TY  - JOUR
A1  - Leung, Tsz Yan
A1  - Leutbecher, Martin
A1  - Reich, Sebastian
A1  - Shepherd, Theodore G.
T1  - Forecast verification
BT  - relating deterministic and probabilistic metrics
JF  - Quarterly journal of the Royal Meteorological Society
N2  - 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.
KW  - CRPS
KW  - ensembles
KW  - idealised turbulence
KW  - NWP
KW  - RMSE
KW  - verification
Y1  - 2021
U6  - https://doi.org/10.1002/qj.4120
SN  - 0035-9009
SN  - 1477-870X
VL  - 147
IS  - 739
SP  - 3124
EP  - 3134
PB  - Wiley
CY  - Hoboken
ER  -