The Tropical Cyclone Boundary Layer
4: Thermodynamics
www.cawcr.gov.au
Jeff Kepert
Head, High Impact Weather Research
Oct 2013
The Centre for Australian Weather and Climate Research
A partnership between CSIRO and the Bureau of Meteorology
Observed thermal structure
•
Azimuthal wind
Obs show that the well-mixed
(constant θ) layer is half or less the
depth of the inflow layer in TCs.
Potential temperature
Radial wind
•
Zhang et al (2011, MWR) composite r-z
sections in North Atlantic hurricanes.
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Choice of definitions of BL depth
Which is “correct”?
hinfl: inflow layer depth
hvmax: height of maximum wind speed
zi: mixed layer depth
Ricr: Bulk Richardson number = 0.25
From Zhang et al. (2009)
The Centre for Australian Weather and Climate Research
A partnership between CSIRO and the Bureau of Meteorology
Interesting questions …
Potential temperature
•
Why is the inflow layer so
stable?
•
•
Why is there a surface
superadiabatic layer?
•
contour interval = 0.5 K
This work in collaboration with
Juliane Schwendike and Hamish
Ramsay, Monash University.
•
SST > Ts (by ~2 K), and the
inflow layer is turbulent … so
it should be “well mixed”
These occur over land, but
normally require a very high
skin temperature and light
winds … neither of which exist
in TCs
Where is the top of the BL?
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A partnership between CSIRO and the Bureau of Meteorology
Budget equation for θ
•
Potential temperature budget in axisymmetric cylindrical coordinates:



    Q
4
 u
w
 K H  h   K v

t
r
z
z 
z  C p
horizontal
horizontal
advection
diffusion
vertical
advection
q
potential temperature
u radial wind
v azimuthal wind
w
vertical velocity
r
vertical
diffusion
diabatic
radius
K v vertical turbulent exchange
coefficients for momentum
K H diffusion coefficient
C p specific heat at constant pressure
Q diabatic heating
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A partnership between CSIRO and the Bureau of Meteorology
Budget equation for stability, ∂θ/∂z
•
Budget equation of the lapse rate:
2
 
 2
 2 u  w 
 4        Q
 u
w 2 

 K H  h
  2  Kv

t z
rz
z
z r z z
z  z 
z  z C p

horizontal
advection
differential
horizontal
advection
vertical
advection
horizontal
diffusion
vertical
diffusion
diabatic
stretching
Can’t change the sign of ∂θ/∂z
Can change the sign of ∂θ/∂z
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A partnership between CSIRO and the Bureau of Meteorology
The model
CM1: Axisymmetric TC model of Bryan and Rotunno
(2009)
•
•
•
Non-hydrostatic
Axisymmetric “full-physics” tropical cyclone model
Simulations are time-mean of a quasi-steady state storm at
potential intensity (PI)
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A partnership between CSIRO and the Bureau of Meteorology
CM1 modelled wind structure
Radial
wind
Azimuthal
wind
Vertical
wind
The Centre for Australian Weather and Climate Research
A partnership between CSIRO and the Bureau of Meteorology
Thermal Structure
CM1
Zhang et al. obs
Model has close-to-observed thermal structure.
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A partnership between CSIRO and the Bureau of Meteorology
Vertical advection
Model θ-budget
Red = warming
Blue = cooling
10-3 K s-1
Diabatic term
Log-like scale, 10-3 K s-1
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10-3 K s-1
A partnership between CSIRO and the Bureau of Meteorology
Vertical diffusion
Model θ-budget
Red = warming
Blue = cooling
Log-like scale, 10-3 K s-1
Horizontal advection
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10-3 K s-1
A partnership between CSIRO and the Bureau of Meteorology
Budget equation for ∂θ/∂z
•
Budget equation of the lapse rate:
2
 
 2
 2 u  w 
 4        Q
 u
w 2 

 K H  h
  2  Kv

t z
rz
z
z r z z
z  z 
z  z C p

horizontal
advection
differential
horizontal
advection
vertical
advection
horizontal
diffusion
vertical
diffusion
diabatic
stretching
Can’t change the sign of ∂θ/∂z
Can change the sign of ∂θ/∂z
The Centre for Australian Weather and Climate Research
A partnership between CSIRO and the Bureau of Meteorology
Terms in model ∂θ/∂z-budget
Differential horizontal advection
• Tends to strengthen the observed
stability structure in the core, because
(a) the cyclone is warm cored and (b)
the inflow is a maximum near 100-m
height.
Vertical stretching
• Tends to erode the stability structure
near the surface where ∂w/∂z > 0.
Red = stabilising
Blue = destabilising
The Centre for Australian Weather and Climate Research
A partnership between CSIRO and the Bureau of Meteorology
Terms in model ∂θ/∂z-budget
Vertical diffusion
• Tends to erode the stability
structure, because it mixes
towards constant θ.
Diabatic term
Red = stabilising
Blue = destabilising
The Centre for Australian Weather and Climate Research
A partnership between CSIRO and the Bureau of Meteorology
Model ∂θ/∂z-budget
Horizontal advection
• Horizontal and vertical advection
can’t change the stability – they
just move it around.
Vertical advection
Red = stabilising
Blue = destabilising
The Centre for Australian Weather and Climate Research
A partnership between CSIRO and the Bureau of Meteorology
Fluxes: the CBLAST experiment
• CBLAST: Coupled
Boundary Layers Air Sea
Transfer
• Major field program to
measure air-sea fluxes
• Specially instrumented
aircraft
• Stepped descents
between rainbands (not
eyewall)
• Black et al (2007 BAMS)
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A partnership between CSIRO and the Bureau of Meteorology
The Centre for Australian Weather and Climate Research
Hurricane Boundary Layer at 60 m
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Flux measurements in outer rainbands
• Zhang et al (2009, JAS)
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A partnership between CSIRO and the Bureau of Meteorology
Heat and moisture fluxes
• Zhang et al (2009, JAS)
The Centre for Australian Weather and Climate Research
A partnership between CSIRO and the Bureau of Meteorology
Vertical structure
• Fluxes extend to well above the inversion (stable layer)
• Flux becomes zero (~top of boundary layer) at about 2 zi
• Suggests that the stable layer is not the top of the boundary layer
• Momentum flux is similar to that in textbooks, except deeper
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A partnership between CSIRO and the Bureau of Meteorology
Modelled flow and depth of surface influence
• Two simulation with Kepert and Wang (2001) model, different turbulence
parameterisations. From Kepert (2010a QJRMS)
The Centre for Australian Weather and Climate Research
between CSIRO and the Bureau of Meteorology
• Dots = height where stress drops to 20% Aofpartnership
surface
value.
Thermal structure conclusions
• The main stabilising term is differential advection.
• The inflow decreases with height, and advects cold (low θ) air inwards. So
the cooling is strongest in the lower BL.
• This term reverses (destabilises) right next to the surface because the
inflow max is at about 100-m height … so the differential advection is
reversed right near the surface.
• Main destabilising terms are:
• Vertical diffusion – due to heating from below.
• Differential advection below ~100 m causes the “surface super”.
• One-dimensional thinking is no good for TCBL thermodynamics.
• Constant-θ is not a good definition of the TCBL.
• Mixing is much deeper than constant-θ layer.
• Boundary layer depth a little greater than inflow layer depth
• In axisymmetric storms
• Motion asymmetry is a difficulty
The Centre for Australian Weather and Climate Research
A partnership between CSIRO and the Bureau of Meteorology