Bounded and categorized: Targeting data assimilation for sea ice fractional coverage and nonnegative quantities in a single-column multi-category sea ice model

A rigorous exploration of the sea ice data assimilation (DA) problem using a framework specifically developed for rapid, interpretable hypothesis testing is presented. In many applications, DA is implemented to constrain a modeled estimate of a state with observations. The sea ice DA application is complicated by the wide range of spatiotemporal scales over which key sea ice variables evolve, a variety of physical bounds on those variables, and the particular construction of modern complex sea ice models. By coupling a single-column sea ice model (Icepack) to the Data Assimilation Research Testbed (DART) in a series of observing system simulation experiments (OSSEs), the grid-cell-level response of a complex sea ice model to a range of ensemble Kalman DA methods designed to address the aforementioned complications is explored. The impact on the modeled ice thickness distribution and the bounded nature of both state and prognostic variables in the sea ice model are of particular interest, as these problems are under-examined. Explicitly respecting boundedness has little effect in the winter months, but it correctly accounts for the bounded nature of the observations, particularly in the summer months when the prescribed sea ice concentration (SIC) error is large. Assimilating observations representing each of the individual modeled sea ice thickness categories consistently improves the analyses across multiple diagnostic variables and sea ice mean states. These results elucidate many of the positive and negative results of previous sea ice DA studies, highlight the many counterintuitive aspects of this particular DA application, and motivate better future sea ice analysis products.