Gridded, locally calibrated, probabilistic temperature forecasts based on ensemble model output statistics

Abstract

We propose a further refinement of the the non‐homogeneous Gaussian regression approach for temperature, which transforms the output of an ensemble prediction system into predictive Gaussian distributions at each location of interest. Model fitting is partly done within a regression framework using a penalized version of the least‐squares loss function. This is conceptually simpler than the original approach and at the same time is able to prevent overfitting. While calibration is initially performed at observation locations only, geostatistical methods are used to provide predictive distributions on the entire grid. The incorporation of land‐use information in this interpolation scheme further improves predictive performance, even though a simpler statistical model than in the original approach is used. The assessment of predictive performance and calibration is carried out with dynamical forecasts of 2 m temperatures by the COSMO‐DE‐EPS, an application of the COSMO (Consortium for Small‐scale Modeling) model system which covers Germany and neighbouring countries.

Spatial Postprocessing of Ensemble Forecasts for Temperature Using Nonhomogeneous Gaussian Regression

“…where |T | denotes the number of days in the training period. At locations without an observation station, predictive means and variances are obtained by spatial interpolation as described in Scheuerer and König (2014). We refer to this inclusion of the local climatology as NGR c .…”

“…. , b M in (2) are estimated by weighted least squares using a penalized version of the loss function to prevent overfitting, see Scheuerer and König (2014) for details. The parameters of the variance function, c and d, are subsequently estimated via CRPS minimization as in (3) above.…”

“…In order to check whether this assumption is appropriate or whether correlation strengths vary strongly over the domain considered here, we study the probability integral transforms (PITs) of predicted temperature differences between close-by stations (a motivation and interpretation for that is given in the Appendix). Specifically, we focus on the NGR c model and its spatial extensions where we can assume that the univariate predictive distributions have no local biases and reflect the local prediction uncertainty reasonably well (Scheuerer and König, 2014). Figure 4 depicts, for each station, the mean absolute deviations of the PIT values from 0.5 over all verification days and all temperature differences between this station and stations within a 50 km neighborhood.…”

“…By merging ensemble BMA and GOP, calibrated probabilistic forecasts of entire weather fields are produced. We propose a similar conceptualization, combining the NGR methods of Gneiting et al (2005) and Scheuerer and König (2014) with a Gaussian random field error model in an approach we refer to as spatial NGR.…”

Spatial ensemble post‐processing with standardized anomalies

“…Several techniques exist to overcome this limitation and to produce statistical forecasts for an arbitrary point in a region. Statistical forecasts from the observation sites can be interpolated to arbitrary locations (Hacker and Rife, ; Glahn et al , ), observations can be interpolated on to the NWP grid to post‐process every grid point (Schefzik et al , ) or statistical forecasts representative of a whole region (Scheuerer and Büermann, ; Scheuerer and König, ) can be produced. The latter forecasts cover several stations simultaneously by using anomalies.…”