Cloud Condensate Control Variable Transform and Background Errors

We will present progress on work to add cloud condensate control variable to a 4D-VAR analysis system at ECMWF. First, in 4D-VAR the linear physics scheme needs prognostic cloud variables to be able to use additional cloud information from observations, and in the current phase of our development the additional prognostic variable is cloud condensate (cloud liquid water and ice). Second, it is necessary to describe the relationship of cloud condensate background errors to the errors in other variables, and we have found a physical-statistical balance relationship between cloud condensate, humidity (and temperature) errors which are included as a change of variable from total to “unbalanced” cloud condensate. Third, the normalization of cloud condensate by its background error standard deviation requires particular attention because of the spatial inhomogeneity of the cloud field and the non-Gaussian errors. In this presentation we will focus on the formulation of cloud condensate background errors.