Model Uncertainty Quantification for Data Assimilation in partially observed multi-scale systems
The success of any data assimilation scheme and quality of its outputs are highly dependent on uncertainty quantification of model outputs and observations. Quantifying model uncertainty remains a particularly challenging task, especially for partially observed non-linear systems with non-Gaussian uncertainties. Stochastic parameterisation methods have been receiving increasing attention to quantify model uncertainty due to unresolved sub-grid scale processes. However, these are generally only applicable when knowledge of the true sub-grid scale process or full observations of the coarse scale process are available, which represents rather unrealistic conditions. We present a methodology for estimating the statistics of sub-grid scale processes using only partial observations of the coarse scale process, and without relying on Gaussian assumptions which are often invoked. Additive errors are estimated over a training period by minimising their conditional variance, constrained by available observations. Special is that these errors are binned conditioned on the previous model state during the minimisation process, allowing for the recovery of complex error structures. We present the theory behind the approach along with numerical experiments using the multi-scale Lorenz 96’ model. Results demonstrate improved analyses and forecasts with the proposed method compared to two existing methods for accounting for model uncertainty in Data Assimilation.
Dr. Sahani Pathiraja Universitaet Potsdam