化方案设置。本研究从同化频率、晴空数据处理阈值以及边界层杂波处理高度3个方面进行了研究。结果显示,高频同化可以抑制虚假回波,并有利于获得更准确的对流预报结果。将可靠晴空回波识别阈值设为-10 dBZ并剔除边界层内的低值回波可以有效改进对流触发的预报效果。为以后C波段相控阵雷达同化应用提供了新的同化方案思路。     

集合卡尔曼滤波数据同化在一维波动方程中的应用

简要回顾了集合卡尔曼滤波(EnKF：Ensemble Kalman Filter)数据同化方法的发展历史,并介绍了EnKF数据同化方法的基本原理,利用一维非线性波动方程进行了数值试验。EnKF数据同化方法的实现过程简单可行。避免了EKF中协方差演变方程预报过程中出现的计算不准确和关于协方差矩阵的大量数据的存储问题,最主要的是EnKF可以有效控制模式变量估计误差方差的增长,改善预报效果。