Incorporating non-Gaussian observation errors into variational methods

The observation error has been assumed to be Gaussian in most data assimilation (DA) applications. One of the reasons is that we typically do not have access to the actual shape of the observation error probability density function (pdf). Recently, we have developed a new method, the Deconvolution-based Observation Error Estimation (DOEE), that allows us to derive a fully non-Gaussian pdf even for observations with complicated representation error.

With DOEE, we can now explore the effect of non-Gaussian observation error in assimilation using non-parametric DA methods, e.g., particle (flow) filters. However, most of the operational weather forecasting centers are still based on variational DA methods, e.g., 4D-Var, in which the DA algorithms are constructed based on Gaussian observation errors. In this presentation, we will propose a novel way, called the evolving-Gaussian method, to account for non-Gaussian observation errors in incremental 4D-Var. The evolving-Gaussian method essentially uses a different Gaussian observation error pdf in each outer loop to locally approximate the gradient of the cost-function. One advantage of the evolving-Gaussian method is that we do not require changing the cost-function for different observation error pdfs, such that it can be easily implemented in a full-scale operational weather forecasting system without adding to the computational cost. We will demonstrate the evolving-Gaussian method in the ECMWF system with the assimilation of satellite microwave radiances, which have non-Gaussian observation errors due to the representation errors. The preliminary results indicate promising signs of improvement for the 12-h forecast of the low-level water vapor, cloud and precipitation, especially in the tropics.