Forecast verification
- The philosophy of forecast verification is rather different between deterministic and probabilistic verification metrics: generally speaking, deterministic metrics measure differences, whereas probabilistic metrics assess reliability and sharpness of predictive distributions. This article considers the root-mean-square error (RMSE), which can be seen as a deterministic metric, and the probabilistic metric Continuous Ranked Probability Score (CRPS), and demonstrates that under certain conditions, the CRPS can be mathematically expressed in terms of the RMSE when these metrics are aggregated. One of the required conditions is the normality of distributions. The other condition is that, while the forecast ensemble need not be calibrated, any bias or over/underdispersion cannot depend on the forecast distribution itself. Under these conditions, the CRPS is a fraction of the RMSE, and this fraction depends only on the heteroscedasticity of the ensemble spread and the measures of calibration. The derived CRPS-RMSE relationship for the caseThe philosophy of forecast verification is rather different between deterministic and probabilistic verification metrics: generally speaking, deterministic metrics measure differences, whereas probabilistic metrics assess reliability and sharpness of predictive distributions. This article considers the root-mean-square error (RMSE), which can be seen as a deterministic metric, and the probabilistic metric Continuous Ranked Probability Score (CRPS), and demonstrates that under certain conditions, the CRPS can be mathematically expressed in terms of the RMSE when these metrics are aggregated. One of the required conditions is the normality of distributions. The other condition is that, while the forecast ensemble need not be calibrated, any bias or over/underdispersion cannot depend on the forecast distribution itself. Under these conditions, the CRPS is a fraction of the RMSE, and this fraction depends only on the heteroscedasticity of the ensemble spread and the measures of calibration. The derived CRPS-RMSE relationship for the case of perfect ensemble reliability is tested on simulations of idealised two-dimensional barotropic turbulence. Results suggest that the relationship holds approximately despite the normality condition not being met.…
Verfasserangaben: | Tsz Yan LeungORCiD, Martin LeutbecherORCiDGND, Sebastian ReichORCiDGND, Theodore G. ShepherdORCiDGND |
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DOI: | https://doi.org/10.1002/qj.4120 |
ISSN: | 0035-9009 |
ISSN: | 1477-870X |
Titel des übergeordneten Werks (Englisch): | Quarterly journal of the Royal Meteorological Society |
Untertitel (Englisch): | relating deterministic and probabilistic metrics |
Verlag: | Wiley |
Verlagsort: | Hoboken |
Publikationstyp: | Wissenschaftlicher Artikel |
Sprache: | Englisch |
Datum der Erstveröffentlichung: | 07.07.2021 |
Erscheinungsjahr: | 2021 |
Datum der Freischaltung: | 23.01.2024 |
Freies Schlagwort / Tag: | CRPS; NWP; RMSE; ensembles; idealised turbulence; verification |
Band: | 147 |
Ausgabe: | 739 |
Seitenanzahl: | 11 |
Erste Seite: | 3124 |
Letzte Seite: | 3134 |
Fördernde Institution: | U.K. Engineering and Physical Sciences Research CouncilUK Research & Innovation (UKRI)Engineering & Physical Sciences Research Council (EPSRC) [EP/L016613/1]; European Research CouncilEuropean Research Council (ERC)European Commission [339390]; Deutsche ForschungsgemeinschaftGerman Research Foundation (DFG) [SFB 1114/2/235221301] |
Organisationseinheiten: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik |
DDC-Klassifikation: | 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik |
Peer Review: | Referiert |
Publikationsweg: | Open Access / Hybrid Open-Access |
Lizenz (Deutsch): | CC-BY - Namensnennung 4.0 International |