Assimilating Measurements with State-Dependent Non-Gaussian Errors

Most data assimilation techniques used for environmental models have a Bayesian interpretation. If we choose a prior distribution for prior model variables (typically a Gaussian) and a likelihood function based on assumed observation uncertainty (also typically a Gaussian), we can arrive at numerical methods that either solve for parts of the posterior distribution or draw samples from it. This presentation highlights new developments and model implementations that adopt “nonparametric” choices for priors and likelihoods—meaning no specific distribution shape is assumed. Moving beyond parametric assumptions has many practical advantages for the diverse modeling applications in geoscience. Nonparametric choices for the prior can lead to greater physical fidelity in ensemble members updated during data assimilation and used to initialize dynamical models. Nonparametric choices for the likelihood can lead to a more optimal use of novel datasets (e.g., assimilating images instead of point measurements) and the removal of ad hoc quality control algorithms. In addition to describing new research directions on this topic, we will survey progress made for several atmospheric and marine science applications, with a focus on convective-scale modeling, hurricanes, and coupled sea ice-ocean modeling.