Metrics
Brier Skill Score
CRPSS
Reliability plot
Relative Economic Value
Relative Mean Error
Relative Operating Characteristic score
References
References
Verification software
Miscellaneous
LateX users
Metrics
Brier Skill Score
CRPSS
Reliability plot
Relative Economic Value
Relative Mean Error
Relative Operating Characteristic score
References
References
Verification software
Miscellaneous
LateX users
The Continuous Ranked Probability Score (CRPS) measures the integral square difference between the cumulative distribution function (cdf) of the forecast $\mathrm{F}_S \left( q \right)$, and the corresponding cdf of the observed variable $\mathrm{F}_Q \left( q \right)$,
\begin{equation} \mathrm{CRPS} = \int_{-\infty}^{\infty} \left\lbrace \mathrm{F}_S \left( q \right) - \mathrm{F}_Q \left( q \right) \right\rbrace \mathrm{d} q \textrm{.} \end{equation}
The mean CRPS comprises the CRPS averaged across $J$ pairs of forecasts and observations,
\begin{equation} \overline{\mathrm{CRPS}} = \frac{1}{J} \sum \limits_{j=1}^{J} \mathrm{CRPS}_j \textrm{.} \end{equation}
The Continuous Ranked Probability Skill Score (CRPSS) is a function of the ratio of the mean CRPS of the main prediction system, $\overline{\mathrm{CRPS}}$, and a reference system, $\mathrm{\overline{CRPS}_{\mathrm{ref}}}$,
\begin{eqnarray} \mathrm{CRPSS} &=& \frac{ \mathrm{\overline{CRPS}} - \mathrm{\overline{CRPS}}_\mathrm{ref} }{ \mathrm{\overline{CRPS}}_\mathrm{perfect} - \mathrm{\overline{CRPS}}_\mathrm{ref} } \\ &=& \frac{ \mathrm{\overline{CRPS}} - \mathrm{\overline{CRPS}}_\mathrm{ref} }{ 0 - \mathrm{\overline{CRPS}}_\mathrm{ref} } \nonumber \\ &=& \frac{ \mathrm{\overline{CRPS}}_\mathrm{ref} - \mathrm{\overline{CRPS}} }{ \mathrm{\overline{CRPS}}_\mathrm{ref} } \nonumber \\ &=& 1 - \frac{ \mathrm{\overline{CRPS}} }{ \mathrm{\overline{CRPS}}_\mathrm{ref} } \nonumber \end{eqnarray}