CDFt
Downscaling or bias correction of CDF through CDFtransformation
Downscales (or corrects the model outputs) cumulative distribution function (CDF) of a climate variable from large to localscale by applying a equivalent of proportionality transformation : i.e., based on a CDF representing a variable at large scale (i.e., low spatial resolution) and the equivalent CDF at a local scale (e.g., modeled at a weather station), this method finds a mathematical transformation allowing to go from the large to the localscale CDF. Hence, when a new largescale CDF is given, a new localscale CDF is downscaled based on this transformation.
 Keywords
 models, distribution, math, nonparametric
Usage
CDFt(ObsRp, DataGp, DataGf, npas=100, dev=2)
Arguments
 ObsRp
 Observed time series of the variable (e.g., temperature) at the local scale to be used for estimation of the calibration localscale CDF.
 DataGp
 Largescale time series to be used for estimation of the calibration largescale CDF.
 DataGf
 Largescale time series to be used for estimation of the largescale CDF to be downscaled.
 npas
 Number of "cuts" for which quantiles will be empirically estimated (Default is 100).
 dev
 Coefficient of development (of the difference between the mean of the largescale historical data and the mean of the largescale future data to be downscaled). This development is used to extend range of data on which the quantiles will be calculated for the CDF to be downscaled (Default is 2).
Details
For details on the mathematical formulation of the transformation used to translate the largescale CDF to the localscale one, see the reference below. Note that in this R package, the largescale data (i.e., DataGp and DataGf) are automatically transformed to have the same mean as the ObsRp time series. This avoid to get out of the range of applicability of the CDFt method. However, the largescale output CDFs have their initial mean (i.e., not centered).
P.A. Michelangeli, M. Vrac, H. Loukos. "Probabilistic downscaling approaches: Application to wind cumulative distribution functions", Geophys. Res. Lett., doi:10.1029/2009GL038401, 2009.
Value

A message is returned if the "dev" parameter is too small to capture the whole range of the downscaled CDF. Otherwise, CDFt returns a list with components
 DS
 Downscaled time series generated by "Quantilematching" method performed between largescale CDF to be downscaled, and the localscale downscaled CDF. Note that the length of this array is equal to the length of DataGf
 x
 an array containing values of the variable (e.g., temperature) where the downscaled (and other) CDF has been estimated.
 FRp
 an array containing the values of the localscale CDF used for calibration, evaluated at the points in x.
 FGp
 an array containing the values of the largescale CDF used for calibration, evaluated at the points in x.
 FGf
 an array containing the values of the largescale CDF used for downscalingn, evaluated at the points in x.
 FRf
 an array containing the values of the downscaled CDF evaluated at the points in x.
See Also
Examples
## Example
### Generation of example data
O < rnorm(2100,mean=0,sd=1)
Gp < rnorm(300,mean=3,sd=1)
Gf < rnorm(300,mean=4,sd=1)
### Call of the CDFt method
CT < CDFt(O,Gp,Gf)
x < CT$x
FGp < CT$FGp
FGf < CT$FGf
FRp < CT$FRp
FRf < CT$FRf
ds < CT$DS
### Plot the results
par(mfrow=c(1,2))
plot(x, FGp,type="l",lty=2,ylim=c(0,1),xlab="x",ylab="CDF(x)")
lines(x,FGf,type="l",lty=2,col=2)
lines(x,FRp,type="l")
lines(x,FRf,type="l",col=2)
plot(Gf,ds,xlab="Largescale data", ylab="Downscaled data")