easyVerification (version 0.1.8)

EnsRocss: Skill score for area under the ROC curve

Description

Computes the skill score for the area under the ROC curve compared to an arbitrary reference forecast (generally climatological forecast).

Usage

EnsRocss(ens, ens.ref, obs)

Arguments

ens

n x j matrix of n probability forecasts for j categories

ens.ref

n x j matrix of reference forecast for j categories

obs

n x j matrix of occurence of n verifying observations in j categories

Value

• a list with the ROC area skill score for forecast category i in cati and the standard deviation of this skill score for category i in cati.sigma if a reference forecast with zero association is used (see details).

Details

For the traditional ROC area skill score where the reference forecast has zero association with the observations, the standard error $\sigma$ of the ROC area skill score is given by the following formula after Broecker (2012).

$$\sigma^2 = \frac{1}{3} \left(\frac{1}{N_0} + \frac{1}{N_1} + \frac{1}{N_0 N_1} \right)$$

Where $\sigma$ is the standard error, $N_1$ the number of events, and $N_0$ the number of non-events in category i. Please note the factor 2 difference to the formulation of the standard error for the ROC area in the original manuscript due to the conversion of the ROC area to the ROC area skill score.

References

Br"ocker, J. (2012). Probability forecasts. Forecast Verification: A Practitioner's Guide in Atmospheric Science, Second Edition, 119-139.

See Also

veriApply, EnsRoca

Examples

tm <- toymodel()

## compute ROC skill score for forecasts of x <= 0, 0 <= x < 1, and x > 1
## skill score is computed using climatological forecast as reference
veriApply("EnsRocss", tm$fcst, tm$obs, threshold=c(0,1))