• Bister, M., and K. A. Emanuel, 1998: Dissipative heating and hurricane intensity. Meteor. Atmos. Phys., 65, 233240, https://doi.org/10.1007/BF01030791.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Bister, M., and K. A. Emanuel, 2002: Low frequency variability of tropical cyclone potential intensity 1. Interannual to interdecadal variability. J. Geophys. Res., 107, 4801, https://doi.org/10.1029/2001JD000776.

    • Search Google Scholar
    • Export Citation
  • Bryan, G. H., 2008: On the computation of pseudoadiabatic entropy and equivalent potential temperature. Mon. Wea. Rev., 136, 52395245, https://doi.org/10.1175/2008MWR2593.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Bryan, G. H., and R. Rotunno, 2009: Evaluation of an analytical model for the maximum intensity of tropical cyclones. J. Atmos. Sci., 66, 30423060, https://doi.org/10.1175/2009JAS3038.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Camargo, S. J., K. A. Emanuel, and A. H. Sobel, 2007: Use of a genesis potential index to diagnose ENSO effects on tropical cyclone genesis. J. Climate, 20, 48194834, https://doi.org/10.1175/JCLI4282.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Chavas, D. R., K. A. Reed, and J. A. Knaff, 2017: Physical understanding of the tropical cyclone wind-pressure relationship. Nat. Commun., 8, 1360, https://doi.org/10.1038/s41467-017-01546-9.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Cronin, T. W., and D. R. Chavas, 2019: Dry and semidry tropical cyclones. J. Atmos. Sci., 76, 21932212, https://doi.org/10.1175/JAS-D-18-0357.1.

    • Search Google Scholar
    • Export Citation
  • Emanuel, K. A., 1986: An air–sea interaction theory for tropical cyclones. Part I: Steady-state maintenance. J. Atmos. Sci., 43, 585605, https://doi.org/10.1175/1520-0469(1986)043<0585:AASITF>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Emanuel, K. A., 1987: The dependence of hurricane intensity on climate. Nature, 326, 483485, https://doi.org/10.1038/326483a0.

  • Emanuel, K. A., 1988a: The maximum intensity of hurricanes. J. Atmos. Sci., 45, 11431155, https://doi.org/10.1175/1520-0469(1988)045<1143:TMIOH>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Emanuel, K. A., 1988b: Observational evidence of slantwise convective adjustment. Mon. Wea. Rev., 116, 18051816, https://doi.org/10.1175/1520-0493(1988)116<1805:OEOSCA>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Emanuel, K. A., 1994: Atmospheric Convection. Oxford University Press, 580 pp.

  • Emanuel, K. A., 2003: Tropical cyclones. Annu. Rev. Earth Planet. Sci., 31, 75104, https://doi.org/10.1146/annurev.earth.31.100901.141259.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Emanuel, K. A., 2013: Downscaling CMIP5 climate models shows increased tropical cyclone activity over the 21st century. Proc. Natl. Acad. Sci. USA, 110, 12 21912 224, https://doi.org/10.1073/pnas.1301293110.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Emanuel, K. A., C. DesAutels, C. Holloway, and R. Korty, 2004: Environmental control of tropical cyclone intensity. J. Atmos. Sci., 61, 843858, https://doi.org/10.1175/1520-0469(2004)061<0843:ECOTCI>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Emanuel, K. A., R. Sundararajan, and J. Williams, 2008: Hurricanes and global warming: Results from downscaling IPCC AR4 simulations. Bull. Amer. Meteor. Soc., 89, 347368, https://doi.org/10.1175/BAMS-89-3-347.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Emanuel, K. A., S. Solomon, D. Folini, S. Davis, and C. Cagnazzo, 2013: Influence of tropical tropopause layer cooling on Atlantic hurricane activity. J. Climate, 26, 22882301, https://doi.org/10.1175/JCLI-D-12-00242.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Garner, S., 2015: The relationship between hurricane potential intensity and CAPE. J. Atmos. Sci., 72, 141163, https://doi.org/10.1175/JAS-D-14-0008.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Gilford, D. M., S. Solomon, and K. A. Emanuel, 2017: On the seasonal cycles of tropical cyclone potential intensity. J. Climate, 30, 60856096, https://doi.org/10.1175/JCLI-D-16-0827.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Hartmann, D. L., and K. Larson, 2002: An important constraint on tropical cloud-climate feedback. Geophys. Res. Lett., 29, 1951, https://doi.org/10.1029/2002GL015835.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Knutson, T. R., and R. E. Tuleya, 2004: Impact of CO2-induced warming on simulated hurricane intensity and precipitation: Sensitivity to the choice of climate model and convective parameterization. J. Climate, 17, 34773495, https://doi.org/10.1175/1520-0442(2004)017<3477:IOCWOS>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Knutson, T. R., and Coauthors, 2010: Tropical cyclones and climate change. Nat. Geosci., 3, 157163, https://doi.org/10.1038/ngeo779.

  • Merlis, T. M., and I. M. Held, 2019: Aquaplanet simulations of tropical cyclones. Curr. Climate Change Rep., 5, 185195, https://doi.org/10.1007/s40641-019-00133-y.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Merlis, T. M., W. Zhou, I. M. Held, and M. Zhao, 2016: Surface temperature dependence of tropical cyclone-permitting simulations in a spherical model with uniform thermal forcing. Geophys. Res. Lett., 43, 28592865, https://doi.org/10.1002/2016GL067730.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Nolan, D. S., E. D. Rappin, and K. A. Emanuel, 2007: Tropical cyclogenesis sensitivity to environmental parameters in radiative–convective equilibrium. Quart. J. Roy. Meteor. Soc., 133, 20852107, https://doi.org/10.1002/qj.170.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Persing, J., and M. T. Montgomery, 2003: Hurricane superintensity. J. Atmos. Sci., 60, 23492371, https://doi.org/10.1175/1520-0469(2003)060<2349:HS>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Ramsay, H. A., M. S. Singh, and D. R. Chavas, 2020: Response of tropical cyclone formation and intensification rates to climate warming in idealized simulations. J. Adv. Model. Earth Syst., 12, e2020MS002086, https://doi.org/10.1029/2020MS002086.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Richter, I., and S.-P. Xie, 2008: Muted precipitation increase in global warming simulations: A surface evaporation perspective. J. Geophys. Res., 113, D24118, https://doi.org/10.1029/2008JD010561.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Romps, D. M., 2014: An analytical model for tropical relative humidity. J. Climate, 27, 74327449, https://doi.org/10.1175/JCLI-D-14-00255.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Romps, D. M., 2016: Clausius–Clapeyron scaling of CAPE from analytical solutions to RCE. J. Atmos. Sci., 73, 37193737, https://doi.org/10.1175/JAS-D-15-0327.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Rousseau-Rizzi, R., and K. Emanuel, 2019: An evaluation of hurricane superintensity in axisymmetric numerical models. J. Atmos. Sci., 76, 16971708, https://doi.org/10.1175/JAS-D-18-0238.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Rousseau-Rizzi, R., and K. Emanuel, 2021: A weak temperature gradient framework to quantify the causes of potential intensity variability in the tropics. Climate, 34, 86698682, https://doi.org/10.1175/JCLI-D-21-0139.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Rousseau-Rizzi, R., R. Rotunno, and G. Bryan, 2021: A thermodynamic perspective on steady-state tropical cyclones. J. Atmos. Sci., 78, 583593, https://doi.org/10.1175/JAS-D-20-0140.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Seeley, J. T., and D. M. Romps, 2015: Why does tropical convective available potential energy (CAPE) increase with warming? Geophys. Res. Lett., 42, 10 42910 437, https://doi.org/10.1002/2015GL066199.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Singh, M. S., and P. A. O’Gorman, 2013: Influence of entrainment on the thermal stratification in simulations of radiative-convective equilibrium. Geophys. Res. Lett., 40, 43984403, https://doi.org/10.1002/grl.50796.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Smith, R. K., M. T. Montgomery, and S. Vogl, 2008: A critique of Emanuel’s hurricane model and potential intensity theory. Quart. J. Roy. Meteor. Soc., 134, 551561, https://doi.org/10.1002/qj.241.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Sobel, A. H., and S. J. Camargo, 2011: Projected future seasonal changes in tropical summer climate. J. Climate, 24, 473487, https://doi.org/10.1175/2010JCLI3748.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Sobel, A. H., S. J. Camargo, T. M. Hall, C.-Y. Lee, M. K. Tippett, and A. A. Wing, 2016: Human influence on tropical cyclone intensity. Science, 353, 242246, https://doi.org/10.1126/science.aaf6574.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Sobel, A. H., S. J. Camargo, and M. Previdi, 2019: Aerosol versus greenhouse gas effects on tropical cyclone potential intensity and the hydrologic cycle. J. Climate, 32, 55115527, https://doi.org/10.1175/JCLI-D-18-0357.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Tang, B., and K. Emanuel, 2012: A ventilation index for tropical cyclones. Bull. Amer. Meteor. Soc., 93, 19011912, https://doi.org/10.1175/BAMS-D-11-00165.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Vecchi, G. A., and B. J. Soden, 2007: Increased tropical Atlantic wind shear in model projections of global warming. Geophys. Res. Lett., 34, L08702, https://doi.org/10.1029/2006GL028905.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Vecchi, G. A., S. Fueglistaler, I. M. Held, T. R. Knutson, and M. Zhao, 2013: Impacts of atmospheric temperature trends on tropical cyclone activity. J. Climate, 26, 38773891, https://doi.org/10.1175/JCLI-D-12-00503.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Wang, S., S. J. Camargo, A. H. Sobel, and L. M. Polvani, 2014: Impact of the tropopause temperature on the intensity of tropical cyclones: An idealized study using a mesoscale model. J. Atmos. Sci., 71, 43334348, https://doi.org/10.1175/JAS-D-14-0029.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Wing, A. A., K. Emanuel, and S. Solomon, 2015: On the factors affecting trends and variability in tropical cyclone potential intensity. Geophys. Res. Lett., 42, 86698677, https://doi.org/10.1002/2015GL066145.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Zhou, W., I. M. Held, and S. T. Garner, 2014: Parameter study of tropical cyclones in rotating radiative–convective equilibrium with column physics and resolution of a 25-km GCM. J. Atmos. Sci., 71, 10581069, https://doi.org/10.1175/JAS-D-13-0190.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
All Time Past Year Past 30 Days
Abstract Views 173 173 173
Full Text Views 29 29 29
PDF Downloads 33 33 33

The Connection between Carnot and CAPE Formulations of TC Potential Intensity

View More View Less
  • 1 a Lorenz Center, Department of Earth and Planetary Sciences, Massachusetts Institute of Technology, Cambridge, Massachusetts
  • | 2 b Department of Atmospheric and Oceanic Sciences, McGill University, Montreal, Quebec, Canada
  • | 3 c NOAA/Geophysical Fluid Dynamics Laboratory, Princeton, New Jersey
© Get Permissions Rent on DeepDyve
Restricted access

Abstract

Tropical cyclone (TC) potential intensity (PI) theory has a well-known form, consistent with a Carnot cycle interpretation of TC energetics, which relates PI to mean environmental conditions: the difference between surface and TC outflow temperatures and the air–sea enthalpy disequilibrium. PI has also been defined as a difference in convective available potential energy (CAPE) between two parcels, and quantitative assessments of future changes make use of a numerical algorithm based on this definition. Here, an analysis shows the conditions under which these Carnot and CAPE-based PI definitions are equivalent. There are multiple conditions, not previously enumerated, which in particular reveal a role for irreversible entropy production from surface evaporation. This mathematical analysis is verified by numerical calculations of PI’s sensitivity to large changes in surface-air relative humidity. To gain physical insight into the connection between the CAPE and Carnot formulations of PI, we use a recently developed analytic theory for CAPE to derive, starting from the CAPE-based definition, a new approximate formula for PI that nearly recovers the previous Carnot PI formula. The derivation shows that the difference in undilute buoyancies of saturated and environmental parcels that determines CAPE PI can in fact be expressed as a difference in the parcels’ surface moist static energy, providing a physical link between the Carnot and CAPE formulations of PI. This combination of analysis and physical interpretation builds confidence in previous numerical CAPE-based PI calculations that use climate model projections of the future tropical environment.

© 2022 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Timothy M. Merlis, timothy.merlis@mcgill.ca

Abstract

Tropical cyclone (TC) potential intensity (PI) theory has a well-known form, consistent with a Carnot cycle interpretation of TC energetics, which relates PI to mean environmental conditions: the difference between surface and TC outflow temperatures and the air–sea enthalpy disequilibrium. PI has also been defined as a difference in convective available potential energy (CAPE) between two parcels, and quantitative assessments of future changes make use of a numerical algorithm based on this definition. Here, an analysis shows the conditions under which these Carnot and CAPE-based PI definitions are equivalent. There are multiple conditions, not previously enumerated, which in particular reveal a role for irreversible entropy production from surface evaporation. This mathematical analysis is verified by numerical calculations of PI’s sensitivity to large changes in surface-air relative humidity. To gain physical insight into the connection between the CAPE and Carnot formulations of PI, we use a recently developed analytic theory for CAPE to derive, starting from the CAPE-based definition, a new approximate formula for PI that nearly recovers the previous Carnot PI formula. The derivation shows that the difference in undilute buoyancies of saturated and environmental parcels that determines CAPE PI can in fact be expressed as a difference in the parcels’ surface moist static energy, providing a physical link between the Carnot and CAPE formulations of PI. This combination of analysis and physical interpretation builds confidence in previous numerical CAPE-based PI calculations that use climate model projections of the future tropical environment.

© 2022 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Timothy M. Merlis, timothy.merlis@mcgill.ca
Save