Diagnosing non-Gaussianity of forecast and analysis errors in a convective scale model

R. Legrand, Y. Michel, T. Montmerle
2015 Nonlinear Processes in Geophysics Discussions  
In numerical weather prediction, the problem of estimating initial conditions is usually based on a Bayesian framework. Two common derivations respectively lead to the Kalman filter and to variational approaches. They rely on either assumptions of linearity or assumptions of Gaussianity of the probability density functions of both observation and background errors. In practice, linearity and Gaussianity of errors are tied to one another, in the sense that a nonlinear model will yield
more » ... ll yield non-Gaussian probability density functions, and that standard methods may perform poorly in the context of non-Gaussian probability density functions. <br><br> This study aims to describe some aspects of non-Gaussianity of forecast and analysis errors in a convective scale model using a Monte-Carlo approach based on an ensemble of data assimilations. For this purpose, an ensemble of 90 members of cycled perturbed assimilations has been run over a highly precipitating case of interest. Non-Gaussianity is measured using the <i>K</i><sup>2</sup>-statistics from the D'Agostino test, which is related to the sum of the squares of univariate skewness and kurtosis. <br><br> Results confirm that specific humidity is the least Gaussian variable according to that measure, and also that non-Gaussianity is generally more pronounced in the boundary layer and in cloudy areas. The mass control variables used in our data assimilation, namely vorticity and divergence, also show distinct non-Gaussian behavior. It is shown that while non-Gaussianity increases with forecast lead time, it is efficiently reduced by the data assimilation step especially in areas well covered by observations. Our findings may have implication for the choice of the control variables.
doi:10.5194/npgd-2-1061-2015 fatcat:a5g7i7pkrze2je2mzfd7z2tjkm