Nancy Nichols, University of Reading
The error of representation: treatment and estimation
Coauthors
Daniel Hodyss, Elizabeth Satterfield, Sarah KingAbstract:
The numerical simulation of geophysical systems invariably leads to approximations on a mesh that is coarser than is required to resolve all of the important physical processes. Representation error arises from the inability of the forecast model to simulate accurately the climatology of the truth. We present a rigorous framework for understanding this error of representation and show that contemporary data assimilation systems cannot precisely identify representation error using standard estimation procedures. A new gain matrix for the data assimilation problem is derived that gives the best approach to Bayesian data assimilation for forecast models that represent the true system using a truncated state space. This new data assimilation algorithm is the optimal scheme in the case where the distributions on the true attractor and the forecast attractors are separately Gaussian and there exists a linear map between them. The results of this theory are illustrated in a simple Gaussian multivariate model.