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Tropical Cyclone Theory

by Kerry Emanuel and Adam Sobel

Motivation

Predicting the response of tropical cyclones to changing climate should be aided by a
better understanding of the factors that control their rate of generation, their intensification, and their demise, as well as related phenomena such as flooding and storm surges. Development and testing of comprehensive theories for these and other aspects of tropical cyclones is of fundamental scientific interest, and also is needed to help us predict how climate change might affect tropical cyclones and their effects on society.

Research Summary 

Research to date has established a few fundamental principles and, perhaps more
importantly, has delineated important questions that must be answered to achieve a
comprehensive understanding of the phenomenon. Early investigators (e.g. Riehl, 1950, Kleinschmidt, 1951) established that mature tropical cyclones are maintained against frictional dissipation by enthalpy (heat) transfer from the ocean to the atmosphere. In nature, most of this enthalpy transfer is accomplished by the evaporation of seawater. In this process, the latent heat of vaporization is supplied by the ocean, which acts as very large heat capacitor for the atmosphere on the time scales of tropical cyclones. (By contrast, the land surface has a vanishingly small effective heat capacity on tropical cyclone time scales, which explains why virtually all such storms dissipate when they move over land.) The mature tropical cyclone, approximated as a steady, circularly symmetric vortex, may be idealized as an ideal Carnot heat engine, as illustrated in Figure 1. As air spirals into the eyewall region (A to B in Figure 1), it undergoes a nearly isothermal expansion, acquiring enthalpy from the sea surface
and does so. It then ascends in the eyewall, undergoing a nearly (moist) adiabatic expansion. Enthalpy acquired from the sea is either exported from the system or lost by infrared radiation to space, at the comparatively low temperature of the tropical tropopause region. In a closed cycle, the air would slowly subside and compress under the influence of radiative cooling, following the (moist) adiabatic temperature profile of the tropical environment. The thermodynamic efficiency of the cycle is proportional to the difference between the sea surface and tropopause temperatures.

A common misconception about tropical cyclones is that they are powered by the latent
heat released as air ascends and expands in the eyewall. But this is an internal energy conversion and so does not bear on the overall energetics of the system. In fact, perfectly dry hurricanes have been simulated numerically (Mrowiec et al., 2011). In this case, the ascent and decent are dry adiabatic, and the radiative-convective equilibrium of the storm environment is likewise characterized by dry adiabatic lapse rates of temperature.

Image removed.

Figure : Energy cycle of a mature tropical cyclone. Air undergoes isothermal expansion as it spirals into the eyewall between A and B, acquiring enthalpy from the underlying ocean. From B to C the air expands (moist) adiabatically, while from C to D it undergoes a nearly isothermal compression, returning to the surface along a (moist) adiabat from D to A. In the steady state, the mechanical wind energy generated in this cycle is dissipated by friction, mostly in the atmospheric boundary layer.

 

While the basic energy cycle helps explain the maintenance of tropical cyclone against frictional dissipation of wind, it does not by itself explain how such storms come into being in the first place, nor does it fully explain how storms, once initiated, intensify. It has been shown (e.g. Emanuel, 1989) that tropical cyclones cannot arise spontaneously but must be set off by some independent process or processes. Understanding those processes is an important endeavor known as the “genesis problem” in the science of tropical cyclones. There are many unresolved theoretical issues pertaining to tropical cyclones.

These include:

  • What environmental and physical parameters determine the maximum achievable intensity of tropical cyclones? There are many related issues that must be resolved to answer this question. These include, but may not be limited to
    • The physics of air-sea enthalpy and momentum transport at high wind speeds, including such factors as waves and sea spray (Fairall et al., 1994, Edson et al., 1996, Andreas and Emanuel, 2001)
    • The existence and magnitude of supergradient winds in the boundary layer (Smith et al., 2008, Bryan and Rotunno, 2009a)
    • Horizontal mixing by atmospheric eddies (Bryan and Rotunno, 2009b)
    • Radial structure of the “outflow temperature” (Emanuel and Rotunno 2011)
  • What environmental factors control the actual (as opposed to potential) intensity of tropical cyclones? Answering this question involves such issues as
    • Response of the upper ocean to tropical cyclones; especially, cooling of the sea surface by vertical mixing in the ocean (Khain and Ginis, 1991)
    • Interaction of tropical cyclones with environmental winds, which may serve to import low entropy air into the storm core (Tang and Emanuel, 2010)
    • The time it takes for storms to intensify, as they are more likely to reach their maximum potential intensities if they have time to do so before reaching land or colder ocean surfaces.
  • How do Tropical Cyclones, once initiated, intensify? (Emanuel, 1997, Smith and Montgomery, 2009)
  • How do tropical cyclones form? This is one of the great, largely unsolved problems of tropical meteorology. While empirical necessary conditions for tropical cyclone formation have been known for many decades (e.g., Palmen 1948; Gray 1979), a fundamental understanding of genesis remains elusive.
  • What controls the sizes of tropical cyclones? While there have been recent advances in empirical knowledge of storm size distributions (e.g. Chavas and Emanuel, 2010), there is almost no theoretical understanding of storm size.
  • What determines the level of tropical cyclone activity in a given climate state?

This is a subject of intense theoretical as well as modeling-based research, and involves many of the issues described above. The term “tropical cyclone activity” includes the frequency and intensity of events as well as their characteristic tracks, regions of genesis, and horizontal dimensions. These statistics of the tropical cyclone distribution are known to vary with natural variations of the large-scale climate such as ENSO (e.g., Camargo et al. 2010, and references therein), and it is natural to expect that they will vary with anthropogenic global warming as well. However, our understanding of how climate variations control TC statistics is based largely on empirical methods (which are limited by the observational record and contain no true analog for global warming) and now, to an increasing extent, global high-resolution numerical models (e.g., Knutson et al. 2010). Theory is so far silent on several of these important questions; there is no existing theory, for example, which predicts the average number of tropical cyclones thaform in a year under a given climate.

Implications

Tropical cyclones are, by far, the major source of insured losses by natural catastrophes worldwide, and are a leading cause of damage and mortality from natural phenomena. Even small changes in their levels of activity owing to climate change may have important societal consequences. Successful prediction of the response of tropical cyclone activity to climate change is predicated not just on better numerical simulations but on much improved theoretical understanding of these storms.

References

  • Andreas, E. L., and K. Emanuel, 2001: Effects of sea spray on tropical cyclone intensity. J. Atmos. Sci., 58, 3741-3751.
  • Bryan, G. H., and R. Rotunno, 2009a: Evaluation of an analytical model for the maximum intensity of tropical cyclones. J. Atmos. Sci., 66, 3042-3060.
  • ——, 2009b: The maximum intensity of tropical cyclones in axisymmetric numerical model simulations. Mon. Wea. Rev., 137, 1770-1789. doi:10.1175/2008MWR2709.1.
  • Camargo, S. J., A. H. Sobel, A. Barnston, and P. Klotzbach 2010: The influence of natural climate variability, and seasonal forecasts of tropical cyclone activity. Global Perspectives on Tropical Cyclones, 2nd edition, J. C. L. Chan and J. D. Kepert, Eds.,
    World Scientific, 325-360.
  • Chavas, D. R., and K. A. Emanuel, 2010: A QuickSCAT climatology of tropical cyclone size. Geophys. Res. Lett., 37, 10.1029/2010GL044558.
  • Edson, J. B., S. Anquentin, P. G. Mestayer, and J. F. Sini, 1996: Spray droplet modeling: 2. An interactive Eulerian-Lagrangian model of evaporating spray droplets. J. Geophys. Res., 101, 1279-1293.
  • Emanuel, K. A., 1989: The finite-amplitude nature of tropical cyclogenesis. J. Atmos. Sci., 46, 3431-3456.
  • ——, 1997: Some aspects of hurricane inner-core dynamics and energetics. J. Atmos. Sci., 54, 1014-1026.
  • Emanuel, K., and R. Rotunno, 2011: Self-Stratification of Tropical Cyclone Outflow. Part I: Implications for Storm Structure. J. Atmos. Sci, in press
  • Fairall, C. W., J. D. Kepert, and G. J. Holland, 1994: The effect of sea spray on surface energy transports over the ocean. Global Atmos. Ocean Sys., 2, 121-142.
  • Gray, W.M., 1979: Hurricanes: Their formation, structure and likely role in the tropical circulation. Meteorology Over Tropical Oceans. D. B. Shaw (Ed.), Roy. Meteor. Soc., James Glaisher House, Grenville Place, Bracknell, Berkshire, RG12 1BX, pp.155-218
  • Khain, A., and I. Ginis, 1991: The mutual response of a moving tropical cyclone and the ocean. Beitr. Phys. Atmosph., 64, 125-141.
  • Kleinschmidt, E., Jr., 1951: Gundlagen einer Theorie des tropischen Zyklonen. Archiv fur Meteorologie, Geophysik und Bioklimatologie, Serie A, 4, 53-72.
  • Knutson, T. R., J. L. McBride, J. Chan, K. Emanuel, G. Holland, C. Landsea, I. Held, J. P. Kossin, A. K. Srivastava, and M. Sugi, 2010: Tropical cyclones and climate change. Nature Geoscience, 3, 157-163.
  • Mrowiec, A. A., S. T. Garner, and O. M. Pauluis, 2011: Axisymmetric hurricane in a dry atmosphere: Theoretical framework and numerical experiments. J. Atmos. Sci., 68, in press.
  • Palmen, E. H., 1948: On the formation and structure of tropical cyclones. Geophysica , Univ. of Helsinki, 3, pp. 26-38.
  • Riehl, H., 1950: A model for hurricane formation. J. Appl. Phys., 21, 917-925.
  • Smith, R. K., and M. T. Montgomery, 2009: Tropical cyclone spin-up revisited. Quart. J. Roy. Meteor. Soc., 135, 1321-1335.
  • 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, 551-561.
  • Tang, B., and K. Emanuel, 2010: Midlevel ventilation's constraint on tropical cyclone intensity. J. Atmos. Sci., 67, 1817-1830.
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