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Wikipedia / Maximum potential intensity

The maximum potential intensity of a tropical cyclone is the theoretical limit of the strength of a tropical cyclone.

Maximum potential intensity

Due to surface friction, the inflow only partially conserves angular momentum. Thus, the sea surface lower boundary acts as both a source (evaporation) and sink (friction) of energy for the system. This fact leads to the existence of a theoretical upper bound on the strongest wind speed that a tropical cyclone can attain. Because evaporation increases linearly with wind speed (just as climbing out of a pool feels much colder on a windy day), there is a positive feedback on energy input into the system known as the Wind-Induced Surface Heat Exchange (WISHE) feedback., and is given by

are the surface exchange coefficients (dimensionless) of enthalpy and momentum, respectively. is the saturation enthalpy is the enthalpy of boundary layer air overlying the surface.

The maximum potential intensity is predominantly a function of the background environment alone (i.e. without a tropical cyclone), and thus this quantity can be used to determine which regions on Earth can support tropical cyclones of a given intensity, and how these regions may evolve in time. Specifically, the maximum potential intensity has three components, but its variability in space and time.

Derivation

A tropical cyclone may be viewed as a heat engine that converts input heat energy from the surface into mechanical energy that can be used to do mechanical work against surface friction. At equilibrium, the rate of net energy production in the system must equal the rate of energy loss due to frictional dissipation at the surface, i.e.

, is given by

is the density of near-surface air ([kg/m3 is the near surface wind speed ([m/s]).

is given by

is the total rate of heat input into the system per unit surface area. Given that a tropical cyclone may be idealized as a Carnot heat engine, the Carnot heat engine efficiency is given by

Heat (enthalpy) per unit mass is given by

is the concentration of water vapor. The first component corresponds to sensible heat and the second to latent heat.

, is given by

), which occurs near the surface within the tropical cyclone and is recycled to the system.

Thus, the total rate of net energy production per unit surface area is given by

in the denominator of the Carnot efficiency.

An alternative definition for the maximum potential intensity, which is mathematically equivalent to the above formulation, is

where CAPE stands for the Convective Available Potential Energy is the CAPE of an air parcel lifted from saturation at sea level in reference to the environmental sounding is the CAPE of the boundary layer air, and both quantities are calculated at the radius of maximum wind.

Characteristic values and variability on Earth

varies with wind speed and may decrease at high wind speeds within the boundary layer of a mature hurricane. may vary at high wind speeds due to the effect of sea spray on evaporation within the boundary layer.

, is . However, this quantity varies significantly across space and time, particularly within the seasonal cycle, spanning a range of . ) as well as in the thermodynamic structure of the troposphere, which are controlled by the large-scale dynamics of the tropical climate. These processes are modulated by factors including the sea surface temperature (and underlying ocean dynamics), background near-surface wind speed, and the vertical structure of atmospheric radiative heating. The nature of this modulation is complex, particularly on climate time-scales (decades or longer). On shorter time-scales, variability in the maximum potential intensity is commonly linked to sea surface temperature perturbations from the tropical mean, as regions with relatively warm water have thermodynamic states much more capable of sustaining a tropical cyclone than regions with relatively cold water. is weak in comparison.

Empirical limit

An empirical limit on tropical cyclone intensity can also be computed using the following formula:

is the maximum potential velocity in meters per second is the sea surface temperature is a reference temperature (30 ˚C, the graph generated by this function corresponds to the 99th percentile of empirical tropical cyclone intensity data.

See also

References