scholarly journals A Consistent Hybrid Variational-Smoothing Data Assimilation Method: Application to a Simple Shallow-Water Model of the Turbulent Midlatitude Ocean

2011 ◽  
Vol 139 (11) ◽  
pp. 3333-3347 ◽  
Author(s):  
Monika Krysta ◽  
Eric Blayo ◽  
Emmanuel Cosme ◽  
Jacques Verron
Keyword(s):  
Data Assimilation ◽  
Shallow Water ◽  
Covariance Matrix ◽  
Hybrid Method ◽  
Water Model ◽  
Shallow Water Model ◽  
Background Error ◽  
Error Covariance Matrix ◽  
Error Covariance ◽  
The Matrix

Abstract In the standard four-dimensional variational data assimilation (4D-Var) algorithm the background error covariance matrix remains static over time. It may therefore be unable to correctly take into account the information accumulated by a system into which data are gradually being assimilated. A possible method for remedying this flaw is presented and tested in this paper. A hybrid variational-smoothing algorithm is based on a reduced-rank incremental 4D-Var. Its consistent coupling to a singular evolutive extended Kalman (SEEK) smoother ensures the evolution of the matrix. In the analysis step, a low-dimensional error covariance matrix is updated so as to take into account the increased confidence level in the state vector it describes, once the observations have been introduced into the system. In the forecast step, the basis spanning the corresponding control subspace is propagated via the tangent linear model. The hybrid method is implemented and tested in twin experiments employing a shallow-water model. The background error covariance matrix is initialized using an EOF decomposition of a sample of model states. The quality of the analyses and the information content in the bases spanning control subspaces are also assessed. Several numerical experiments are conducted that differ with regard to the initialization of the matrix. The feasibility of the method is illustrated. Since improvement due to the hybrid method is not universal, configurations that benefit from employing it instead of the standard 4D-Var are described and an explanation of the possible reasons for this is proposed.

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 Assimilation of Stratospheric Temperature and Ozone with an Ensemble Kalman Filter in a Chemistry–Climate Model

2011 ◽  
Vol 139 (11) ◽  
pp. 3389-3404 ◽  
Author(s):  
Thomas Milewski ◽  
Michel S. Bourqui
Keyword(s):  
Kalman Filter ◽  
Data Assimilation ◽  
Covariance Matrix ◽  
Ensemble Kalman Filter ◽  
Climate Model ◽  
Observation Error ◽  
Background Error ◽  
Error Covariance Matrix ◽  
Error Covariance ◽  
Analysis Error

Abstract A new stratospheric chemical–dynamical data assimilation system was developed, based upon an ensemble Kalman filter coupled with a Chemistry–Climate Model [i.e., the intermediate-complexity general circulation model Fast Stratospheric Ozone Chemistry (IGCM-FASTOC)], with the aim to explore the potential of chemical–dynamical coupling in stratospheric data assimilation. The system is introduced here in a context of a perfect-model, Observing System Simulation Experiment. The system is found to be sensitive to localization parameters, and in the case of temperature (ozone), assimilation yields its best performance with horizontal and vertical decorrelation lengths of 14 000 km (5600 km) and 70 km (14 km). With these localization parameters, the observation space background-error covariance matrix is underinflated by only 5.9% (overinflated by 2.1%) and the observation-error covariance matrix by only 1.6% (0.5%), which makes artificial inflation unnecessary. Using optimal localization parameters, the skills of the system in constraining the ensemble-average analysis error with respect to the true state is tested when assimilating synthetic Michelson Interferometer for Passive Atmospheric Sounding (MIPAS) retrievals of temperature alone and ozone alone. It is found that in most cases background-error covariances produced from ensemble statistics are able to usefully propagate information from the observed variable to other ones. Chemical–dynamical covariances, and in particular ozone–wind covariances, are essential in constraining the dynamical fields when assimilating ozone only, as the radiation in the stratosphere is too slow to transfer ozone analysis increments to the temperature field over the 24-h forecast window. Conversely, when assimilating temperature, the chemical–dynamical covariances are also found to help constrain the ozone field, though to a much lower extent. The uncertainty in forecast/analysis, as defined by the variability in the ensemble, is large compared to the analysis error, which likely indicates some amount of noise in the covariance terms, while also reducing the risk of filter divergence.

An improved variational Data Assimilation method for ocean models with limited number of observations.

2020 ◽  
Author(s):  
Lewis Sampson ◽  
Jose M. Gonzalez-Ondina ◽  
Georgy Shapiro
Keyword(s):  
Data Assimilation ◽  
Covariance Matrix ◽  
Observational Data ◽  
Inner Product ◽  
Product Analysis ◽  
Background Error ◽  
Error Covariance Matrix ◽  
Error Covariance ◽  
Ocean Prediction ◽  
The Stability

<p>Data assimilation (DA) is a critical component for most state-of-the-art ocean prediction systems, which optimally combines model data and observational measurements to obtain an improved estimate of the modelled variables, by minimizing a cost function. The calculation requires the knowledge of the background error covariance matrix (BECM) as a weight for the quality of the model results, and an observational error covariance matrix (OECM) which weights the observational data.</p><p>Computing the BECM would require knowing the true values of the physical variables, which is not feasible. Instead, the BECM is estimated from model results and observations by using methods like National Meteorological Centre (NMC) or the Hollingsworth and Lönnberg (1984) (H-L). These methods have some shortcomings which make them unfit in some situations, which includes being fundamentally one-dimensional and making a suboptimal use of observations.</p><p>We have produced a novel method for error estimation, using an analysis of observations minus background data (innovations), which attempts to improve on some of these shortcomings. In particular, our method better infers information from observations, requiring less data to produce statistically robust results. We do this by minimizing a linear combination of functions to fit the data using a specifically tailored inner product, referred to as an inner product analysis (IPA).</p><p>We are able to produce quality BECM estimations even in data sparse domains, with notably better results in conditions of scarce observational data. By using a sample of observations, with decreasing sample size, we show that the stability and efficiency of our method, when compared to that of the H-L approach, does not deteriorate nearly as much as the number of data points decrease. We have found that we are able to continually produce error estimates with a reduced set of data, whereas the H-L method will begin to produce spurious values for smaller samples.</p><p>Our method works very well in combination with standard tools like NEMOVar by providing the required standard deviations and length-scales ratios. We have successfully ran this in the Arabian Sea for multiple seasons and compared the results with the H-L (in optimal conditions, when plenty of data is available), spatially the methods perform equally well. When we look at the root mean square error (RMSE) we see very similar performances, with each method giving better results for some seasons and worse for others.</p>

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 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.

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