A time-parallel approach to strong-constraint four-dimensional variational data assimilation

Accounting for Model Error in Variational Data Assimilation: A Deterministic Formulation

Monthly Weather Review ◽

10.1175/2010mwr3192.1 ◽

2010 ◽

Vol 138 (9) ◽

pp. 3369-3386 ◽

Cited By ~ 27

Author(s):

Alberto Carrassi ◽

Stéphane Vannitsem

Keyword(s):

Data Assimilation ◽

Deterministic Model ◽

Model Error ◽

Variational Data Assimilation ◽

Noise Model ◽

Actual State ◽

Strong Constraint ◽

Variational Assimilation ◽

Uncorrelated Noise ◽

Practical Applications

Abstract In data assimilation, observations are combined with the dynamics to get an estimate of the actual state of a natural system. The knowledge of the dynamics, under the form of a model, is unavoidably incomplete and model error affects the prediction accuracy together with the error in the initial condition. The variational assimilation theory provides a framework to deal with model error along with the uncertainties coming from other sources entering the state estimation. Nevertheless, even if the problem is formulated as Gaussian, accounting for model error requires the estimation of its covariances and correlations, which are difficult to estimate in practice, in particular because of the large system dimension and the lack of enough observations. Model error has been therefore either neglected or assumed to be an uncorrelated noise. In the present work, an approach to account for a deterministic model error in the variational assimilation is presented. Equations for its correlations are first derived along with an approximation suitable for practical applications. Based on these considerations, a new four-dimensional variational data assimilation (4DVar) weak-constraint algorithm is formulated and tested in the context of a linear unstable system and of the three-component Lorenz model, which has chaotic dynamics. The results demonstrate that this approach is superior in skill to both the strong-constraint and a weak-constraint variational assimilation that employs the uncorrelated noise model error assumption.

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Cycling the Representer Algorithm for Variational Data Assimilation with the Lorenz Attractor

Monthly Weather Review ◽

10.1175/mwr3281.1 ◽

2007 ◽

Vol 135 (2) ◽

pp. 373-386 ◽

Cited By ~ 9

Author(s):

H. E. Ngodock ◽

S. R. Smith ◽

G. A. Jacobs

Keyword(s):

Data Assimilation ◽

Variational Data Assimilation ◽

Lorenz Attractor ◽

Strong Constraint ◽

Strongly Nonlinear ◽

Time Period ◽

Representer Method ◽

The Cost ◽

Solution Accuracy ◽

Perturbation Magnitude

Abstract Realistic dynamic systems are often strongly nonlinear, particularly those for the ocean and atmosphere. Applying variational data assimilation to these systems requires a tangent linearization of the nonlinear dynamics about a background state for the cost function minimization. The tangent linearization may be accurate for limited time scales. Here it is proposed that linearized assimilation systems may be accurate if the assimilation time period is less than the tangent linear accuracy time limit. In this paper, the cycling representer method is used to test this assumption with the Lorenz attractor. The outer loops usually required to accommodate the linear assimilation for a nonlinear problem may be dropped beyond the early cycles once the solution (and forecast used as the background in the tangent linearization) is sufficiently accurate. The combination of cycling the representer method and limiting the number of outer loops significantly lowers the cost of the overall assimilation problem. In addition, this study shows that weak constraint assimilation corrects tangent linear model inaccuracies and allows extension of the limited assimilation period. Hence, the weak constraint outperforms the strong constraint method. Assimilated solution accuracy at the first cycle end is computed as a function of the initial condition error, model parameter perturbation magnitude, and outer loops. Results indicate that at least five outer loops are needed to achieve solution accuracy in the first cycle for the selected error range. In addition, this study clearly shows that one outer loop in the first cycle does not preclude accuracy convergence in future cycles.

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Development and evaluation of a high-resolution reanalysis of the East Australian Current region using the Regional Ocean Modelling System (ROMS 3.4) and Incremental Strong-Constraint 4-Dimensional Variational data assimilation (IS4D-Var)

10.5194/gmd-2016-44 ◽

2016 ◽

Author(s):

Colette Kerry ◽

Brian Powell ◽

Moninya Roughan ◽

Peter Oke

Keyword(s):

High Resolution ◽

Data Assimilation ◽

Water Column ◽

Marked Improvement ◽

Variational Data Assimilation ◽

Surface Velocity ◽

East Australian Current ◽

Strong Constraint ◽

Ocean Modelling ◽

Modelling System

Abstract. As with other western boundary currents globally, the East Australian Current (EAC) is inherently dynamic making it a challenge to model and predict. For the EAC region, we combine a high-resolution state-of-the-art numerical ocean model with a variety of traditional and newly available observations using an advanced variational data assimilation scheme. The numerical model is configured using the Regional Ocean Modelling System (ROMS 3.4) and takes boundary forcing from the BlueLink ReANalysis (BRAN3). For the data assimilation we use an Incremental Strong-Constraint 4-Dimensional Variational (IS4D-Var) scheme. This paper describes the data assimilative model configuration that achieves an optimised minimisation of the difference between the modelled solution and the observations to give a dynamically-consistent `best-estimate' of the ocean state over a 2-year period. The reanalysis is shown to represent both assimilated and non-assimilated observations well. It achieves mean spatially-averaged RMS residuals with the observations of 7 cm for SSH and 0.4 °C for SST over the assimilation period. The time-mean RMS residual for subsurface temperature measured by Argo floats is a maximum of 1 °C between water depths of 100–300 m and smaller throughout the rest of the water column. Velocities at several offshore and continental shelf moorings are well represented in the reanalysis with complex correlations between 0.8–1 for all observations in the upper 500 m. Surface radial velocities from a high-frequency radar array are assimilated and the reanalysis provides surface velocity estimates with complex correlations with observed velocities of 0.8–1 across the radar footprint. Comparison with independent (non-assimilated) shipboard CTD cast observations shows a marked improvement in the representation of the subsurface ocean in the reanalysis, with the RMS residual in potential density reduced to about half of the residual with the free-running model in the upper eddy-influenced part of the water column. This shows that information is successfully propagated from observed variables to unobserved regions as the assimilation system uses the model dynamics to determine covariance, such that the ocean state better fits and is in balance with the observations. This is the first study to generate a reanalysis of the region at such a high resolution, making use of an unprecedented observational data set and using an assimilation method that uses the time-evolving model physics to adjust the model in a dynamically consistent way. As such, the reanalysis potentially represents a marked improvement in our ability to capture important circulation dynamics in the EAC. The reanalysis is being used to study EAC dynamics, observation impact in state-estimation and as forcing for a variety of downscaling studies.

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