SUMMARYMost operational assimilation schemes rely on linear estimation theory. Under this assumption, it is shown how simple consistency diagnostics can be obtained for the covariances of observation, background and estimation errors in observation space. Those diagnostics are shown to be nearly cost-free since they only combine quantities available after the analysis, i.e. observed values and their background and analysis counterparts in observation space. A first application of such diagnostics is presented on analyses provided by the French 4D-Var assimilation. A procedure to refine background and observation-error variances is also proposed and tested in a simple toy analysis problem. The possibility to diagnose cross-correlations between observation errors is also investigated in this same simple framework. A spectral interpretation of the diagnosed covariances is finally presented, which allows us to highlight the role of the scale separation between background and observation errors.

SUMMARYFollowing the a posteriori diagnosis approach proposed by some authors, a practical computation of the expectation of sub-parts of the value of a cost function at the minimum is shown to be feasible by using a randomization technique based on a perturbation of observations or background fields. These computations allow the tuning of observation-error weighting parameters by applying a simple iterative fixed-point procedure.The procedure is first tested in a simplified variational scheme on a circular domain and then in a similar scheme but with the addition of the vertical coordinate. The relationship between the proposed approach and the Generalized Cross Validation is also shown. A test in the French Action de Recherche Petite Echelle Grande Echelle (ARPEGE) three-dimensional variational framework with both simulated observations and background fields is finally performed. It shows that a complete description of observation-error parameters can be retrieved with only a few iterations and, thus, at a reasonable cost.

AROME-France is a convective-scale numerical weather prediction system running operationally at Météo-France since the end of 2008. It uses a 3D-Var assimilation scheme to determine its initial conditions. Climatological background-error covariances of such a system are calculated using differences between forecasts from an AROME ensemble assimilation. These statistics are compared with the lowerresolution ALADIN-France system ones: they provide 3D-Var analysis increments that are more intense and more localized, in accordance with the actual AROME model resolution. AROME ensemble-assimilation (ENS DA) covariances have also been compared with covariances calculated with an AROME ensemble of forecasts run in spin-up mode (ENS SU). On the one hand, ENS SU appears to be a reasonable approximation of ENS DA compared with ALADIN-France covariances, by representing a large part of the small-scale variance increase. On the other hand, ENS DA allows for a fully cycled development of small-scale forecast perturbations, which leads to a further enhancement of small-scale covariances. This aspect is shown to be beneficial in terms of assimilation diagnostics and forecast performance and in a case study.

Several networks of Global Positioning System receiving stations over Europe send their data to several processing centers to generate atmospheric Zenith Total Delay (ZTD) observations. Thanks to the efforts of the Targeting Optimal Use of Global Positioning System Humidity measurements in meteorology project, these observations combining surface pressure and total precipitable water information in the atmosphere have been delivered to the operational meteorological centers in near real‐time since 2004. This paper presents forecast impact trials of such ZTD observations in a global Four‐Dimensional Variational (4DVAR) assimilation and forecasting system. The implementation of the ZTD assimilation in the 4DVAR system is described, including a preprocessing developed specifically for the ZTD data. The preprocessing involves a time averaging procedure of the observations in order to ensure consistency with the resolution of the 4DVAR, a bias correction, and a station selection based on χ2 tests of the normality of the observation minus first‐guess differences. Three forecast trials were conducted: winter, spring, and summer 2005. These trials cover various meteorological conditions and a total of about 10 weeks of assimilation. All three trials suggest a positive impact of the ZTD data in helping constrain the synoptic circulation in 1 to 4 day forecasts. In the spring and the summer trials, the impact of the ZTD data also shows positively on the prediction of precipitation patterns as indicated by improved Quantitative Precipitation Forecast scores for total precipitation forecasts over France between +12 and +36 hours. We also assess in this paper ZTD observation and background errors.

Flow-dependent background-error variances can be estimated by means of an ensemble of assimilations. However, the finite size of the ensemble implies a sampling noise, which is detrimental for the variance estimation. This article presents a filtering procedure for ensemble-estimated variance fields, which relies on an estimate of spectral signal/noise ratios.It is first demonstrated that the sampling noise covariance can be expressed analytically as a simple function of the background-error covariance. The resulting formula shows in particular that the spatial structure of the sampling noise is closely related to the spatial structure of background error (i.e. to its correlation function). It is then explained how this relation can be used to calculate an objective filter.Investigations are first conducted in a highly idealized 1D framework, to show that the proposed filter is able to remove most of the sampling noise, while extracting the signal of interest. Application to an ensemble of Météo-France Arpège forecasts is then considered. This objective filter reveals a vertical-level dependence, with a larger signal/noise ratio near the surface, and a scale separation between signal and noise which is more pronounced in altitude. The results also indicate that, after applying such an optimized filter, variance estimates obtained from a six-member ensemble have a residual estimation error variance around 10%.Some insights are then given into the spatio-temporal dynamics of the variance field. It is observed that the globally averaged background-error variance is fairly stable in time, while spatial patterns of the variance field are closely linked to the meteorological situation, with high values found in the vicinity of troughs.Finally, impact studies in the Arpège system show that the filtering of vorticity variances has a positive impact on the quality of the NWP system.

Following the a posteriori diagnosis approach proposed by some authors, a practical computation of the expectation of sub-parts of the value of a cost function at the minimum is shown to be feasible by using a randomization technique based on a perturbation of observations or background fields. These computations allow the tuning of observation-error weighting parameters by applying a simple iterative fixed-point procedure.The procedure is first tested in a simplified variational scheme on a circular domain and then in a similar scheme but with the addition of the vertical coordinate. The relationship between the proposed approach and the Generalized Cross Validation is also shown. A test in the French Action de Recherche Petite Echelle Grande Echelle (ARPEGE) three-dimensional variational framework with both simulated observations and background fields is finally performed. It shows that a complete description of observation-error parameters can be retrieved with only a few iterations and, thus, at a reasonable cost. = hTr(R7' [I'jE(caeyT)r; + E ( c y~y )~ -E{(l'jxa)cYT} -E[cy(rjxa)T}]), since r j x ay? = r j x a + rjxTr j x Ty? = rjea -€ 9 , and using the fact that E(Tr(.)} = Tr{E(.)} and the linearity properties of the expectation operator E. J J J

SUMMARYDesroziers and Ivanov proposed a method to tune error variances used for data assimilation. The implementation of this algorithm implies the computation of the trace of certain matrices which are not explicitly known. A method proposed by Girard, allowing an approximate estimation of the traces without explicit knowledge of the matrices, was then used. This paper proposes a new implementation of the Desroziers and Ivanov algorithm, including a new computation scheme for the required traces. This method is compared to Girard's in two aspects: its use in the implementation of the tuning algorithm, and the computation of a quantification of the observation impacts on the analysis known as Degrees of Freedom for Signal. Those results are illustrated by studies utilizing the French data assimilation/numerical weather-prediction system ARPEGE. The impact of a first quasioperational tuning of variances on forecasts is shown and discussed.

SUMMARYThe method for tuning observational or background error statistics is presented and some of its properties are exposed using theoretical considerations and experiments carried out in a simplified framework. In particular, the method is shown to be equivalent to a maximum-likelihood evaluation and its efficiency is seen to depend on the number of observations. The results of several experiments carried out with the variational assimilation system of the French numerical weather-prediction system ARPEGE, both with simulated and actual datasets involving satellite radiances, are also presented. The temporal stability of the results and their consistency with the known quality of the measurements are shown.