Variational data assimilation in the tropics: The impact of a background-error constraint

2004 ◽  
Vol 130 (596) ◽  
pp. 103-125 ◽  
Author(s):  
Nedjeljka Žagar ◽  
Nils Gustafsson ◽  
Erland Källén
Keyword(s):  
Data Assimilation ◽  
Variational Data Assimilation ◽  
Background Error ◽  
The Tropics ◽  
Error Constraint ◽  
The Impact

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 Singular-Vector-Based Covariance Propagation in a Quasigeostrophic Assimilation System

2005 ◽  
Vol 133 (5) ◽  
pp. 1295-1310 ◽  
Author(s):  
Alexander Beck ◽  
Martin Ehrendorfer
Keyword(s):  
Kalman Filter ◽  
Data Assimilation ◽  
Variational Data Assimilation ◽  
Dynamic Information ◽  
Dynamic Background ◽  
Background Error ◽  
Singular Vectors ◽  
Reduced Rank ◽  
The Impact ◽  
Static Background

Abstract Variational data assimilation systems require the specification of the covariances of background and observation errors. Although the specification of the background-error covariances has been the subject of intense research, current operational data assimilation systems still rely on essentially static and thus flow-independent background-error covariances. At least theoretically, it is possible to use flow-dependent background-error covariances in four-dimensional variational data assimilation (4DVAR) through exploiting the connection between variational data assimilation and estimation theory. This paper reports on investigations concerning the impact of flow-dependent background-error covariances in an idealized 4DVAR system that, based on quasigeostrophic dynamics, assimilates artificial observations. The main emphasis is placed on quantifying the improvement in analysis quality that is achievable in 4DVAR through the use of flow-dependent background-error covariances. Flow dependence is achieved through dynamical error-covariance evolution based on singular vectors in a reduced-rank approach, referred to as reduced-rank Kalman filter (RRKF). The RRKF yields partly dynamic background-error covariances through blending static and dynamic information, where the dynamic information is obtained from error evolution in a subspace of dimension k (defined here through the singular vectors) that may be small compared to the dimension of the model’s phase space n, which is equal to 1449 in the system investigated here. The results show that the use of flow-dependent background-error covariances based on the RRKF leads to improved analyses compared to a system using static background-error statistics. That latter system uses static background-error covariances that are carefully tuned given the model dynamics and the observational information available. It is also shown that the performance of the RRKF approaches the performance of the extended Kalman filter, as k approaches n. Results therefore support the hypothesis that significant analysis improvement is possible through the use of flow-dependent background-error covariances given that a sufficiently large number (here on the order of n/10) of singular vectors is used.

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 Strongly Coupled Data Assimilation Experiments with Linearized Ocean–Atmosphere Balance Relationships

2018 ◽  
Vol 146 (4) ◽  
pp. 1233-1257 ◽  
Author(s):  
Andrea Storto ◽  
Matthew J. Martin ◽  
Bruno Deremble ◽  
Simona Masina
Keyword(s):  
Data Assimilation ◽  
General Circulation ◽  
Circulation Model ◽  
Variational Data Assimilation ◽  
Global Ocean ◽  
Background Error ◽  
Near Surface ◽  
Strongly Coupled ◽  
Coupled Data Assimilation ◽  
The Impact

Coupled data assimilation is emerging as a target approach for Earth system prediction and reanalysis systems. Coupled data assimilation may be indeed able to minimize unbalanced air–sea initialization and maximize the intermedium propagation of observations. Here, we use a simplified framework where a global ocean general circulation model (NEMO) is coupled to an atmospheric boundary layer model [Cheap Atmospheric Mixed Layer (CheapAML)], which includes prognostic prediction of near-surface air temperature and moisture and allows for thermodynamic but not dynamic air–sea coupling. The control vector of an ocean variational data assimilation system is augmented to include 2-m atmospheric parameters. Cross-medium balances are formulated either through statistical cross covariances from monthly anomalies or through the application of linearized air–sea flux relationships derived from the tangent linear approximation of bulk formulas, which represents a novel solution to the coupled assimilation problem. As a proof of concept, the methodology is first applied to study the impact of in situ ocean observing networks on the near-surface atmospheric analyses and later to the complementary study of the impact of 2-m air observations on sea surface parameters, to assess benefits of strongly versus weakly coupled data assimilation. Several forecast experiments have been conducted for the period from June to December 2011. We find that especially after day 2 of the forecasts, strongly coupled data assimilation provides a beneficial impact, particularly in the tropical oceans. In most areas, the use of linearized air–sea balances outperforms the statistical relationships used, providing a motivation for implementing coupled tangent linear trajectories in four-dimensional variational data assimilation systems. Further impacts of strongly coupled data assimilation might be found by retuning the background error covariances.

Impact Assessment of Simulated Doppler Wind Lidars with a Multivariate Variational Assimilation in the Tropics

2008 ◽  
Vol 136 (7) ◽  
pp. 2443-2460 ◽  
Author(s):  
Nedjeljka Žagar ◽  
Ad Stoffelen ◽  
Gert-Jan Marseille ◽  
Christophe Accadia ◽  
Peter Schlüssel
Keyword(s):  
Data Assimilation ◽  
Variational Data Assimilation ◽  
Forecast Errors ◽  
Horizontal Line ◽  
Wind Vector ◽  
Background Error ◽  
Horizontal Structure ◽  
Tropical Conditions ◽  
The Tropics

Abstract This paper deals with the dynamical aspect of variational data assimilation in the tropics and the role of the background-error covariances in the observing system simulation experiments for the tropics. The study uses a model that describes the horizontal structure of the potential temperature and wind fields in regions of deep tropical convection. The assimilation method is three- and four-dimensional variational data assimilation. The background-error covariance model for the assimilation is a multivariate model that includes the mass–wind couplings representative of equatorial inertio-gravity modes and equatorial Kelvin and mixed Rossby–gravity modes in addition to those representative of balanced equatorial Rossby waves. Spectra of the background errors based on these waves are derived from the tropical forecast errors of the European Centre for Medium-Range Weather Forecasts (ECMWF) model. Tropical mass–wind (im)balances are illustrated by studying the potential impact of the spaceborne Doppler wind lidar (DWL) Atmospheric Dynamic Mission (ADM)-Aeolus, which measures horizontal line-of-sight (LOS) wind components. Several scenarios with two DWLs of ADM-Aeolus type are compared under different flow conditions and using different assumptions about the quality of the background-error covariances. Results of three-dimensional variational data assimilation (3DVAR) illustrate the inefficiency of multivariate assimilation in the tropics. The consequence for the assimilation of LOS winds is that the missing part of the wind vector can hardly be reconstructed from the mass-field observations and applied balances as in the case of the midlatitudes. Results of four-dimensional variational data assimilation (4DVAR) show that for large-scale tropical conditions and using reliable background-error statistics, differences among various DWL scenarios are not large. As the background-error covariances becomes less reliable, horizontal scales become smaller and the flow becomes less zonal, the importance of obtaining information about the wind vector increases. The added value of another DWL satellite increases as the quality of the background-error covariances deteriorates and it can be more than twice as large as in the case of reliable covariances.

scholarly journals Intercomparison of Variational Data Assimilation and the Ensemble Kalman Filter for Global Deterministic NWP. Part I: Description and Single-Observation Experiments

2010 ◽  
Vol 138 (5) ◽  
pp. 1550-1566 ◽  
Author(s):  
Mark Buehner ◽  
P. L. Houtekamer ◽  
Cecilien Charette ◽  
Herschel L. Mitchell ◽  
Bin He
Keyword(s):  
Kalman Filter ◽  
Data Assimilation ◽  
Ensemble Kalman Filter ◽  
Forecast Model ◽  
Variational Data Assimilation ◽  
Spatial Covariance ◽  
4D Flow ◽  
Background Error ◽  
Single Observation ◽  
The Impact

Abstract An intercomparison of the Environment Canada variational and ensemble Kalman filter (EnKF) data assimilation systems is presented in the context of global deterministic NWP. In an EnKF experiment having the same spatial resolution as the inner loop in the four-dimensional variational data assimilation system (4D-Var), the mean of each analysis ensemble is used to initialize the higher-resolution deterministic forecasts. Five different variational data assimilation experiments are also conducted. These include both 4D-Var and 3D-Var (with first guess at appropriate time) experiments using either (i) prescribed background-error covariances similar to those used operationally, which are static in time and include horizontally homogeneous and isotropic correlations; or (ii) flow-dependent covariances computed from the EnKF background ensembles with spatial covariance localization applied. The fifth variational data assimilation experiment is a new approach called the Ensemble-4D-Var (En-4D-Var). This approach uses 4D flow-dependent background-error covariances estimated from EnKF ensembles to produce a 4D analysis without the need for tangent-linear or adjoint versions of the forecast model. In this first part of a two-part paper, results from a series of idealized assimilation experiments are presented. In these experiments, only a single observation or vertical profile of observations is assimilated to explore the impact of various fundamental differences among the EnKF and the various variational data assimilation approaches considered. In particular, differences in the application of covariance localization in the EnKF and variational approaches are shown to have a significant impact on the assimilation of satellite radiance observations. The results also demonstrate that 4D-Var and the EnKF can both produce similar 4D background-error covariances within a 6-h assimilation window. In the second part, results from medium-range deterministic forecasts for the study period of February 2007 are presented for the EnKF and the five variational data assimilation approaches considered.

A New Approach for Estimating the Observation Impact in Ensemble–Variational Data Assimilation

2018 ◽  
Vol 146 (2) ◽  
pp. 447-465 ◽  
Author(s):  
Mark Buehner ◽  
Ping Du ◽  
Joël Bédard
Keyword(s):  
Data Assimilation ◽  
Forecast Error ◽  
Forecast Model ◽  
Variational Data Assimilation ◽  
Observation Error ◽  
New Approach ◽  
Regional Prediction ◽  
Observation Impact ◽  
Adjoint Approach ◽  
The Impact

Abstract Two types of approaches are commonly used for estimating the impact of arbitrary subsets of observations on short-range forecast error. The first was developed for variational data assimilation systems and requires the adjoint of the forecast model. Comparable approaches were developed for use with the ensemble Kalman filter and rely on ensembles of forecasts. In this study, a new approach for computing observation impact is proposed for ensemble–variational data assimilation (EnVar). Like standard adjoint approaches, the adjoint of the data assimilation procedure is implemented through the iterative minimization of a modified cost function. However, like ensemble approaches, the adjoint of the forecast step is obtained by using an ensemble of forecasts. Numerical experiments were performed to compare the new approach with the standard adjoint approach in the context of operational deterministic NWP. Generally similar results are obtained with both approaches, especially when the new approach uses covariance localization that is horizontally advected between analysis and forecast times. However, large differences in estimated impacts are obtained for some surface observations. Vertical propagation of the observation impact is noticeably restricted with the new approach because of vertical covariance localization. The new approach is used to evaluate changes in observation impact as a result of the use of interchannel observation error correlations for radiance observations. The estimated observation impact in similarly configured global and regional prediction systems is also compared. Overall, the new approach should provide useful estimates of observation impact for data assimilation systems based on EnVar when an adjoint model is not available.

scholarly journals Interpretation of Adaptive Observing Guidance for Atlantic Tropical Cyclones

2007 ◽  
Vol 135 (12) ◽  
pp. 4006-4029 ◽  
Author(s):  
C. A. Reynolds ◽  
M. S. Peng ◽  
S. J. Majumdar ◽  
S. D. Aberson ◽  
C. H. Bishop ◽  
...  
Keyword(s):  
Data Assimilation ◽  
Total Energy ◽  
Tropical Cyclones ◽  
Error Variance ◽  
Naval Research ◽  
Error Statistics ◽  
Background Error ◽  
Analysis Error ◽  
The Impact ◽  
Perturbation Growth

Abstract Adaptive observing guidance products for Atlantic tropical cyclones are compared using composite techniques that allow one to quantitatively examine differences in the spatial structures of the guidance maps and relate these differences to the constraints and approximations of the respective techniques. The guidance maps are produced using the ensemble transform Kalman filter (ETKF) based on ensembles from the National Centers for Environmental Prediction and the European Centre for Medium-Range Weather Forecasts (ECMWF), and total-energy singular vectors (TESVs) produced by ECMWF and the Naval Research Laboratory. Systematic structural differences in the guidance products are linked to the fact that TESVs consider the dynamics of perturbation growth only, while the ETKF combines information on perturbation evolution with error statistics from an ensemble-based data assimilation scheme. The impact of constraining the SVs using different estimates of analysis error variance instead of a total-energy norm, in effect bringing the two methods closer together, is also assessed. When the targets are close to the storm, the TESV products are a maximum in an annulus around the storm, whereas the ETKF products are a maximum at the storm location itself. When the targets are remote from the storm, the TESVs almost always indicate targets northwest of the storm, whereas the ETKF targets are more scattered relative to the storm location and often occur over the northern North Atlantic. The ETKF guidance often coincides with locations in which the ensemble-based analysis error variance is large. As the TESV method is not designed to consider spatial differences in the likely analysis errors, it will produce targets over well-observed regions, such as the continental United States. Constraining the SV calculation using analysis error variance values from an operational 3D variational data assimilation system (with stationary, quasi-isotropic background error statistics) results in a modest modulation of the target areas away from the well-observed regions, and a modest reduction of perturbation growth. Constraining the SVs using the ETKF estimate of analysis error variance produces SV targets similar to ETKF targets and results in a significant reduction in perturbation growth, due to the highly localized nature of the analysis error variance estimates. These results illustrate the strong sensitivity of SVs to the norm (and to the analysis error variance estimate used to define it) and confirm that discrepancies between target areas computed using different methods reflect the mathematical and physical differences between the methods themselves.

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