Abstract
It has long been known that hurricanes, the strongest and most destructive atmospheric events, do not occur below a sea surface temperature near 26 C. The detailed dependence of hurricane power on ocean temperature is of increasing interest and concern in the prospect of continuing global warming. The hurricane power was usefully quantified by Emanuel in 2005 with the definition and tabulations of the power dissipation index, PDI. This is the integral over the relevant sea areas of the cube of the maximum windspeed, representiting the power dissipated over one year. In his important 2005 paper Emanuel found that the PDI for the North Atlantic increased strongly in recent decades and showed in plots a close correlation of PDI with sea surface temperature. A critical temperature Tc, and a linear T-Tc power law dependence, typical of a continuous phase transition, for hurricanes have prcviously (Wolf, 2020) been inferred from plots of the power dissipation index PDI vs sea surface temperature T. This implies that tropical cyclone formation can usefully be regarded as a second order phase transition of the warm ocean-atmosphere system, driven by disequilibrium in atmospheric water content. We here show that the theory of phase transitions allows a precise prediction of the temperature dependence of hurricane power and windspeed on ocean surface temperature. We find that the wind velocity transition of the hurricane is in the same universality class as the Ising Model, the uniaxial antiferromagenet and the vapor- liquid transition of simple fluids, and shares their critical exponent. An implication for the applicability of potential intensity theory is noted.
Highlights
IntroductionAn important aspect of the tropical climate is the hurricane. These storms, that generate copious rainfall, occur primarily in the low latitudes of the North Atlantic in the warmest part of the year
The Power Dissipation IndexAn important aspect of the tropical climate is the hurricane
We confirm an alternative view [2] of extensive and closely fitted data sets [3, 4] of the hurricane Power Dissipation Index vs measured sea surface temperature T. These data provide excellent detailed fits if the measured temperatures are subjected to offsets that are equivalent to choosing a critical temperature for a tropical cyclone, via fitting law Eq (3), with linear dependence on (T- Tc)
Summary
An important aspect of the tropical climate is the hurricane. These storms, that generate copious rainfall, occur primarily in the low latitudes of the North Atlantic in the warmest part of the year. Eq 3 with nominal exponent 1.0 was used to fit all of the data compiled by Emanuel [3, 4] Those data cover hurricanes over 70 years in tropical portions of the North Atlantic, North Pacific, West Pacific, and Indian Oceans. (Data from the other tropical basins are of lower availability and quality, so Emanuel’s work focused on, but was not limited to, northern hemisphere storms Those total data cover hurricanes over 70 years in tropical portions of the North Atlantic, North Pacific, West Pacific, and Indian Oceans.) Remarkably detailed fits were shown, with two accurately overlain curves vs time, representing the PDI, a quantity rising from zero to with values in units of 1011 m3/s2, and “temperature”. Such an idea is supported by the detailed structures, the eye and eyewall regions, following accurate circular forms uncharacteristic of the underlying thunderstorms
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