How far can the statistical error estimation problem be closed by collocated data?
<p>Accurate specification of the error statistics required for data assimilation remains an ongoing challenge, partly because their estimation is an underdetermined problem that requires statistical assumptions. Even with the common assumption that background and observation errors are uncorre...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Copernicus Publications
2023-09-01
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| Series: | Nonlinear Processes in Geophysics |
| Online Access: | https://npg.copernicus.org/articles/30/375/2023/npg-30-375-2023.pdf |
| _version_ | 1797681430149464064 |
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| author | A. Vogel A. Vogel R. Ménard |
| author_facet | A. Vogel A. Vogel R. Ménard |
| author_sort | A. Vogel |
| collection | DOAJ |
| description | <p>Accurate specification of the error statistics required for data assimilation remains an ongoing challenge, partly because their estimation is an
underdetermined problem that requires statistical assumptions. Even with the common assumption that background and observation errors are
uncorrelated, the problem remains underdetermined. One natural question that could arise is as follows: can the increasing amount of overlapping observations
or other datasets help to reduce the total number of statistical assumptions, or do they introduce more statistical unknowns? In order to answer
this question, this paper provides a conceptual view on the statistical error estimation problem for multiple collocated datasets, including a
generalized mathematical formulation, an illustrative demonstration with synthetic data, and guidelines for setting up and solving the
problem. It is demonstrated that the required number of statistical assumptions increases linearly with the number of datasets. However, the number
of error statistics that can be estimated increases quadratically, allowing for an estimation of an increasing number of error cross-statistics
between datasets for more than three datasets. The presented generalized estimation of full error covariance and cross-covariance matrices between
datasets does not necessarily accumulate the uncertainties of assumptions among error estimations of multiple datasets.</p> |
| first_indexed | 2024-03-11T23:44:43Z |
| format | Article |
| id | doaj.art-274716b7d7384c3e8455e78864596981 |
| institution | Directory Open Access Journal |
| issn | 1023-5809 1607-7946 |
| language | English |
| last_indexed | 2024-03-11T23:44:43Z |
| publishDate | 2023-09-01 |
| publisher | Copernicus Publications |
| record_format | Article |
| series | Nonlinear Processes in Geophysics |
| spelling | doaj.art-274716b7d7384c3e8455e788645969812023-09-19T10:24:53ZengCopernicus PublicationsNonlinear Processes in Geophysics1023-58091607-79462023-09-013037539810.5194/npg-30-375-2023How far can the statistical error estimation problem be closed by collocated data?A. Vogel0A. Vogel1R. Ménard2Air Quality Research Division, Environment and Climate Change Canada (ECCC), Dorval, Quebec, CanadaRhenish Institute for Environmental Research at the University of Cologne (RIU), Cologne, GermanyAir Quality Research Division, Environment and Climate Change Canada (ECCC), Dorval, Quebec, Canada<p>Accurate specification of the error statistics required for data assimilation remains an ongoing challenge, partly because their estimation is an underdetermined problem that requires statistical assumptions. Even with the common assumption that background and observation errors are uncorrelated, the problem remains underdetermined. One natural question that could arise is as follows: can the increasing amount of overlapping observations or other datasets help to reduce the total number of statistical assumptions, or do they introduce more statistical unknowns? In order to answer this question, this paper provides a conceptual view on the statistical error estimation problem for multiple collocated datasets, including a generalized mathematical formulation, an illustrative demonstration with synthetic data, and guidelines for setting up and solving the problem. It is demonstrated that the required number of statistical assumptions increases linearly with the number of datasets. However, the number of error statistics that can be estimated increases quadratically, allowing for an estimation of an increasing number of error cross-statistics between datasets for more than three datasets. The presented generalized estimation of full error covariance and cross-covariance matrices between datasets does not necessarily accumulate the uncertainties of assumptions among error estimations of multiple datasets.</p>https://npg.copernicus.org/articles/30/375/2023/npg-30-375-2023.pdf |
| spellingShingle | A. Vogel A. Vogel R. Ménard How far can the statistical error estimation problem be closed by collocated data? Nonlinear Processes in Geophysics |
| title | How far can the statistical error estimation problem be closed by collocated data? |
| title_full | How far can the statistical error estimation problem be closed by collocated data? |
| title_fullStr | How far can the statistical error estimation problem be closed by collocated data? |
| title_full_unstemmed | How far can the statistical error estimation problem be closed by collocated data? |
| title_short | How far can the statistical error estimation problem be closed by collocated data? |
| title_sort | how far can the statistical error estimation problem be closed by collocated data |
| url | https://npg.copernicus.org/articles/30/375/2023/npg-30-375-2023.pdf |
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