Compute the spread to error ratio (
SPR) for probabilistic forecasts -
not unlike the functions in SpecsVerification.
SPR > 1 indicates
overdispersion (underconfidence), whereas
SPR < 1 indicates
overconfidence in the forecasts.
n x k matrix of n forecasts for k ensemble members
vector with n verifying observations
Here we define the spread-error rate as the square root of the ratio of mean ensemble variance to the mean squared error of the ensemble mean with the verifying observations. We inflate the intra ensemble sample variance to account for the finite ensemble size as in Weigel (2011).
Weigel, A.P. (2012). Ensemble forecasts. Forecast Verification: A Practitioner's Guide in Atmospheric Science, Second Edition, 141-166.
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