Incorporation of a New Non-Gaussian Solver in the Static Component of the Hybrid GSI System

Current data assimilation for numerical environmental prediction at operational centers is based on Bayesian statistics and probability, which are inherently tied to a Gaussian assumption of the probability density function (PDF) of the observation and background errors. In reality, the errors associated with key fields linked to the prediction of high-impact weather (clouds and precipitation) exhibit PDF error distributions that are non-Gaussian.

As way to address this problem, we can employ the “mixed distribution” approach whereby a lognormal and a Gaussian distribution are combined to form a new distribution. The objective of the mixed distribution approach is to find an analysis solution 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. This can allow for the simultaneous assimilation of observations that update control variables with associated Gaussian and lognormal error distributions in their background counterparts. In addition, standard procedures, such as rejecting “lognormal” observations to later assimilate them separately or to transform lognormal variables into a Gaussian can be avoided.

With the objective of advancing data assimilation and to address the non-Gaussian aspects associated with the assimilation of clouds and humidity related observations, (e.g. microwave radiances, lightning flash rate, and specific humidity or cloud hydrometeor profiles), the hybrid Gridpoint Statistical Interpolation (GSI) system is being augmented to include a novel mixed Gaussian-lognormal solver in its static component. Through this addition, GSI is capable of producing a non-Gaussian deterministic analysis and to simultaneously assimilate Gaussian and non-Gaussian observations. Even though, this new solver is model agnostic, initial testing is being done for convection allowing model resolution analysis. In addition, a new static error covariance matrix for lognormal cloud and humidity control variables modeled via flow dependent length-scale calculations can also be used with GSI. The methodology for inclusion of the mixed-distribution approach in GSI and initial tests with this new non-Gaussian solver and background error covariance matrix will be covered.