Ackerman, A. S., Hobbs, P. V., and Toon, O. B.: A model for particle
microphysics, turbulent mixing, and radiative transfer in the
stratocumulus-topped marine boundary layer and comparisons with measurements,
J. Atmos. Sci., 52, 1204–1236, 1995. a

Ackerman, A. S., vanZanten, M. C., Stevens, B., Savic-Jovcic, V., Bretherton,
C. S., Chlond, A., Golaz, J.-C., Jiang, H., Khairoutdinov, M., Krueger,
S. K., Lewellen, D. C., Lock, A., Moeng, C.-H., Nakamura, K., Petters, M. D.,
Snider, J. R., Weinbrecht, S., and Zulauf, M.: Large-Eddy Simulations of a
Drizzling, Stratocumulus-Topped Marine Boundary Layer, Mon. Weather
Rev., 137, 1083–1110, https://doi.org/10.1175/2008MWR2582.1,
2009. a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r

Andrejczuk, M., Reisner, J., Henson, B., Dubey, M., and Jeffery, C.: The
potential impacts of pollution on a nondrizzling stratus deck: Does aerosol
number matter more than type?, J. Geophys. Res.-Atmos.,
113, D19204, https://doi.org/10.1029/2007JD009445,
2008. a, b

Andrejczuk, M., Grabowski, W., Reisner, J., and Gadian, A.: Cloud-aerosol
interactions for boundary layer stratocumulus in the Lagrangian Cloud Model,
J. Geophys. Res.-Atmos., 115, D22214, https://doi.org/10.1029/2010JD014248, 2010. a

Arabas, S. and Pawlowska, H.: Adaptive method of lines for multi-component aerosol condensational growth and CCN activation, Geosci. Model Dev., 4, 15–31, https://doi.org/10.5194/gmd-4-15-2011, 2011. a

Arabas, S. and Shima, S.-I.: Large-eddy simulations of trade wind cumuli using
particle-based microphysics with Monte Carlo coalescence, J.
Atmos. Sci., 70, 2768–2777, 2013. a

Arabas, S., Jaruga, A., Pawlowska, H., and Grabowski, W. W.: libcloudph++ 1.0: a single-moment bulk, double-moment bulk, and particle-based warm-rain microphysics library in C++, Geosci. Model Dev., 8, 1677–1707, https://doi.org/10.5194/gmd-8-1677-2015, 2015. a, b, c, d, e, f, g, h, i

Arabas, S., Jaruga, A., Dziekan, P., Waruszewski, M., and Jarecka, D.:
libcloudphx++ code v2.1.0, Zenodo, https://doi.org/10.5281/zenodo.2790277, 2019. a

Arakawa, A. and Lamb, V. R.: Computational design of the basic dynamical
processes of the UCLA general circulation model, General circulation models
of the atmosphere, 17, 173–265, 1977. a

Chen, J.-P.: Numerical simulations of the redistribution of atmospheric trace
chemicals through cloud processes, PhD thesis, Pennsylvania State
University, 1992. a

Clark, T. L. and Farley, R. D.: Severe Downslope Windstorm Calculations in Two
and Three Spatial Dimensions Using Anelastic Interactive Grid Nesting: A
Possible Mechanism for Gustiness, J. Atmos. Sci., 41,
329–350, https://doi.org/10.1175/1520-0469(1984)041<0329:SDWCIT>2.0.CO;2,
1984. a, b

Davis, M. H.: Collisions of small cloud droplets: Gas kinetic effects,
J. Atmos. Sci., 29, 911–915, 1972. a

Dziekan, P. and Pawlowska, H.: Stochastic coalescence in Lagrangian cloud microphysics, Atmos. Chem. Phys., 17, 13509–13520, https://doi.org/10.5194/acp-17-13509-2017, 2017. a, b, c, d

Dziekan, P. and Waruszewski, M.: University of Warsaw Lagrangian Cloud Model
code v1.0, Zenodo, https://doi.org/10.5281/zenodo.2791156, 2019. a

Gillespie, D. T.: The stochastic coalescence model for cloud droplet growth,
J. Atmos. Sci., 29, 1496–1510, 1972. a, b

Grabowski, W. W.: Extracting Microphysical Impacts in Large-Eddy Simulations of
Shallow Convection, J. Atmos. Sci., 71, 4493–4499,
https://doi.org/10.1175/JAS-D-14-0231.1,
2014. a

Grabowski, W. W. and Abade, G. C.: Broadening of Cloud Droplet Spectra through
Eddy Hopping: Turbulent Adiabatic Parcel Simulations, J.
Atmos. Sci., 74, 1485–1493, https://doi.org/10.1175/JAS-D-17-0043.1, 2017. a

Grabowski, W. W. and Smolarkiewicz, P. K.: Two-Time-Level Semi-Lagrangian
Modeling of Precipitating Clouds, Mon. Weather Rev., 124, 487–497,
https://doi.org/10.1175/1520-0493(1996)124<0487:TTLSLM>2.0.CO;2,
1996. a, b, c

Grabowski, W. W., Dziekan, P., and Pawlowska, H.: Lagrangian condensation microphysics with Twomey CCN activation, Geosci. Model Dev., 11, 103–120, https://doi.org/10.5194/gmd-11-103-2018, 2018a. a, b, c

Grabowski, W. W., Morrison, H., Shima, S.-i., Abade, G., Pawlowska, H., and
Dziekan, P.: Modeling of cloud microphysics: Can we do better?, B. of
Am. Meteorol. Soc., 100, 655–672,
https://doi.org/10.1175/BAMS-D-18-0005.1, 2018b. a, b

Grinstein, F. F., Margolin, L. G., and Rider, W. J.: Implicit large eddy
simulation: computing turbulent fluid dynamics, Cambridge university press,
2007. a

Hall, W. D.: A detailed microphysical model within a two-dimensional dynamic
framework: Model description and preliminary results, J.
Atmos. Sci., 37, 2486–2507, 1980. a

Hoffmann, F.: The Effect of Spurious Cloud Edge Supersaturations in Lagrangian
Cloud Models: An Analytical and Numerical Study, Mon. Weather Rev., 144,
107–118, https://doi.org/10.1175/MWR-D-15-0234.1,
2016. a

Hoffmann, F., Raasch, S., and Noh, Y.: Entrainment of aerosols and their
activation in a shallow cumulus cloud studied with a coupled LCM–LES
approach, Atmos. Res., 156, 43–57,
https://doi.org/10.1016/j.atmosres.2014.12.008,
2015. a

Hoffmann, F., Noh, Y., and Raasch, S.: The route to raindrop formation in a
shallow cumulus cloud simulated by a Lagrangian cloud model, J. the
Atmos. Sci., 74, 2125–2142, 2017. a

Jaruga, A., Arabas, S., Jarecka, D., Pawlowska, H., Smolarkiewicz, P. K., and Waruszewski, M.: libmpdata++ 1.0: a library of parallel MPDATA solvers for systems of generalised transport equations, Geosci. Model Dev., 8, 1005–1032, https://doi.org/10.5194/gmd-8-1005-2015, 2015. a, b, c, d, e

Jaruga, A., Arabas, S., Jarecka, D., Waruszewski, M., and Dziekan, P.:
libmpdata++ code v1.2.0, Zenodo, https://doi.org/10.5281/zenodo.2787740, 2019. a

Khairoutdinov, M. F. and Randall, D. A.: Cloud resolving modeling of the ARM
summer 1997 IOP: Model formulation, results, uncertainties, and
sensitivities, J. Atmos. Sci., 60, 607–625, 2003. a

Khvorostyanov, V. I. and Curry, J. A.: Terminal Velocities of Droplets and
Crystals: Power Laws with Continuous Parameters over the Size Spectrum,
J. Atmospheric Sciences, 59, 1872–1884,
https://doi.org/10.1175/1520-0469(2002)059<1872:TVODAC>2.0.CO;2,
2002. a

Klein, R., Achatz, U., Bresch, D., Knio, O. M., and Smolarkiewicz, P. K.:
Regime of validity of soundproof atmospheric flow models, J.
Atmos. Sci., 67, 3226–3237, 2010. a

Lilly, D. K.: On the numerical simulation of buoyant convection, Tellus, 14,
148–172, 1962. a

Lipps, F. B. and Hemler, R. S.: A Scale Analysis of Deep Moist Convection and
Some Related Numerical Calculations, J. Atmos. Sci.,
39, 2192–2210, https://doi.org/10.1175/1520-0469(1982)039<2192:ASAODM>2.0.CO;2,
1982. a, b, c, d, e

Margolin, L., Smolarkiewicz, P., and Wyszogradzki, A.: Dissipation in implicit
turbulence models: A computational study, J. Appl. Mech., 73,
469–473, 2006. a

Margolin, L. G. and Rider, W. J.: A rationale for implicit turbulence
modelling, Int. J. Numer. Meth. Fl., 39,
821–841, 2002. a

Morrison, H., Witte, M., Bryan, G. H., Harrington, J. Y., and Lebo, Z. J.:
Broadening of modeled cloud droplet spectra using bin microphysics in an
Eulerian spatial domain, J. Atmos. Sci., 75, 4005–4030,
https://doi.org/10.1175/JAS-D-18-0055.1,
2018. a

Naumann, A. K. and Seifert, A.: A Lagrangian drop model to study warm rain
microphysical processes in shallow cumulus, J. Adv. Model.
Earth Sy., 7, 1136–1154, 2015. a

Petters, M. D. and Kreidenweis, S. M.: A single parameter representation of hygroscopic growth and cloud condensation nucleus activity, Atmos. Chem. Phys., 7, 1961-1971, https://doi.org/10.5194/acp-7-1961-2007, 2007. a, b

RAMS Technical Description: The Regional AtmosphericModeling System, Technical
Description,
available at: http://www.atmet.com/html/docs/rams/rams_techman.pdf, last access: 26 June 2019. a

Riechelmann, T., Noh, Y., and Raasch, S.: A new method for large-eddy
simulations of clouds with Lagrangian droplets including the effects of
turbulent collision, New J. Phys., 14, 065008, https://doi.org/10.1088/1367-2630/14/6/065008, 2012. a, b

Schmidt, H. and Schumann, U.: Coherent structure of the convective boundary
layer derived from large-eddy simulations, J. Fluid Mech., 200,
511–562, 1989. a, b

Schwenkel, J., Hoffmann, F., and Raasch, S.: Improving collisional growth in Lagrangian cloud models: development and verification of a new splitting algorithm, Geosci. Model Dev., 11, 3929–3944, https://doi.org/10.5194/gmd-11-3929-2018, 2018. a

Shima, S.-I., Kusano, K., Kawano, A., Sugiyama, T., and Kawahara, S.: The
super-droplet method for the numerical simulation of clouds and
precipitation: A particle-based and probabilistic microphysics model coupled
with a non-hydrostatic model, Q. J. Roy. Meteor.
Soc., 135, 1307–1320, 2009. a, b, c, d, e, f, g, h, i

Smagorinsky, J.: General circulation experiments with the primitive equations:
I. The basic experiment, Mon. Weather Rev., 91, 99–164, 1963. a

Smolarkiewicz, P. and Margolin, L.: Variational methods for elliptic problems
in fluid models, in: Proc. ECMWF Workshop on Developments in numerical
methods for very high resolution global models, 137–159, 2000. a

Smolarkiewicz, P. K.: Multidimensional positive definite advection transport
algorithm: an overview, Int. J. Numer. Meth. Fl., 50, 1123–1144, https://doi.org/10.1002/fld.1071,
2006. a, b

Smolarkiewicz, P. K.: Modeling atmospheric circulations with soundproof
equations, in: Proc. of the ECMWF Workshop on Nonhydrostatic Modelling, 8-10
November, 2010, Reading, UK, p 1–15, 2011. a

Smolarkiewicz, P. K. and Szmelter, J.: A nonhydrostatic unstructured-mesh
soundproof model for simulation of internal gravity waves, Acta Geophys.,
59, 1109, https://doi.org/10.2478/s11600-011-0043-z, 2011. a

Smolarkiewicz, P. K., Kühnlein, C., and Wedi, N. P.: A consistent framework
for discrete integrations of soundproof and compressible PDEs of atmospheric
dynamics, J. Comput. Phys., 263, 185–205,
https://doi.org/10.1016/j.jcp.2014.01.031,
2014. a

Smolarkiewicz, P. K., Kühnlein, C., and Wedi, N. P.: Semi-implicit
integrations of perturbation equations for all-scale atmospheric dynamics,
J. Comput. Phys., 376, 145–159, 2019. a

Stevens, B., Feingold, G., Cotton, W. R., and Walko, R. L.: Elements of the
microphysical structure of numerically simulated nonprecipitating
stratocumulus, J. Atmos. Sci., 53, 980–1006, 1996. a

Stevens, B., Lenschow, D. H., Vali, G., Gerber, H., Bandy, A., Blomquist, B.,
Brenguier, J. L., Bretherton, C. S., Burnet, F., Campos, T., Chai, S.,
Faloona, I., Friesen, D., Haimov, S., Laursen, K., Lilly, D. K., Loehrer,
S. M., Malinowski, S. P., Morley, B., Petters, M. D., Rogers, D. C., Russell,
L., Savic-Jovcic, V., Snider, J. R., Straub, D., Szumowski, M. J., Takagi,
H., Thornton, D. C., Tschudi, M., Twohy, C., Wetzel, M., and van Zanten,
M. C.: Dynamics and Chemistry of Marine Stratocumulus–DYCOMS-II, B.
Am. Meteorol. Soc., 84, 579–594,
https://doi.org/10.1175/BAMS-84-5-579,
2003. a

Stevens, D. E., Ackerman, A. S., and Bretherton, C. S.: Effects of domain size
and numerical resolution on the simulation of shallow cumulus convection,
J. Atmos. Sci., 59, 3285–3301, 2002. a

Unterstrasser, S., Hoffmann, F., and Lerch, M.: Collection/aggregation algorithms in Lagrangian cloud microphysical models: rigorous evaluation in box model simulations, Geosci. Model Dev., 10, 1521–1548, https://doi.org/10.5194/gmd-10-1521-2017, 2017. a, b