Hurricane Superintensity John Persing and Michael Montgomery JAS, 1 October 2003 Kristen Corbosiero AT 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 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 Ψ o ∂χ/∂r 2 = –C k /C d (1 + c|V|)|V|(χ sea – χ) Entropy balance Ψ o ∂R 2 /∂r 2 = 2(1+c|V|)|V|rV Momentum balance Ψ o = radial streamfunction (inflow) χ ≡ (SST – T out )(s inflow – s env ) s env = c p lnΘ e C k, C d = air-sea exchange coefficients for entropy and angular momentum c = empirical constant V = tangential wind speed R = 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 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 V t 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

V max from E-MPI as a function of SST and T outflow The boxes denote the range of E- MPI values in the simulations, while the stars are the actual superintense results

RunDefault2x4x8x Max V t Max Daily V t Median V t Mean RMW Min SLP Median SLP Max W Max Daily W V t = 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

RunDefault2x4x8x Max V t Max Daily V t Median V t Mean RMW Min SLP Median SLP Max W Max Daily W 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 ( Θ e ) for the default run The Θ e 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 Θ e develops in two steps: 1)Elimination of the initial mid-level Θ e 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 Θ e 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 Θ e 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 Θ e -height space Downdraft air is indistinguishable from PBL inflow air by the time it reaches the eyewall Parcels with lower trajectories have the highest Θ e Parcels increase their Θ e 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 trivial 2) 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 Θ e 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 Θ e 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 Adiabatic expansion Adiabatic compression Isothermal compression

How does high Θ e 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

Isothermal expansion Adiabatic compression How does high Θ e 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 Cooling phase

How does high Θ e 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 + Δ Θ e = SST + ( Θ e,out – Θ e,sfc ) Δ Θ e ≈ 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 Θ e (right) from Braun (2002) Maximum Θ e 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 Θ e 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 Θ e was K higher than the eyewall The eye has a significant vertical gradient of Θ e, 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?

Θ e (red) and 2-D streamlines (blue) overlaid with q l >.3 g kg -1 (light green) and q l >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