This study expands the pool of verification methods for probabilistic weather and climate predictions by a decomposition of the quantile score (QS). The QS is a proper score function and evaluates predictive quantiles on a set of forecast-observation pairs. We introduce a decomposition of the QS in reliability, resolution and uncertainty and discuss the biases of the decomposition. Further, a reliability diagram for quantile forecasts is presented. Verification with the QS and its decomposition is illustrated on precipitation forecasts derived from the mesoscale weather prediction ensemble COSMO-DE-EPS of the German Meteorological Service. We argue that the QS is ready to become as popular as the Brier score in forecast verification.

Statistical postprocessing is an integral part of an ensemble prediction system. This study compares methods used to derive probabilistic quantitative precipitation forecasts based on the high-resolution version of the German-focused Consortium for Small-Scale Modeling (COSMO-DE) time-lagged ensemble (COSMO-DE-TLE). The investigation covers the period from July 2008 to June 2011 for a region over northern Germany with rain gauge measurements from 445 stations. The investigated methods provide pointwise estimates of the predictive distribution using logistic and quantile regression, and full predictive distributions using parametric mixture models. All mixture models use a point mass at zero to represent the probability of precipitation. The amount of precipitation is modeled by either a gamma, lognormal, or inverse Gaussian distribution. Furthermore, an adaptive tail using a generalized Pareto distribution (GPD) accounts for a better representation of extreme precipitation. The predictive probabilities, quantiles, and distributions are evaluated using the Brier, the quantile verification, and the continuous ranked probability scores. Baseline predictions and covariates are based on first-guess estimates from the COSMO-DE-TLE. Predictive performance is largely improved by statistical postprocessing due to an increase in reliability and resolution. The mixture models show some deficiencies. The inverse Gaussian fails to provide calibrated predictive distributions, whereas the lognormal and gamma mixtures perform well within the bulk of the distribution. Both mixtures provide significantly less skill for the extremal quantiles (0.99-0.999). Their representation is largely improved by incorporating an adaptive GPD tail. Even more stable estimates are obtained if the annual cycle is included in the postprocessing and training is performed on almost 3 yr of data.

Kinetic energy spectra derived from commercial aircraft observations of horizontal wind velocities exhibit a k −5/3 wavenumber dependence on the mesoscale that merges into a k −3 dependence on the macroscale. In this study, spectral analysis is applied to evaluate the mesoscale ensemble prediction system using the convection-permitting NWP model COSMO-DE (COSMO-DE-EPS). One-dimensional wavenumber spectra of the kinetic energy are derived from zonal and meridional wind velocities, as well as from vertical velocities. Besides a general evaluation, the model spectra reveal important information about spin-up effects and effective resolution. The COSMO-DE-EPS well reproduces the spectral k −5/3 dependence of the mesoscale horizontal kinetic energy spectrum. Due to the assimilation of high-resolution meteorological observations (mainly rain radar), there is no signif cant spin-up of the model simulations within the f rst few hours after initialization. COSMO-DE-EPS features an effective resolution of a factor of about 4 to 5 of the horizontal grid spacing. This is slightly higher in comparison to other limited area models. Kinetic energy spectra derived from vertical velocities exhibit a much f atter wavenumber dependence leading to relatively large spectral energy on smaller scales. This is in good agreement with similar models and also suggested by observations of temporal variance spectra of the vertical velocity.

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