Hurricane Superintensity

John Persing and Michael Montgomery

JAS, 1 October 2003

Kristen CorbosieroAT796

18 April 2007

Outline

1. Superintense relative to what?

MPI theories (Energetic & Thermodynamic)

2. Motivation for the current study

3. Superintensity in the Rotunno-Emanuel model

4. The eye as a latent heat reservoir

5. Three-dimensional modeling and observational evidence for superintensity

6. Summary and conclusions

NHC Official Forecast track and intensity

errors for the Atlantic Ocean

http://www.nhc.noaa.gov/verification/

Maximum Potential Intensity (MPI) theories were

formulated to try to get a handle on what processes determine the upper bound on

intensity

MPI Theory

• Modern MPI theory led by Kerry Emanuel (1986, 1988, 1995, 1998) and Greg Holland (1997)

• Both theories assume moist adiabatic ascent in the eyewall and are governed by SST, surface RH, and the thermal structure of the upper troposphere

Figure 1, Camp and Montgomery (2001)

Holland MPI, T-MPI (T for thermodynamic), relies heavily on prescribed environmental and eye

soundings, and convective instability (CAPE) that develops in the eyewall

Emanuel MPI, E-MPI (E for energetic), relies on air-sea heat and momentum exchange (WISHE)

E-MPI is based on a balance between frictional dissipation and energy production in the inflowing boundary layer air, or a point balance between moist entropy and angular momentum

Ψo ∂χ/∂r2 = –Ck/Cd (1 + c|V|)|V|(χsea – χ) Entropy balance

Ψo ∂R2/∂r2 = 2(1+c|V|)|V|rV Momentum balance

Ψo = radial streamfunction (inflow)χ ≡ (SST – Tout)(sinflow – senv)senv = cplnΘe

Ck, Cd = air-sea exchange coefficients for entropy and angular momentumc = empirical constantV = tangential wind speedR = angular momentum

Entropy lost due to radial advection = Entropy gain from ocean

Momentum gain from inflow = Momentum lost to ocean due to friction

These two balance equations can be combined (with some fancy algebra) to get an equation for the maximum tangential wind of

an axisymmetric, steady state vortex (Equations 2-5)

Current E-MPI maps from http://wxmaps.org/pix/hurpot.html

K-R

I

Most tropical cyclones do not reach their 2-D, symmetric, steady state derived E-MPI

Among the factors neglected are vertical wind shear, convective asymmetries, secondary eyewalls, sea

spray and wind-induced ocean cooling

Motivation

• Hausman (2001) documented a systematic increase in intensity with increasing resolution using an axisymmetric hurricane model (Ooyama 2001)

• The simulations converged at ~1 km resolution to an intensity of nearly 140 m s-1 which far exceeded the E-MPI

• Based on this and other high resolution simulations that exhibited superintensity, Persing and Montgomery (2001) used the axisymmetric model of Rotunno and Emanuel (1987) to investigate the assumptions of E-MPI and document those assumptions that are violated in the simulations and that can explain superintensity

20-21 day average fields of the 4x resolution (3.75 km) run with the Rotunno Emanuel (1987) model

This 2-D, non-hydrostatic model produces realistic hurricane structure

Time series of maximum Vt from the model

(solid), E-MPI, (dotted) and simplified MPI from

Equation 6 (dashed)

The 2x, 4x and 8x runs all exceed their MPI

around day 5 and reach an approximate steady

state at day 10

The default run reaches steady state at its MPI around day 9, but then exceeds the MPI and reaches a new steady

state by day 20

Vmax from E-MPI as a function of SST and Toutflow

The boxes denote the range of

E- MPI values in the simulations, while the stars are the actual superintense

results

Run Default 2x 4x 8x

Max Vt 71.77 87.74 100.20 101.90

Max Daily Vt 67.81 83.75 95.96 96.79

Median Vt 62.04 80.21 90.42 87.51

Mean RMW 43.89 22.23 26.14 22.91

Min SLP 935.0 906.5 894.2 901.8

Median SLP 952.9 917.7 910.1 922.9

Max W 8.32 13.20 22.80 30.18

Max Daily W 4.77 7.58 10.86 13.58Vt = tangential wind (m s-1)

RMW = radius of maximum wind (km)SLP = sea level pressure (hPa)

W = updraft velocity (m s-1)

Default = 15 km horizontal resolution

Run Default 2x 4x 8x

Max Vt 71.77 87.74 100.20 101.90

Max Daily Vt 67.81 83.75 95.96 96.79

Median Vt 62.04 80.21 90.42 87.51

Mean RMW 43.89 22.23 26.14 22.91

Min SLP 935.0 906.5 894.2 901.8

Median SLP 952.9 917.7 910.1 922.9

Max W 8.32 13.20 22.80 30.18

Max Daily W 4.77 7.58 10.86 13.58• Convergence in intensity is reached by the 4x simulation, but not in updraft strength

• Intensity changes can not be explained solely in terms of the shrinking of the RMW

Default run (15 km) temperature and

potential temperature (Θ)

anomalies

This run had two steady states, one at its MPI (day 12, top) and one well above it (day 28,

bottom)

There is a substantial

difference in eye structure between

the two states

Equivalent potential temperature (Θe) for the default run

The Θe maximum that develops by day 18 at 3 km inside the 20 km radius is a possible source of heat to

eyewall convection if mixed outward (a violation of MPI theory!)

The reservoir of high Θe develops in two steps:

1)Elimination of the initial mid-level Θe minimum by convectively forced subsidence

2)Strong upward moisture flux under the eye

The 4x run (3.75 km) resolves the storm evolution

in much greater detail including:

1) The concentration of strong subsidence just inside the eyewall

2) The large and deep 360+ K Θe reservoir in the eye

3) The eyewall updrafts are not moist neutral (violation!)

Figure 17 of Rotunno and Emanuel (1987)

The ultimate source of high Θe in the 4x run (3.75 km) run is

upward moisture flux from the ocean

at significantly reduced surface

pressures

The heat flux is actually slightly

negative in the eye due to subsidence

warming

Moisture flux

Heat flux

4x run (3.75 km)half day trajectories in

radius-height space

There are 3 source regions for air entering

the eyewall updraft:

1) From the eye (dotted)

2) From boundary layer (PBL) inflow (solid)

3) From low level inflow above the PBL (dashed)

4x run (3.75 km)half day trajectories in

Θe-height space

Downdraft air is indistinguishable from PBL inflow air by the time it reaches the

eyewall

Parcels with lower trajectories have the

highest Θe

Parcels increase their Θe as they rise in the

eyewall above the PBL, requiring an additional source of heat other than the ocean…the

eye!

The waviness of the trajectories in the eye

and on the inner edge of the eyewall indicate

parcels are detraining into the eye and being

reintroduced to the eyewall frequently.

Thus, 2 key assumptions of MPI theory have been

violated:

1) Entropy exchange between the eye and eyewall is trivial2) The eyewall updraft is moist neutral

1.3 km resolution MM5 simulation

Hurricane Bob (1991) from Braun (2002) also

shows the eye as a source of air for eyewall updrafts

4x run Θe before and after addition of a heat sink in lower eye to mimic the elimination of

the eye heat reservoir

The storm weakened from 90 to 55 m s-1, but was still above its E-MPI

Secondary circulation from the model and calculated from Eliassen’s (1951) balanced vortex

model using the model derived heat and momentum forcings

The model is evolving largely in hydrostatic and gradient wind balance

How does high Θe air from the eye produce a stronger storm?

How does high Θe air from the eye produce a stronger storm?

• E-MPI theory assumes that all of the heat added to the eyewall is in the PBL from the ocean in a near perfect Carnot engine

Isothermal expansion

Adiabaticexpansion

Adiabaticcompression

Isothermal compression

How does high Θe air from the eye produce a stronger storm?

• E-MPI theory assumes that all of the heat added to the eyewall is in the PBL from the ocean in a near perfect Carnot engine

Warming phase

Cooling phase

Cooling phase

Isothermal expansion

Adiabaticcompression

How does high Θe air from the eye produce a stronger storm?

• Add eyewall to the warming phase and consider the warming of a parcel relative to the moist adiabat at the top and bottom of the eyewall

Warming phase

Warming phase

Cooling phase

Cooling phase

How does high Θe air from the eye produce a stronger storm?

• Persing and Montgomery suggests the following ad hoc modification of SST in E-MPI theory:

SST’ = SST + ΔΘe = SST + (Θe,out – Θe,sfc)

• ΔΘe ≈ 8 K in the 4x simulation, increasing the SST from 26° to 34° C, increasing the MPI to ~80 m s-1

• This value is still slightly below the actual model intensity of 90 m s-1, but much greater than the E-MPI of 55 m s-1, and provides the largest increase in intensity of any of the assumptions tested

Evidence of superintensity

(eye turbo-boost) in 3-D models

Invertible moist potential vorticity

(left) and Θe

(right) from Braun (2002)

Maximum Θe is located on the SE,

outward advecting side of

the cyclonic eyewall

mesovortex (+)

5 km MM5 idealized TC simulation of

Frank and Ritchie (2001)

E-MPI would be ~65 m s-1

Dropsondes reveal low level eye Θe can be higher than in

the eyewall

Left: Hurricane Jimena Willoughby (1998)

Below: Hurricane Isabel Aberson et al. (2006)

Dropsonde composites by LeeJoice (2000) found that in the 0-3 km layer, eye Θe was

5-10 K higher than the eyewall

The eye has a significant vertical gradient of Θe, while

the eyewall does not

Is most of the mixing accomplished by large

mesovortices, small misovortices, instabilities

or waves?

Is mixing continuous or are there large, transient mixing

events that temporally deplete the eye

reservoir?

Θe (red) and 2-D streamlines (blue) overlaid with ql >.3 g kg-1 (light green) and ql>1 g kg-1 (dark green)

in height-angular momentum space

Summary and Conclusions

• At high spatial resolution, 2-D axisymmetric hurricane simulations produce steady state storms that greatly exceed their E-MPI

• The cause of this superintensity was found to be the entrainment of high entropy air from the low level eye into the eyewall updraft

• In the real world, in the face of the many negative influences on intensity (vertical wind shear, convective asymmetries, and ocean feedbacks), this additional source of heating may be important factor in TC intensity