An adaptive background error inflation method for assimilating all-sky radiances

An adaptive background error inflation (ABEL) method is proposed for assimilating all-sky satellite brightness temperatures with an ensemble Kalman filter. This empirical cloud-scene-dependent covariance inflation method is designed to mitigate the model's difficulties in initiating convection in the observed cloudy regions where the background prior estimated from the ensemble mean incorrectly simulates clear-sky conditions. This new approach calculates a spatially varying, flow-dependent, multiplicative ensemble covariance inflation factor based on error statistics produced by a well-constructed, off-line observing system simulation experiment (OSSE) that assimilates similar all-sky radiance observations but were generated by the model, in which case the truth is known for all the state variables and the assimilated radiances. The adaptive inflation factor is a linear function of a cloud parameter which is only applied to the observed cloudy regions where there are less or no cloud in the prior ensemble mean estimates. The performance of ABEI is evaluated through assimilating synthetic and real-data all-sky radiance experiments from the Advanced Baseline Imager on board GOES-16 for Hurricanes Karl of 2010 and Harvey of 2017 . Assimilation experiments with ABEI allow adaptive inflation of the ensemble covariance in the model-simulated clear-sky regions when there are observed clouds while avoiding unnecessarily large ensemble spread in other cloud scenarios. This new approach alleviates the difficulty in estimating the appropriate inflation factors in the model state space using the innovation statistics in the observation space (radiance) with a highly nonlinear observation operator. It serves as an alternative to existing methods using spatially varying adaptive inflations; their relative performance and potential combinations are to be further assessed in the future.