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Joël Arnault, Thomas Rummler, Florian Baur, Sebastian Lerch, Sven Wagner, Benjamin Fersch, Zhenyu Zhang, Noah Kerandi, Christian Keil, and Harald Kunstmann

1. Introduction Numerical atmospheric models generally consider terrestrial hydrological processes as only being vertical, in order to estimate the surface heat fluxes for constraining the atmospheric lower boundary condition. This is, for example, the case for the Weather Research and Forecasting (WRF) Model ( Skamarock and Klemp 2008 ) coupled with the Noah land surface model (LSM; Chen and Dudhia 2001 ). In this approach, the lateral redistribution of soil moisture according to the

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Tobias Kremer, Elmar Schömer, Christian Euler, and Michael Riemer

settings have been used for the parameterization schemes: inter alia a turbulent kinetic energy-based turbulence scheme, a shallow-convection scheme with mass-flux closure after Tiedtke (1989) , and a single-moment ice microphysics scheme (including graupel). The parameterization schemes are described in Doms et al. (2011) and more details on the setup of the simulation are given in Euler et al. (2019) . Our simulation domain spans from 22° to 54°N and from 40° to 70°W. Boundary and initial

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Peter Vogel, Peter Knippertz, Andreas H. Fink, Andreas Schlueter, and Tilmann Gneiting

, 2019 : Resolving Sahelian thunderstorms improves mid-latitude weather forecasts . Nat. Commun. , 10 , 3487 , https://doi.org/10.1038/s41467-019-11081-4 . 10.1038/s41467-019-11081-4 Pantillon , F. , P. Knippertz , J. H. Marsham , and C. E. Birch , 2015 : A parameterization of convective dust storms for models with mass-flux convection schemes . J. Atmos. Sci. , 72 , 2545 – 2561 , https://doi.org/10.1175/JAS-D-14-0341.1 . 10.1175/JAS-D-14-0341.1 Park , Y.-Y. , R. Buizza , and

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Stephan Rasp, Tobias Selz, and George C. Craig

assumptions about how convection behaves. The main purpose of this study is to test the applicability of the CC06 theory outside of its comfort zone. a. The CC06 theory The aim of the CC06 theory is to derive a minimally simple model of convective variability. Under the quasi-equilibrium assumption, the large-scale state prescribes the mean mass flux in a certain domain 〈 M 〉 1 —through a closure assumption in a parameterization. The mean mass flux of an individual cloud 〈 m 〉 is determined solely by

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Gabriel Wolf and Volkmar Wirth

of RWPs at any given time; rather, it can only be derived by reference to a sequence of consecutive points in time. This is in contrast to diagnostics involving some form of a flux, which by design is a vector and may be designed such as to indicate the direction of propagation. In this study we make use of wave activity and its associated flux. The concept of wave activity and wave activity flux is attractive, because it involves a conservation relation for conservative flows, in distinct

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Volkmar Wirth, Michael Riemer, Edmund K. M. Chang, and Olivia Martius

conservation of total energy following the 3D flow); is the velocity vector, ω is the pressure vertical velocity, and α is the specific volume. In (3) , the first two terms on the right-hand side represent baroclinic and barotropic conversion, respectively. The third term on the right-hand side also represents an energy transfer between the mean flow and the eddies, but averages out to zero in the time mean. Following Orlanski and Sheldon (1993) , the energy flux can be written as follows: where

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Roderick van der Linden, Andreas H. Fink, Joaquim G. Pinto, and Tan Phan-Van

predictability, which is not studied here. The operational analyses were used to calculate vertically integrated moisture flux vectors (cf. Peixoto and Oort 1992 ) between the surface pressure and the 300-hPa pressure level. The use of surface pressure ensures the corrections for orography and moisture flux convergence were computed using a centered finite-difference approach. The vertically averaged potential vorticity between the 500- and 200-hPa pressure levels was determined from the operational

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Christian Euler, Michael Riemer, Tobias Kremer, and Elmar Schömer

. 2018 ). For our numerical simulation, COSMO is used in default settings: the heating rate due to radiation is calculated by the parameterization scheme of Ritter and Geleyn (1992) . Surface heat, moisture and momentum fluxes are parameterized by a turbulent kinetic energy-based surface transfer scheme formulated in conservative thermodynamic variables. While the parameterization of deep convection is turned off, a shallow convection scheme after Tiedtke (1989) is used. Microphysical processes

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Tobias Selz

-base upward mass flux) is randomly drawn from a distribution. The total upward mass flux M is given by the sum of the individual updrafts (clouds) in the grid box. An ensemble of convective realizations (microstates) consistent with the larger-scale environment (macrostate) can be created by using different random seeds. A similar closure assumption as for a conventional convection scheme is used to determine the ensemble average of the total upward mass flux . We refer to Craig and Cohen (2006) for

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Julian F. Quinting and Christian M. Grams

trajectories has significantly advanced our understanding of WCBs and their effect on the large-scale flow (e.g., Eckhardt et al. 2004 ; Grams et al. 2011 ; Madonna et al. 2014b ; Martínez-Alvarado et al. 2016 ). The inflow of WCBs is located in a cyclone’s warm sector ahead of the cold front (label 1 in Fig. 1 ). At this stage, air parcels still reside predominantly in the planetary boundary layer. WCB inflow is typically characterized by strong moisture flux convergence and a band of high water

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