Current data assimilation efforts in operational centers are done under the Gaussianity assumption of the probability density function (PDF) of the background errors, but the processes involved in clouds and precipitation are highly non-linear and can give rise to non-Gaussian background error distributions. In reality, even when obtaining good-quality data, and advancing the physics in some parameterizations used in NWP, the PDF of the background errors still show significant departures from the pure Gaussian form.
An alternative approach is to combine a lognormal and Gaussian distribution to form a mixed distribution. This approach can allow for the simultaneous assimilation of variables with Gaussian and lognormal error distributions, rather than rejecting lognormal observations to later assimilate them, separately or to transform lognormal variables into Gaussian. The objective of the mixed distribution approach is to find an analysis with the correct covariances between random variables, as opposed to finding the mode of the best Gaussian approximation or the median of a lognormal distribution.
With the objective of advancing hybrid data assimilation and to address the non-Gaussian aspects associated with the incorporation of microwave radiances and cloud hydrometeors, the hybrid Gridpoint Statistical Interpolation system is being augmented to include a lognormal and subsequently a mixed Gaussian-lognormal background error representation. Preliminary results showing the benefit of the formerly mentioned background error representations in convective-scale weather forecasting with the RAP+HRRR model will be presented.