1. Analysis of Axisymmetric Hurricanes in
Statistical Equilibrium
Gregory J. Hakim
University of Washington
29th Conference on Hurricanes and Tropical Meteorology
Sponsors: NSF & ONR
Gregory J. Hakim AMS 2010: Axisymmetric Hurricanes in Statistical Equilibrium

2. Motivation
Basic understanding of “intrinsic” tropical cyclone variability
remove variability due to environment (SST & shear)
remove variability due to asymmetries (motion, etc.)
isolate predictable components
Numerical modeling
provides necessarily control to answer these questions
very long simulations
3D (WRF) (Bonnie Brown poster P2.76)
here: axisymmetric
Gregory J. Hakim AMS 2010: Axisymmetric Hurricanes in Statistical Equilibrium

3. Method
Idealized axisymmetric modeling
modified version of Bryan and Rotunno (2009) model (r14)
examine the mean and variability of the equilibrium solution
compare mean with maximum potential intensity (MPI)
History
Rotunno & Emanuel (1987): test of Emanuel (1986)
Persing & Montgomery (2003): superintensity
Bryan & Rotunno (2009): superintensity sensitivity
Gregory J. Hakim AMS 2010: Axisymmetric Hurricanes in Statistical Equilibrium

4. Superintensity
Bryan & Rotunno (2009)
simulated intensity exceeds E-MPI
Persing & Montgomery (2003): high entropy air in eye
Bryan & Rotunno (2009): radial mixing parameterization
“realistic value” lh ∼ 1500 m.
Gregory J. Hakim AMS 2010: Axisymmetric Hurricanes in Statistical Equilibrium

5. Maximum wind speed for “standard configuration”
80
70
60
50
wind speed (m/s)
40
30
20
10
0
0 2 4 6 8 10 12 14
time (days)
SST = 26.3◦ C; Rayleigh damping “radiation”; warm rain; lh = 1500 m
little variability
Gregory J. Hakim AMS 2010: Axisymmetric Hurricanes in Statistical Equilibrium

6. Maximum wind speed for “standard configuration”
80
70
60
50
wind speed (m/s)
40
30
20
10
0
0 20 40 60 80 100 120
time (days)
SST = 26.3◦ C; Rayleigh damping “radiation”; warm rain; lh = 1500 m
storm decays; not in equilibrium
Gregory J. Hakim AMS 2010: Axisymmetric Hurricanes in Statistical Equilibrium

7. Why does the storm dissipate?
angular momentum (lines) & relative humidity (colors)
t = 15 days t = 25 days
Problems with Rayleigh damping “radiation”
Only damps existing perturbations; cannot create new
Small outflow radius; dry air descends to small r
Environment not in rad-conv equilibrium
Gregory J. Hakim AMS 2010: Axisymmetric Hurricanes in Statistical Equilibrium

8. Method
Modifications
Explicit radiation: RRTM-G longwave parameterization
Thompson et al. (2008) microphysics (6 class; 2-moment)
E-MPI modified to include ice (pseudoadiabatic entropy)
no initial disturbance (cf. initial vortex in previous work)
Gregory J. Hakim AMS 2010: Axisymmetric Hurricanes in Statistical Equilibrium

9. Maximum wind speed with radiation
120
100
80
wind speed (m/s)
60
40
20
0
0 2 4 6 8 10 12 14
time (days)
convection develops from rest; superintense storm by day 10
Gregory J. Hakim AMS 2010: Axisymmetric Hurricanes in Statistical Equilibrium

10. Maximum wind speed with radiation
120
100
80
wind speed (m/s)
60
40
20
0
0 50 100 150 200 250 300 350 400 450 500
time (days)
superintense storm is transient; replaced by “equilibrium” storm
Gregory J. Hakim AMS 2010: Axisymmetric Hurricanes in Statistical Equilibrium

11. E-MPI
140
67 +/− 8.1 m/s
70 +/− 3.9 m/s
120
100
wind speed (m/s)
80
60
40
20
0
0 20 40 60 80 100 120
time (days)
periods of superintensity (days), but not in mean.
Gregory J. Hakim AMS 2010: Axisymmetric Hurricanes in Statistical Equilibrium

12. Sensitivity to turbulence mixing parameterization (lh )
160
equilibrium storm
transient storm
Bryan & Rotunno (2009)
140
120
wind speed (m/s)
100
80
60
40
0 500 1000 1500 2000 2500 3000
lh (m)
lh sensitivity
transient storm sensitive as in Bryan and Rotunno (2009)
equilibrium storm is insensitive
implies standard sfc drag and vertical mixing are sufficient
Gregory J. Hakim AMS 2010: Axisymmetric Hurricanes in Statistical Equilibrium

13. Variability
Examine the variability of the equilibrium storm
dominant structures
dominant timescales
Gregory J. Hakim AMS 2010: Axisymmetric Hurricanes in Statistical Equilibrium

14. Surface azimuthal wind r –t diagram
bands of stronger wind propagate inward
dominant time scale?
Gregory J. Hakim AMS 2010: Axisymmetric Hurricanes in Statistical Equilibrium

15. Surface azimuthal wind power spectrum
power spectrum; AR-1 (e-folding corr); AR-1 (lag-1 corr)
5
10
4
10
3
10
2
10
power
1
10
0
10
−1
10
−2
10
32 16 8 4 2 1 0.5 0.25 0.125
period (days)
Two “peaks”
∼1–3 hours: “random” convection
4–8 days: organized convective bands
Gregory J. Hakim AMS 2010: Axisymmetric Hurricanes in Statistical Equilibrium

16. Radius of maximum wind time series
160
140
120
radius (km)
100
80
60
40
20
50 100 150 200 250 300 350 400 450 500
time (days)
rapid jumps from ∼30 km to ∼60–100 km.
analog of eyewall replacement
Gregory J. Hakim AMS 2010: Axisymmetric Hurricanes in Statistical Equilibrium

17. Composite mean “eyewall replacement” (131 events)
radius max winds (m) wind (m/s) & pressure (hPa)
50 12
45 10
maximum wind (m/s) & central pressure (hPa) anomalies
40 8
35 6
radius of maximum wind (km)
30 4
25 2
20 0
15 −2
10 −4
5 −6
0 −8
−50 −40 −30 −20 −10 0 10 20 30 40 50 −50 −40 −30 −20 −10 0 10 20 30 40 50
time (hours) time (hours)
RMW moves inward at ∼0.2 m/s and slows
asymmetric response in wind & pressure
(initially) slower weakening and faster intensification
Gregory J. Hakim AMS 2010: Axisymmetric Hurricanes in Statistical Equilibrium

18. Azimuthal wind regressed onto maximum wind
8
200
150
6
100
50 4
0
2
−50
−100
0
−150
−2
−200
50 100 150 200 250 300 350
sample size = 3759 (most of field is significant at 99%)
4–8 day timescale apparent
bands originate > 200 km radius
range in r sets timescale?
bands move inward 2 m/s; slowing to ∼ 0.2 m/s near eye
Gregory J. Hakim AMS 2010: Axisymmetric Hurricanes in Statistical Equilibrium

19. Conclusions: Axisymmetric Hurricanes in Statistical Equilibrium
Genesis
superintense storm develops spontaneously from rest
suggests instability to symmetric convection
suggests damping by asymmetries is important
Mean state
“real” radiation critical for storm dynamics
equilibrium storm average intensity matches E-MPI
equilibrium storm insensitive to radial mixing
Variability
“eyewall replacement cycles”: convective bands at large r
average “return time” ∼4–8 days
Gregory J. Hakim AMS 2010: Axisymmetric Hurricanes in Statistical Equilibrium