crpsDecompostion: Decompostion of Continuous Ranked Probability Score

In verification: Weather Forecast Verification Utilities

Description

The CRPS measures the distance between the predicted and the observed cumulative density functions (CDFs) of scalar variables. Furthermore, the crpsDecomposition function provides the reliability and resolution terms obtained by the CRPS decomposition proposed by Hersbach. The alpha, beta matrices and Heavisides vectors of outliers calculated in the CRPS decomposition are also returned. To speed up calculation time, these matrices/vectors can then be used to recalculate the CRPS's in a bootstrap by using the crpsFromAlphaBeta function.

Usage

      crpsDecomposition(obs, eps)
      crpsFromAlphaBeta(alpha,beta,heaviside0,heavisideN)
       

Arguments

obs	Vector of observations
eps	Matrix of ensemble forecast. Each column represent a member.
alpha	Matrix of alpha (returned from crpsDecomposition)
beta	Vector of beta (returned from crpsDecomposition)
heaviside0	Vector of Heaviside for outlier i=0 (returned from crpsDecomposition)
heavisideN	Vector of Heaviside for outlier i=N (returned from crpsDecomposition)

Value

CRPS	CRPS score
CRPSpot	The potential CRPS (Resolution - Uncertainty)
Reli	The Reliability term of the CRPS
alpha	Matrix (Nobservation rows x Nmember +1 columns) of alpha used in the CRPS decomposition.
beta	Matrix (Nobservation rows x Nmember +1 columns) of beta used in the CRPS decomposition.
heaviside0	Vector (Nobservation length) of Heaviside for outlier i=0 used in the CRPS decomposition
heavisideN	Vector (Nobservation length) of Heaviside for outlier i=N used in the CRPS decomposition

Author(s)

Ronald Frenette <[e-mail]>

References

G. Candille, P. L. Houtekamer, and G. Pellerin: Verification of an Ensemble Prediction System against Observations, Monthly Weather Review,135, pp. 2688-2699

Hershcach, Hans, 2000. Decomposition of the Continuous Ranked Probability Score for Ensemble Prediction Systems. Weather and Forecasting, 15, (5) pp. 559-570.

Examples

data(precip.ensemble)
x <- precip.ensemble[seq(5,5170,5),]

#Observations are in the column
obs<-x[,3]

#Forecast values of ensemble are in the column 4 to 54
eps<-x[,4:54]

#CRPS calculation 
c<-crpsDecomposition(obs,eps)

#CRPS with alpha and beta
#Resampling indices
nObs<-length(obs)
i<-sample(seq(nObs),nObs,replace=TRUE)
crps2<-crpsFromAlphaBeta(c$alpha[i,],c$beta[i,],c$heaviside0[i],c$heavisideN[i])

verification documentation built on May 2, 2019, 1:24 a.m.