Four-dimensional variational data assimilation: A new formulation of the background-error covariance matrix based on a potential-vorticity representation

2003 ◽  
Vol 129 (593) ◽  
pp. 2777-2796 ◽  
Author(s):  
M. J. P. Cullen
Keyword(s):  
Data Assimilation ◽  
Covariance Matrix ◽  
Potential Vorticity ◽  
Variational Data Assimilation ◽  
Background Error ◽  
Error Covariance Matrix ◽  
Background Error Covariance ◽  
Error Covariance ◽  
New Formulation

scholarly journals Generalized background error covariance matrix model (GEN_BE v2.0)

2015 ◽  
Vol 8 (3) ◽  
pp. 669-696 ◽  
Author(s):  
G. Descombes ◽  
T. Auligné ◽  
F. Vandenberghe ◽  
D. M. Barker ◽  
J. Barré
Keyword(s):  
Data Assimilation ◽  
Covariance Matrix ◽  
Chemical Species ◽  
Variational Data Assimilation ◽  
Control Variables ◽  
Background Error ◽  
Error Covariance Matrix ◽  
Background Error Covariance ◽  
Error Covariance ◽  
The Impact

Abstract. The specification of state background error statistics is a key component of data assimilation since it affects the impact observations will have on the analysis. In the variational data assimilation approach, applied in geophysical sciences, the dimensions of the background error covariance matrix (B) are usually too large to be explicitly determined and B needs to be modeled. Recent efforts to include new variables in the analysis such as cloud parameters and chemical species have required the development of the code to GENerate the Background Errors (GEN_BE) version 2.0 for the Weather Research and Forecasting (WRF) community model. GEN_BE allows for a simpler, flexible, robust, and community-oriented framework that gathers methods used by some meteorological operational centers and researchers. We present the advantages of this new design for the data assimilation community by performing benchmarks of different modeling of B and showing some of the new features in data assimilation test cases. As data assimilation for clouds remains a challenge, we present a multivariate approach that includes hydrometeors in the control variables and new correlated errors. In addition, the GEN_BE v2.0 code is employed to diagnose error parameter statistics for chemical species, which shows that it is a tool flexible enough to implement new control variables. While the generation of the background errors statistics code was first developed for atmospheric research, the new version (GEN_BE v2.0) can be easily applied to other domains of science and chosen to diagnose and model B. Initially developed for variational data assimilation, the model of the B matrix may be useful for variational ensemble hybrid methods as well.

scholarly journals The “ABC-DA system” (v1.4): a variational data assimilation system for convective scale assimilation research with a study of the impact of a balance constraint

2020 ◽  
Author(s):  
Ross Noel Bannister
Keyword(s):  
Data Assimilation ◽  
Covariance Matrix ◽  
Variational Data Assimilation ◽  
Background Error ◽  
Error Covariance Matrix ◽  
Background Error Covariance ◽  
Error Covariance ◽  
Convective Scale ◽  
Data Assimilation System ◽  
Assimilation System

Abstract. Following the development of the simplified atmospheric convective-scale "toy" model (the ABC model, named after its three key parameters: the pure gravity wave frequency, A, the controller of the acoustic wave speed, B, and the constant of proportionality between pressure and density perturbations, C), this paper introduces its associated variational data assimilation system, ABC-DA. The purpose of ABC-DA is to permit quick and efficient research into data assimilation methods suitable for convective scale systems. The system can also be used as an aid to teach and demonstrate data assimilation principles. ABC-DA is flexible, configurable and is efficient enough to be run on a personal computer. The system can run a number of assimilation methods (currently 3DVar and 3DFGAT have been implemented), with user configurable observation networks. Observation operators for direct observations and wind speeds are part of the system, although these can be expanded relatively easily. A key feature of any data assimilation system is how it specifies the background error covariance matrix. ABC-DA uses a control variable transform method to allow this to be done efficiently. This version of ABC-DA mirrors many operational configurations, by modelling multivariate error covariances with uncorrelated control parameters, and spatial error covariances with special uncorrelated spatial patterns separately for each parameter. The software developed (amongst other things) does model runs, calibration tasks associated with the background error covariance matrix, testing and diagnostic tasks, single data assimilation runs, multi-cycle assimilation/forecast experiments, and has associated visualisation software. As a demonstration, the system is used to tackle a scientific question concerning the role of geostrophic balance (GB) to model background error covariances between mass and wind fields. This question arises because, although GB is a very useful mechanism that is successfully exploited in larger scale assimilation systems, its use is questionable at convective scales due to the typically larger Rossby numbers where GB is not so relevant. A series of identical twin experiments is done in cycled assimilation configurations. One experiment exploits GB to represent mass-wind covariances in a mirror of an operational set-up (with use of an additional vertical regression (VR) step, as used operationally). This experiment performs badly where assimilation error accumulates over time. Two further experiments are done: one that does not use GB, and another that does but without the VR step. Turning off GB impairs the performance, and turning off VR improves the performance in general. It is concluded that there is scope to further improve the way that the background error covariance matrices are calibrated, with some directions discussed.

scholarly journals Generalized Background Error covariance matrix model (GEN_BE v2.0)

2014 ◽  
Vol 7 (4) ◽  
pp. 4291-4352
Author(s):  
G. Descombes ◽  
T. Auligné ◽  
F. Vandenberghe ◽  
D. M. Barker
Keyword(s):  
Data Assimilation ◽  
Covariance Matrix ◽  
Chemical Species ◽  
Variational Data Assimilation ◽  
Control Variables ◽  
Background Error ◽  
Error Covariance Matrix ◽  
Background Error Covariance ◽  
Error Covariance ◽  
The Impact

Abstract. The specification of state background error statistics is a key component of data assimilation since it affects the impact observations will have on the analysis. In the variational data assimilation approach, applied in geophysical sciences, the dimensions of the background error covariance matrix (B) are usually too large to be explicitly determined and B needs to be modeled. Recent efforts to include new variables in the analysis such as cloud parameters and chemical species have required the development of the code to GENerate the Background Errors (GEN_BE) version 2.0 for the Weather Research and Forecasting (WRF) community model to allow for a simpler, flexible, robust, and community-oriented framework that gathers methods used by meteorological operational centers and researchers. We present the advantages of this new design for the data assimilation community by performing benchmarks and showing some of the new features on data assimilation test cases. As data assimilation for clouds remains a challenge, we present a multivariate approach that includes hydrometeors in the control variables and new correlated errors. In addition, the GEN_BE v2.0 code is employed to diagnose error parameter statistics for chemical species, which shows that it is a tool flexible enough to involve new control variables. While the generation of the background errors statistics code has been first developed for atmospheric research, the new version (GEN_BE v2.0) can be easily extended to other domains of science and be chosen as a testbed for diagnostic and new modeling of B. Initially developed for variational data assimilation, the model of the B matrix may be useful for variational ensemble hybrid methods as well.

scholarly journals The ABC-DA system (v1.4): a variational data assimilation system for convective-scale assimilation research with a study of the impact of a balance constraint

2020 ◽  
Vol 13 (8) ◽  
pp. 3789-3816
Author(s):  
Ross Noel Bannister
Keyword(s):  
Data Assimilation ◽  
Covariance Matrix ◽  
Variational Data Assimilation ◽  
Background Error ◽  
Error Covariance Matrix ◽  
Background Error Covariance ◽  
Error Covariance ◽  
Convective Scale ◽  
Data Assimilation System ◽  
Assimilation System

Abstract. Following the development of the simplified atmospheric convective-scale “toy” model (the ABC model, named after its three key parameters: the pure gravity wave frequency A, the controller of the acoustic wave speed B, and the constant of proportionality between pressure and density perturbations C), this paper introduces its associated variational data assimilation system, ABC-DA. The purpose of ABC-DA is to permit quick and efficient research into data assimilation methods suitable for convective-scale systems. The system can also be used as an aid to teach and demonstrate data assimilation principles. ABC-DA is flexible and configurable, and is efficient enough to be run on a personal computer. The system can run a number of assimilation methods (currently 3DVar and 3DFGAT have been implemented), with user configurable observation networks. Observation operators for direct observations and wind speeds are part of the current system, and these can, for example, be expanded relatively easily to include operators for Doppler winds. A key feature of any data assimilation system is how it specifies the background error covariance matrix. ABC-DA uses a control variable transform method to allow this to be done efficiently. This version of ABC-DA mirrors many operational configurations by modelling multivariate error covariances with uncorrelated control parameters, each with special uncorrelated spatial patterns. The software developed performs (amongst other things) model runs, calibration tasks associated with the background error covariance matrix, testing and diagnostic tasks, single data assimilation runs, and multi-cycle assimilation/forecast experiments, and it also has associated visualisation software. As a demonstration, the system is used to tackle a scientific question concerning the role of geostrophic balance (GB) to model background error covariances between mass and wind fields. This question arises because although GB is a very useful mechanism that is successfully exploited in larger-scale assimilation systems, its use is questionable at convective scales due to the typically larger Rossby numbers where GB is not so relevant. A series of identical twin experiments is done in cycled assimilation configurations. One experiment exploits GB to represent mass–wind covariances in a mirror of an operational set-up (with use of an additional vertical regression (VR) step, as used operationally). This experiment performs badly where error accumulates over time. Two further experiments are done: one that does not use GB and another that does but without the VR step. Turning off GB impairs the performance, and turning off VR improves the performance in general. It is concluded that there is scope to further improve the way that the background error covariance matrices are represented at convective scale. Ideas for further possible developments of ABC-DA are discussed.

Ocean spectral data assimilation without background error covariance matrix

2016 ◽  
Vol 66 (9) ◽  
pp. 1143-1163 ◽  
Author(s):  
Peter C. Chu ◽  
Chenwu Fan ◽  
Tetyana Margolina
Keyword(s):  
Data Assimilation ◽  
Spectral Data ◽  
Covariance Matrix ◽  
Background Error ◽  
Error Covariance Matrix ◽  
Background Error Covariance ◽  
Error Covariance

scholarly journals A Hybrid Variational-Ensemble data assimilation scheme with systematic error correction for limited area ocean model

2016 ◽  
Author(s):  
Paolo Oddo ◽  
Andrea Storto ◽  
Srdjan Dobricic ◽  
Aniello Russo ◽  
Craig Lewis ◽  
...  
Keyword(s):  
Data Assimilation ◽  
Systematic Error ◽  
Error Correction ◽  
Covariance Matrix ◽  
Limited Area ◽  
Hybrid Scheme ◽  
Background Error ◽  
Error Covariance Matrix ◽  
Background Error Covariance ◽  
Error Covariance

Abstract. A hybrid variational-ensemble data assimilation scheme to estimate the vertical and horizontal parts of the background-error covariance matrix for an ocean variational data assimilation system is presented and tested in a limited area ocean model implemented in the western Mediterranean Sea. An extensive dataset collected during the Recognized Environmental Picture Experiments conducted in June 2014 by the Centre for Maritime Research and Experimentation has been used for assimilation and validation. The hybrid scheme is used to both correct the systematic error introduced in the system from the external forcing (initial, lateral and surface open boundary conditions) and model parameterization and improve the representation of small scale errors in the Background Error Covariance matrix. An ensemble system is run off-line for further use in the hybrid scheme, generated through perturbation of assimilated observations. Results of four different experiments have been compared. The reference experiment uses the classical static formulation of the background error covariance matrix and has no systematic error correction. The other three experiments account, or not, for systematic error correction and hybrid daily estimates of the background error covariance matrix combining the static and the ensemble derived errors statistics. Results show that the hybrid scheme when used in conjunction with the systematic error correction reduce the mean absolute error of temperature and salinity misfit by 55 % and 42 % respectively versus statistics arising from standard climatological covariances without systematic error correction.

scholarly journals Impact of different estimations of the background-error covariance matrix on climate reconstructions based on data assimilation

2018 ◽  
Author(s):  
Veronika Valler ◽  
Jörg Franke ◽  
Stefan Brönnimann
Keyword(s):  
Data Assimilation ◽  
Covariance Matrix ◽  
Sampling Error ◽  
Localization Length ◽  
Background Error ◽  
Error Covariance Matrix ◽  
Background Error Covariance ◽  
Error Covariance ◽  
Sample Covariance ◽  
Temporal Localization

Abstract. Data assimilation has been adapted in paleoclimatology to reconstruct past climate states. A key component of the assimilation system is the background-error covariance matrix, which controls how the information from observations spreads into the model space. In ensemble-based approaches, the background-error covariance matrix can be estimated from the ensemble. Due to the usually limited ensemble size, the background-error covariance matrix is subject to the so-called sampling error. We test different methods to reduce the effect of sampling error in a published paleo data assimilation setup. For this purpose, we conduct a set of experiments, where we assimilate early instrumental data and proxy records stored in trees, to investigate the effect of 1) the applied localization function and localization length scale; 2) multiplicative and additive inflation techniques; 3) temporal localization of monthly data, which applies if several time steps are estimated together in the same assimilation window. We find that the estimation of the background-error covariance matrix can be improved by additive inflation where the background-error covariance matrix is not only calculated from the sample covariance, but blended with a climatological covariance matrix. Implementing a temporal localization for monthly resolved data also led to a better reconstruction.

scholarly journals A hybrid variational-ensemble data assimilation scheme with systematic error correction for limited-area ocean models

Ocean Science ◽  
2016 ◽  
Vol 12 (5) ◽  
pp. 1137-1153 ◽  
Author(s):  
Paolo Oddo ◽  
Andrea Storto ◽  
Srdjan Dobricic ◽  
Aniello Russo ◽  
Craig Lewis ◽  
...  
Keyword(s):  
Data Assimilation ◽  
Systematic Error ◽  
Error Correction ◽  
Covariance Matrix ◽  
Limited Area ◽  
Hybrid Scheme ◽  
Background Error ◽  
Error Covariance Matrix ◽  
Background Error Covariance ◽  
Error Covariance

Abstract. A hybrid variational-ensemble data assimilation scheme to estimate the vertical and horizontal parts of the background error covariance matrix for an ocean variational data assimilation system is presented and tested in a limited-area ocean model implemented in the western Mediterranean Sea. An extensive data set collected during the Recognized Environmental Picture Experiments conducted in June 2014 by the Centre for Maritime Research and Experimentation has been used for assimilation and validation. The hybrid scheme is used to both correct the systematic error introduced in the system from the external forcing (initialisation, lateral and surface open boundary conditions) and model parameterisation, and improve the representation of small-scale errors in the background error covariance matrix. An ensemble system is run offline for further use in the hybrid scheme, generated through perturbation of assimilated observations. Results of four different experiments have been compared. The reference experiment uses the classical stationary formulation of the background error covariance matrix and has no systematic error correction. The other three experiments account for, or not, systematic error correction and hybrid background error covariance matrix combining the static and the ensemble-derived errors of the day. Results show that the hybrid scheme when used in conjunction with the systematic error correction reduces the mean absolute error of temperature and salinity misfit by 55 and 42 % respectively, versus statistics arising from standard climatological covariances without systematic error correction.

scholarly journals Impact of different estimations of the background-error covariance matrix on climate reconstructions based on data assimilation

2019 ◽  
Vol 15 (4) ◽  
pp. 1427-1441 ◽  
Author(s):  
Veronika Valler ◽  
Jörg Franke ◽  
Stefan Brönnimann
Keyword(s):  
Data Assimilation ◽  
Covariance Matrix ◽  
Sampling Error ◽  
Localization Length ◽  
Background Error ◽  
Error Covariance Matrix ◽  
Background Error Covariance ◽  
Error Covariance ◽  
Sample Covariance ◽  
Temporal Localization

Abstract. Data assimilation has been adapted in paleoclimatology to reconstruct past climate states. A key component of some assimilation systems is the background-error covariance matrix, which controls how the information from observations spreads into the model space. In ensemble-based approaches, the background-error covariance matrix can be estimated from the ensemble. Due to the usually limited ensemble size, the background-error covariance matrix is subject to the so-called sampling error. We test different methods to reduce the effect of sampling error in a published paleoclimate data assimilation setup. For this purpose, we conduct a set of experiments, where we assimilate early instrumental data and proxy records stored in trees, to investigate the effect of (1) the applied localization function and localization length scale; (2) multiplicative and additive inflation techniques; (3) temporal localization of monthly data, which applies if several time steps are estimated together in the same assimilation window. We find that the estimation of the background-error covariance matrix can be improved by additive inflation where the background-error covariance matrix is not only calculated from the sample covariance but blended with a climatological covariance matrix. Implementing a temporal localization for monthly resolved data also led to a better reconstruction.

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