\begin{thebibliography}{}

\bibitem[B{\"o}ing et~al., 2012]{boing2012}
B{\"o}ing, S.~J., Jonker, H.~J., Siebesma, A.~P., and Grabowski, W.~W. (2012).
\newblock Influence of the subcloud layer on the development of a deep
  convective ensemble.
\newblock {\em Journal of the Atmospheric Sciences}, 69(9):2682--2698.

\bibitem[Boucher et~al., 2020]{boucher2020}
Boucher, O., Denvil, S., Levavasseur, G., Cozic, A., Caubel, A., Foujols,
  M.-A., Meurdesoif, Y., Balkanski, Y., Checa-Garcia, R., Hauglustaine, D.,
  et~al. (2020).
\newblock Ipsl ipsl-cm6a-lr-inca model output prepared for cmip6 rfmip
  piclim-aer.

\bibitem[Brown et~al., 2002]{brown2002}
Brown, A., Cederwall, R.~T., Chlond, A., Duynkerke, P.~G., Golaz, J.-C.,
  Khairoutdinov, M., Lewellen, D., Lock, A., MacVean, M., Moeng, C.-H., et~al.
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\newblock Large-eddy simulation of the diurnal cycle of shallow cumulus
  convection over land.
\newblock {\em Quarterly Journal of the Royal Meteorological Society: A journal
  of the atmospheric sciences, applied meteorology and physical oceanography},
  128(582):1075--1093.

\bibitem[Bryan, 2005]{bryan2005}
Bryan, G.~H. (2005).
\newblock Spurious convective organization in simulated squall lines owing to
  moist absolutely unstable layers.
\newblock {\em Monthly weather review}, 133(7):1978--1997.

\bibitem[Couvreux et~al., 2021]{couvreux2021}
Couvreux, F., Hourdin, F., Williamson, D., Roehrig, R., Volodina, V.,
  Villefranque, N., Rio, C., Audouin, O., Salter, J., Bazile, E., et~al.
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\newblock Process-based climate model development harnessing machine learning:
  I. a calibration tool for parameterization improvement.
\newblock {\em Journal of Advances in Modeling Earth Systems},
  13(3):e2020MS002217.

\bibitem[Couvreux et~al., 2012]{couvreux2012}
Couvreux, F., Rio, C., Guichard, F., Lothon, M., Canut, G., Bouniol, D., and
  Gounou, A. (2012).
\newblock Initiation of daytime local convection in a semi-arid region analysed
  with high-resolution simulations and amma observations.
\newblock {\em Quarterly Journal of the Royal Meteorological Society},
  138(662):56--71.

\bibitem[Daleu et~al., 2015]{daleu2015}
Daleu, C.~L., Plant, R., Woolnough, S.~J., Sessions, S., Herman, M., Sobel, A.,
  Wang, S., Kim, D., Cheng, A., Bellon, G., et~al. (2015).
\newblock Intercomparison of methods of coupling between convection and
  large-scale circulation: 1. comparison over uniform surface conditions.
\newblock {\em Journal of Advances in Modeling Earth Systems}, 7(4):1576--1601.

\bibitem[Diallo et~al., 2017]{diallo2017}
Diallo, F., Hourdin, F., Rio, C., Traore, A.-K., Mellul, L., Guichard, F., and
  Kergoat, L. (2017).
\newblock The surface energy budget computed at the grid-scale of a climate
  model challenged by station data in west africa.
\newblock {\em Journal of Advances in Modeling Earth Systems}, 9(7):2710--2738.

\bibitem[Dirmeyer et~al., 2012]{dirmeyer2012}
Dirmeyer, P.~A., Cash, B.~A., Kinter, J.~L., Jung, T., Marx, L., Satoh, M.,
  Stan, C., Tomita, H., Towers, P., Wedi, N., et~al. (2012).
\newblock Simulating the diurnal cycle of rainfall in global climate models:
  Resolution versus parameterization.
\newblock {\em Climate dynamics}, 39:399--418.

\bibitem[Dorrestijn et~al., 2013]{dorrestijn2013}
Dorrestijn, J., Crommelin, D.~T., Siebesma, A.~P., and Jonker, H.~J. (2013).
\newblock Stochastic parameterization of shallow cumulus convection estimated
  from high-resolution model data.
\newblock {\em Theoretical and Computational Fluid Dynamics}, 27:133--148.

\bibitem[Emanuel, 1991]{emanuel1991}
Emanuel, K.~A. (1991).
\newblock A scheme for representing cumulus convection in large-scale models.
\newblock {\em Journal of Atmospheric Sciences}, 48(21):2313--2329.

\bibitem[Feng et~al., 2015]{feng2015}
Feng, Z., Hagos, S., Rowe, A.~K., Burleyson, C.~D., Martini, M.~N., and
  de~Szoeke, S.~P. (2015).
\newblock Mechanisms of convective cloud organization by cold pools over
  tropical warm ocean during the amie/dynamo field campaign.
\newblock {\em Journal of Advances in Modeling Earth Systems}, 7(2):357--381.

\bibitem[Grandpeix and Lafore, 2010]{GL10I}
Grandpeix, J.-Y. and Lafore, J.-P. (2010).
\newblock A density current parameterization coupled with emanuel’s
  convection scheme. part i: The models.
\newblock {\em Journal of the Atmospheric Sciences}, 67(4):881--897.

\bibitem[Grandpeix et~al., 2010]{GL10II}
Grandpeix, J.-Y., Lafore, J.-P., and Cheruy, F. (2010).
\newblock A density current parameterization coupled with emanuel’s
  convection scheme. part ii: 1d simulations.
\newblock {\em Journal of the Atmospheric Sciences}, 67(4):898--922.

\bibitem[Grandpeix et~al., 2004]{grandpeix2004}
Grandpeix, J.-Y., Phillips, V., and Tailleux, R. (2004).
\newblock Improved mixing representation in emanuel's convection scheme.
\newblock {\em Quarterly Journal of the Royal Meteorological Society: A journal
  of the atmospheric sciences, applied meteorology and physical oceanography},
  130(604):3207--3222.

\bibitem[Grant et~al., 2018]{grant2018}
Grant, L.~D., Lane, T.~P., and van~den Heever, S.~C. (2018).
\newblock The role of cold pools in tropical oceanic convective systems.
\newblock {\em Journal of the Atmospheric Sciences}, 75(8):2615--2634.

\bibitem[Guichard et~al., 2004]{guichard2004}
Guichard, F., Petch, J., Redelsperger, J.-L., Bechtold, P., Chaboureau, J.-P.,
  Cheinet, S., Grabowski, W., Grenier, H., Jones, C., K{\"o}hler, M., et~al.
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\newblock Modelling the diurnal cycle of deep precipitating convection over
  land with cloud-resolving models and single-column models.
\newblock {\em Quarterly Journal of the Royal Meteorological Society: A journal
  of the atmospheric sciences, applied meteorology and physical oceanography},
  130(604):3139--3172.

\bibitem[Haerter and Schlemmer, 2018]{haerter2018}
Haerter, J.~O. and Schlemmer, L. (2018).
\newblock Intensified cold pool dynamics under stronger surface heating.
\newblock {\em Geophysical Research Letters}, 45(12):6299--6310.

\bibitem[Hourdin et~al., 2002]{hourdin2002}
Hourdin, F., Couvreux, F., and Menut, L. (2002).
\newblock Parameterisation of the dry convective boundary layer based on a mass
  flux representation of thermals.
\newblock {\em Journal of the Atmospheric Sciences}, 59:1105--1123.

\bibitem[Hourdin et~al., 2013]{hourdin2013}
Hourdin, F., Foujols, M.-A., Codron, F., Guemas, V., Dufresne, J.-L., Bony, S.,
  Denvil, S., Guez, L., Lott, F., Ghattas, J., et~al. (2013).
\newblock Impact of the lmdz atmospheric grid configuration on the climate and
  sensitivity of the ipsl-cm5a coupled model.
\newblock {\em Climate Dynamics}, 40:2167--2192.

\bibitem[{Hourdin} et~al., 2019]{hourdin2019}
{Hourdin}, F., {Jam}, A., {Rio}, C., {Couvreux}, F., {Sandu}, I., {Lefebvre},
  M.-P., {Brient}, F., and {Idelkadi}, A. (2019).
\newblock {Unified Parameterization of Convective Boundary Layer Transport and
  Clouds With the Thermal Plume Model}.

\bibitem[Hourdin et~al., 2006]{hourdin2006}
Hourdin, F., Musat, I., Bony, S., Braconnot, P., Codron, F., Dufresne, J.-L.,
  Fairhead, L., Filiberti, M.-A., Friedlingstein, P., Grandpeix, J.-Y., et~al.
  (2006).
\newblock The lmdz4 general circulation model: climate performance and
  sensitivity to parametrized physics with emphasis on tropical convection.
\newblock {\em Climate Dynamics}, 27:787--813.

\bibitem[Hourdin et~al., 2020]{Hourdin2020}
Hourdin, F., Rio, C., Grandpeix, J.-Y., Madeleine, J.-B., Cheruy, F., Rochetin,
  N., Jam, A., Musat, I., Idelkadi, A., Fairhead, L., et~al. (2020).
\newblock Lmdz6a: The atmospheric component of the ipsl climate model with
  improved and better tuned physics.
\newblock {\em Journal of Advances in Modeling Earth Systems},
  12(7):e2019MS001892.

\bibitem[{Hourdin} et~al., 2020]{hourdin2020etoa}
{Hourdin}, F., {Rio}, C., {Jam}, A., {Traore}, A.-K., and {Musat}, I. (2020).
\newblock {Convective Boundary Layer Control of the Sea Surface Temperature in
  the Tropics}.
\newblock {\em J. of Adv. in Modeling Earth Systems}, 12(6):e01988.

\bibitem[Hourdin et~al., 2021]{hourdin2021}
Hourdin, F., Williamson, D., Rio, C., Couvreux, F., Roehrig, R., Villefranque,
  N., Musat, I., Fairhead, L., Diallo, F.~B., and Volodina, V. (2021).
\newblock Process-based climate model development harnessing machine learning:
  Ii. model calibration from single column to global.
\newblock {\em Journal of Advances in Modeling Earth Systems},
  13(6):e2020MS002225.

\bibitem[{Jam} et~al., 2013]{jam2013}
{Jam}, A., {Hourdin}, F., {Rio}, C., and {Couvreux}, F. (2013).
\newblock {Resolved Versus Parametrized Boundary-Layer Plumes. Part III:
  Derivation of a Statistical Scheme for Cumulus Clouds}.
\newblock 147:421--441.

\bibitem[Jeevanjee and Romps, 2013]{jeevanjee2013}
Jeevanjee, N. and Romps, D.~M. (2013).
\newblock Convective self-aggregation, cold pools, and domain size.
\newblock {\em Geophysical Research Letters}, 40(5):994--998.

\bibitem[Kendon et~al., 2012]{kendon2012}
Kendon, E.~J., Roberts, N.~M., Senior, C.~A., and Roberts, M.~J. (2012).
\newblock Realism of rainfall in a very high-resolution regional climate model.
\newblock {\em Journal of Climate}, 25(17):5791--5806.

\bibitem[Khairoutdinov and Randall, 2006]{khairoutdinov2006}
Khairoutdinov, M. and Randall, D. (2006).
\newblock High-resolution simulation of shallow-to-deep convection transition
  over land.
\newblock {\em Journal of the atmospheric sciences}, 63(12):3421--3436.

\bibitem[Khairoutdinov and Randall, 2003]{khairoutdinov2003}
Khairoutdinov, M.~F. and Randall, D.~A. (2003).
\newblock Cloud resolving modeling of the arm summer 1997 iop: Model
  formulation, results, uncertainties, and sensitivities.
\newblock {\em Journal of the Atmospheric Sciences}, 60(4):607--625.

\bibitem[Kurowski et~al., 2018]{kurowski2018}
Kurowski, M.~J., Suselj, K., Grabowski, W.~W., and Teixeira, J. (2018).
\newblock Shallow-to-deep transition of continental moist convection: Cold
  pools, surface fluxes, and mesoscale organization.
\newblock {\em Journal of the Atmospheric Sciences}, 75(12):4071--4090.

\bibitem[Lac et~al., 2018]{lac2018}
Lac, C., Chaboureau, J.-P., Masson, V., Pinty, J.-P., Tulet, P., Escobar, J.,
  Leriche, M., Barthe, C., Aouizerats, B., Augros, C., et~al. (2018).
\newblock Overview of the meso-nh model version 5.4 and its applications.
\newblock {\em Geoscientific Model Development}, 11(5):1929--1969.

\bibitem[Lafore and Moncrieff, 1989]{lafore1989}
Lafore, J.-P. and Moncrieff, M.~W. (1989).
\newblock A numerical investigation of the organization and interaction of the
  convective and stratiform regions of tropical squall lines.
\newblock {\em Journal of Atmospheric Sciences}, 46(4):521--544.

\bibitem[Legay et~al., 2025]{legay2025}
Legay, A., Deremble, B., and Burchard, H. (2025).
\newblock Derivation and implementation of a non-local term to improve the
  oceanic convection representation within the k--$\epsilon$ parameterization.
\newblock {\em Journal of Advances in Modeling Earth Systems},
  17(1):e2024MS004243.

\bibitem[Lothon et~al., 2011]{lothon2011}
Lothon, M., Campistron, B., Chong, M., Couvreux, F., Guichard, F., Rio, C., and
  Williams, E. (2011).
\newblock Life cycle of a mesoscale circular gust front observed by a c-band
  doppler radar in west africa.
\newblock {\em Monthly weather review}, 139(5):1370--1388.

\bibitem[Meyer and Haerter, 2020]{meyer2020}
Meyer, B. and Haerter, J.~O. (2020).
\newblock Mechanical forcing of convection by cold pools: Collisions and energy
  scaling.
\newblock {\em Journal of Advances in Modeling Earth Systems},
  12(11):e2020MS002281.

\bibitem[Pantillon et~al., 2015]{pantillon2015}
Pantillon, F., Knippertz, P., Marsham, J.~H., and Birch, C.~E. (2015).
\newblock A parameterization of convective dust storms for models with
  mass-flux convection schemes.
\newblock {\em Journal of the Atmospheric Sciences}, 72(6):2545--2561.

\bibitem[Provod et~al., 2016]{provod2016}
Provod, M., Marsham, J., Parker, D., and Birch, C. (2016).
\newblock A characterization of cold pools in the west african sahel.
\newblock {\em Monthly Weather Review}, 144(5):1923--1934.

\bibitem[Qian et~al., 1998]{qian1998}
Qian, L., Young, G.~S., and Frank, W.~M. (1998).
\newblock A convective wake parameterization scheme for use in general
  circulation models.
\newblock {\em Monthly weather review}, 126(2):456--469.

\bibitem[Randall et~al., 2003]{randall2003}
Randall, D., Khairoutdinov, M., Arakawa, A., and Grabowski, W. (2003).
\newblock Breaking the cloud parameterization deadlock.
\newblock {\em Bulletin of the American Meteorological Society},
  84(11):1547--1564.

\bibitem[Redelsperger et~al., 2006]{redelsperger2006}
Redelsperger, J.-L., Diedhiou, A., Flamant, C., Janicot, S., Lafore, J.-P.,
  Lebel, T., Polcher, J., Bourl{\`e}s, B., Caniaux, G., de~Rosnay, P., et~al.
  (2006).
\newblock Amma, une {\'e}tude multidisciplinaire de la mousson ouest-africaine.
\newblock {\em La meteorologie}, 54:22--32.

\bibitem[Rio and Hourdin, 2008]{rio2008}
Rio, C. and Hourdin, F. (2008).
\newblock A thermal plume model for the convective boundary layer:
  Representation of cumulus clouds.
\newblock {\em Journal of the atmospheric sciences}, 65(2):407--425.

\bibitem[Rio et~al., 2010]{rio2010}
Rio, C., Hourdin, F., Couvreux, F., and Jam, A. (2010).
\newblock Resolved versus parametrized boundary-layer plumes. part ii:
  continuous formulations of mixing rates for mass-flux schemes.
\newblock {\em Boundary-layer meteorology}, 135:469--483.

\bibitem[Rio et~al., 2009]{rio2009}
Rio, C., Hourdin, F., Grandpeix, J.-Y., and Lafore, J.-P. (2009).
\newblock Shifting the diurnal cycle of parameterized deep convection over
  land.
\newblock {\em Geophysical Research Letters}, 36(7).

\bibitem[Rochetin et~al., 2014]{rochetin2014}
Rochetin, N., Grandpeix, J.-Y., Rio, C., and Couvreux, F. (2014).
\newblock Deep convection triggering by boundary layer thermals. part ii:
  Stochastic triggering parameterization for the lmdz gcm.
\newblock {\em Journal of the Atmospheric Sciences}, 71(2):515--538.

\bibitem[Rochetin et~al., 2021]{rochetin2021}
Rochetin, N., Hohenegger, C., Touz{\'e}-Peiffer, L., and Villefranque, N.
  (2021).
\newblock A physically based definition of convectively generated density
  currents: Detection and characterization in convection-permitting
  simulations.
\newblock {\em Journal of Advances in Modeling Earth Systems},
  13(7):e2020MS002402.

\bibitem[Rotunno et~al., 1988]{rotunno1988}
Rotunno, R., Klemp, J.~B., and Weisman, M.~L. (1988).
\newblock A theory for strong, long-lived squall lines.
\newblock {\em Journal of Atmospheric Sciences}, 45(3):463--485.

\bibitem[Sadourny, 1984]{sadourny1984}
Sadourny, R. (1984).
\newblock January and july performances of the lmd general circulation model.
\newblock {\em New perspectives in climate modeling}.

\bibitem[Siebesma et~al., 2003]{siebesma2003}
Siebesma, A.~P., Bretherton, C.~S., Brown, A., Chlond, A., Cuxart, J.,
  Duynkerke, P.~G., Jiang, H., Khairoutdinov, M., Lewellen, D., Moeng, C.-H.,
  et~al. (2003).
\newblock A large eddy simulation intercomparison study of shallow cumulus
  convection.
\newblock {\em Journal of the Atmospheric Sciences}, 60(10):1201--1219.

\bibitem[Stephens et~al., 2010]{stephens2010}
Stephens, G.~L., L'Ecuyer, T., Forbes, R., Gettelmen, A., Golaz, J.-C.,
  Bodas-Salcedo, A., Suzuki, K., Gabriel, P., and Haynes, J. (2010).
\newblock Dreary state of precipitation in global models.
\newblock {\em Journal of Geophysical Research: Atmospheres}, 115(D24).

\bibitem[Strauss et~al., 2019]{strauss2019}
Strauss, C., Ricard, D., Lac, C., and Verrelle, A. (2019).
\newblock Evaluation of turbulence parametrizations in convective clouds and
  their environment based on a large-eddy simulation.
\newblock {\em Quarterly Journal of the Royal Meteorological Society},
  145(724):3195--3217.

\bibitem[Tan et~al., 2018]{tan2018}
Tan, J., Oreopoulos, L., Jakob, C., and Jin, D. (2018).
\newblock Evaluating rainfall errors in global climate models through cloud
  regimes.
\newblock {\em Climate Dynamics}, 50:3301--3314.

\bibitem[Tompkins, 2001]{tompkins2001}
Tompkins, A.~M. (2001).
\newblock Organization of tropical convection in low vertical wind shears: The
  role of cold pools.
\newblock {\em Journal of the atmospheric sciences}, 58(13):1650--1672.

\bibitem[Torri and Kuang, 2019]{torri2019}
Torri, G. and Kuang, Z. (2019).
\newblock On cold pool collisions in tropical boundary layers.
\newblock {\em Geophysical Research Letters}, 46(1):399--407.

\bibitem[Touz{\'e}-Peiffer et~al., 2022]{touze2022}
Touz{\'e}-Peiffer, L., Vogel, R., and Rochetin, N. (2022).
\newblock Cold pools observed during eurec 4 a: Detection and characterization
  from atmospheric soundings.
\newblock {\em Journal of Applied Meteorology and Climatology}, 61(5):593--610.

\bibitem[Vogel et~al., 2021]{vogel2021}
Vogel, R., Konow, H., Schulz, H., and Zuidema, P. (2021).
\newblock A climatology of trade-wind cumulus cold pools and their link to
  mesoscale cloud organization.
\newblock {\em Atmospheric Chemistry and Physics}, 21(21):16609--16630.

\bibitem[Weisman and Rotunno, 2004]{weisman2004}
Weisman, M.~L. and Rotunno, R. (2004).
\newblock “a theory for strong long-lived squall lines” revisited.
\newblock {\em Journal of the Atmospheric Sciences}, 61(4):361--382.

\bibitem[Williamson et~al., 2013]{williamson2013}
Williamson, D., Goldstein, M., Allison, L., Blaker, A., Challenor, P., Jackson,
  L., and Yamazaki, K. (2013).
\newblock History matching for exploring and reducing climate model parameter
  space using observations and a large perturbed physics ensemble.
\newblock {\em Climate dynamics}, 41:1703--1729.

\bibitem[Yamada, 1983]{yamada1983}
Yamada, T. (1983).
\newblock Simulations of nocturnal drainage flows by a $q^2l$ turbulence
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\newblock 40:91--106.

\bibitem[Young et~al., 1995]{young1995}
Young, G.~S., Perugini, S.~M., and Fairall, C. (1995).
\newblock Convective wakes in the equatorial western pacific during toga.
\newblock {\em Monthly Weather Review}, 123(1):110--123.

\bibitem[Zuidema et~al., 2017]{zuidema2017}
Zuidema, P., Torri, G., Muller, C., and Chandra, A. (2017).
\newblock A survey of precipitation-induced atmospheric cold pools over oceans
  and their interactions with the larger-scale environment.
\newblock {\em Surveys in Geophysics}, 38(6):1283--1305.

\end{thebibliography}
