Exploring Bounded Nonparametric Ensemble Filter Impacts on Sea Ice Data Assimilation

Abstract Standard ensemble Kalman filter algorithms have Gaussian assumptions built into their formulations. Gaussian assumptions make these algorithms susceptible to biased solutions when prior distributions or likelihoods are non-Gaussian. Sea ice poses a unique application for testing ensemble Kalman filter algorithms because sea ice observations are nonnegative and doubly bounded, leading to non-Gaussian distributions. Four different ensemble Kalman filter algorithms are tested in observing system simulation experiments (OSSEs) to evaluate their ability to update different sea ice fields: 1) ensemble adjustment Kalman filter, 2) ensemble Kalman filter with perturbed observations, 3) rank histogram filter (RHF), and 4) bounded RHF. The bounded RHF, an extension of the standard RHF, was recently developed to properly respect bounds (singly and doubly bounded) on distributions in observation space. Compared to the other ensemble Kalman filter algorithms, the bounded RHF pulls the ensemble closer to the true value and respects the bounds. Most notably during winter when sea ice concentration is near its upper bound of one, the bounded RHF provides updates in the observation space that are more uniformly distributed around zero compared to the other algorithms. One common finding among all ensemble Kalman filter algorithms tested is the overdispersive nature of sea ice thickness. This was linked back to the method used to create the initial ensemble spread for our free forecasts in our OSSEs. Improving our ability to assimilate sea ice observations within our coupled Earth system modeling frameworks will help improve future projections of the climate and processes related to the cryosphere.