DressEnsemble {SpecsVerification}

Transform an ensemble forecast to a continuous forecast distribution by kernel dressing.

Description

Transform an ensemble forecast to a continuous forecast distribution by kernel dressing.

Usage

DressEnsemble(ens, dressing.method = "silverman", parameters = NA)

Arguments

ens

a N*R matrix representing N time instances of real-valued R-member ensemble forecasts

dressing.method

One of "silverman" (default), "akd", "akd.fit". See Details.

parameters

A list, containing the parameters for the dressing method. See Details.

Details

The dressing methods currently implemented and their required parameters are:

"silverman" (default)

No parameters are given. At time instance ‘n' each ensemble member is replaced by a Gaussian kernel with mean ens[n, k] and variance (4 / 3 / K)^0.4 * var(ens[n, ]). This method is called "Silverman’s rule of thumb" and provides a simple non-parametric method for smoothing a discrete ensemble.

"akd"

Affine Kernel Dressing. The required parameters are list(r1, r2, a, s1, s2). The 'k'-th ensemble member at time instance 'n' is dressed with a Gaussian kernel with mean r1 + r2 * mean(ens[n,]) + a * ens[n, k] and variance (4 / 3 / K)^0.4 * (s1 + s2 * a^2 * var(ens[n,])). Negative variances are set to zero. Note that parameters = list(r1=0, r2=0, a=1, s1=0, s2=1) yields the same dressed ensemble as dressing.method="silverman".

"akd.fit"

Affine Kernel Dressing with fitted parameters. The required parameters is list(obs), where 'obs' is a vector of observations which are used to optimize the parameters r1, r2, a, s1, s2 by CRPS minimization. See ?FitAkdParameters for more information.

Value

The function returns a list with elements 'ens' (a N*R matrix, where ens[t,r] is the mean of the r-th kernel at time instance t) and 'ker.wd' (a N*R matrix, where ker.wd[t,r] is the standard deviation of the r-th kernel at time t)

References

Silverman, B.W. (1998). Density Estimation for Statistics and Data Analysis. London: Chapman & Hall/CRC. ISBN 0-412-24620-1. Broecker J. and Smith L. (2008). From ensemble forecasts to predictive distribution functions. Tellus (2008), 60A, 663–678. doi: 10.1111/j.1600-0870.2008.00333.x.

See Also

DressCrps, DressIgn, GetDensity, FitAkdParameters

Examples

data(eurotempforecast)
d.silverman <- DressEnsemble(ens)
d.akd <- DressEnsemble(ens, dressing.method="akd", 
                       parameters=list(r1=0, r2=0, a=1, 
                                       s1=0, s2=0))
d.akd.fit <- DressEnsemble(ens, dressing.method="akd.fit", 
                           parameters=list(obs=obs))