pith. sign in

arxiv: 2308.05015 · v3 · submitted 2023-08-07 · ⚛️ physics.flu-dyn · physics.ao-ph

Immersion freezing in particle-based aerosol-cloud microphysics: a probabilistic perspective on singular and time-dependent models

Sylwester Arabas , Jeffrey H. Curtis , Israel Silber , Ann M. Fridlind , Daniel A. Knopf , Matthew West , Nicole Riemer This is my paper

Pith reviewed 2026-05-24 07:53 UTC · model grok-4.3

classification ⚛️ physics.flu-dyn physics.ao-ph
keywords immersion freezingice nucleationsingular parameterizationtime-dependent parameterizationparticle-based microphysicsaerosol-cloud interactionscloud modelingcooling rate dependence
0
0 comments X

The pith

Singular immersion freezing models apply only under limited ambient cooling rates.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper contrasts singular and time-dependent parameterizations for immersion freezing of cloud droplets containing ice-nucleating particles. It demonstrates through box-model tests that the singular approach functions as a time-integrated version of the time-dependent one but holds only for restricted cooling-rate profiles. Two-dimensional prescribed-flow simulations then show how applying singular models outside chamber-like conditions affects frozen-fraction evolution and particle sampling in super-particle methods. The work concludes that time-dependent, water-activity-based formulations integrate more readily with detailed aerosol composition and collisional processes in particle-based cloud microphysics.

Core claim

The singular approach constitutes a time-integrated form of a more general time-dependent approach and is only applicable under a limited range of ambient cooling rates. The time-dependent approach is suitable for integration with particle-based model components that resolve detailed aerosol composition and collisional growth or breakup. Flow-coupled aerosol-budget-resolving simulations reveal both the benefits and the sampling challenges of modeling cloud condensation nuclei activation and immersion freezing on insoluble ice nuclei with super-particle methods.

What carries the argument

Singular versus time-dependent parameterization of immersion freezing, viewed probabilistically within particle-based aerosol-cloud microphysics.

If this is right

  • Singular models produce incorrect frozen fractions when ambient cooling rates depart from the narrow range for which they were calibrated.
  • Time-dependent formulations remain consistent across cooling-rate variations and couple directly to water-activity-based nucleation rates.
  • Super-particle representations of sparse INPs require careful attribute-space sampling to avoid statistical bias in nucleation events.
  • Aerosol-budget-resolving simulations can track collisional processing of INPs when the time-dependent approach is used.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Cloud models that embed singular parameterizations may underestimate or overestimate ice formation in regions with strong vertical motion or turbulence.
  • Extending the analysis to three-dimensional large-eddy simulations would test whether the cooling-rate limitation persists under realistic flow variability.
  • The sampling challenges identified for sparse INPs likely apply to other rare-event processes such as homogeneous freezing or droplet coalescence.

Load-bearing premise

Parameterizations derived from cloud-chamber experiments can be directly applied to ambient cloud flow regimes without additional validation of cooling-rate dependence.

What would settle it

A side-by-side comparison of frozen-fraction evolution under a range of controlled cooling-rate profiles that match both chamber experiments and ambient cloud flows, using the same immersed surface spectrum, would show whether the singular model deviates systematically outside its claimed validity range.

Figures

Figures reproduced from arXiv: 2308.05015 by Ann M. Fridlind, Daniel A. Knopf, Israel Silber, Jeffrey H. Curtis, Matthew West, Nicole Riemer, Sylwester Arabas.

Figure 1
Figure 1. Figure 1: Conceptual representation of the aerosol-cloud droplet activation and immersion freezing processes and their numerical implementation. Left: Depiction of the physical processes. Right: Numerical implementation using super-particles. See section 2.3 and 4 for discussion. 2.3.1 Time-dependent scheme using ABIFM parameterization The time-dependent Monte-Carlo model explored herein uses the stochastic water-ac… view at source ↗
Figure 2
Figure 2. Figure 2: The INAS ns(T) curve with parameters from Niemand et al. (2012) (black filled squares) and a set of three ABIFM curves corresponding to three different cooling rates c plotted (teal solid lines). the multiplicities (stemming from coarser size-spectral resolution), the larger will be the spread among different Monte-Carlo realizations of the process. 2.3.2 Singular scheme using INAS parameterization The sin… view at source ↗
Figure 3
Figure 3. Figure 3: Two-dimensional probability densities as a function of immersed insoluble surface area S and freezing tem￾perature T, p(S, T), used for sampling the initial conditions for the box model simulations presented in Section 3.3, using geometric standard deviation σg = exp(0.05) (top), σg = exp(0.25) (middle), and σg = exp(1.25) (bottom). The marginals with respect to S and T are shown above and on the right, re… view at source ↗
Figure 4
Figure 4. Figure 4: Schematic of operation of time-dependent (top) and singular (bottom) immersion freezing models. Left: parti￾cle attribute sampling strategy at initialization. Middle: evolving particle dynamics of super-particles during the simulations. Right: aggregation of results as frozen fractions as a function of time. Gray line on the temperature plot indicates ice melt￾ing point. 3.2 Response of simulated frozen fr… view at source ↗
Figure 5
Figure 5. Figure 5: Temporal evolution of prescribed temperature and resulting frozen fractions calculated using the singular scheme and the time-dependent scheme. Three realizations are shown for each case. (a) Linear temperature decrease, with temperature gradient comparable to the experimental conditions that were used to derive the parameterizations. (b) Linear temperature decrease, temperature gradient lower than in case… view at source ↗
Figure 6
Figure 6. Figure 6: Detailed view of one singular and one time-dependent realizations depicted in panel (f) of [PITH_FULL_IMAGE:figures/full_fig_p014_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Frozen fraction as a function of temperature comparing simulations using singular (INAS, black markers) and time-dependent (ABIFM, teal symbols) parameterizations. For reference, the broken lines indicate the analytic cumulative distribution functions corresponding to monodisperse particle populations with surface areas equal to the median (red), 10 times the median (burgundy) and 1/10 of the median (yello… view at source ↗
Figure 8
Figure 8. Figure 8: Frozen fraction as a function of temperature comparing simulations using singular (INAS, black markers) and time-dependent (ABIFM, teal symbols) parameterizations. Diagrams constructed as in [PITH_FULL_IMAGE:figures/full_fig_p017_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Flow field pattern visualized with arrows depicting air velocity. Initial relative humidity field plotted with colored filled cells. qv = (7.5−6.66) = 0.84 g/kg (where the minuends are the values from the original setup of Morrison & Grabowski, 2007, used for warm-rain simulations, and the subtrahends are arbitrarily chosen for the relative humidity pro￾file to roughly match). The dry-air density profile i… view at source ↗
Figure 10
Figure 10. Figure 10: Renderings of snapshots of the prescribed-flow simulations at t = 600s, t = 1800s and t = 6000s, with super-droplets depicted as solid spheres colored by: (a) (wet) radius (from yellow: aerosol to blue: droplets), (b) immersed surface area (for time-dependent scheme, values of zero correspond to INP-void super-particles) and (c) freezing temperature (for singular scheme, INP-void particles plotted with ye… view at source ↗
Figure 11
Figure 11. Figure 11: Aggregated results from twelve prescribed-flow simulations, performed for three different stream-function am￾plitudes A and for both singular (solid lines) and time-dependent (dashed lines) immersion freezing representations, for two different values of the random seed each. Panel (a) depicts the time evolution of ice concentration, with the initial spinup period (freezing disabled) indicated with gray li… view at source ↗
read the original abstract

Cloud droplets containing ice-nucleating particles (INPs) may freeze at temperatures above the homogeneous freezing threshold temperature. This process, referred to as immersion freezing, is one of the modulators of aerosol-cloud interactions in the Earth's atmosphere. In modeling studies, immersion freezing is often described using either so-called "singular" or "time-dependent" parameterizations. Here, we juxtapose both approaches and discuss them in the context of probabilistic particle-based cloud microphysics modeling. First, using a box model, we contrast how both parameterizations respond to different idealized ambient cooling rate profiles and quantify the impact of the polydispersity of the immersed surface spectrum on the frozen fraction evolution. Second, using a prescribed-flow two-dimensional cloud model, we illustrate the implications of applying the singular model in simulations with flow regimes relevant to ambient cloud conditions rather than to the cloud-chamber experiments on which these parameterizations are built upon. We discuss the critical role of the attribute-space sampling strategy for particle-based model simulations in modeling heterogeneous ice nucleation which is contingent on the presence of relatively sparse immersed INPs. The key takeaways include: (i) The singular approach, constituting a time-integrated form of a more general time-dependent approach, is only applicable under a limited range of ambient cooling rates. (ii) The time-dependent approach, especially when based on water-activity, is suitable for integration with particle-based model components of detailed aerosol composition and collisional growth/breakup. (iii) A flow-coupled aerosol-budget-resolving simulation shows the benefits and challenges of modeling cloud condensation nuclei activation and immersion freezing on insoluble ice nuclei with super-particle methods.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 2 minor

Summary. The manuscript compares singular and time-dependent parameterizations for immersion freezing within particle-based aerosol-cloud microphysics. Box-model experiments with idealized cooling-rate profiles quantify differences in frozen-fraction evolution arising from polydispersity of the immersed surface spectrum. A prescribed-flow two-dimensional cloud model then illustrates consequences of applying the singular parameterization under ambient-relevant flows, stressing the importance of attribute-space sampling for sparse INPs. Central claims are that the singular approach is a time-integrated form of the time-dependent model and is applicable only under a limited range of cooling rates, while the time-dependent (especially water-activity-based) approach integrates more readily with detailed aerosol and collisional processes.

Significance. If substantiated, the result would guide parameterization choice in cloud microphysics, particularly for super-particle methods. The dual use of controlled box-model cooling profiles and 2D flow simulations bridges chamber-derived parameterizations to ambient regimes, and the explicit treatment of sampling strategies for sparse INPs is a practical contribution.

major comments (1)
  1. [prescribed-flow two-dimensional cloud model] In the prescribed-flow two-dimensional cloud model section, the distribution of instantaneous cooling rates experienced by super-particles is not reported. Without this mapping to the box-model threshold range, it remains unclear whether the illustrated differences arise from cooling-rate mismatch or from attribute-space sampling of sparse INPs or the prescribed flow itself; this step is load-bearing for the limited-applicability claim.
minor comments (2)
  1. [Abstract] The abstract states that the box model 'quantifies the impact' of polydispersity but does not name the quantitative metric (e.g., difference in frozen fraction at a given temperature or integrated error).
  2. [box-model experiments] The precise numerical bounds defining the 'limited range of ambient cooling rates' for which the singular model holds are not tabulated or stated explicitly with reference to the box-model results.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their constructive comments. We address the single major comment below.

read point-by-point responses

  1. Referee: In the prescribed-flow two-dimensional cloud model section, the distribution of instantaneous cooling rates experienced by super-particles is not reported. Without this mapping to the box-model threshold range, it remains unclear whether the illustrated differences arise from cooling-rate mismatch or from attribute-space sampling of sparse INPs or the prescribed flow itself; this step is load-bearing for the limited-applicability claim.

    Authors: We agree that the distribution of instantaneous cooling rates experienced by super-particles in the 2D prescribed-flow simulation was not reported and that providing this information would strengthen the connection to the box-model results. In the revised manuscript we will add a new panel (or supplementary figure) showing the histogram of cooling rates sampled by the super-particles together with a quantitative mapping onto the range of idealized cooling-rate profiles examined in the box-model section. This addition will allow readers to assess the degree to which the observed differences are attributable to cooling-rate regimes outside the singular-model validity range versus attribute-space sampling effects. revision: yes

Circularity Check

0 steps flagged

No circularity: paper contrasts established parameterizations via external benchmarks

full rationale

The paper's core claim—that the singular model is a time-integrated form of the time-dependent model and only applicable under limited cooling rates—is advanced through direct numerical comparison of two published parameterizations against idealized cooling profiles (box model) and prescribed ambient flows (2D model). No step reduces a prediction to a fitted input by construction, invokes a self-citation as the sole justification for a uniqueness theorem, or renames a known result as a new derivation. The attribute-space sampling discussion and water-activity formulation are presented as independent modeling choices, not derived from the authors' prior outputs. The derivation chain therefore remains self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review yields no explicit free parameters, axioms, or invented entities beyond standard microphysics assumptions; no new entities postulated.

pith-pipeline@v0.9.0 · 5856 in / 1059 out tokens · 36550 ms · 2026-05-24T07:53:24.914553+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

134 extracted references · 134 canonical work pages

  1. [1]

    \ Albuquerque, D

    Abade_and_Albuquerque_2024 APACrefauthors Abade, G. \ Albuquerque, D. APACrefauthors \ 2024 . Persistent mixed-phase states in adiabatic cloud parcels under idealised conditions Persistent mixed-phase states in adiabatic cloud parcels under idealised conditions . Q. J. Royal Meteorol. Soc. . APACrefDOI doi:10.1002/qj.4775 APACrefDOI

    work page doi:10.1002/qj.4775 2024

  2. [2]

    , Grabowski, W

    Abade_et_al_2018 APACrefauthors Abade, G. , Grabowski, W. \ Pawlowska, H. APACrefauthors \ 2018 . Broadening of Cloud Droplet Spectra through Eddy Hopping: Turbulent Entraining Parcel Simulations Broadening of cloud droplet spectra through eddy hopping: Turbulent entraining parcel simulations . J. Atmos. Sci. 75 . APACrefDOI doi:10.1175/JAS-D-18-0078.1 APACrefDOI

    work page doi:10.1175/jas-d-18-0078.1 2018

  3. [3]

    , Aller, J

    Alpert_et_al_2011 APACrefauthors Alpert, P. , Aller, J. \ Knopf, D. APACrefauthors \ 2011 . Ice nucleation from aqueous NaCl droplets with and without marine diatoms Ice nucleation from aqueous nacl droplets with and without marine diatoms . Atmos. Chem. Phys. 11 . APACrefDOI doi:10.5194/acp-11-5539-2011 APACrefDOI

    work page doi:10.5194/acp-11-5539-2011 2011

  4. [4]

    \ Knopf, D

    Alpert_and_Knopf_2016 APACrefauthors Alpert, P. \ Knopf, D. APACrefauthors \ 2016 . Analysis of isothermal and cooling-rate-dependent immersion freezing by a unifying stochastic ice nucleation model Analysis of isothermal and cooling-rate-dependent immersion freezing by a unifying stochastic ice nucleation model . Atmos. Chem. Phys. 16 . APACrefDOI doi:10...

    work page doi:10.5194/acp-16-2083-2016 2016

  5. [5]

    \ Rosenfeld, D

    Andreae_and_Rosenfeld_2008 APACrefauthors Andreae, M. \ Rosenfeld, D. APACrefauthors \ 2008 . Aerosol–cloud–precipitation interactions. Part 1. The nature and sources of cloud-active aerosols Aerosol–cloud–precipitation interactions. part 1. the nature and sources of cloud-active aerosols . Earth-Sci. Rev. 89 13--41 . APACrefDOI doi:10.1016/j.earscirev.20...

    work page doi:10.1016/j.earscirev.2008.03.001 2008

  6. [6]

    , Jaruga, A

    Arabas_et_al_2015 APACrefauthors Arabas, S. , Jaruga, A. , Pawlowska, H. \ Grabowski, W. APACrefauthors \ 2015 . libcloudph++ 1.0: a single-moment bulk, double-moment bulk, and particle-based warm-rain microphysics library in C++ libcloudph++ 1.0: a single-moment bulk, double-moment bulk, and particle-based warm-rain microphysics library in C++ . Geosci. ...

    work page doi:10.5194/gmd-8-1677-2015 2015

  7. [7]

    , Ackerman, A

    Avramov_et_al_2011 APACrefauthors Avramov, A. , Ackerman, A. , Fridlind, A. , van Diedenhoven, B. , Botta, G. , Aydin, K. Wolde, M. APACrefauthors \ 2011 . Towards ice formation closure in Arctic mixed-phase boundary layer clouds during ISDAC Towards ice formation closure in arctic mixed-phase boundary layer clouds during ISDAC . J. Geophys. Res. 116 D00T...

    work page doi:10.1029/2011jd015910 2011

  8. [8]

    , Zeman, C

    Banderler_et_al_2023 APACrefauthors Banderier, H. , Zeman, C. , Leutwyler, D. , Rüdisühli, S. \ Schär, C. APACrefauthors \ 2023 . Reduced floating-point precision in regional climate simulations: An ensemble-based statistical verification Reduced floating-point precision in regional climate simulations: An ensemble-based statistical verification . EGUsphe...

    work page doi:10.5194/egusphere-2023-2263 2023

  9. [9]

    \ Hoose, C

    Barrett_and_Hoose_2022 APACrefauthors Barrett, A. \ Hoose, C. APACrefauthors \ 2023 . Microphysical Pathways Active within Thunderstorms and Their Sensitivity to CCN Concentration and Wind Shear Microphysical pathways active within thunderstorms and their sensitivity to CCN concentration and wind shear . J. Geophys. Res. Atmos. 128 . APACrefDOI doi:10.102...

    work page doi:10.1029/2022jd036965 2023

  10. [10]

    , Banaśkiewicz, J

    Bartman_et_al_2022_PyMPDATA APACrefauthors Bartman, P. , Banaśkiewicz, J. , Drenda, S. , Manna, M. , Olesik, M. , Rozwoda, P. Arabas, S. APACrefauthors \ 2022 . PyMPDATA v1: Numba -accelerated implementation of MPDATA with examples in Python , Julia and Matlab PyMPDATA v1: Numba -accelerated implementation of MPDATA with examples in Python , Julia and Mat...

    work page doi:10.21105/joss.03896 2022

  11. [11]

    , Bulenok, O

    Bartman_et_al_2022_PySDM APACrefauthors Bartman, P. , Bulenok, O. , Górski, K. , Jaruga, A. , Łazarski, G. , Olesik, M. Arabas, S. APACrefauthors \ 2022 . PySDM v1: particle-based cloud modelling package for warm-rain microphysics and aqueous chemistry PySDM v1: particle-based cloud modelling package for warm-rain microphysics and aqueous chemistry . J. O...

    work page doi:10.21105/joss.03219 2022

  12. [12]

    , Ault, A

    Bauer_et_al_2013 APACrefauthors Bauer, S. , Ault, A. \ Prather, K. APACrefauthors \ 2013 . Evaluation of aerosol mixing state classes in the GISS -model E - MATRIX climate model using single particle mass spectrometry measurements Evaluation of aerosol mixing state classes in the GISS -model E - MATRIX climate model using single particle mass spectrometry...

    work page doi:10.1002/jgrd.50700 2013

  13. [13]

    , Wright, D

    Bauer_et_al_2008 APACrefauthors Bauer, S. , Wright, D. , Koch, D. , Lewis, E. , McGraw, R. , Chang, L S. Ruedy, R. APACrefauthors \ 2008 . MATRIX ( M ulticonfiguration A erosol TR acker of m IX ing state): A n aerosol microphysical module for global atmospheric models MATRIX ( M ulticonfiguration A erosol TR acker of m IX ing state): A n aerosol microphys...

    work page doi:10.5194/acp-8-6003-2008 2008

  14. [14]

    , Quaas, J

    Bellouin_et_al_2020 APACrefauthors Bellouin, N. , Quaas, J. , Gryspeerdt, E. , Kinne, S. , Stier, P. , Watson-Parris, D. Stevens, B. APACrefauthors \ 2020 . Bounding Global Aerosol Radiative Forcing of Climate Change Bounding global aerosol radiative forcing of climate change . Rev. Geophys. 58 . APACrefDOI doi:10.1029/2019RG000660 APACrefDOI

    work page doi:10.1029/2019rg000660 2020

  15. [15]

    APACrefauthors \ 1953

    Bigg_1953b APACrefauthors Bigg, E. APACrefauthors \ 1953 . The formation of atmospheric ice crystals by the freezing of droplets The formation of atmospheric ice crystals by the freezing of droplets . Q. J. Royal Meteorol. Soc. . APACrefDOI doi:10.1002/qj.49707934207 APACrefDOI

    work page doi:10.1002/qj.49707934207 1953

  16. [16]

    APACrefauthors \ 1953

    Bigg_1953a APACrefauthors Bigg, E. APACrefauthors \ 1953 . The Supercooling of Water The supercooling of water . Proc. Phys. Soc. B 66 . APACrefDOI doi:10.1088/0370-1301/66/8/309 APACrefDOI

    work page doi:10.1088/0370-1301/66/8/309 1953

  17. [17]

    \ Seifert, A

    Brdar_and_Seifert_2018 APACrefauthors Brdar, S. \ Seifert, A. APACrefauthors \ 2018 . McSnow : A Monte-Carlo Particle Model for Riming and Aggregation of Ice Particles in a Multidimensional Microphysical Phase Space McSnow : A Monte-Carlo particle model for riming and aggregation of ice particles in a multidimensional microphysical phase space . J. Adv. M...

    work page doi:10.1002/2017ms001167 2018

  18. [18]

    , McCluskey, C

    Burrows_et_al_2022 APACrefauthors Burrows, S. , McCluskey, C. , Cornwell, G. , Steinke, I. , Zhang, K. , Zhao, B. DeMott, P. APACrefauthors \ 2022 . Ice-Nucleating Particles That Impact Clouds and Climate: Observational and Modeling Research Needs Ice-nucleating particles that impact clouds and climate: Observational and modeling research needs . Rev. Geo...

    work page doi:10.1029/2021rg000745 2022

  19. [19]

    APACrefauthors \ 1959

    Carte_1959 APACrefauthors Carte, A. APACrefauthors \ 1959 . Probability of Freezing Probability of freezing . Proc. Phys. Soc. 73 . APACrefDOI doi:10.1088/0370-1328/73/2/126 APACrefDOI

    work page doi:10.1088/0370-1328/73/2/126 1959

  20. [20]

    , Brient, F

    Ceppi_et_al_2017 APACrefauthors Ceppi, P. , Brient, F. , Zelinka, M. \ Hartmann, D. APACrefauthors \ 2017 . Cloud feedback mechanisms and their representation in global climate models Cloud feedback mechanisms and their representation in global climate models . WIREs Clim. Change. 8 . APACrefDOI doi:10.1002/wcc.465 APACrefDOI

    work page doi:10.1002/wcc.465 2017

  21. [21]

    , Möhler, O

    Conolly_et_al_2009 APACrefauthors Connolly, P. , Möhler, O. , Field, P. , Saathoff, H. , Burgess, R. , Choularton, T. \ Gallagher, M. APACrefauthors \ 2009 . Studies of heterogeneous freezing by three different desert dust samples Studies of heterogeneous freezing by three different desert dust samples . Atmos. Chem. Phys. 9 . APACrefDOI doi:10.5194/acp-9...

    work page doi:10.5194/acp-9-2805-2009 2009

  22. [22]

    , McCluskey, C

    Cornwell_et_al_2021 APACrefauthors Cornwell, G. , McCluskey, C. , DeMott, P. , Prather, K. \ Burrows, S. APACrefauthors \ 2021 . Development of Heterogeneous Ice Nucleation Rate Coefficient Parameterizations From Ambient Measurements Development of heterogeneous ice nucleation rate coefficient parameterizations from ambient measurements . Geophys. Res. Le...

    work page doi:10.1029/2021gl095359 2021

  23. [23]

    , Michelotti, M

    Curtis_et_al_2016 APACrefauthors Curtis, J. , Michelotti, M. , Riemer, N. , Heath, M. \ West, M. APACrefauthors \ 2016 . Accelerated simulation of stochastic particle removal processes in particle-resolved aerosol models Accelerated simulation of stochastic particle removal processes in particle-resolved aerosol models . J. Comp. Phys. 322 . APACrefDOI do...

    work page doi:10.1016/j.jcp.2016.06.029 2016

  24. [24]

    , Riemer, N

    Curtis_et_al_2024 APACrefauthors Curtis, J. , Riemer, N. \ West, M. APACrefauthors \ 2024 . Explicit stochastic advection algorithms for the regional scale particle-resolved atmospheric aerosol model WRF-PartMC (v1.0) Explicit stochastic advection algorithms for the regional scale particle-resolved atmospheric aerosol model WRF-PartMC (v1.0) . EGUsphere ....

    work page doi:10.5194/egusphere-2024-825 2024

  25. [25]

    , Mackay, J

    deJong_et_al_2023_GMD APACrefauthors de Jong, E. , Mackay, J. , Bulenok, O. , Jaruga, A. \ Arabas, S. APACrefauthors \ 2023 . Breakups are Complicated: An Efficient Representation of Collisional Breakup in the Superdroplet Method Breakups are complicated: An efficient representation of collisional breakup in the superdroplet method . Geosci. Model Dev. 16...

    work page doi:10.5194/gmd-16-4193-2023 2023

  26. [26]

    , Singer, C

    deJong_et_al_2023_JOSS APACrefauthors de Jong, E. , Singer, C. , Azimi, S. , Bartman, P. , Bulenok, O. , Derlatka, K. Arabas, S. APACrefauthors \ 2023 . New developments in PySDM and PySDM-examples v2: collisional breakup, immersion freezing, dry aerosol initialization, and adaptive time-stepping New developments in PySDM and PySDM-examples v2: collisiona...

    work page doi:10.21105/joss.04968 2023

  27. [27]

    , Huffman, J

    Despres_et_al_2012 APACrefauthors Després, V. , Huffman, J. , Burrows, S. , Hoose, C. , Safatov, A. , Buryak, G. Jaenicke, R. APACrefauthors \ 2012 . Primary biological aerosol particles in the atmosphere: a review Primary biological aerosol particles in the atmosphere: a review . Tellus B 64 . APACrefDOI doi:10.3402/tellusb.v64i0.15598 APACrefDOI

    work page doi:10.3402/tellusb.v64i0.15598 2012

  28. [28]

    , Riemer, N

    DeVille_et_al_2019 APACrefauthors DeVille, L. , Riemer, N. \ West, M. APACrefauthors \ 2019 . Convergence of a Generalized Weighted Flow Algorithm for Stochastic Particle Coagulation Convergence of a generalized weighted flow algorithm for stochastic particle coagulation . J. Comp. Dyn. 2019 . APACrefDOI doi:10.3934/jcd.2019003 APACrefDOI

    work page doi:10.3934/jcd.2019003 2019

  29. [29]

    \ Pawlowska, H

    Dziekan_and_Pawlowska_2017 APACrefauthors Dziekan, P. \ Pawlowska, H. APACrefauthors \ 2017 . Stochastic coalescence in L agrangian cloud microphysics Stochastic coalescence in L agrangian cloud microphysics . Atmos. Chem. Phys. 17 . APACrefDOI doi:10.5194/acp-17-13509-2017 APACrefDOI

    work page doi:10.5194/acp-17-13509-2017 2017

  30. [30]

    \ Feingold, G

    Ervens_and_Feingold_2013 APACrefauthors Ervens, B. \ Feingold, G. APACrefauthors \ 2013 . Sensitivities of immersion freezing: Reconciling classical nucleation theory and deterministic expressions Sensitivities of immersion freezing: Reconciling classical nucleation theory and deterministic expressions . Geophys. Res. Lett. 40 . APACrefDOI doi:10.1002/grl...

    work page doi:10.1002/grl.50580 2013

  31. [31]

    APACrefauthors \ 1958

    Fletcher_1958 APACrefauthors Fletcher, N. APACrefauthors \ 1958 . Time lag in ice crystal nucleation in the atmosphere. Part II theoretical Time lag in ice crystal nucleation in the atmosphere. part ii theoretical . Bull. Obs. Puy de Dôme 1 . APACrefURL https://web.archive.org/web/*/https://www.phys.unsw.edu.au/music/people/publications/Fletcher1958b.pdf ...

    work page 1958

  32. [32]

    APACrefauthors \ 1969

    Fletcher_1969 APACrefauthors Fletcher, N. APACrefauthors \ 1969 . Active Sites and Ice Crystal Nucleation Active sites and ice crystal nucleation . J. Atmos. Sci. 26 . APACrefDOI doi:10.1175/1520-0469(1969)026<1266:ASAICN>2.0.CO;2 APACrefDOI

    work page doi:10.1175/1520-0469(1969)026 1969

  33. [33]

    , Brooks, S

    Fornea_et_al_2009 APACrefauthors Fornea, A. , Brooks, S. , Dooley, J. \ Saha, A. APACrefauthors \ 2009 . Heterogeneous freezing of ice on atmospheric aerosols containing ash, soot, and soil Heterogeneous freezing of ice on atmospheric aerosols containing ash, soot, and soil . J. Geophys. Res. Atmos. 114 D13 . APACrefDOI doi:10.1029/2009JD011958 APACrefDOI

    work page doi:10.1029/2009jd011958 2009

  34. [34]

    \ Ackerman, A

    Fridlind_and_Ackerman_2018 APACrefauthors Fridlind, A. \ Ackerman, A. APACrefauthors \ 2018 . Simulations of Arctic Mixed-Phase Boundary Layer Clouds: Advances in Understanding and Outstanding Questions Simulations of arctic mixed-phase boundary layer clouds: Advances in understanding and outstanding questions . C. Andronache\ ( ), Mixed-Phase Clouds: Obs...

    work page doi:10.1016/b978-0-12-810549-8.00007-6 2018

  35. [35]

    , Van Diedenhoven, B

    Fridlind_et_al_2012 APACrefauthors Fridlind, A. , Van Diedenhoven, B. , Ackerman, A. , Avramov, A. , Mrowiec, A. , Morrison, H. Shupe, M. APACrefauthors \ 2012 . A FIRE-ACE/SHEBA Case Study of Mixed-Phase Arctic Boundary Layer Clouds: Entrainment Rate Limitations on Rapid Primary Ice Nucleation Processes A FIRE-ACE/SHEBA case study of mixed-phase arctic b...

    work page doi:10.1175/jas-d-11-052.1 2012

  36. [36]

    , Welti, A

    Frostenberg_et_al_2022 APACrefauthors Frostenberg, H. , Welti, A. , Luhr, M. , Savre, J. , Thomson, E. \ Ickes, L. APACrefauthors \ 2023 . The chance of freezing – a conceptional study to parameterize temperature-dependent freezing by including randomness of ice-nucleating particle concentrations The chance of freezing – a conceptional study to parameteri...

    work page doi:10.5194/acp-23-10883-2023 2023

  37. [37]

    , Kampf, C

    Froechlich_Nowoisky_et_al_2016 APACrefauthors Fröhlich-Nowoisky, J. , Kampf, C. , Weber, B. , Huffman, J. , Pöhlker, C. , Andreae, M. Pöschl, U. APACrefauthors \ 2016 . Bioaerosols in the Earth system: Climate, health, and ecosystem interactions Bioaerosols in the earth system: Climate, health, and ecosystem interactions . Atmos. Res. 182 346--376 . APACr...

    work page doi:10.1016/j.atmosres.2016.07.018 2016

  38. [38]

    \ Arnold, R

    Gedzelman_and_Arnold_1993 APACrefauthors Gedzelman, S. \ Arnold, R. APACrefauthors \ 1993 . The Form of Cyclonic Precipitation and Its Thermal Impact The form of cyclonic precipitation and its thermal impact . Mon. Wea. Rev. 121 . APACrefDOI doi:10.1175/1520-0493(1993)121<1957:TFOCPA>2.0.CO;2 APACrefDOI

    work page doi:10.1175/1520-0493(1993)121 1993

  39. [39]

    \ Arnold, R

    Gedzelman_and_Arnold_1994 APACrefauthors Gedzelman, S. \ Arnold, R. APACrefauthors \ 1994 . Modeling the isotopic composition of precipitation Modeling the isotopic composition of precipitation . J. Geophys. Res. Atmos. 99 D5

    work page 1994

  40. [40]

    APACrefauthors \ 1998

    Grabowski_1998 APACrefauthors Grabowski, W. APACrefauthors \ 1998 . Toward Cloud Resolving Modeling of Large-Scale Tropical Circulations: A Simple Cloud Microphysics Parameterization Toward cloud resolving modeling of large-scale tropical circulations: A simple cloud microphysics parameterization . J. Atmos. Sci. 55 . APACrefDOI doi:10.1175/1520-0469(1998...

    work page doi:10.1175/1520-0469(1998)055 1998

  41. [41]

    APACrefauthors \ 1999

    Grabowski_1999 APACrefauthors Grabowski, W. APACrefauthors \ 1999 . A parameterization of cloud microphysics for long-term cloud-resolving modeling of tropical convection A parameterization of cloud microphysics for long-term cloud-resolving modeling of tropical convection . Atmos. Res. 52 . APACrefDOI doi:10.1016/S0169-8095(99)00029-0 APACrefDOI

    work page doi:10.1016/s0169-8095(99)00029-0 1999

  42. [42]

    , Dziekan, P

    Grabowski_et_al_2018 APACrefauthors Grabowski, W. , Dziekan, P. \ Pawlowska, H. APACrefauthors \ 2018 . Lagrangian condensation microphysics with T womey CCN activation Lagrangian condensation microphysics with T womey CCN activation . Geosci. Model Dev. . APACrefDOI doi:10.5194/gmd-11-103-2018 APACrefDOI

    work page doi:10.5194/gmd-11-103-2018 2018

  43. [43]

    , Morrison, H

    Grabowski_et_al_2019 APACrefauthors Grabowski, W. , Morrison, H. , Shima, S. , Abade, G. , Dziekan, P. \ Pawlowska, H. APACrefauthors \ 2019 . Modeling of Cloud Microphysics: Can We Do Better? Modeling of cloud microphysics: Can we do better? Bull. Am. Meteorol. Soc. 100 . APACrefDOI doi:10.1175/BAMS-D-18-0005.1 APACrefDOI

    work page doi:10.1175/bams-d-18-0005.1 2019

  44. [44]

    , Murray, B

    Herbert_et_al_2014 APACrefauthors Herbert, R. , Murray, B. , Whale, T. , Dobbie, S. \ Atkinson, J. APACrefauthors \ 2014 . Representing time-dependent freezing behaviour in immersion mode ice nucleation Representing time-dependent freezing behaviour in immersion mode ice nucleation . Atmos. Chem. Phys. 14 . APACrefDOI doi:10.5194/acp-14-8501-2014 APACrefDOI

    work page doi:10.5194/acp-14-8501-2014 2014

  45. [45]

    \ Feingold, G

    Hoffmann_et_al_2019 APACrefauthors Hoffmann, F. \ Feingold, G. APACrefauthors \ 2019 . Entrainment and Mixing in Stratocumulus: Effects of a New Explicit Subgrid-Scale Scheme for Large-Eddy Simulations with Particle-Based Microphysics Entrainment and mixing in stratocumulus: Effects of a new explicit subgrid-scale scheme for large-eddy simulations with pa...

    work page doi:10.1175/jas-d-18-0318.1 2019

  46. [46]

    \ Feingold, G

    Hoffmann_and_Feingold_2023 APACrefauthors Hoffmann, F. \ Feingold, G. APACrefauthors \ 2023 . A Note on Aerosol Processing by Droplet Collision-Coalescence A note on aerosol processing by droplet collision-coalescence . Geophys. Res. Lett. . APACrefDOI doi:10.1029/2023GL103716 APACrefDOI

    work page doi:10.1029/2023gl103716 2023

  47. [47]

    \ M\"ohler, O

    Hoose_and_Moehler_2012 APACrefauthors Hoose, C. \ M\"ohler, O. APACrefauthors \ 2012 . Heterogeneous ice nucleation on atmospheric aerosols: a review of results from laboratory experiments Heterogeneous ice nucleation on atmospheric aerosols: a review of results from laboratory experiments . Atmos. Chem. Phys. 12 . APACrefDOI doi:10.5194/acp-12-9817-2012 ...

    work page doi:10.5194/acp-12-9817-2012 2012

  48. [48]

    \ Douglas, R

    Isaac_and_Douglas_1972 APACrefauthors Isaac, G. \ Douglas, R. APACrefauthors \ 1972 . Another ``Time Lag'' in the Activation of Atmospheric Ice Nuclei Another ``time lag'' in the activation of atmospheric ice nuclei . J. Appl. Meteorol. 11 . APACrefDOI doi:10.1175/1520-0450(1972)011<0490:ALITAO>2.0.CO;2 APACrefDOI

    work page doi:10.1175/1520-0450(1972)011 1972

  49. [49]

    \ Pawlowska, H

    Jaruga_and_Pawlowska_2018 APACrefauthors Jaruga, A. \ Pawlowska, H. APACrefauthors \ 2018 . libcloudph++ 2.0: aqueous-phase chemistry extension of the particle-based cloud microphysics scheme libcloudph++ 2.0: aqueous-phase chemistry extension of the particle-based cloud microphysics scheme . Geosci. Model Dev. 11 . APACrefDOI doi:10.5194/gmd-11-3623-2018...

    work page doi:10.5194/gmd-11-3623-2018 2018

  50. [50]

    \ Pfister, L

    Jensen_and_Pfister_2004 APACrefauthors Jensen, E. \ Pfister, L. APACrefauthors \ 2004 . Transport and freeze-drying in the tropical tropopause layer Transport and freeze-drying in the tropical tropopause layer . J. Geophys. Res. Atmos. 109 . APACrefDOI doi:10.1029/2003JD004022 APACrefDOI

    work page doi:10.1029/2003jd004022 2004

  51. [51]

    , Ladino, L

    Kanji_et_al_2017 APACrefauthors Kanji, Z. , Ladino, L. , Wex, H. , Boose, Y. , Burkert-Kohn, M. , Cziczo, D. \ Kr\"amer, M. APACrefauthors \ 2017 . Overview of Ice Nucleating Particles Overview of ice nucleating particles . Meteorol. Monogr. 58 . APACrefDOI doi:10.1175/AMSMONOGRAPHS-D-16-0006.1 APACrefDOI

    work page doi:10.1175/amsmonographs-d-16-0006.1 2017

  52. [52]

    \ Marcolli, C

    Kaercher_and_Marcolli_2021 APACrefauthors K\"archer, B. \ Marcolli, C. APACrefauthors \ 2021 . Aerosol--cloud interactions: the representation of heterogeneous ice activation in cloud models Aerosol--cloud interactions: the representation of heterogeneous ice activation in cloud models . Atmos. Chem. Phys. 21 . APACrefDOI doi:10.5194/acp-21-15213-2021 APACrefDOI

    work page doi:10.5194/acp-21-15213-2021 2021

  53. [53]

    , Marcolli, C

    Kaufmann_et_al_2017 APACrefauthors Kaufmann, L. , Marcolli, C. , Luo, B. \ Peter, T. APACrefauthors \ 2017 . Refreeze experiments with water droplets containing different types of ice nuclei interpreted by classical nucleation theory Refreeze experiments with water droplets containing different types of ice nuclei interpreted by classical nucleation theor...

    work page doi:10.5194/acp-17-3525-2017 2017

  54. [54]

    APACrefauthors \ 1969

    Kessler_1969 APACrefauthors Kessler, E. APACrefauthors \ 1969 . On the Distribution and Continuity of Water Substance in Atmospheric Circulations On the distribution and continuity of water substance in atmospheric circulations . Meteorol. Monogr. 10 . APACrefDOI doi:10.1007/978-1-935704-36-2_1 APACrefDOI

    work page doi:10.1007/978-1-935704-36-2_1 1969

  55. [55]

    , Ovtchinnikov, M

    Khain_et_al_2000 APACrefauthors Khain, A. , Ovtchinnikov, M. , Pinsky, M. , Pokrovsky, A. \ Krugliak, H. APACrefauthors \ 2000 . Notes on the state-of-the-art numerical modeling of cloud microphysics Notes on the state-of-the-art numerical modeling of cloud microphysics . Atmos. Res. 55 . APACrefDOI doi:10.1016/S0169-8095(00)00064-8 APACrefDOI

    work page doi:10.1016/s0169-8095(00)00064-8 2000

  56. [56]

    , Mahrt, F

    Kilchhofer_et_al_2021 APACrefauthors Kilchhofer, K. , Mahrt, F. \ Kanji, Z. APACrefauthors \ 2021 . The Role of Cloud Processing for the Ice Nucleating Ability of Organic Aerosol and Coal Fly Ash Particles The role of cloud processing for the ice nucleating ability of organic aerosol and coal fly ash particles . J. Geophys. Res. Atmos. 126 . APACrefDOI do...

    work page doi:10.1029/2020jd033338 2021

  57. [57]

    \ Alpert, P

    Knopf_and_Alpert_2013 APACrefauthors Knopf, D. \ Alpert, P. APACrefauthors \ 2013 . A water activity based model of heterogeneous ice nucleation kinetics for freezing of water and aqueous solution droplets A water activity based model of heterogeneous ice nucleation kinetics for freezing of water and aqueous solution droplets . Faraday Discuss. 165 . APAC...

    work page doi:10.1039/c3fd00035d 2013

  58. [58]

    \ Alpert, P

    Knopf_and_Alpert_2023 APACrefauthors Knopf, D. \ Alpert, P. APACrefauthors \ 2023 . Atmospheric ice nucleation Atmospheric ice nucleation . Nat. Rev. Phys. 5 203--217 . APACrefDOI doi:10.1038/s42254-023-00570-7 APACrefDOI

    work page doi:10.1038/s42254-023-00570-7 2023

  59. [59]

    , Alpert, P

    Knopf_et_al_2018 APACrefauthors Knopf, D. , Alpert, P. \ Wang, B. APACrefauthors \ 2018 . The role of organic aerosol in atmospheric ice nucleation: A review The role of organic aerosol in atmospheric ice nucleation: A review . ACS Earth and Space Chemistry 2 3 168--202 . APACrefDOI doi:10.1021/acsearthspacechem.7b00120 APACrefDOI

    work page doi:10.1021/acsearthspacechem.7b00120 2018

  60. [60]

    , Alpert, P

    Knopf_et_al_2020 APACrefauthors Knopf, D. , Alpert, P. , Zipori, A. , Reicher, N. \ Rudich, Y. APACrefauthors \ 2020 . Stochastic nucleation processes and substrate abundance explain time-dependent freezing in supercooled droplets Stochastic nucleation processes and substrate abundance explain time-dependent freezing in supercooled droplets . npj Clim. At...

    work page doi:10.1038/s41612-020-0106-4 2020

  61. [61]

    , Barry, K R

    Knopf_et_al_2021 APACrefauthors Knopf, D. , Barry, K R. , Brubaker, T A. , Jahl, L G. , K. A., L J. , Li, J. Liu, X. APACrefauthors \ 2021 . Aerosol-Ice Formation Closure: A Southern Great Plains Field Campaign Aerosol-ice formation closure: A southern great plains field campaign . Bull. Am. Meteorol. Soc. 102 . APACrefDOI doi:10.1175/BAMS-D-20-0151.1 APACrefDOI

    work page doi:10.1175/bams-d-20-0151.1 2021

  62. [62]

    , Charnawskas, J

    Knopf_et_al_2022 APACrefauthors Knopf, D. , Charnawskas, J. , Wang, P. , Wong, B. , Tomlin, J. , Jankowski, K. Wang, J. APACrefauthors \ 2022 . Micro-spectroscopic and freezing characterization of ice-nucleating particles collected in the marine boundary layer in the eastern North Atlantic Micro-spectroscopic and freezing characterization of ice-nucleatin...

    work page doi:10.5194/acp-22-5377-2022 2022

  63. [63]

    , Silber, I

    Knopf_et_al_2023 APACrefauthors Knopf, D. , Silber, I. , Riemer, N. , Fridlind, A. \ Ackerman, A. APACrefauthors \ 2023 . A 1D Model for Nucleation of Ice from Aerosol Particles: An Application to a Mixed-Phase Arctic Stratus Cloud Layer A 1D model for nucleation of ice from aerosol particles: An application to a mixed-phase arctic stratus cloud layer . J...

    work page doi:10.1029/2023ms003663 2023

  64. [64]

    , Wang, P

    Knopf_et_al_2023_ACP APACrefauthors Knopf, D. , Wang, P. , Wong, B. , Tomlin, J. , Veghte, D. , Lata, N. Wang, J. APACrefauthors \ 2023 . Physicochemical characterization of free troposphere and marine boundary layer ice-nucleating particles collected by aircraft in the eastern North Atlantic Physicochemical characterization of free troposphere and marine...

    work page doi:10.5194/acp-23-8659-2023 2023

  65. [65]

    APACrefauthors \ 2002

    Koop_2002 APACrefauthors Koop, T. APACrefauthors \ 2002 . The Water Activity of Aqueous Solutions in Equilibrium with Ice The water activity of aqueous solutions in equilibrium with ice . Bull. Chem. Soc. Japan 75 12 2587--2588 . APACrefDOI doi:10.1246/bcsj.75.2587 APACrefDOI

    work page doi:10.1246/bcsj.75.2587 2002

  66. [66]

    , Devi, J

    Kotalczyk_et_al_2017 APACrefauthors Kotalczyk, G. , Devi, J. \ Kruis, F. APACrefauthors \ 2017 . A time-driven constant-number Monte Carlo method for the GPU -simulation of particle breakage based on weighted simulation particles A time-driven constant-number Monte Carlo method for the GPU -simulation of particle breakage based on weighted simulation part...

    work page doi:10.1016/j.powtec.2017.05.002 2017

  67. [67]

    APACrefauthors \ 2019

    Kubota_2019 APACrefauthors Kubota, N. APACrefauthors \ 2019 . Random distribution active site model for ice nucleation in water droplets Random distribution active site model for ice nucleation in water droplets . Cryst. Eng. Comm. 21 . APACrefDOI doi:10.1039/C9CE00246D APACrefDOI

    work page doi:10.1039/c9ce00246d 2019

  68. [68]

    \ Malila, J

    Laaksonen_and_Malila_2022 APACrefauthors Laaksonen, A. \ Malila, J. APACrefauthors \ 2022 . Ice nucleation Ice nucleation . Nucleation of Water Nucleation of water \ ( 209-248). Elsevier . APACrefDOI doi:10.1016/B978-0-12-814321-6.00018-X APACrefDOI

    work page doi:10.1016/b978-0-12-814321-6.00018-x 2022

  69. [69]

    \ Mason, B

    Langham_and_Mason_1958 APACrefauthors Langham, E. \ Mason, B. APACrefauthors \ 1958 . The heterogeneous and homogeneous nucleation of supercooled water The heterogeneous and homogeneous nucleation of supercooled water . Proc. Royal Soc. A . APACrefDOI doi:10.1098/rspa.1958.0207 APACrefDOI

    work page doi:10.1098/rspa.1958.0207 1958

  70. [70]

    , Zhang, B

    Lata_et_al_2021 APACrefauthors Lata, N. , Zhang, B. , Schum, S. , Mazzoleni, L. , Brimberry, R. , Marcus, M. China, S. APACrefauthors \ 2021 . Aerosol Composition, Mixing State, and Phase State of Free Tropospheric Particles and Their Role in Ice Cloud Formation Aerosol composition, mixing state, and phase state of free tropospheric particles and their ro...

    work page doi:10.1021/acsearthspacechem.1c00315 2021

  71. [71]

    \ Morrison, H

    Lebo_and_Morrison_2013 APACrefauthors Lebo, Z J. \ Morrison, H. APACrefauthors \ 2013 . A Novel Scheme for Parameterizing Aerosol Processing in Warm Clouds A novel scheme for parameterizing aerosol processing in warm clouds . J. Atmos. Sci. 70 . APACrefDOI doi:10.1175/JAS-D-13-045.1 APACrefDOI

    work page doi:10.1175/jas-d-13-045.1 2013

  72. [72]

    \ Matsoukas, T

    Lee_and_Matsoukas_2000 APACrefauthors Lee, K. \ Matsoukas, T. APACrefauthors \ 2000 . Simultaneous coagulation and break-up using constant- N Monte Carlo Simultaneous coagulation and break-up using constant- N Monte Carlo . Powder Tech. 110 . APACrefDOI doi:10.1016/S0032-5910(99)00270-3 APACrefDOI

    work page doi:10.1016/s0032-5910(99)00270-3 2000

  73. [73]

    Leonard_and_Im_1999 APACrefauthors Leonard, J. \ Im, J. APACrefauthors \ 1999 . Modelling Solid Nucleation and Growth In Supercooled Liquid Modelling solid nucleation and growth in supercooled liquid . Mat. Res. Soc. Symp. Proc. 580 . APACrefDOI doi:10.1557/proc-580-233 APACrefDOI

    work page doi:10.1557/proc-580-233 1999

  74. [74]

    APACrefauthors \ 1950

    Levine_1950 APACrefauthors Levine, J. APACrefauthors \ 1950 . Statistical explanation of spontaneous freezing of water droplets. Statistical explanation of spontaneous freezing of water droplets. Washington . APACrefURL https://web.archive.org/web/*/https://core.ac.uk/download/pdf/42803258.pdf APACrefURL NACA Tech. Note 2234

    work page arXiv 1950

  75. [75]

    , Mehlig, B

    Li_et_al_2022 APACrefauthors Li, X Y. , Mehlig, B. , Svensson, G. , Brandenburg, A. \ Haugen, N E L. APACrefauthors \ 2022 . Collision fluctuations of lucky droplets with superdroplets Collision fluctuations of lucky droplets with superdroplets . J. Atmos. Sci. . APACrefDOI doi:10.1175/JAS-D-20-0371.1 APACrefDOI

    work page doi:10.1175/jas-d-20-0371.1 2022

  76. [76]

    , van den Heever, S C

    Marinescu_et_al_2021 APACrefauthors Marinescu, P J. , van den Heever, S C. , Heikenfeld, M. , Barrett, A I. , Barthlott, C. , Hoose, C. Zhang, Y. APACrefauthors \ 2021 . Impacts of Varying Concentrations of Cloud Condensation Nuclei on Deep Convective Cloud Updrafts—A Multimodel Assessment Impacts of varying concentrations of cloud condensation nuclei on ...

    work page doi:10.1175/jas-d-20-0200.1 2021

  77. [77]

    APACrefauthors \ 1961

    Marshall_1961 APACrefauthors Marshall, J. APACrefauthors \ 1961 . Heterogeneous nucleations is a stochastic process Heterogeneous nucleations is a stochastic process . Nubila: rivista di fisica delle nubi 4 . APACrefURL https://web.archive.org/web/*/https://cma.entecra.it/Astro2_sito/doc/Nubila_1_1961.pdf APACrefURL

    work page 1961

  78. [78]

    , Nishizawa, S

    Matsushima_et_al_2023 APACrefauthors Matsushima, T. , Nishizawa, S. \ Shima, S. APACrefauthors \ 2023 . Overcoming computational challenges to realize meter- to submeter-scale resolution in cloud simulations using the super-droplet method Overcoming computational challenges to realize meter- to submeter-scale resolution in cloud simulations using the supe...

    work page doi:10.5194/gmd-16-6211-2023 2023

  79. [79]

    \ Corrsin, S

    Maxey_and_Corrsin_1986 APACrefauthors Maxey, M. \ Corrsin, S. APACrefauthors \ 1986 . Gravitational Settling of Aerosol Particles in Randomly Oriented Cellular Flow Fields Gravitational settling of aerosol particles in randomly oriented cellular flow fields . J. Atmos. Sci. 43 . APACrefDOI doi:10.1175/1520-0469(1986)043<1112:GSOAPI>2.0.CO;2 APACrefDOI

    work page doi:10.1175/1520-0469(1986)043 1986

  80. [80]

    APACrefauthors \ 1967

    Michel_1967 APACrefauthors Michel, B. APACrefauthors \ 1967 . From the Nucleation of Ice Crystals in Clouds to the Formation of Frazil Ice in Rivers From the nucleation of ice crystals in clouds to the formation of frazil ice in rivers . International Conference on Low Temperature Science, 1966, Sapporo, Japan. International conference on low temperature ...

    work page 1967

Showing first 80 references.