Multi-Model Ensemble Approaches to Data Assimilation Using the 4D-Local Ensemble Transform Kalman Filter

摘要

Uncertainties in the numerical prediction using a computational model of a physical system arise from two primary sources: (i) errors within the model itself; and (ii) imperfect knowledge of (a) the initial conditions to start the model and (b) boundary conditions and the forcing that is required to run the model. One way to examine these uncertainties is the multi-model approach, i.e., to compare results from multiple models. However, the multi- model approach cannot completely address either (i) or (ii) due to lack of knowledge of the real state. Another way is to compare the results with the 'observations' that sample the real state. However, the observations introduce another source of uncertainties, i.e., (iii) imperfect knowledge and/or improper assumptions within the observations including sampling error. The ultimate objective of this project is to develop a framework for two purposes: one is the maximum reduction of the reducible uncertainties and the other is the diagnosis of the irreducible uncertainties in the numerical prediction. We will use a data-assimilation approach, which is ideal for this problem. Data assimilation is a method that was developed to primarily address the issues related to (ii-a) above by merging the observations into the numerical prediction. It attempts to optimally combine the 'background' (or 'forecast') information obtained by a short-term forecast using a numerical model with the observations taken within the forecast time window. The resulting state is the so-called 'analysis', whose uncertainties are expected to be smaller than both the background and the observations. Some of these uncertainties are reducible by improving the data assimilation method. Other uncertainties are irreducible.