Abstract.We study the characteristics of a statistical ensemble of mesoscale simulations in order to estimate the model error in the simulation of CO 2 concentrations. The ensemble consists of ten members and the reference simulation using the operationnal short range forecast PEARP, perturbed using the Singular Vector technique. We then used this ensemble of simulations as the initial and boundary conditions for the meso scale model (Méso-NH) simulations, which uses CO 2 fluxes from the ISBA-A-gs land surface model. The final ensemble represents the model dependence to the boundary conditions, conserving the physical properties of the dynamical schemes, but excluding the intrinsic error of the model. First, the variance of our ensemble is estimated over the domain, with associated spatial and temporal correlations. Second, we extract the signal from noisy horizontal correlations, due to the limited size ensemble, using diffusion equation modelling. The computational cost of such ensemble limits the number of members (simulations) especially when running online the carbon flux and the atmospheric models. In the theory, 50 to 100 members would be required to explore the overall sensitivity of the ensemble. The present diffusion model allows us to extract a significant part of the noisy error, and makes this study feasable with a limited number of simulations. Finally, we compute the diagonal and non-diagonal terms of the observation error covariance matrix and introduced it into our CO 2 flux matrix inversion for 18 days of the 2005 intensive campaign CERES over the South West of France. Variances are based on model-data mismatch to ensure we treat model bias as well as ensemble dispersion, whereas spatial and temporal covariances are estimated with our method.The horizontal structure of the ensemble variance maniCorrespondence to: T. Lauvaux (thomas.lauvaux@lsce.ipsl.fr) fests the discontinuities of the mesoscale structures during the day, but remains locally driven during the night. On the vertical, surface layer variance shows large correlations with the upper levels in the boundary layer (> 0.6), dropping to 0.4 with the lower levels of the free troposphere. Large temporal correlations were found during the afternoon (> 0.5 for several hours), reduced during the night. The diffusion equation model extracted relevant error covariance signals horizontally, with reduced correlations over mountain areas and during the night over the continent. The posterior error reduction on the inverted CO 2 fluxes accounting for the model error correlations illustrates the predominance of the temporal over the spatial correlations when using tower-based CO 2 concentration observations.

ABSTRACT:As the background-error covariance matrix is a key component of any assimilation system, its modelling is an important step. Usually, this matrix is decomposed into correlations and standard deviations matrices. An interesting method for modelling the correlation matrix of the background error for complex geometry, like an ocean grid, consists in computing correlation functions using a diffusion operator. The background-error correlation functions can be estimated for example from an ensemble of perturbed forecasts. The diffusion operator is able to represent heterogeneous correlation functions at a reasonable numerical cost. But a first challenge resides in the determination of the local diffusion tensor corresponding to the local correlation function. Then the second challenge resides in the determination of the normalization to make sure that the matrix modelled through the diffusion operator is a correlation matrix. In this article, we propose to build a background-error correlation matrix using a diffusion operator based on a local diffusion tensor. The estimation of this local tensor is performed using an ensemble of perturbed forecasts. A validation within a randomization method illustrates the feasibility and the accuracy of the proposed method. In particular, it is shown that the local geographical variations of diagnosed correlation functions (through an ensemble of perturbed forecast) are well represented. This is first illustrated in an analytical one-dimensional framework. In that context, the diffusion field and the normalization field are deduced from a given correlation length-scale field. The resulting length-scales are shown to correspond to the initial length-scale when the given length-scale field spectrum is red. The approximate normalization, computed from the local length-scale, is close to the true normalization under the same condition of a red spectrum.Then, the method is illustrated in a real context using an ensemble of perturbed forecasts from the MOCAGE-PALM assimilation system. In that case, length-scale and anisotropy diagnosis reveal the complexity of the correlation of stratospheric ozone forecast errors. The local diffusion tensor deduced from these diagnoses is shown be able to represent such an existing heterogeneity and anisotropy. As in the one-dimensional case, the approximate normalization, based on the local diffusion tensor, appears to be a really good approximation of the true normalization.

Abstract. Accurate and temporally resolved fields of freetroposphere ozone are of major importance to quantify the intercontinental transport of pollution and the ozone radiative forcing. We consider a global chemical transport model (MOdèle de Chimie Atmosphérique à Grande Échelle, MOCAGE) in combination with a linear ozone chemistry scheme to examine the impact of assimilating observations from the Microwave Limb Sounder (MLS) and the Infrared Atmospheric Sounding Interferometer (IASI). The assimilation of the two instruments is performed by means of a variational algorithm (4D-VAR) and allows to constrain stratospheric and tropospheric ozone simultaneously. The analysis is first computed for the months of August and November 2008 and validated against ozonesonde measurements to verify the presence of observations and model biases. Furthermore, a longer analysis of 6 months (July-December 2008) showed that the combined assimilation of MLS and IASI is able to globally reduce the uncertainty (root mean square error, RMSE) of the modeled ozone columns from 30 to 15 % in the upper troposphere/lower stratosphere (UTLS, 70-225 hPa). The assimilation of IASI tropospheric ozone observations (1000-225 hPa columns, TOC -tropospheric O 3 column) decreases the RMSE of the model from 40 to 20 % in the tropics (30 • S-30 • N), whereas it is not effective at higher latitudes. Results are confirmed by a comparison with additional ozone data sets like the Measurements of OZone and wAter vapour by aIrbus in-service airCraft (MOZAIC) data, the Ozone Monitoring Instrument (OMI) total ozone columns and several high-altitude surface measurements. Finally, the analysis is found to be insensitive to the assimilation parameters. We conclude that the combination of a simplified ozone chemistry scheme with frequent satellite observations is a valuable tool for the longterm analysis of stratospheric and free-tropospheric ozone.

Background-error covariances can be estimated from an ensemble of forecast differences. The finite size of the ensemble induces a sampling noise in the calculated statistics. It is shown formally that a wavelet diagonal approach amounts to locally averaging the correlations, and its ability to spatially filter this sampling noise is thus investigated experimentally. This is first studied in a simple analytical one-dimensional framework. The capacity of a wavelet diagonal approach to model the scale variations over the domain is illustrated. Moreover, the sampling noise appears to be better filtered than when only using a Schur filter, in particular for small ensembles.The filtering properties are then illustrated for an ensemble of Météo-France Arpège forecasts. This is done both for the 'time-averaged correlations', and for the 'correlations of the day'. It is shown that the wavelets are able to extract some length-scale variations that are related to the meteorological situation.