Estimation of the observation standard deviation error formula thanks to the a posteriori diagnosis

Within the UERRA project, a daily precipitation reanalysis at a 5,5km resolution has been realized from 1961 to 2015. The reanalysis was obtained by the MESCAN analysis system which combines an a priori estimate of the atmosphere – called background – and observations using an optimum interpolation (OI) scheme. Such method requires the specification of observations and background errors. In general, constant standard deviation errors are used but more errors are made when high precipitation are observed. Then, to take this effect into account and to avoid a model over-estimation in case of light precipitation, a variable formula of the observation standard deviation error was purposed with a small value for null precipitation and greater values when precipitation are higher, following a linear equation.

Desroziers et al proposed a method to determine observations and background errors called a posteriori diagnosis. To use this iterative method, the analysis has to be ran several times until it converged. In this study, the a posteriori diagnosis is used per precipitation class to determine the observation standard deviation error formula. MESCAN was tested using the French operational model AROME at 1,3km resolution and the atmopsheric UERRA analysis downscaled to 5,5km background and combined to the French observational network over the 2016-2018 period. The observation standard deviation error formula obtained by the a posteriori diagnosis is then used in the MESCAN analysis system to produce precipitation analysis over the 2016-2018 period. Results are compared to UERRA precipitation reanalysis over independant observations by comparing bias, RMSE and scores per precipitation class.