The last decade has seen the success of stochastic parameterizations in short-term, medium-range, and seasonal forecasts: operational weather centers now routinely use stochastic parameterization schemes to represent model inadequacy better and to improve the quantification of forecast uncertainty. Developed initially for numerical weather prediction, the inclusion of stochastic parameterizations not only provides better estimates of uncertainty, but it is also extremely promising for reducing long-standing climate biases and is relevant for determining the climate response to external forcing. This article highlights recent developments from different research groups that show that the stochastic representation of unresolved processes in the atmosphere, oceans, land surface, and cryosphere of comprehensive weather and climate models 1) gives rise to more reliable probabilistic forecasts of weather and climate and 2) reduces systematic model bias. We make a case that the use of mathematically stringent methods for the derivation of stochastic dynamic equations will lead to substantial improvements in our ability to accurately simulate weather and climate at all scales. Recent work in mathematics, statistical mechanics, and turbulence is reviewed; its relevance for the climate problem is demonstrated; and future research directions are outlined.

Large-eddy simulations (LES) with the newThis is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited. R. Heinze et al.at building confidence in the model's ability to simulate small-to mesoscale variability in turbulence, clouds and precipitation. The results are encouraging: the high-resolution model matches the observed variability much better at small-to mesoscales than the coarser resolved reference model. In its highest grid resolution, the simulated turbulence profiles are realistic and column water vapour matches the observed temporal variability at short time-scales. Despite being somewhat too large and too frequent, small cumulus clouds are well represented in comparison with satellite data, as is the shape of the cloud size spectrum. Variability of cloud water matches the satellite observations much better in ICON than in the reference model. In this sense, it is concluded that the model is fit for the purpose of using its output for parametrization development, despite the potential to improve further some important aspects of processes that are also parametrized in the high-resolution model.

A 1000-yr integration of a coupled ocean-atmosphere model (ECHO-G) has been analyzed to describe decadal to multidecadal variability in equatorial Pacific sea surface temperature (SST) and thermocline depth (Z20), and their relationship to decadal modulations of El Niño-Southern Oscillation (ENSO) behavior. Although the coupled model is characterized by an unrealistically regular 2-yr ENSO period, it exhibits significant modulations of ENSO amplitude on decadal to multidecadal time scales. The authors' main finding is that the structures in SST and Z20 characteristic of tropical Pacific decadal variability (TPDV) in the model are due to an asymmetry between the anomaly patterns associated with the model's El Niño and La Niña states, with this asymmetry reflecting a nonlinearity in ENSO variability. As a result, the residual (i.e., the sum) of the composite El Niño and La Niña patterns exhibits a nonzero dipole structure across the equatorial Pacific, with positive perturbation values in the east and negative values in the west for SST and Z20. During periods when ENSO variability is strong, this difference manifests itself as a rectified change in the mean state. For comparison, a similar analysis was applied to a gridded SST dataset spanning the period 1871-1999. The data confirms that the asymmetry between the SST anomaly patterns associated with El Niño and La Niña for the model is realistic. However, ENSO in the observations is weaker and not as regular as in the model, and thus the changes due to ENSO asymmetries for the observations can only be detected in the Niño-12 region.

Atmospheric reanalyses covering the European region are mainly available as part of relatively coarse global reanalyses. The aim of this article is to present the development and evaluation of a next generation regional reanalysis for the European CORDEX EUR-11 domain with a horizontal grid spacing of approximately 6 km. In this context, a reanalysis is understood to be an assimilation of heterogeneous observations with a physical model such as a numerical weather prediction (NWP) model. The reanalysis system presented here is based on the NWP model COSMO by the German Meteorological Service (Deutscher Wetterdienst) using a continuous nudging scheme. In order to assess the added value of data assimilation, a dynamical downscaling experiment has been conducted, i.e. an identical model set-up but without data assimilation. Both systems have been evaluated for a 1 year test period, employing standard measures such as analysis increments, biases, or log-odds ratios, as well as tests for distributional characteristics. An important aspect is the evaluation from different perspectives and with independent measurements such as satellite infrared brightness temperatures using forward operators, integrated water vapour from GPS stations, and ceilometer cloud cover. It can be shown that the reanalysis better resolves local extreme events; this is basically an effect of the higher spatio-temporal resolution, as known from dynamical downscaling approaches. However, an important criterion for regional reanalyses is the coherence with independent observations of high temporal and spatial resolution, resulting in significant improvement over dynamical downscaling. The system is intended to become operational within a year, continuously reprocessing and evaluating longer time periods. The reanalysis data are planned to become available to the research community within a year.

Abstract. Probability distributions of multivariate random variables are generally more complex compared to their univariate counterparts which is due to a possible nonlinear dependence between the random variables. One approach to this problem is the use of copulas, which have become popular over recent years, especially in fields like econometrics, finance, risk management, or insurance. Since this newly emerging field includes various practices, a controversial discussion, and vast field of literature, it is difficult to get an overview. The aim of this paper is therefore to provide an brief overview of copulas for application in meteorology and climate research. We examine the advantages and disadvantages compared to alternative approaches like e.g. mixture models, summarize the current problem of goodness-of-fit (GOF) tests for copulas, and discuss the connection with multivariate extremes. An application to station data shows the simplicity and the capabilities as well as the limitations of this approach. Observations of daily precipitation and temperature are fitted to a bivariate model and demonstrate, that copulas are valuable complement to the commonly used methods.