GEORGE H. BRYAN and RICHARD ROTUNNO 2009, J. Atmos. Sci., 66, 148-158 The Influence of Near-Surface, High-Entropy Air in Hurricane Eyes on Maximum Hurricane Intensity GEORGE H. BRYAN and RICHARD ROTUNNO 2009, J. Atmos. Sci., 66, 148-158

Outline Introduction Methodology Results with the RE87 environment Simulations in other environments Interpretation Summary

Introduction Maximum potential intensity theory of Emanuel (1986,1995) (E-MPI) can be significantly weaker than simulated and observed TC intensity. The locally high-entropy air at low levels in the tropical cyclone’s eye can provide an additional source of energy that is not considered in E-MPI. (Persing and Montgomery 2003)—”superintensity” mechanism It is not clear to us that this process has any significant effect on maximum azimuthally averaged hurricane intensity. The total magnitude of θe transport from the eye to the eyewall and its effect on average θe in the eyewall has never been quantified clearly.

Methodology Nonhydrostatic axisymmetric numerical model developed by Rotunno and Emanuel (1987)(hereafter RE87) is used. The configuration of Control simulation is identical to PM03 except for the initial sounding. Estimates of E-MPI use the “local PBL balance” method from PM03. T0 (outflow temperature) is the average temperature along the parcel trajectory as it passes between r=200-300km through the maximum tangential winds.

Initial soundings Warmer in the BL Cooler above

Simulations Diff=30 CE : surface exchange coefficient for entropy

Results with the RE87 environment Rm Near the surface in the eye, θe is 12 K higher than θe at the radius of maximum winds. θe budget shows that the ultimate source of the high-θe anomaly is the upward flux of entropy from the sea surface in the eye. There is very little difference in maximum intensity compared to Control (Fig. c). The difference in vmax is only 3 m/s.

Contour of v is 75 m/s. 3 After the surface fluxes in the eye are turned off, the high-θe anomaly is quickly eradicated (in about 8 h). The maximum sustained winds are hardly affected. vmax decreases by only 2 m/s.

Simulations in other environments

In the simulations without the eye fluxes, vmax is again slightly weaker than in simulations that retain these fluxes. Of all experiments vmax in all simulations is 25–30 m/s higher than E-MPI. Out of all simulations in which eye fluxes are included, the largest θe anomaly is 25 K (in which θe in the eye is compared to θe at rm) which is comparable to observations. This feature above has a negligible impact on maximum axisymmetric intensity.

Interpretation The PM03 mechanism clearly affects the intensity of individual, unsteady, nonaxisymmetric features as measured by local buoyancy and/or updraft intensity. The focus here is on the steady, axisymmetric intensity, which these simulations show to be barely affected by the PM03 mechanism and the PM03 mechanism can be reasonably neglected in analytic MPI theories. Shutting off the surface flux in the eye is a direct way rather than inserting a heat sink (8K/day) in the low-level eye to evaluate PM03 mechanism.

1) Magnitude of surface fluxes R=200km r R Surface fluxes in the eye are very important ??(Fig a) A much larger potential impact from the surface fluxes is suggested in the region well beyond the radius of maximum winds (i.e., for 50 km<r<100 km in Fig.b). (Fig. c) show that 97.5% of the surface entropy input into the cyclone comes from outside the eye. Surface fluxes in the eye have negligible effect on the energetics of simulated axisymmetric TCs.

0< r<rf, CE is set to 0 Regardless of the environment used, vmax does not decrease until surface fluxes are set to zero inside the nominal eyewall region (shaded region in Fig.). Surface fluxes over a broad region (specifically, from the eyewall to r=R) are important to the energetics, and thus to the intensity, of hurricanes. eyewall Rm

2) Entropy transport steady flow mass-conservation flux-form integral for control volume

JordanControl are small and therefore negligible 3.5 The total flux of θe through the right boundary rm balances the total flux of θe from the sea surface. No net enhancement of θe for parcels that pass through the eye and then back into the eyewall. (if =0)

Feyesurf is one order of magnitude smaller than surface fluxes in the eyewall and three orders of magnitude smaller than the surface entropy flux between r2 and R(=200km). The mass flux from the eye to the eyewall is only 8% of the total upward mass flux at z=H in the eyewall. Average θe in the eyewall is only a few tenths of a degree Kelvin higher as compared to simulations without the PM03 mechanism.

3) A sensitivity test These results support our hypothesis that surface fluxes in the eye would have to be at least one order of magnitude higher than typical values to have a significant positive effect on maximum axisymmetric hurricane intensity.

Summary Although the PM03 mechanism does occur in the numerical simulations, it is too small (~4%) in magnitude to significantly affect the maximum axisymmetric intensity of hurricanes. Total surface entropy fluxes in the eye are negligible compared to total surface fluxes near and outside the eyewall, and therefore the total magnitude of θe flux between the eye and eyewall is a negligible component of the θe budget in the eyewall. Additional numerical simulations could be undertaken in different environments (i.e., with different soundings and/or Ts). Furthermore, a similar set of numerical simulations could be undertaken in three dimensions. (Yang et al.2007) The neglect of surface fluxes in the eye is not an inherent limitation of E-MPI.

Thank you!

Conceptually, θe is the potential temperature an air parcel would have if all the water vapor were condensed by lifting the parcel to zero pressure. (Typically, the ice phase is neglected, and any freezing of the condensed water at low temperatures is not considered; this assumption is also made herein.)

Bryan(2008) pd is the partial pressure of dry air, rv is the mixing ratio of water vapor

Emanuel (1986) the “a priori” method of Emanuel (1986), which uses only parameters from an environmental sounding Ts is SST TB is at the top of the boudary layer(z=h) and is constant with radius T0 is mean outflow temperature q*a is the ambient saturated mixing ratio at the top of the surface layer r0 is the the radius at which surface tangential winds vanish

TB (Emanuel 1986)

PM03 the “local PBL balance” method