| DOI: | 10.1175/JCLI-D-17-0197.1
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| Scopus记录号: | 2-s2.0-85041696202
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| 论文题名: | Ensemble averaging and the curse of dimensionality |
| 作者: | Christiansen B.
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| 刊名: | Journal of Climate
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| ISSN: | 8948755
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| 出版年: | 2018
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| 卷: | 31, 期:4 | | 起始页码: | 1587
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| 结束页码: | 1596
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| 语种: | 英语
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| 英文关键词: | Climate models
; Ensembles
; Error analysis
; Model comparison
; Statistics
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| Scopus关键词: | Error analysis
; Error statistics
; Errors
; Statistics
; Vector spaces
; Curse of dimensionality
; Ensemble averaging
; Ensembles
; Geometric properties
; High dimensional spaces
; Individual models
; Model comparison
; Multi-model ensemble
; Climate models
; climate modeling
; CMIP
; ensemble forecasting
; error analysis
; statistical analysis
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| 英文摘要: | When comparing climate models to observations, it is often observed that the mean over many models has smaller errors than most or all of the individual models. This paper will show that a general consequence of the nonintuitive geometric properties of high-dimensional spaces is that the ensemble mean often outperforms the individual ensemble members. This also explains why the ensemble mean often has an error that is 30% smaller than the median error of the individual ensemble members. The only assumption that needs to be made is that the observations and the models are independently drawn from the same distribution. An important and relevant property of high-dimensional spaces is that independent random vectors are almost always orthogonal. Furthermore, while the lengths of random vectors are large and almost equal, the ensemble mean is special, as it is located near the otherwise vacant center. The theory is first explained by an analysis of Gaussian- and uniformly distributed vectors in high-dimensional spaces. A subset of 17 models from the CMIP5 multimodel ensemble is then used to demonstrate the validity and robustness of the theory in realistic settings. © 2018 American Meteorological Society. |
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| 资源类型: | 期刊论文
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| 标识符: | http://119.78.100.158/handle/2HF3EXSE/111685
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| Appears in Collections: | 气候减缓与适应
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作者单位: | Danish Meteorological Institute, Copenhagen, Denmark
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| Recommended Citation: | |
Christiansen B.. Ensemble averaging and the curse of dimensionality[J]. Journal of Climate,2018-01-01,31(4)
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