  Weather prediction today is performed with numerical weather prediction (NWP)
models. These are deterministic simulation models describing the dynamics of
the atmosphere, and evolving the current conditions forward in time to obtain a
prediction for future atmospheric states. To account for uncertainty in NWP
models it has become common practice to employ ensembles of NWP forecasts.
However, NWP ensembles often exhibit forecast biases and dispersion errors,
thus require statistical postprocessing to improve reliability of the ensemble
forecasts. This work proposes an extension of a recently developed
postprocessing model utilizing autoregressive information present in the
forecast error of the raw ensemble members. The original approach is modified
to let the variance parameter depend on the ensemble spread, yielding a
two-fold heteroscedastic model. Furthermore, an additional high-resolution
forecast is included into the postprocessing model, yielding improved
predictive performance. Finally, it is outlined how the autoregressive model
can be utilized to postprocess ensemble forecasts with higher forecast
horizons, without the necessity of making fundamental changes to the original
model. We accompany the new methodology by an implementation within the R
package ensAR to make our method available for other researchers working in
this area. To illustrate the performance of the heteroscedastic extension of
the autoregressive model, and its use for higher forecast horizons we present a
case study for a data set containing 12 years of temperature forecasts and
observations over Germany. The case study indicates that the autoregressive
model yields particularly strong improvements for forecast horizons beyond 24
hours.
