The error of representation: basic understanding
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 clim...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Stockholm University Press
2015-01-01
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| Series: | Tellus: Series A, Dynamic Meteorology and Oceanography |
| Subjects: | |
| Online Access: | http://www.tellusa.net/index.php/tellusa/article/view/24822/pdf_9 |
| _version_ | 1811252615654146048 |
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| author | Daniel Hodyss Nancy Nichols |
| author_facet | Daniel Hodyss Nancy Nichols |
| author_sort | Daniel Hodyss |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-12T16:37:19Z |
| format | Article |
| id | doaj.art-19e75f5a3d384bc2903b7d05abb28de9 |
| institution | Directory Open Access Journal |
| issn | 1600-0870 |
| language | English |
| last_indexed | 2024-04-12T16:37:19Z |
| publishDate | 2015-01-01 |
| publisher | Stockholm University Press |
| record_format | Article |
| series | Tellus: Series A, Dynamic Meteorology and Oceanography |
| spelling | doaj.art-19e75f5a3d384bc2903b7d05abb28de92022-12-22T03:24:55ZengStockholm University PressTellus: Series A, Dynamic Meteorology and Oceanography1600-08702015-01-0167011710.3402/tellusa.v67.2482224822The error of representation: basic understandingDaniel Hodyss0Nancy Nichols1 Marine Meteorology Division, Naval Research Laboratory, Monterey, CA, USA School of Mathematical and Physical Sciences, University of Reading, Reading, UKRepresentation 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.http://www.tellusa.net/index.php/tellusa/article/view/24822/pdf_9Representation errordata assimilationcorrelated observationsmodel errorBayesian |
| spellingShingle | Daniel Hodyss Nancy Nichols The error of representation: basic understanding Tellus: Series A, Dynamic Meteorology and Oceanography Representation error data assimilation correlated observations model error Bayesian |
| title | The error of representation: basic understanding |
| title_full | The error of representation: basic understanding |
| title_fullStr | The error of representation: basic understanding |
| title_full_unstemmed | The error of representation: basic understanding |
| title_short | The error of representation: basic understanding |
| title_sort | error of representation basic understanding |
| topic | Representation error data assimilation correlated observations model error Bayesian |
| url | http://www.tellusa.net/index.php/tellusa/article/view/24822/pdf_9 |
| work_keys_str_mv | AT danielhodyss theerrorofrepresentationbasicunderstanding AT nancynichols theerrorofrepresentationbasicunderstanding AT danielhodyss errorofrepresentationbasicunderstanding AT nancynichols errorofrepresentationbasicunderstanding |