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subpixel scales. To bridge the gap between satellite and ground-based observations, airborne measurements of spectral irradiance are a useful tool for direct model evaluation. In this regard, some airborne campaigns were conducted, operating instruments to measure the spectral solar radiation reflected by clouds, e.g., Wendisch and Keil (1999) , Wendisch et al. (2005 , 2007) , Jacob et al. (2010) , or Smith et al. (2017) . In spite of that, the natural variability of clouds might not be covered
subpixel scales. To bridge the gap between satellite and ground-based observations, airborne measurements of spectral irradiance are a useful tool for direct model evaluation. In this regard, some airborne campaigns were conducted, operating instruments to measure the spectral solar radiation reflected by clouds, e.g., Wendisch and Keil (1999) , Wendisch et al. (2005 , 2007) , Jacob et al. (2010) , or Smith et al. (2017) . In spite of that, the natural variability of clouds might not be covered
atmosphere’s scale-dependence behavior appropriately, shortcomings in the numerics or parameterizations are likely. In the case of kinetic energy, the evaluation of scaling exponents has provided valuable insights into model performance ( Skamarock 2004 ; Hamilton et al. 2008 ; Bierdel et al. 2012 ; Fang and Kuo 2015 ). For water vapor, Schemann et al. (2013) investigated the scaling behaviors of a GCM, an NWP model, and a large-eddy simulation (LES) and the implication for cloud parameterizations
atmosphere’s scale-dependence behavior appropriately, shortcomings in the numerics or parameterizations are likely. In the case of kinetic energy, the evaluation of scaling exponents has provided valuable insights into model performance ( Skamarock 2004 ; Hamilton et al. 2008 ; Bierdel et al. 2012 ; Fang and Kuo 2015 ). For water vapor, Schemann et al. (2013) investigated the scaling behaviors of a GCM, an NWP model, and a large-eddy simulation (LES) and the implication for cloud parameterizations
analysis are therefore made up of values obtained from different lead times of the forecasts. This is acceptable to us since we are not interested in evaluating model performance at a fixed forecast horizon. We have found that the statistical robustness of our results is considerably enhanced when combining consecutive ensemble runs compared to an analysis based on a single ensemble only. Fig . 1. For the sensitivity analysis in section 3 , we combine four consecutive forecast ensembles, here
analysis are therefore made up of values obtained from different lead times of the forecasts. This is acceptable to us since we are not interested in evaluating model performance at a fixed forecast horizon. We have found that the statistical robustness of our results is considerably enhanced when combining consecutive ensemble runs compared to an analysis based on a single ensemble only. Fig . 1. For the sensitivity analysis in section 3 , we combine four consecutive forecast ensembles, here
regression and the limitations of this approach. In section 4 we evaluate the performance of the models during Northern Hemisphere winter and demonstrate their applicability to an operational ECMWF ensemble forecast of a WCB event during January 2011. The study ends with concluding remarks and an outlook in section 5 . 2. Data a. Predictor dataset The predictor selection as well as the development and evaluation of the logistic regression models is based on ECMWF’s interim reanalysis data (ERA
regression and the limitations of this approach. In section 4 we evaluate the performance of the models during Northern Hemisphere winter and demonstrate their applicability to an operational ECMWF ensemble forecast of a WCB event during January 2011. The study ends with concluding remarks and an outlook in section 5 . 2. Data a. Predictor dataset The predictor selection as well as the development and evaluation of the logistic regression models is based on ECMWF’s interim reanalysis data (ERA
the perturbation method is applicable in any atmospheric model that allows for calculation of the relevant physical process information. The observational data used to evaluate the forecasts and the selected case studies in which the parameterization is tested will be introduced briefly as well as the analysis strategy for the suggested method. a. Physically based stochastic perturbations in the boundary layer We propose a concept of process-based model error representation in terms of a
the perturbation method is applicable in any atmospheric model that allows for calculation of the relevant physical process information. The observational data used to evaluate the forecasts and the selected case studies in which the parameterization is tested will be introduced briefly as well as the analysis strategy for the suggested method. a. Physically based stochastic perturbations in the boundary layer We propose a concept of process-based model error representation in terms of a
of forecast errors and uncertainties from small to large scales ( Grams et al. 2018 ). On the medium range, the representation of WCBs in NWP models was first evaluated by Madonna et al. (2015) for three winter periods [December–February (DJF)] in the operational high resolution deterministic forecast of the ECMWF Integrated Forecasting System (IFS) model. They used a novel feature-based verification technique that was originally developed to verify precipitation forecasts ( Wernli et al. 2008
of forecast errors and uncertainties from small to large scales ( Grams et al. 2018 ). On the medium range, the representation of WCBs in NWP models was first evaluated by Madonna et al. (2015) for three winter periods [December–February (DJF)] in the operational high resolution deterministic forecast of the ECMWF Integrated Forecasting System (IFS) model. They used a novel feature-based verification technique that was originally developed to verify precipitation forecasts ( Wernli et al. 2008
Aerosol Effects on Clouds and Precipitation over Central Europe in Different Weather Regimesprecipitation to changes in the aerosol content and thermodynamical conditions of the atmosphere. Nevertheless, we have evaluated the respective reference runs at least in a qualitative way to ensure that the COSMO model simulates the main weather characteristics on the analyzed days reasonably well. The simulated 24-h precipitation amount of the reference runs with continental CCN displayed in Fig. 5 show good agreement with observations ( Fig. 4 ) for all days. Not only the convective or stratiform
precipitation to changes in the aerosol content and thermodynamical conditions of the atmosphere. Nevertheless, we have evaluated the respective reference runs at least in a qualitative way to ensure that the COSMO model simulates the main weather characteristics on the analyzed days reasonably well. The simulated 24-h precipitation amount of the reference runs with continental CCN displayed in Fig. 5 show good agreement with observations ( Fig. 4 ) for all days. Not only the convective or stratiform
-tropopause, the tropospheric-deep, and the divergent terms, respectively. e. Computation of LWA and its budget from model data First, LWA is calculated using the algorithm of Ghinassi et al. (2018) . Thereafter, the terms in the budget equations, (9) and (15) , are computed as follows. For a given time step n we consider data at time n − 1, n , and n + 1. The time derivatives are computed using centered differences between time steps n + 1 and n − 1. We then evaluate the integrals for T C and
-tropopause, the tropospheric-deep, and the divergent terms, respectively. e. Computation of LWA and its budget from model data First, LWA is calculated using the algorithm of Ghinassi et al. (2018) . Thereafter, the terms in the budget equations, (9) and (15) , are computed as follows. For a given time step n we consider data at time n − 1, n , and n + 1. The time derivatives are computed using centered differences between time steps n + 1 and n − 1. We then evaluate the integrals for T C and
