Factors Controlling the Intensity of Idealized Hurricanes in Numerical Models* Richard Rotunno NCAR *Based on: Bryan, G. H., and R. Rotunno, 2008: The influence of near-surface, high-entropy air in hurricane eyes on maximum hurricane intensity. The Journal of the Atmospheric Sciences, in press. Bryan, G. H., and R. Rotunno, 2008: The maximum intensity of tropical cyclones in axisymmetric numerical model simulations. Submitted to Monthly Weather Review. Rotunno, R., Y. Chen, W. Wang, C. Davis, J. Dudhia and G. J. Holland, 2008: Resolved turbulence in a three-dimensional model of an idealized tropicaI cyclone. Submitted to Geophysical Research Letters.

Hurricane is a heat engine it depends on the temperature of the heat reservoir and the heat sink; the transfer of Heat to the hurricane and the drag of the ocean on the hurricane wind enter as a ratio; finally the relative humidity of The air below the lowest clouds is a factor (if RH=1 the air would be saturated and there could be no evaporative heat transfer).

Tangential Velocity from an Axisymmetric Numerical Model Bryan and Rotunno (2008 MWR)

Rotunno and Emanuel 1987 (RE87) / Axisymmetric Numerical Model Vortex Amplifies under Moist-Neutral Conditions Steady State Intensity Agrees with Theory (E-PI) Bryan and Rotunno (2008 MWR)

Persing and Montgomery (2003, JAS) using RE87 Model: Vmax Sensitive to Grid Resolution 7.5 15 Bryan and Rotunno (2008 MWR): RE87 paper RE87 code Vmax Sensitive to 7.5 15

Numerical Model Axisymmetric version of Bryan and Fritsch (2002, MWR) cloud model Uses newly developed, more accurate numerical techniques (compared to the RE87 model) Governing equations conserve mass and energy for saturated flows Includes dissipative heating Following RE87, new simulations use SST = 26C, moist-neutral initial sounding, same grid-staggering, simple microphysics, sea-surface transfer, and domain . New simulations at high grid resolution ( RE87 grid resolution ) (PM03 grid resolution ) Bryan and Rotunno (2008 MWR)

Numerical Models 3D Axisymmetric Turbulent fluxes represented by 37km Turbulent fluxes represented by mixing-length theory Turbulent fluxes computed, but high resolution required

Sensitivity to Turbulence Length Scales essentially inviscid PM03 RE87 Bryan and Rotunno (2008 MWR)

Sensitivity of Wind Speed to Turbulence Mixing Length lh Bryan and Rotunno (2008 MWR)

Evaluation of the “High-Entropy Reservoir”* shaded: black dot: location of vmax black line: trajectory default configuration: no surface fluxes in eye: *Persing and Montgomery (2003) Bryan and Rotunno (2008 JAS)

Structure of and Angular Momentum Bryan and Rotunno (2008 MWR)

Horizontal Diffusion Weakens Gradients of and Bryan and Rotunno (2008 MWR)

Vmax , E-PI vs Bryan and Rotunno (2009 in prep)

1. Moist slantwise neutrality 2. PBL Model Components of E-PI 1. Moist slantwise neutrality 2. PBL Model 3. Gradient-wind and hydrostatic balance Bryan and Rotunno (2009 in prep)

Flow with small horizontal diffusion not in gradient-wind balance Bryan and Rotunno (2009 in prep)

Rotating Flow Above a Stationary Disk* * Bödewadt (1940) (Schlichting 1968 Boundary Layer Theory); see also Rott and Lewellen 1966 Prog Aero Sci)

There are no observations of radial turbulent fluxes in a hurricane What is ? There are no observations of radial turbulent fluxes in a hurricane

Numerical Models 3D Axisymmetric Turbulent fluxes represented by 37km Turbulent fluxes represented by mixing-length theory Turbulent fluxes computed, but high resolution required

Weather Research and Forecast (WRF) Forecasts Radar Reflectivity at z=3km WRF ELDORA Davis et al. (2008 MWR)

Domain Idealized TC: WRF Model Physics: f-plane zero env wind 6075km Idealized TC: f-plane zero env wind fixed SST Nested Grids 1500km WRF Model Physics: WSM3 simple ice No radiation Relax to initial temp. Cd (Donelan) Ce (Carlson-Boland) Ce/Cd ~ 0.65 YSU PBL LES PBL 1000km 111km 333km 37km Check the vertical grid spacing! 50 vertical levels Dz=60m~1km Ztop=27km Rotunno et al. (2008 GRL)

Initial Condition (after RE87) Axisymmetric initial vortex Initial sounding WRF neutral Rotunno et al. (2008 GRL)

Instantaneous Maximum 10-m Wind Speed NOTE: Red to green: shift from PBL to TKE Rotunno et al. (2008 GRL)

10-m Wind Speed t=9.75d y[km] y[km] max=61.5 max=86.7 max=86.2 Rotunno et al. (2008 GRL)

10-m Wind Speed instantaneous 1-min average Max=85.5 Max=82.3 Max=83.7 37km 37 km Rotunno et al. (2008 GRL)

10-m Tangentially Averaged Wind Speed vs Grid Interval Rotunno et al. (2008 GRL)

Eddy Kinetic Energy Spectra Change x-axis ticks to 1/meter Change color to be consistent KE on a circle with max ke_mean Rotunno et al. (2008 GRL)

grid-scale waves & turbulence Estimation of Eddy Viscosity for Axisymmetric Models LES grid-scale grid-scale subgrid-scale TC Vortex grid-scale azimuthal average grid-scale waves & turbulence

Conclusions Treatment of turbulence in numerical models of hurricanes is as important for intensity prediction as other factors (e.g. sea-surface transfer, ocean-wave drag, cloud physics…) Quantitative information needed on turbulent transfer in hurricanes Observations are expensive, LES so far inconclusive