- Invited
- Access by Xinjiang University
Framework for idealized climate simulations with spatiotemporal stochastic clouds and planetary-scale circulations
Phys. Rev. Fluids 7, 010502 – Published 20 January, 2022
DOI: https://doi.org/10.1103/PhysRevFluids.7.010502
Abstract
In climate predictions, clouds are the leading source of uncertainty. This is partly because, to simulate the fluid dynamics of climate over the entire globe, a large grid spacing must be used, so clouds are a subgrid-scale parametrization rather than a resolved feature. Here, a framework is investigated with finer grid spacing of or so that some clouds are not subgrid-scale; instead, clouds evolve on the numerical grid. This cloud evolution is achieved using stochastic modeling. Hence, the framework is idealized in the sense that the full fluid dynamics of cloud circulations is still not resolved, and simplified vertical structures are used. Nevertheless, the fluid dynamics model includes evolving clouds that interactively adjust in size, shape, lifetime, and regional coverage. In addition, different cloud types are included with different roles in the climate system, including deep convective clouds and also boundary-layer clouds such as shallow cumulus and stratocumulus clouds. Other basic aspects of the idealized climate system are planetary-scale circulations (e.g., Walker circulation) and radiation. With these ingredients (evolving clouds, planetary-scale circulations, and radiation), the framework has the potential for idealized investigations of climate change with interactive cloud–radiative feedback of individual clouds. Here, the formulation of the model equations is presented, and numerical simulations are shown to illustrate the model dynamics and climate change.
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Cloud Physics Invited Papers
Physical Review Fluids publishes a collection of papers associated with invited talks presented at the mini-symposium on the Cloud Physics at the 73rd Annual Meeting of the APS Division of Fluid Dynamics.
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References (67)
- G. W. Petty, A First Course in Atmospheric Radiation (Sundog Pub, Madison, WI, 2006).
- J. D. Neelin, Climate Change and Climate Modeling (Cambridge University Press, New York, NY, 2010).
- IPCC, Climate Change 2013: The Physical Science Basis. Working Group I Contribution to the Fifth Assessment Report of the Intergovernmental Panel on Climate Change, edited by T. Stocker, D. Qin, M. Plattner, G.-K. Tignor, S. Allen, J. Boschung, A. Nauels, Y. Xia, B. Bex, and P. Midgley (Cambridge University Press, New York, NY, 2013).
- R. D. Cess, G. L. Potter, J. P. Blanchet, G. J. Boer, A. D. Del Genio, M. Deque, V. Dymnikov, V. Galin, W. L. Gates, S. J. Ghan et al., Intercomparison and interpretation of climate feedback processes in 19 atmospheric general circulation models, J. Geophys. Res. 95, 16601 (1990).
- G. L. Stephens, Cloud feedbacks in the climate system: A critical review, J. Climate 18, 237 (2005).
- S. Bony and J. Dufresne, Marine boundary layer clouds at the heart of tropical cloud feedback uncertainties in climate models, Geophys. Res. Lett. 32, L20806 (2005).
- S. Bony, B. Stevens, D. M. Frierson, C. Jakob, M. Kageyama, R. Pincus, T. G. Shepherd, S. C. Sherwood, A. P. Siebesma, A. H. Sobel et al., Clouds, circulation and climate sensitivity, Nat. Geosci. 8, 261 (2015).
- B. Stevens, Atmospheric moist convection, Annu. Rev. Earth Planet. Sci. 33, 605 (2005).
- B. Stevens, C.-H. Moeng, A. S. Ackerman, C. S. Bretherton, A. Chlond, S. de Roode, J. Edwards, J.-C. Golaz, H. Jiang, M. Khairoutdinov et al., Evaluation of large-eddy simulations via observations of nocturnal marine stratocumulus, Mon. Weather Rev. 133, 1443 (2005).
- S. N. Stechmann, Multiscale eddy simulation for moist atmospheric convection: Preliminary investigation, J. Comput. Phys. 271, 99 (2014).
- G. Matheou, D. Chung, and J. Teixeira, Large-eddy simulation of a stratocumulus cloud, Phys. Rev. Fluids 2, 090509 (2017).
- J. P. Mellado, Cloud-top entrainment in stratocumulus clouds, Annu. Rev. Fluid Mech. 49, 145 (2017).
- S. N. Stechmann and H. R. Ogrosky, The Walker circulation, diabatic heating, and outgoing longwave radiation, Geophys. Res. Lett. 41, 9097 (2014).
- E.-S. Chung, A. Timmermann, B. J. Soden, K.-J. Ha, L. Shi, and V. O. John, Reconciling opposing walker circulation trends in observations and model projections, Nat. Clim. Change 9, 405 (2019).
- C. J. Muller, P. A. O'Gorman, and L. E. Back, Intensification of precipitation extremes with warming in a cloud-resolving model, J. Clim. 24, 2784 (2011).
- D. M. Romps, Response of tropical precipitation to global warming, J. Atmos. Sci. 68, 123 (2011).
- M. Khairoutdinov and C.-E. Yang, Cloud-resolving modelling of aerosol indirect effects in idealised radiative-convective equilibrium with interactive and fixed sea surface temperature, Atmos. Chem. Phys. 13, 4133 (2013).
- C. Muller and Y. Takayabu, Response of precipitation extremes to warming: What have we learned from theory and idealized cloud-resolving simulations, and what remains to be learned? Environ. Res. Lett. 15, 035001 (2020).
- C. S. Bretherton, Challenges in numerical modeling of tropical circulations, in The Global Circulation of the Atmosphere, edited by T. Schneider and A. H. Sobel (Princeton University Press, Princeton, NJ, 2007), Chap. 11, pp. 302–330.
- W. W. Grabowski and P. K. Smolarkiewicz, CRCP: A Cloud Resolving Convection Parameterization for modeling the tropical convecting atmosphere, Physica D 133, 171 (1999).
- S. Hottovy and S. N. Stechmann, A spatiotemporal stochastic model for tropical precipitation and water vapor dynamics, J. Atmos. Sci. 72, 4721 (2015).
- S. N. Stechmann and S. Hottovy, Cloud regimes as phase transitions, Geophys. Res. Lett. 43, 6579 (2016).
- F. Ahmed and J. D. Neelin, Explaining scales and statistics of tropical precipitation clusters with a stochastic model, J. Atmos. Sci. 76, 3063 (2019).
- B. Khouider and A. Bihlo, A new stochastic model for the boundary layer clouds and stratocumulus phase transition regimes: Open cells, closed cells, and convective rolls, J. Geophys. Res. Atmos. 124, 367 (2019).
- D. L. Monroy and G. G. Naumis, Description of mesoscale pattern formation in shallow convective cloud fields by using time-dependent ginzburg-landau and Swift-Hohenberg stochastic equations, Phys. Rev. E 103, 032312 (2021).
- J. D. Neelin and N. Zeng, A quasiequilibrium tropical circulation model—formulation, J. Atmos. Sci. 57, 1741 (2000).
- J. Wei-Bing Lin and J. Neelin, Influence of a stochastic moist convective parameterization on tropical climate variability, Geophys. Res. Lett. 27, 3691 (2000).
- B. Khouider and A. J. Majda, A nonoscillatory balanced scheme for an idealized tropical climate model: Part I: Algorithm and validation, Theor. Comput. Fluid Dyn. 19, 331 (2005).
- B. Khouider and A. J. Majda, Multicloud convective parameterizations with crude vertical structure, Theor. Comput. Fluid Dyn. 20, 351 (2006).
- J. Biello, B. Khouider, and A. J. Majda, A stochastic multicloud model for tropical convection, Commun. Math. Sci. 8, 187 (2010).
- Y. Frenkel, A. J. Majda, and S. N. Stechmann, Cloud-radiation feedback and atmosphere-ocean coupling in a stochastic multicloud model, Dyn. Atmos. Oceans 71, 35 (2015).
- Y. Chen and S. N. Stechmann, Multi-model communication and data assimilation for mitigating model error and improving forecasts, Chin. Ann. Math. Ser. B 40, 689 (2019).
- A. J. Majda, in Introduction to PDEs and Waves for the Atmosphere and Ocean, Courant Lecture Notes in Mathematics Vol. 9 (American Mathematical Society, Providence, RI, 2003), pp. x+234.
- S. N. Stechmann, A. J. Majda, and B. Khouider, Nonlinear dynamics of hydrostatic internal gravity waves, Theor. Comput. Fluid Dyn. 22, 407 (2008).
- M. A. Kelly and D. A. Randall, A two-box model of a zonal atmospheric circulation in the tropics, J. Climate 14, 3944 (2001).
- E. A. Mueller and S. N. Stechmann, Shallow-cloud impact on climate and uncertainty: A simple stochastic model, Math. Climate Weather Forecast. 6, 16 (2020).
- R. Marchand and T. Ackerman, A cloud-resolving model with an adaptive vertical grid for boundary layer clouds, J. Atmos. Sci. 68, 1058 (2011).
- W. W. Grabowski, Towards global large eddy simulation: Super-parameterization revisited, J. Meteorol. Soc. Jpn. 94, 327 (2016).
- H. Parishani, M. S. Pritchard, C. S. Bretherton, M. C. Wyant, and M. Khairoutdinov, Toward low-cloud-permitting cloud superparameterization with explicit boundary layer turbulence, J. Adv. Model. Earth Syst. 9, 1542 (2017).
- D. H. Marsico and S. N. Stechmann, Expanding grids for efficient cloud dynamics simulations across scales, Math. Climate Weather Forecast. 6, 38 (2020).
- M. L. Waite and B. Khouider, Boundary layer dynamics in a simple model for convectively coupled gravity waves, J. Atmos. Sci. 66, 2780 (2009).
- J. A. Biello and A. J. Majda, Boundary layer dissipation and the nonlinear interaction of equatorial baroclinic and barotropic Rossby waves, Geophys. Astrophys. Fluid Dynam. 98, 85 (2004).
- R. Neggers, B. Stevens, and J. Neelin, A simple equilibrium model for shallow-cumulus-topped mixed layers, Theor. Comput. Fluid Dyn. 20, 305 (2006).
- A. H. Sobel and J. D. Neelin, The boundary layer contribution to intertropical convergence zones in the quasiequilibrium tropical circulation model framework, Theor. Comput. Fluid Dyn. 20, 323 (2006).
- B. Stevens, Bulk boundary-layer concepts for simplified models of tropical dynamics, Theor. Comput. Fluid Dyn. 20, 279 (2006).
- S. N. Stechmann and S. Hottovy, Unified spectrum of tropical rainfall and waves in a simple stochastic model, Geophys. Res. Lett. 44, 10,713 (2017).
- N. A. Phillips, Energy transformations and meridional circulations associated with simple baroclinic waves in a two-level, quasigeostrophic model, Tellus 6, 273 (1954).
- N. A. Phillips, The general circulation of the atmosphere: A numerical experiment, Q. J. R. Meteorol. Soc. 82, 123 (1956).
- I. M. Held, The gap between simulation and understanding in climate modeling, Bull. Am. Meteorol. Soc. 86, 1609 (2005).
- G. Vallis, Atmospheric and Oceanic Fluid Dynamics: Fundamentals and Large-scale Circulation (Cambridge University Press, New York, NY, 2006).
- R. Hu, T. K. Edwards, L. M. Smith, and S. N. Stechmann, Initial investigations of precipitating quasigeostrophic turbulence with phase changes, Res. Math. Sci. 8, 6 (2021).
- B. E. Mapes and R. A. Houze Jr., Diabatic divergence profiles in western Pacific mesoscale convective systems, J. Atmos. Sci. 52, 1807 (1995).
- G. N. Kiladis, M. C. Wheeler, P. T. Haertel, K. H. Straub, and P. E. Roundy, Convectively coupled equatorial waves, Rev. Geophys. 47, RG2003 (2009).
- R. Rogers and M. Yau, A Short Course in Cloud Physics (Butterworth–Heinemann, Burlington, 1989).
- J. D. Neelin, O. Peters, and K. Hales, The transition to strong convection, J. Atmos. Sci. 66, 2367 (2009).
- R. Salmon, Lectures on Geophysical Fluid Dynamics (Oxford University Press, New York, NY, 1998).
- A. J. Majda and P. R. Kramer, Simplified models for turbulent diffusion: Theory, numerical modelling, and physical phenomena, Phys. Rep. 314, 237 (1999).
- T. DelSole, Stochastic models of quasigeostrophic turbulence, Surv. Geophys. 25, 107 (2004).
- A. J. Majda and M. J. Grote, Explicit off-line criteria for stable accurate time filtering of strongly unstable spatially extended systems, Proc. Natl. Acad. Sci. USA 104, 1124 (2007).
- A. J. Majda and M. J. Grote, Mathematical test models for superparametrization in anisotropic turbulence, Proc. Natl. Acad. Sci. USA 106, 5470 (2009).
- W. W. Grabowski and P. K. Smolarkiewicz, Two-time-level semi-Lagrangian modeling of precipitating clouds, Mon. Weather Rev. 124, 487 (1996).
- M. E. Peters and C. S. Bretherton, A simplified model of the Walker circulation with an interactive ocean mixed layer and cloud–radiative feedbacks, J. Climate 18, 4216 (2005).
- C. W. Gardiner, Handbook of Stochastic Methods: For Physics, Chemistry & the Natural Sciences, Springer Series in Synergetics Vol. 13 (Springer–Verlag, Berlin, 2004).
- J. L. Torchinsky and S. N. Stechmann, EZ Parallel version 1.0, Github Repository (2020).
- O. Peters, J. D. Neelin, and S. W. Nesbitt, Mesoscale convective systems and critical clusters, J. Atmos. Sci. 66, 2913 (2009).
- G. A. Vecchi, B. J. Soden, A. T. Wittenberg, I. M. Held, A. Leetmaa, and M. J. Harrison, Weakening of tropical Pacific atmospheric circulation due to anthropogenic forcing, Nature (London) 441, 73 (2006).
- M. L. L'Heureux, S. Lee, and B. Lyon, Recent multidecadal strengthening of the Walker circulation across the tropical Pacific, Nat. Clim. Change 3, 571 (2013).