Linear post‐processing approaches are proposed and fundamental mechanisms are analyzed by which the probabilistic skill of an ensemble forecast can be improved. The ensemble mean of the corrected forecast is a linear function of the ensemble mean(s) of the predictor(s). Likewise, the ensemble spread of the corrected forecast depends linearly on that of the uncorrected forecast. The regression coefficients are obtained by maximizing the likelihood function for the error distribution. Comparing different calibration approaches on simple systems that exhibit chaotic features (the Kuramoto–Sivashinsky equation, the spatially extended Lorenz system), four correction mechanisms are identified: the ensemble‐mean scaling and nudging using the predictor(s), and the ensemble‐spread scaling and nudging. Ensemble‐spread corrections turn out to yield improvement only when ‘reliability’ constraints are imposed on the corrected forecast. First of all climatological reliability is enforced and is satisfied when the total variability of the forecast is equal to the variability of the observations. Second, ensemble reliability or calibration of the ensembles is enforced such that the squared error of the ensemble mean coincides with the ensemble variance.In terms of continuous ranked probability skill score, spread calibration provides much more gain in skill than the traditional ensemble‐mean calibration and extends for lead times far beyond the error‐doubling time. The skill performance is better than or as good as the benchmark calibration method which derives from statistical assumptions –non‐homogeneous Gaussian regression. In addition to the member‐by‐member nature of the approach, benefits compared with the benchmark method can be pinpointed. In particular, although the post‐processing methods are performed for each lead time, location and variable independently, they preserve the rank correlations and thus take dependencies across space, time, and different variables into account. In addition, higher‐order ensemble moments like kurtosis and skewness correspond to those of the uncorrected forecasts.

Motivated by recent observations of phase-segregated binary Bose-Einstein condensates, we propose a method to calculate the excess energy due to the interface tension of a trapped configuration. By this method one should be able to numerically reproduce the experimental data by means of a simple Thomas-Fermi approximation, combined with interface excess terms and the Laplace equation. Using the Gross-Pitaevskii theory, we find expressions for the interface excesses which are accurate in a very broad range of the interspecies and intraspecies interaction parameters. We also present finite-temperature corrections to the interface tension which, aside from the regime of weak segregation, turn out to be small.

Using the regional climate model ALARO-0, the Royal Meteorological Institute of Belgium and Ghent University have performed two simulations of the past observed climate within the framework of the Coordinated Regional Climate Downscaling Experiment (CORDEX). The ERA-Interim reanalysis was used to drive the model for the period 1979–2010 on the EURO-CORDEX domain with two horizontal resolutions, 0.11 and 0.44°. ALARO-0 is characterised by the new microphysics scheme 3MT, which allows for a better representation of convective precipitation. In Kotlarski et al. (2014) several metrics assessing the performance in representing seasonal mean near-surface air temperature and precipitation are defined and the corresponding scores are calculated for an ensemble of models for different regions and seasons for the period 1989–2008. Of special interest within this ensemble is the ARPEGE model by the Centre National de Recherches Météorologiques (CNRM), which shares a large amount of core code with ALARO-0. Results show that ALARO-0 is capable of representing the European climate in an acceptable way as most of the ALARO-0 scores lie within the existing ensemble. However, for near-surface air temperature, some large biases, which are often also found in the ARPEGE results, persist. For precipitation, on the other hand, the ALARO-0 model produces some of the best scores within the ensemble and no clear resemblance to ARPEGE is found, which is attributed to the inclusion of 3MT. Additionally, a jackknife procedure is applied to the ALARO-0 results in order to test whether the scores are robust, meaning independent of the period used to calculate them. Periods of 20 years are sampled from the 32-year simulation and used to construct the 95 % confidence interval for each score. For most scores, these intervals are very small compared to the total ensemble spread, implying that model differences in the scores are significant.

The interfacial profiles and interfacial tensions of phase-separated binary mixtures of Bose-Einstein condensates are studied theoretically. The two condensates are characterized by their respective healing lengths ${\xi }_1$ and ${\xi }_2$ and by the interspecies repulsive interaction $K$. An exact solution to the Gross-Pitaevskii (GP) equations is obtained for the special case ${\xi }_2/{\xi }_1=1/2$ and $K=3/2$. Furthermore, applying a double-parabola approximation (DPA) to the energy density featured in GP theory allows us to define a DPA model, which is much simpler to handle than GP theory but nevertheless still captures the main physics. In particular, a compact analytic expression for the interfacial tension is derived that is useful for all ${\xi }_1,{\xi }_2$, and $K$. An application to wetting phenomena is presented for condensates adsorbed at an optical wall. The wetting phase boundary obtained within the DPA model nearly coincides with the exact one in GP theory.

Wheat yield variability will increase in the future due to the projected increase in extreme weather events and long-term climate change effects. Currently, regional agricultural statistics are used to monitor wheat yield. Remotely sensed vegetation indices have a higher spatio-temporal resolution and could give more insight into crop yield. In this paper, we (i) evaluate the possibility to use Normalized Difference Vegetation Index (NDVI) time series to estimate wheat yield in Latvia and (ii) determine which weather variables impact wheat yield changes using both ALARO-0 and REMO Regional Climate Models (RCM) output. The integral from NDVI series (aNDVI) for winter and spring wheat fields is used as a predictor to model regional wheat yield from 2014 to 2018. A correlation analysis between weather variables, wheat yield and aNDVI was used to elucidate which weather variables impact wheat yield changes in Latvia. Our results indicate that high temperatures in June for spring wheat and in July for winter wheat had a negative correlation with yield. A linear regression yield model explained 71% of the variability with a residual standard error of 0.55 Mg/ha. When RCM data were added as predictor variables to the wheat yield empirical model a random forest approach resulted in better results compared to a linear regression approach, the explained variance increased up to 97% and the residual standard error decreased to 0.17 Mg/ha. We conclude that NDVI time series and RCM output enabled regional crop yield and weather impact monitoring at higher spatio-temporal resolutions than regional statistics.