Comparing climate time series – Part 3: Discriminant analysis
In parts I and II of this paper series, rigorous tests for equality of stochastic processes were proposed. These tests provide objective criteria for deciding whether two processes differ, but they provide no information about the nature of those differences. This paper develops a systematic and opt...
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ftdoajarticles:oai:doaj.org/article:0a713d59b6514075a18d5322c9179b18 2023-05-15T17:34:07+02:00 Comparing climate time series – Part 3: Discriminant analysis T. DelSole M. K. Tippett 2022-05-01T00:00:00Z https://doi.org/10.5194/ascmo-8-97-2022 https://doaj.org/article/0a713d59b6514075a18d5322c9179b18 EN eng Copernicus Publications https://ascmo.copernicus.org/articles/8/97/2022/ascmo-8-97-2022.pdf https://doaj.org/toc/2364-3579 https://doaj.org/toc/2364-3587 doi:10.5194/ascmo-8-97-2022 2364-3579 2364-3587 https://doaj.org/article/0a713d59b6514075a18d5322c9179b18 Advances in Statistical Climatology, Meteorology and Oceanography, Vol 8, Pp 97-115 (2022) Oceanography GC1-1581 Meteorology. Climatology QC851-999 Probabilities. Mathematical statistics QA273-280 article 2022 ftdoajarticles https://doi.org/10.5194/ascmo-8-97-2022 2022-12-30T21:29:54Z In parts I and II of this paper series, rigorous tests for equality of stochastic processes were proposed. These tests provide objective criteria for deciding whether two processes differ, but they provide no information about the nature of those differences. This paper develops a systematic and optimal approach to diagnosing differences between multivariate stochastic processes. Like the tests, the diagnostics are framed in terms of vector autoregressive (VAR) models, which can be viewed as a dynamical system forced by random noise. The tests depend on two statistics, one that measures dissimilarity in dynamical operators and another that measures dissimilarity in noise covariances. Under suitable assumptions, these statistics are independent and can be tested separately for significance. If a term is significant, then the linear combination of variables that maximizes that term is obtained. The resulting indices contain all relevant information about differences between data sets. These techniques are applied to diagnose how the variability of annual-mean North Atlantic sea surface temperature differs between climate models and observations. For most models, differences in both noise processes and dynamics are important. Over 40 % of the differences in noise statistics can be explained by one or two discriminant components, though these components can be model dependent. Maximizing dissimilarity in dynamical operators identifies situations in which some climate models predict large-scale anomalies with the wrong sign. Article in Journal/Newspaper North Atlantic Directory of Open Access Journals: DOAJ Articles Advances in Statistical Climatology, Meteorology and Oceanography 8 1 97 115 |
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Open Polar |
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Directory of Open Access Journals: DOAJ Articles |
op_collection_id |
ftdoajarticles |
language |
English |
topic |
Oceanography GC1-1581 Meteorology. Climatology QC851-999 Probabilities. Mathematical statistics QA273-280 |
spellingShingle |
Oceanography GC1-1581 Meteorology. Climatology QC851-999 Probabilities. Mathematical statistics QA273-280 T. DelSole M. K. Tippett Comparing climate time series – Part 3: Discriminant analysis |
topic_facet |
Oceanography GC1-1581 Meteorology. Climatology QC851-999 Probabilities. Mathematical statistics QA273-280 |
description |
In parts I and II of this paper series, rigorous tests for equality of stochastic processes were proposed. These tests provide objective criteria for deciding whether two processes differ, but they provide no information about the nature of those differences. This paper develops a systematic and optimal approach to diagnosing differences between multivariate stochastic processes. Like the tests, the diagnostics are framed in terms of vector autoregressive (VAR) models, which can be viewed as a dynamical system forced by random noise. The tests depend on two statistics, one that measures dissimilarity in dynamical operators and another that measures dissimilarity in noise covariances. Under suitable assumptions, these statistics are independent and can be tested separately for significance. If a term is significant, then the linear combination of variables that maximizes that term is obtained. The resulting indices contain all relevant information about differences between data sets. These techniques are applied to diagnose how the variability of annual-mean North Atlantic sea surface temperature differs between climate models and observations. For most models, differences in both noise processes and dynamics are important. Over 40 % of the differences in noise statistics can be explained by one or two discriminant components, though these components can be model dependent. Maximizing dissimilarity in dynamical operators identifies situations in which some climate models predict large-scale anomalies with the wrong sign. |
format |
Article in Journal/Newspaper |
author |
T. DelSole M. K. Tippett |
author_facet |
T. DelSole M. K. Tippett |
author_sort |
T. DelSole |
title |
Comparing climate time series – Part 3: Discriminant analysis |
title_short |
Comparing climate time series – Part 3: Discriminant analysis |
title_full |
Comparing climate time series – Part 3: Discriminant analysis |
title_fullStr |
Comparing climate time series – Part 3: Discriminant analysis |
title_full_unstemmed |
Comparing climate time series – Part 3: Discriminant analysis |
title_sort |
comparing climate time series – part 3: discriminant analysis |
publisher |
Copernicus Publications |
publishDate |
2022 |
url |
https://doi.org/10.5194/ascmo-8-97-2022 https://doaj.org/article/0a713d59b6514075a18d5322c9179b18 |
genre |
North Atlantic |
genre_facet |
North Atlantic |
op_source |
Advances in Statistical Climatology, Meteorology and Oceanography, Vol 8, Pp 97-115 (2022) |
op_relation |
https://ascmo.copernicus.org/articles/8/97/2022/ascmo-8-97-2022.pdf https://doaj.org/toc/2364-3579 https://doaj.org/toc/2364-3587 doi:10.5194/ascmo-8-97-2022 2364-3579 2364-3587 https://doaj.org/article/0a713d59b6514075a18d5322c9179b18 |
op_doi |
https://doi.org/10.5194/ascmo-8-97-2022 |
container_title |
Advances in Statistical Climatology, Meteorology and Oceanography |
container_volume |
8 |
container_issue |
1 |
container_start_page |
97 |
op_container_end_page |
115 |
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1766132847058354176 |