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.

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.

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.