verification (version 1.41)

crpsDecompostion: Decompostion of Continuous Ranked Probability Score

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

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])