Correcting biased observation model error in data assimilation

While the formulation of most data assimilation schemes assumes an unbiased observation model error, in real applications model error with nontrivial biases is unavoidable. A practical example is errors in the radiative transfer model (which is used to assimilate satellite measurements) in the presence of clouds. Together with the dynamical model error, the result is that many (in fact 99%) of the cloudy observed measurements are not being used although they may contain useful information. This paper presents a novel nonparametric Bayesian scheme that is able to learn the observation model error distribution and correct the bias in incoming observations. This scheme can be used in tandem with any data assimilation forecasting system. The proposed model error estimator uses nonparametric likelihood functions constructed with data-driven basis functions based on the theory of kernel embeddings of conditional distributions developed in the machine learning community. Numerically, positive results are shown with two examples. The first example is designed to produce a bimodality in the observation model error (typical of "cloudy" observations) by introducing obstructions to the observations that occur randomly in space and time. The second example, which is physically more realistic, is to assimilate cloudy satellite brightness temperature-like quantities, generated from a stochastic multicloud model for tropical convection and a simple radiative transfer model.