SpecsVerification (version 0.5-3)

DressEnsemble: 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.

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)

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.

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. 10.1111/j.1600-0870.2008.00333.x.

See Also

DressCrps, DressIgn, GetDensity, FitAkdParameters

Examples

# NOT RUN {
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))
# }