Hurricanes in other climates:Thermodynamic genesis factors

Robert KortyTexas A&M

Geologic evidence

sand layer from a prehistoric hurricane

Photo courtesy of Kam-biu Liu, LSU.Photo courtesy of Jon Woodruff.

Sedimentary core from Nicaragua… …from Massachusetts.

Hurricane Carol

Great New EnglandHurricane

Great Colonial Hurricane

Great SeptemberGale

Tropical cyclone genesis studies

Observations analyzed in work by Gray (1968, 1979)Revisited by Emanuel and Nolan (2004), Camargo et al. (2007)

Dynamic constraints• low vertical wind shear• incipient vortex (supply of vorticity)

Thermodynamic requirements• enthalpy flux from ocean to atmosphere• sounding supportive of deep convection• mid-tropospheric humidity

1

2 3

4

Thermodynamic speed limit for hurricanes

First Law of ThermodynamicsThe internal energy dU changes when:

1. heat dQ is exchanged between a parcel and its environment2. work is done by a parcel on its environment (or vice-versa)

For a cyclic process in which the internal energy does not change (you end up where you started), then any heating dQ must be balanced by work done to or by the system dW. In this case

This cycle has a maximum efficiency, the Carnot engine. This is the physics that sets the speed limit on how intense a tropical storm can be.

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dQ = dU + dW

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dW = dQ

W total =Qtotal

Thermodynamic speed limit for hurricanes

The heat input at the surface comes from two sources: 1. Fluxes of heat--actually, enthalpy, k--from the ocean2. Dissipative heating from recycled frictional dissipation

Radiative cooling to space is done at convective outflow temperature, To.

This is called the maximum potential intensity.

(Emanuel 1986; Emanuel 1988; Holland 1997; Bister and Emanuel 1998)

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rV =

Ck

CD

Ts −To

To

kocean* − k( )

Thermodynamic speed limit for hurricanes

Sea surface temperature Ts affects limit, but does not independently control it.

These two do:

1.The difference between Ts and To, which is largest where convection is deepest2.Thermodynamic disequilibrium between the saturated ocean surface and the overlying marine boundary layer.

Nothing magic happens when water is 26oC.

In our present climate, the 26oC isotherm is usually found near the region of trade inversions in the subtropics. In others, a different value could be.

€

rV =

Ck

CD

Ts −To

To

kocean* − k( )

Late Quaternary climate forcingsMid-Holocene (6ka)• CO2, CH4: 280 ppm, 650 ppb• Substantial TOA radiation

Last Glacial Maximum (21ka)• CO2, CH4: 185 ppm, 350 ppb; ice• Smaller TOA radiation

Latit

ude

W/m2

Storm season potential intensityLa

titud

e

m/s

Change in potential intensity at LGM

m/s

Latit

ude

weaker at LGMthan Preindustrial

stronger at LGMthan Preindustrial

Change in potential intensity 6000 years ago

m/s

Latit

ude

weaker in mid Holocenethan Preindustrial

stronger in mid Holocenethan Preindustrial

Change in convective outflow T 6000 years ago

oC

Latit

ude

Change in surface temperature 6000 years ago

oC

Latit

ude

Sahel rainfall and cloudiness increase.

Change in surface entropy 6000 years agoLa

titud

e

J/(kg K)warmer, wetter, or bothcooler, drier, or both

Mid tropospheric dryness

• Nascent storms are impeded by dry air in the mid troposphere.

• Downdrafts choke off supply of high entropy boundary layer air.

• Time needed for genesis shortens when entropy deficit is small.

Entropy deficit is related to the saturation deficit, and it is strongly affected by temperature.

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ds = sb − sm ≈ sm* − sm

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sm* − sm ≈

Lv q* − q( )

T

Relative humidity

Tem

pera

ture

Saturation entropy deficit: s* – s

Relative humidity

Tem

pera

ture

Saturation entropy deficit: s* – s

growing entropy deficit

lower inhibition to development

Changes in entropy deficit (ds = sb – sm) at LGMLa

titud

e

Eocene epoch: hot climates---compiled by Huber (2008)

Blue: 18OGreen: Mg/CaRed: TEX86

Eocene epoch: hot climates

Collaboration with Matt Huber (Purdue), who ran CCSM with very high levels of CO2.

CCSM’s climate sensitivity to doubling CO2 is ~2-2.5 K, slightly lower than that of other modeling centers.

Runs with present-day geography and parameters were completed in parallel with others using Eocene continental configurations and pre-industrial trace gas settings.

CO2 levels ranged from 355 ppm to 8960 ppm (32 times larger than pre-industrial levels).

Annual mean surface temperatures (355 ppm)

Annual mean surface temperatures (2240 ppm)

Annual mean surface temperatures (8960 ppm)

Storm season potential intensity (355 ppm)La

titud

e

m/s

Storm season potential intensity (2240 ppm)La

titud

e

m/s

Changes in potential intensity (2240 ppm)La

titud

e

m/s

Storm season potential intensity (8960 ppm)La

titud

e

m/s

Changes in potential intensity (8960 ppm)La

titud

e

m/s

Present climate Weak temperature gradient

Thermal stratification in CAM simulations

Air mass classifications from P*

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P* =ζ a ⋅∇θe

*

ρConvection can be driven by symmetrically unstable slantwise displacements of moist air if e* decreases upward along slanted isosurfaces of M.

Unlike conventional p.v., P* is not conserved, but it is ideally suited to identify regions with constant values of e* (s*) along isosurfaces of absolute angular momentum, M.

Because the absolute vorticity vector points parallel to isosurfaces of constant M, P* will be zero wherever e* is constant along M surfaces.

Fraction of convectively neutral days at 700 mbLa

titud

e

August (355 ppm)

Fraction of convectively neutral days at 700 mbLa

titud

e

August (2240 ppm)

Fraction of convectively neutral days at 700 mbLa

titud

e

August (8960 ppm)

Summary

During the mid Holocene, potential intensities in both hemispheres change inversely with the top of atmosphere (TOA) solar radiation perturbation.

Tropical SST differ little between today and the mid Holocene, but entropy anomalies over land and everywhere aloft follow the sign of the TOA deviation.

The combination yields a change in the thermodynamic “speed limit” that is opposite to the change in local solar radiation.

Saturation entropy deficits, a limiting factor in these models’ storm counts, drop with the colder temperatures at LGM.

This work was advanced by collaborations with:• Suzana Camargo, Columbia• Stephen Cathey, Texas A&M• Kerry Emanuel, MIT• Joe Galewsky, University of New Mexico • Matt Huber, Purdue• Bette Otto-Bliesner, NCAR