A Hybrid Background Error Covariance Model for Assimilating Glider Data into a Coastal Ocean Model

2011 ◽  
Vol 139 (6) ◽  
pp. 1879-1890 ◽  
Author(s):  
Max Yaremchuk ◽  
Dmitri Nechaev ◽  
Chudong Pan
Keyword(s):  
Null Space ◽  
Coastal Ocean ◽  
Ocean Model ◽  
Covariance Operator ◽  
Covariance Model ◽  
Error Statistics ◽  
Background Error ◽  
Background Error Covariance ◽  
Error Covariance ◽  
Coastal Ocean Model

Abstract A hybrid background error covariance (BEC) model for three-dimensional variational data assimilation of glider data into the Navy Coastal Ocean Model (NCOM) is introduced. Similar to existing atmospheric hybrid BEC models, the proposed model combines low-rank ensemble covariances with the heuristic Gaussian-shaped covariances to estimate forecast error statistics. The distinctive features of the proposed BEC model are the following: (i) formulation in terms of inverse error covariances, (ii) adaptive determination of the rank m of with information criterion based on the innovation error statistics, (iii) restriction of the heuristic covariance operator to the null space of , and (iv) definition of the BEC magnitudes through separate analyses of the innovation error statistics in the state space and the null space of . The BEC model is validated by assimilation experiments with simulated and real data obtained during a glider survey of the Monterey Bay in August 2003. It is shown that the proposed hybrid scheme substantially improves the forecast skill of the heuristic covariance model.

Incorporating Ensemble Covariance in the Gridpoint Statistical Interpolation Variational Minimization: A Mathematical Framework

2010 ◽  
Vol 138 (7) ◽  
pp. 2990-2995 ◽  
Author(s):  
Xuguang Wang
Keyword(s):  
Data Assimilation ◽  
Weather Prediction ◽  
Mathematical Framework ◽  
Dependent Manner ◽  
Error Statistics ◽  
Background Error ◽  
Background Error Covariance ◽  
Error Covariance ◽  
Variational Minimization ◽  
Statistical Interpolation

Abstract Gridpoint statistical interpolation (GSI), a three-dimensional variational data assimilation method (3DVAR) has been widely used in operations and research in numerical weather prediction. The operational GSI uses a static background error covariance, which does not reflect the flow-dependent error statistics. Incorporating ensemble covariance in GSI provides a natural way to estimate the background error covariance in a flow-dependent manner. Different from other 3DVAR-based hybrid data assimilation systems that are preconditioned on the square root of the background error covariance, commonly used GSI minimization is preconditioned upon the full background error covariance matrix. A mathematical derivation is therefore provided to demonstrate how to incorporate the flow-dependent ensemble covariance in the GSI variational minimization.

scholarly journals Tensor Formulation of Ensemble-Based Background Error Covariance Matrix Factorization

2015 ◽  
Vol 143 (12) ◽  
pp. 4963-4973 ◽  
Author(s):  
Toshiyuki Ishibashi
Keyword(s):  
Data Assimilation ◽  
Covariance Matrix ◽  
Error Statistics ◽  
Background Error ◽  
Strong Constraint ◽  
Error Covariance Matrix ◽  
Background Error Covariance ◽  
Error Covariance ◽  
Component Form ◽  
Tensor Formulation

Abstract Factorization of a background error covariance matrix (B factorization) constructed from localization matrices and a small ensemble that obeys background error statistics is an efficient method for introducing flow-dependent background error statistics into variational form data assimilation systems. Although there are four types of matrix formulations of B factorization, their derivation processes and relationships are not clarified, and mathematical operability is limited because of their complex matrix forms. In this paper, B factorization in the tensor (component) form is formulated to overcome these shortcomings. The tensor formulation is very simple and directly connects the background error covariance matrix with its factorization. All existing matrix formulations are derived from the tensor formulation as their specific matrix form representations. Using the simplicity of the tensor formulation, the relationships between the strong-constraint four-dimensional variational data assimilation (4DVAR), 4DVAR with the four-dimensional background error covariance, and the weak-constraint 4DVAR are clarified.

A GPU accelerated finite volume coastal ocean model

2017 ◽  
Vol 29 (4) ◽  
pp. 679-690 ◽  
Author(s):  
Xu-dong Zhao ◽  
Shu-xiu Liang ◽  
Zhao-chen Sun ◽  
Xi-zeng Zhao ◽  
Jia-wen Sun ◽  
...  
Keyword(s):  
Finite Volume ◽  
Coastal Ocean ◽  
Ocean Model ◽  
Coastal Ocean Model

Impact of AMSU-A Radiances in a Column Ensemble Kalman Filter

2018 ◽  
Vol 146 (12) ◽  
pp. 3949-3976 ◽  
Author(s):  
Herschel L. Mitchell ◽  
P. L. Houtekamer ◽  
Sylvain Heilliette
Keyword(s):  
Covariance Matrix ◽  
Background Error ◽  
Error Covariance Matrix ◽  
Background Error Covariance ◽  
Error Covariance ◽  
Microwave Sounding Unit ◽  
The Matrix ◽  
Microwave Sounding ◽  
Background Temperature ◽  
The Difference

Abstract A column EnKF, based on the Canadian global EnKF and using the RTTOV radiative transfer (RT) model, is employed to investigate issues relating to the EnKF assimilation of Advanced Microwave Sounding Unit-A (AMSU-A) radiance measurements. Experiments are performed with large and small ensembles, with and without localization. Three different descriptions of background temperature error are considered: 1) using analytical vertical modes and hypothetical spectra, 2) using the vertical modes and spectrum of a covariance matrix obtained from the global EnKF after 2 weeks of cycling, and 3) using the vertical modes and spectrum of the static background error covariance matrix employed to initiate a global data assimilation cycle. It is found that the EnKF performs well in some of the experiments with background error description 1, and yields modest error reductions with background error description 3. However, the EnKF is virtually unable to reduce the background error (even when using a large ensemble) with background error description 2. To analyze these results, the different background error descriptions are viewed through the prism of the RT model by comparing the trace of the matrix , where is the RT model and is the background error covariance matrix. Indeed, this comparison is found to explain the difference in the results obtained, which relates to the degree to which deep modes are, or are not, present in the different background error covariances. The results suggest that, after 2 weeks of cycling, the global EnKF has virtually eliminated all background error structures that can be “seen” by the AMSU-A radiances.

scholarly journals An Unstructured Grid, Finite-Volume Coastal Ocean Model (FVCOM) System

Oceanography ◽  
2006 ◽  
Vol 19 (1) ◽  
pp. 78-89 ◽  
Author(s):  
Changsheng Chen ◽  
Roberet Beardsley ◽  
Geoffrey Cowles
Keyword(s):  
Finite Volume ◽  
Unstructured Grid ◽  
Coastal Ocean ◽  
Ocean Model ◽  
Coastal Ocean Model

Development of Convective-Scale Static Background Error Covariance within GSI-Based Hybrid EnVar System for Direct Radar Reflectivity Data Assimilation

2021 ◽  
Author(s):  
Yongming Wang ◽  
Xuguang Wang
Keyword(s):  
Sampling Errors ◽  
Background Error ◽  
3 Dimensional ◽  
Background Error Covariance ◽  
Error Covariance ◽  
Convective Scale ◽  
Cross Correlations ◽  
Horizontal Momentum ◽  
Reflectivity Data ◽  
Static Background

AbstractA convective-scale static background-error covariance (BEC) matrix is further developed to include the capability of direct reflectivity assimilation and evaluated within the GSI-based 3-dimensional variational (3DVar) and hybrid ensemble-variational (EnVar) methods. Specific developments are summarized as follows: 1) Control variables (CVs) are extended to include reflectivity, vertical velocity, and all hydrometeor types. Various horizontal momentum and moisture CV options are included. 2) Cross-correlations between all CVs are established. 3) A storm intensity-dependent binning method is adopted to separately calculate static error matrices for clear-air and storms with varying intensities. The resultant static BEC matrices are simultaneously applied at proper locations guided by the observed reflectivity. 4) The EnVar is extended to adaptively incorporate static BECs based on the quality of ensemble covariances.Evaluation and examination of the new static BECs are first performed on the 8 May 2003 Oklahoma City supercell. Detailed diagnostics and 3DVar examinations suggest zonal/meridian winds and pseudo-relative humidity are selected horizontal momentum and moisture CVs for direct reflectivity assimilation, respectively; inclusion of cross-correlations favors to spinup and maintain the analyzed storms; application of binning improves characteristics and persistence of the simulated storm. Relative to an experiment using the full ensemble BECs (Exp-PureEnVar), incorporating static BECs in hybrid EnVar reduces spinup time and better analyzes reflectivity distributions while the background ensemble is deficient in sampling errors. Compared to both pure 3DVar and Exp-PureEnVar, hybrid EnVar better predicts reflectivity distributions and better maintains strong mesocyclone. Further examination through the 20 May 2013 Oklahoma supercells confirms these results and additionally demonstrates the effectiveness of adaptive hybridization.

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