The error of representation: basic understanding

• Main Authors: Daniel Hodyss, Nancy Nichols
• Format: Article
• Language: English
• Published: Taylor & Francis Group 2015-01-01
• Series: Tellus: Series A, Dynamic Meteorology and Oceanography
• Subjects: Representation error; data assimilation; correlated observations; model error; Bayesian
• Online Access: http://www.tellusa.net/index.php/tellusa/article/view/24822/pdf_9

Representation error arises from the inability of the forecast model to accurately simulate the climatology of the truth. We present a rigorous framework for understanding this kind of error of representation. This framework shows that the lack of an inverse in the relationship between the true climatology (true attractor) and the forecast climatology (forecast attractor) leads to the error of representation. A new gain matrix for the data assimilation problem is derived that illustrates the proper approaches one may take to perform Bayesian data assimilation when the observations are of states on one attractor but the forecast model resides on another. This new data assimilation algorithm is the optimal scheme for the situation 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.