Fit the 5 parameters used for affine kernel dressing by minimum CRPS estimation.

`FitAkdParameters(ens, obs)`

ens

a N*R matrix. An archive of R-member ensemble forecasts for N time instances.

obs

a vector of length N. The verifying observations corresponding to the N ensemble forecasts.

The function returns a list of 5 parameters for affine kernel dressing.

Affine Kernel Dressing transforms the discrete K-member forecast ensemble at time instance n, `ens[n, ]`, to a continuous distribution function for the target `y` by the equation:

p(y|ens) = 1 / K * sum dnorm(y, z.i, s) where s = (4/3/K)^0.4 * (s1 + s2 * a^2 * var(ens)) and z.i = r1 + r2 * mean(ens) + a * ens

The parameters r1, r2, a, s1, s2 are fitted by minimizing the continuously ranked probability score (CRPS). The optimization is carried out using the R function `optim(...)`.

Since the evaluation of the CRPS is numerically expensive, the optimization can take a long time. Speed can be increased by optimizing the parameters only for a part of the forecast instances.

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.

DressEnsemble, DressCrps, DressIgn, PlotDressedEns, GetDensity

# NOT RUN { data(eurotempforecast) FitAkdParameters(ens, obs) # }