Forecast verification: Relating deterministic and probabilistic metrics. (3rd August 2021)

• Record Type: Journal Article
• Authors: Leung, Tsz Yan; Leutbecher, Martin; Reich, Sebastian; Shepherd, Theodore G.
• Is Part Of: Quarterly journal of the Royal Meteorological Society. Volume 147:Number 739(2021)
• Page Start: 3124
• Page End: 3134
• Publication Date: 2021-08-03
• Subjects: CRPS -- ensembles -- idealised turbulence -- NWP -- RMSE -- verification; Meteorology -- Periodicals; 551.5
• DOI: 10.1002/qj.4120
• Languages: English
• ISSNs: 0035-9009

Abstract

Abstract: 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 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. Abstract : The philosophy of forecast verification is rather different between deterministic and probabilistic verification metrics, yet some of these metrics can be mathematically related. When the forecast and verifying distributions are normal, the Continuous Ranked Probability Score is a fraction of the root‐mean‐square error, and this fraction depends only on the heteroscedasticity of the ensemble spread and the measures of forecast calibration. The relationship holds approximately in idealised two‐dimensional barotropic turbulence despite the normality condition not being met.