Abstract:
Data assimilation method consists in combining all available pieces of information about a system to obtain optimal estimates of initial states. The different sources of information are weighted according to their accuracy by the means of error covariance matrices. Our purpose here is to evaluate the efficiency of variational data assimilation for the xenon induced oscillations forecasts in nuclear cores. In this paper we focus on the comparison between 3DVAR schemes with optimised background error covariance matrix B and a 4DVAR scheme. Tests were made in twin experiments using a simulation code which implements a mono-dimensional coupled model of xenon dynamics, thermal, and thermal-hydraulic processes. We enlighten the very good efficiency of the 4DVAR scheme as well as good results with the 3DVAR one using a careful multivariate modelling of B.

Abstract:
The problem of variational data assimilation (DA) for a nonlinear evolution model is formulated as an optimal control problem to find the initial condition, boundary conditions and/or model parameters. The input data contain observation and background errors, hence there is an error in the optimal solution. For mildly nonlinear dynamics, the covariance matrix of the optimal solution error can be approximated by the inverse Hessian of the cost function. For problems with strongly nonlinear dynamics, a new statistical method based on the computation of a sample of inverse Hessians is suggested. This method relies on the efficient computation of the inverse Hessian by means of iterative methods (Lanczos and quasi-Newton BFGS) with preconditioning. Numerical examples are presented for the model governed by the Burgers equation with a nonlinear viscous term.

Abstract:
Chemical data assimilation attempts to optimally use noisy observations along with imperfect model predictions to produce a better estimate of the chemical state of the atmosphere. It is widely accepted that a key ingredient for successful data assimilation is a realistic estimation of the background error distribution. Particularly important is the specification of the background error covariance matrix, which contains information about the magnitude of the background errors and about their correlations. Most models currently use diagonal background covariance matrices. As models evolve toward finer resolutions, the diagonal background covariance matrices become increasingly inaccurate, since they captures less of the spatial error correlations. This paper discusses an efficient computational procedure for constructing non-diagonal background error covariance matrices which account for the spatial correlations of errors. The benefits of using the non-diagonal covariance matrices for variational data assimilation with chemical transport models are illustrated.

Abstract:
Chemical data assimilation attempts to optimally use noisy observations along with imperfect model predictions to produce a better estimate of the chemical state of the atmosphere. It is widely accepted that a key ingredient for successful data assimilation is a realistic estimation of the background error distribution. Particularly important is the specification of the background error covariance matrix, which contains information about the magnitude of the background errors and about their correlations. As models evolve toward finer resolutions, the use of diagonal background covariance matrices is increasingly inaccurate, as they captures less of the spatial error correlations. This paper discusses an efficient computational procedure for constructing non-diagonal background error covariance matrices which account for the spatial correlations of errors. The correlation length scales are specified by the user; a correct choice of correlation lengths is important for a good performance of the data assimilation system. The benefits of using the non-diagonal covariance matrices for variational data assimilation with chemical transport models are illustrated.

Abstract:
We investigated the impact of tuning the length scale of the background error covariance in the Weather Research and Forecasting (WRF) three-dimensional variational assimilation (3DVAR) system. In particular, we studied the effect of this parameter on the assimilation of high-resolution surface data for heavy rainfall forecasts associated with mesoscale convective systems over the Korean Peninsula. In the assimilation of high-resolution surface data, the National Meteorological Center method tended to exaggerate the length scale that determined the shape and extent to which observed information spreads out. In this study, we used the difference between observation and background data to tune the length scale in the assimilation of high-resolution surface data. The resulting assimilation clearly showed that the analysis with the tuned length scale was able to reproduce the small-scale features of the ideal field effectively. We also investigated the effect of a double-iteration method with two different length scales, representing large and small-length scales in the WRF-3DVAR. This method reflected the large and small-scale features of observed information in the model fields. The quantitative accuracy of the precipitation forecast using this double iteration with two different length scales for heavy rainfall was high; results were in good agreement with observations in terms of the maximum rainfall amount and equitable threat scores. The improved forecast in the experiment resulted from the development of well-identified mesoscale convective systems by intensified low-level winds and their consequent convergence near the rainfall area.

Abstract:
This paper presents a comparison of two reduced-order, sequential and variational data assimilation methods: the SEEK filter and the R-4D-Var. A hybridization of the two, combining the variational framework and the sequential evolution of covariance matrices, is also preliminarily investigated and assessed in the same experimental conditions. The comparison is performed using the twin-experiment approach on a model of the Tropical Pacific domain. The assimilated data are simulated temperature profiles at the locations of the TAO/TRITON array moorings. It is shown that, in a quasi-linear regime, both methods produce similarly good results. However the hybrid approach provides slightly better results and thus appears as potentially fruitful. In a more non-linear regime, when Tropical Instability Waves develop, the global nature of the variational approach helps control model dynamics better than the sequential approach of the SEEK filter. This aspect is probably enhanced by the context of the experiments in that there is a limited amount of assimilated data and no model error.

Abstract:
In this article we study the influence of different characteristics of our assimilation system on surface ozone analyses over Europe. Emphasis is placed on the evaluation of the background error covariance matrix (BECM). Data assimilation systems require a BECM in order to obtain an optimal representation of the physical state. A posteriori diagnostics are an efficient way to check the consistency of the used BECM. In this study we derived a diagnostic to estimate the BECM. On the other hand, an increasingly used approach to obtain such a covariance matrix is to estimate it from an ensemble of perturbed assimilation experiments. We applied this method, combined with variational assimilation, while analysing the surface ozone distribution over Europe. We first show that the resulting covariance matrix is strongly time (hourly and seasonally) and space dependent. We then built several configurations of the background error covariance matrix with none, one or two of its components derived from the ensemble estimation. We used each of these configurations to produce surface ozone analyses. All the analyses are compared between themselves and compared to assimilated data or data from independent validation stations. The configurations are very well correlated with the validation stations, but with varying regional and seasonal characteristics. The largest correlation is obtained with the experiments using time- and space-dependent correlation of the background errors. Results show that our assimilation process is efficient in bringing the model assimilations closer to the observations than the direct simulation, but we cannot conclude which BECM configuration is the best. The impact of the background error covariances configuration on four-days forecasts is also studied. Although mostly positive, the impact depends on the season and lasts longer during the winter season.

Abstract:
In this article we study the influence of different characteristics of our assimilation system on the surface ozone analyses over Europe. Emphasis is placed on the evaluation of the background error covariance matrix (BECM). Data assimilation systems require a BECM in order to obtain an optimal representation of the physical state. A posteriori diagnostics are an efficient way to check the consistency of the used BECM. In this study we derived a diagnostic to estimate the BECM. On the other hand an increasingly used approach to obtain such a covariance matrix is to estimate it from an ensemble of perturbed assimilation experiments. We applied this method, combined with variational assimilation, while analysing the surface ozone distribution over Europe. We first show that the resulting covariance matrix is strongly time (hourly and seasonally) and space dependent. We then built several configurations of the background error covariance matrix with none, one or two of its components derived from the ensemble estimation. We used each of these configurations to produce surface ozone analyses. All the analyses are compared between themselves and compared to assimilated data or data from independent validation stations. The configurations are very well correlated with the validation stations, but with varying regional and seasonal characteristics. The largest correlation is obtained with the experiments using time and space dependent correlation of the background errors. Results show that our assimilation process is efficient in bringing the model assimilations closer to the observations than the direct simulation, but we cannot conclude which BECM configuration is the best. The impact of the background error covariances configuration on four-days forecasts is also studied. Although mostly positive, the impact depends on the season and lasts longer during the winter season.

Abstract:
To compensate for a poorly known geoid, satellite altimeter data is usually analyzed in terms of anomalies from the time mean record. When such anomalies are assimilated into an ocean model, the bias between the climatologies of the model and data is problematic. An ensemble Kalman filter (EnKF) is modified to account for the presence of a forecast-model bias and applied to the assimilation of TOPEX/Poseidon (T/P) altimeter data. The online bias correction (OBC) algorithm uses the same ensemble of model state vectors to estimate biased-error and unbiased-error covariance matrices. Covariance localization is used but the bias covariances have different localization scales from the unbiased-error covariances, thereby accounting for the fact that the bias in a global ocean model could have much larger spatial scales than the random error.The method is applied to a 27-layer version of the Poseidon global ocean general circulation model with about 30-million state variables. Experiments in which T/P altimeter anomalies are assimilated show that the OBC reduces the RMS observation minus forecast difference for sea-surface height (SSH) over a similar EnKF run in which OBC is not used. Independent in situ temperature observations show that the temperature field is also improved. When the T/P data and in situ temperature data are assimilated in the same run and the configuration of the ensemble at the end of the run is used to initialize the ocean component of the GMAO coupled forecast model, seasonal SSH hindcasts made with the coupled model are generally better than those initialized with optimal interpolation of temperature observations without altimeter data. The analysis of the corresponding sea-surface temperature hindcasts is not as conclusive.