Section: New Results

New methods for data assimilation

Since the beginning, Clime is focused on developing new techniques for data assimilation in geophysical sciences. Clime is active on several of the most challenging theoretical aspects of data assimilation: data assimilation methods based on non-Gaussian assumptions, methods for estimating errors, ensemble filtering techniques, 4D variational assimilation approaches, ensemble-variational methods, etc. This year, we revisited several of these topics. A dual algorithm has been developed for the finite-size ensemble Kalman filter, that shows how to estimate optimal inflation that counteracts sampling errors. A variational method coupled to a subgrid scale statistical model has been introduced and validated to quantify the representativeness errors. We also started to work on ensemble variational methods that are brand new techniques emerging in the meteorological data assimilation field.

Combining inflation-free and iterative ensemble Kalman filters for strongly nonlinear systems

Participants : Marc Bocquet, Pavel Sakov [NERSC, Norway] .

The finite-size ensemble Kalman filter (EnKF-N) is an ensemble Kalman filter (EnKF) which, in perfect model condition, does not require inflation because it partially accounts for the ensemble sampling errors. For the Lorenz '63 and '95 toy-models, it was so far shown to perform as well or better than the EnKF with an optimally tuned inflation. The iterative ensemble Kalman filter (IEnKF) is an EnKF which was shown to perform much better than the EnKF in strongly nonlinear conditions, such as with the Lorenz '63 and '95 models, at the cost of iteratively updating the trajectories of the ensemble members. This study aims at further exploring the two filters, and at combining both into an EnKF that does not require inflation in perfect model condition and which is as efficient as the IEnKF in very nonlinear conditions.

In this study EnKF-N is first introduced and a new implementation is developed. It decomposes EnKF-N into a cheap two-step algorithm that amounts to computing an optimal inflation factor. This offers a justification of the use of the inflation technique in the traditional EnKF and why it can often be efficient. Secondly, the IEnKF is introduced following a new implementation based on the Levenberg-Marquardt optimization algorithm. Then, the two approaches are combined to obtain the finite-size iterative ensemble Kalman filter (IEnKF-N). Several numerical experiments are performed on IEnKF-N with the Lorenz '95 model. These experiments demonstrate its numerical efficiency as well as its performance that offer, at least, the best of both filters.

Accounting for representativeness errors in the inversion of atmospheric constituent emissions: Application to the retrieval of regional carbon monoxide fluxes

Participants : Mohammad Reza Koohkan, Marc Bocquet.

A four-dimensional variational data assimilation system (4D-Var) is developed to retrieve carbon monoxide (CO) fluxes at regional scale, using an air quality network. The air quality stations that monitor CO are proximity stations located close to industrial, urban or traffic sources. The mismatch between the coarsely discretized Eulerian transport model and the observations, inferred to be mainly due to representativeness errors in this context, leads to a bias (averaged simulated concentrations minus observed concentrations) of the same order of magnitude as the concentrations. 4D-Var leads to a mild improvement in the bias because it does not adequately handle the representativeness issue. For this reason, a simple statistical subgrid model is introduced and is coupled to 4D-Var. In addition to CO fluxes, the optimization seeks to jointly retrieve influence coefficients, which quantify each station's representativeness. The method leads to a much better representation of the CO concentration variability, with a significant improvement of statistical indicators. The resulting increase in the total inventory estimate is close to the one obtained from remote sensing data assimilation. This methodology and experiments suggest that information useful at coarse scales can be better extracted from atmospheric constituent observations strongly impacted by representativeness errors.

Real-time data assimilation

Participants : Vivien Mallet, Anne Tilloy, Fabien Brocheton [Numtech] , David Poulet [Numtech] , Cécile Honoré [Airparif] , Édouard Debry [INERIS] .

Based on Verdandi, Polyphemus and the “Urban Air Quality Analysis” software, real-time data assimilation was carried out at urban scale. The Best Linear Unbiased Estimator (BLUE) was computed for every hourly concentration map that the ADMS model computed. A posteriori tests were conducted over Clermont-Ferrand and Paris. We addressed the key issue of the covariance of the state error. The form of the error covariance between two points was determined based on the road network, considering the distance between points along the road and the distance of each point to the road. A few parameters (primarily two decorrelation lengths) were determined thanks to cross validation with several months of simulations and observations. The results showed strong improvements even at locations where no data was assimilated.

At larger scale, the data assimilation library Verdandi was used to apply data assimilation (optimal interpolation) with the air quality model Chimere. This preliminary work will help INERIS to apply optimal interpolation for ozone and particulate matter in the operational platform Prev'air.