The Centre for Australian Weather and Climate ResearchA partnership between CSIRO and the Bureau of Meteorology

The Tropical Cyclone Boundary Layer4: Thermodynamics

Jeff Kepert

Head, High Impact Weather Research

Oct 2013

www.cawcr.gov.au

The Centre for Australian Weather and Climate Research A partnership between CSIRO and the Bureau of Meteorology

Observed thermal structure

• Zhang et al (2011, MWR) composite r-z sections in North Atlantic hurricanes.

Azimuthal wind

Potential temperature

Radial wind

Top of inflow layer

• Obs show that the well-mixed (constant θ) layer is half or less the depth of the inflow layer in TCs.

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Choice of definitions of BL depth

hinfl: inflow layer depth

zi: mixed layer depth

hvmax: height of maximum wind speed

Ricr: Bulk Richardson number = 0.25 From Zhang et al. (2009)

Which is “correct”?

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Interesting questions …

• Why is the inflow layer so stable?

• SST > Ts (by ~2 K), and the inflow layer is turbulent … so it should be “well mixed”

• Why is there a surface superadiabatic layer?

• 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?

Potential temperature

Top of inflo

w laye

r

contour interval = 0.5 K

This work in collaboration with Juliane Schwendike and Hamish Ramsay, Monash University.

The Centre for Australian Weather and Climate Research A partnership between CSIRO and the Bureau of Meteorology

Budget equation for θ

• Potential temperature budget in axisymmetric cylindrical coordinates:

pvhH C

Q

zK

zK

zw

ru

t

4

horizontal advection

vertical advection

horizontal diffusion

vertical diffusion

u

v

w

vK

potential temperature

radial wind

azimuthal wind

vertical velocity

radius

diffusion coefficient

vertical turbulent exchange coefficients for momentum

diabatic

diabatic heating

specific heat at constant pressure

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Budget equation for stability, ∂θ/∂z

• Budget equation of the lapse rate:

pvhH C

Q

zzK

zzK

zz

w

rz

u

zw

zru

zt

2

24

2

22

horizontal advection

vertical advection

differential horizontal advection

stretching

horizontal diffusion

vertical diffusion

diabatic

Can change the sign of ∂θ/∂z

Can’t change the sign of ∂θ/∂z

The Centre for Australian Weather and Climate Research 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)

The Centre for Australian Weather and Climate Research A partnership between CSIRO and the Bureau of Meteorology

CM1 modelled wind structure

Radial wind

Azimuthal wind

Vertical wind

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Thermal Structure

Model has close-to-observed thermal structure.

Zhang et al. obsCM1

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Log-like scale, 10-3 K s-1

Red = warming

Blue = cooling

Model θ-budget

10-3 K s-1

Diabatic term10-3 K s-1

Vertical advection

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Red = warming

Blue = cooling

Log-like scale, 10-3 K s-1

Vertical diffusion

Model θ-budget

10-3 K s-1

Horizontal advection

The Centre for Australian Weather and Climate Research A partnership between CSIRO and the Bureau of Meteorology

Budget equation for ∂θ/∂z

• Budget equation of the lapse rate:

pvhH C

Q

zzK

zzK

zz

w

rz

u

zw

zru

zt

2

24

2

22

horizontal advection

vertical advection

differential horizontal advection

stretching

horizontal diffusion

vertical diffusion

diabatic

Can change the sign of ∂θ/∂z

Can’t 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

• 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.

Differential horizontal advection 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. Red = stabilising

Blue = destabilising

Diabatic term

The Centre for Australian Weather and Climate Research A partnership between CSIRO and the Bureau of Meteorology

Model ∂θ/∂z-budget

Horizontal advection Vertical advection

• Horizontal and vertical advection can’t change the stability – they just move it around.

Red = stabilising

Blue = destabilising

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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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Hurricane Boundary Layer at 60 m

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Flux measurements in outer rainbands

• Zhang et al (2009, JAS)

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Heat and moisture fluxes

• Zhang et al (2009, JAS)

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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

The Centre for Australian Weather and Climate Research 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)

• Dots = height where stress drops to 20% of surface value.

The Centre for Australian Weather and Climate Research A partnership between CSIRO and the Bureau of Meteorology

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