Analysis of Axisymmetric Hurricanes in Statistical Equilibrium

Analysis of Axisymmetric Hurricanes inStatistical 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

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 modelingprovides necessarily control to answer these questionsvery long simulations3D (WRF) (Bonnie Brown poster P2.76)here: axisymmetric


Method

Idealized axisymmetric modeling

modified version of Bryan and Rotunno (2009) model (r14)examine the mean and variability of the equilibrium solutioncompare mean with maximum potential intensity (MPI)

HistoryRotunno & Emanuel (1987): test of Emanuel (1986)Persing & Montgomery (2003): superintensityBryan & Rotunno (2009): superintensity sensitivity


Superintensity

Bryan & Rotunno (2009)

simulated intensity exceeds E-MPIPersing & Montgomery (2003): high entropy air in eyeBryan & Rotunno (2009): radial mixing parameterization

“realistic value” lh ∼ 1500 m.


Maximum wind speed for “standard configuration”

0 2 4 6 8 10 12 140

10

20

30

40

50

60

70

80

time (days)

win

d s

pee

d (

m/s

)

SST = 26.3◦C; Rayleigh damping “radiation”; warm rain; lh = 1500 m

little variability


Maximum wind speed for “standard configuration”

0 20 40 60 80 100 1200

10

20

30

40

50

60

70

80

time (days)

win

d s

pee

d (

m/s

)

SST = 26.3◦C; Rayleigh damping “radiation”; warm rain; lh = 1500 m

storm decays; not in equilibrium


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 newSmall outflow radius; dry air descends to small rEnvironment not in rad-conv equilibrium


Method

ModificationsExplicit radiation: RRTM-G longwave parameterizationThompson 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)


Maximum wind speed with radiation

0 2 4 6 8 10 12 140

20

40

60

80

100

120

time (days)

win

d s

pee

d (

m/s

)

convection develops from rest; superintense storm by day 10


Maximum wind speed with radiation

0 50 100 150 200 250 300 350 400 450 5000

20

40

60

80

100

120

time (days)

win

d s

pee

d (

m/s

)

superintense storm is transient; replaced by “equilibrium” storm


E-MPI

0 20 40 60 80 100 1200

20

40

60

80

100

120

140

time (days)

win

d sp

eed

(m/s

)

67 +/− 8.1 m/s70 +/− 3.9 m/s

periods of superintensity (days), but not in mean.


Sensitivity to turbulence mixing parameterization (lh)

0 500 1000 1500 2000 2500 300040

60

80

100

120

140

160

lh (m)

win

d s

pee

d (

m/s

)

equilibrium stormtransient stormBryan & Rotunno (2009)

lh sensitivitytransient storm sensitive as in Bryan and Rotunno (2009)equilibrium storm is insensitiveimplies standard sfc drag and vertical mixing are sufficient


Variability

Examine the variability of the equilibrium stormdominant structuresdominant timescales


Surface azimuthal wind r–t diagram

bands of stronger wind propagate inwarddominant time scale?


Surface azimuthal wind power spectrumpower spectrum; AR-1 (e-folding corr); AR-1 (lag-1 corr)

32 16 8 4 2 1 0.5 0.25 0.12510

−2

10−1

100

101

102

103

104

105

period (days)

pow

er

Two “peaks”∼1–3 hours: “random” convection4–8 days: organized convective bands


Radius of maximum wind time series

50 100 150 200 250 300 350 400 450 500

20

40

60

80

100

120

140

160

time (days)

rad

ius

(km

)

rapid jumps from ∼30 km to ∼60–100 km.analog of eyewall replacement


Composite mean “eyewall replacement” (131 events)

radius max winds (m) wind (m/s) & pressure (hPa)

−50 −40 −30 −20 −10 0 10 20 30 40 500

5

10

15

20

25

30

35

40

45

50

time (hours)

radi

us o

f max

imum

win

d (k

m)

−50 −40 −30 −20 −10 0 10 20 30 40 50−8

−6

−4

−2

0

2

4

6

8

10

12

time (hours)

max

imum

win

d (m

/s)

& c

entr

al p

ress

ure

(hP

a) a

nom

alie

s

RMW moves inward at ∼0.2 m/s and slowsasymmetric response in wind & pressure

(initially) slower weakening and faster intensification


Azimuthal wind regressed onto maximum wind

50 100 150 200 250 300 350

−200

−150

−100

−50

0

50

100

150

200

−2

0

2

4

6

8

sample size = 3759 (most of field is significant at 99%)4–8 day timescale apparentbands originate > 200 km radius

range in r sets timescale?

bands move inward 2 m/s; slowing to ∼ 0.2 m/s near eye


Conclusions: Axisymmetric Hurricanes in Statistical Equilibrium

Genesissuperintense storm develops spontaneously from restsuggests instability to symmetric convectionsuggests damping by asymmetries is important

Mean state“real” radiation critical for storm dynamicsequilibrium storm average intensity matches E-MPIequilibrium storm insensitive to radial mixing

Variability“eyewall replacement cycles”: convective bands at large raverage “return time” ∼4–8 days


Analysis of Axisymmetric Hurricanes in Statistical Equilibrium

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