Transcript Current understanding and remaining issues on Rapid

A Simplified Dynamical System for
Understanding the Intensity-Dependence of
Intensification Rate of a Tropical Cyclone
Yuqing Wang
International Pacific Research Center and Department of
Atmospheric Sciences, University of Hawaii at Manoa, Honolulu,
Hawaii, USA
Jing Xu
State Key Laboratory of Severe Weather, Chinese Academy of
Meteorological Sciences, CMA, Beijing, China
International Workshop on High Impact Weather Research
20-23 January 2015, Ningbo, China
Outline
• Motivation
• A Carnot heat engine view
• An alternative view based on a simplified
dynamical system for intensity forecast
(LGEM)
• Conclusions
Different intensification rate (IR)
RI of a TC is often
defined as an increase
in the peak 10-m wind
speed of 30 knots (or
roughly 15m/s) in 24 h
Frank Marks (Director of Hurricane Research Division)
“I have often wondered how quickly a TC can intensify and
have questioned my smarter brethren in the TC community
to provide some theoretical basis for a maximum
intensification rate for a TC, such has been proposed and
debated for something like MPI. It seems that it should be
straightforward to use the Navier-Stokes equations and
determine the peak intensity change possible. ….
The question is what controls that rate and what parameters
determine it. That would provide potential bounds to the
problem that would inform modelers as well as forecasters.”
Scatter diagram of the subsequent 24-h IR against the storm intensity
(Vmax) with red and black curves indicating the smoothed 50th and 95th
percentiles of IR for the given storm intensity for Atlantic TCs during
1988-2012.
Xu and Wang (2014)
Tropopause
Outflow
Eyewall
EYE
Outflow
Eyewall
Inflow
Schematic diagram showing the dynamical processes in a strong TC
Wang （2014）
Schubert & Willoughby(1982): If the TC structure is
given, the inner-core inertial stability is proportional
to Vmax of the storm, the intensification rate (IR)
should increase with the increase in TC intensity.
Heating efficiency
A, B, C, D, E indicate increasing
in the inner core inertial stability
B: heating source
V: momentum forcing
Thermodynamic Control of TC Intensity and its change
A Carnot Heat Engine View
Tout
Carnot heat engine
SST
Emanuel 1988
Energy Budget in the Carnot Heat Engine
Rate of Intensity Change = Rate of Energy Input – Dissipation Rate
SST  Tout

Tout

Ck
CD
|V|
k*o
ka

The thermodynamic efficiency of the Carnot heat engine
The surface exchange coefficient
The surface drag coefficient
The near surface wind speed
Enthalpy of the ocean surface
Enthalpy of the atmosphere near the surface
Air density near the surface
At MPI,
Emanuel (1997),
Energy change rate
Dissipation rate
Energy input
Intensification
MPI
Vmpi
|Vmpi|
Ck

 (k**o  k a )
CD
|V|
Wang (2013)
During the intensification stage, the energy growth rate (EGR) of
the dynamical system can be written as
Using the express of Vmpi, the above equation can be rewritten as
The storm IR depends on the storm intensity (the maximum nearsurface wind speed). IR reaches a maximum when
This will lead to maximum IR to occur at an intermediate intensity
The corresponding maximum EGR will be
If we consider that 5% of TCs could
reach their MPI of 120-140 kt. The
lifetime maximum IR could be 69-81
kt, very close to the peak for the 95th
percentile IR in observations.
Energy change rate
- Dissipation rate
Energy input
Intensification
EGRmpi
MPI
Vmpi 
|Vmpir|
|Vmpi|
Ck
 ( k**o  k a )
CD
|V|
Wang and Xu (2015)
20%
20%
>= 0.5
18%
< 30
[30, 40)
> 40
16%
16%
14%
14%
12%
12%
10%
10%
8%
8%
6%
6%
4%
4%
2%
2%
0.1
0.2
0.3
0.4 0.5
Vmax MPI
0.6
0.7
0.8
20%
>= 0.6
18%
0.1
0.2
0.3
0.4 0.5
Vmax MPI
0.6
0.7
0.8
0.3
0.4 0.5
Vmax MPI
0.6
0.7
0.8
20%
>= 0.7
18%
16%
16%
14%
14%
12%
12%
10%
10%
8%
8%
6%
6%
4%
4%
2%
2%
0.1
0.2
>= 0.8
18%
0.3
0.4 0.5
Vmax MPI
0.6
0.7
0.8
0.1
0.2
An alternative Dynamical System based on a logistic
growth equation model (LGEM) of DeMaria (2009)
In DeMaria’s system, IR is mathematically given as
Steady state solution
First term: a linear growth term
Second term: limits the maximum wind to an upper bound (Vmpi)
κ is the time-dependent growth rate, and β (1/24h) and n (2.5)are
positive constants that determine how rapidly and how close the
solution for V can come to Vmpi.
Letting
, we can find that IR reaches a maximum value when
the storm intensity is around Vmpir given by
We use the lifetime maximum intensity of each storm as an estimate for
the steady state intensity Vs
35%
(a)
95th
50th
90
80
30%
25%
70
IRmax (kt/24h)
(b)
60
20%
50
15%
40
30
10%
20
5%
10
0.3
0.4
0.5
0.6
0.7
V Vs
0.8
0.9
1.0
0.3
0.4
0.5
0.6
0.7
0.8
0.9
V Vs
(a) Scatter diagram of the lifetime maximum 24-h IR (IRmax) against the
averaged storm intensity during the 24-h IRmax period normalized by the
lifetime maximum intensity of the storm (namely V/Vs).
(b)The frequency distribution of the lifetime IRmax as a function of the
corresponding normalized storm intensity.
Conclusions
Observations show a strong dependence of IR on TC intensity and
the existence of a preferred intermediate intensity for RI to occur.
This was previously explained as a result of a balance between heat
efficiency and the MPI.
Based the Carnot heat engine, we have developed a simplified
dynamical system model to explain the observed intensitydependence of IR. In this view, the energy input and energy
dissipation rates increase with the storm intensity at quite different
rates, namely linear versus a cubic power of wind speed.
In addition, an alternative simplified dynamical system for TC
intensity change previously developed by DeMaria (2009) was also
used to further demonstrate the nature of the dynamical system that
we newly developed.
Thank you for your attention!
Questions and comments!