The Tropical Cyclone Boundary Layer 4: Thermodynamics

1. The Tropical Cyclone Boundary Layer4: Thermodynamics www.cawcr.gov.au Jeff Kepert Head, High Impact Weather Research Oct 2013

2. Zhang et al (2011, MWR) composite r-z sections in North Atlantic hurricanes. 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 Top of inflow layer The Centre for Australian Weather and Climate ResearchA partnership between CSIRO and the Bureau of Meteorology

3. 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 ResearchA partnership between CSIRO and the Bureau of Meteorology

4. 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? Interesting questions … Potential temperature Top of inflow layer contour interval = 0.5 K This work in collaboration with Juliane Schwendike and Hamish Ramsay, Monash University. The Centre for Australian Weather and Climate ResearchA partnership between CSIRO and the Bureau of Meteorology

5. Budget equation for θ • Potential temperature budget in axisymmetric cylindrical coordinates: horizontal advection horizontal diffusion vertical diffusion diabatic vertical advection radius potential temperature vertical turbulent exchange coefficients for momentum radial wind azimuthal wind diffusion coefficient vertical velocity specific heat at constant pressure diabatic heating The Centre for Australian Weather and Climate ResearchA partnership between CSIRO and the Bureau of Meteorology

6. Budget equation for stability, ∂θ/∂z differential horizontal advection horizontal diffusion vertical diffusion horizontal advection diabatic stretching vertical advection Can’t change the sign of ∂θ/∂z Can change the sign of ∂θ/∂z The Centre for Australian Weather and Climate ResearchA partnership between CSIRO and the Bureau of Meteorology Budget equation of the lapse rate:

7. 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 ResearchA partnership between CSIRO and the Bureau of Meteorology

8. CM1 modelled wind structure Radial wind Azimuthal wind Vertical wind The Centre for Australian Weather and Climate ResearchA partnership between CSIRO and the Bureau of Meteorology

9. Model has close-to-observed thermal structure. Thermal Structure CM1 Zhang et al. obs The Centre for Australian Weather and Climate ResearchA partnership between CSIRO and the Bureau of Meteorology

10. Model θ-budget Vertical advection Red = warming Blue = cooling 10-3 K s-1 Log-like scale, 10-3 K s-1 Diabatic term The Centre for Australian Weather and Climate ResearchA partnership between CSIRO and the Bureau of Meteorology 10-3 K s-1

11. Model θ-budget Vertical diffusion Red = warming Blue = cooling Log-like scale, 10-3 K s-1 Horizontal advection The Centre for Australian Weather and Climate ResearchA partnership between CSIRO and the Bureau of Meteorology 10-3 K s-1

12. Budget equation for ∂θ/∂z differential horizontal advection horizontal diffusion vertical diffusion horizontal advection diabatic stretching vertical advection Can’t change the sign of ∂θ/∂z Can change the sign of ∂θ/∂z The Centre for Australian Weather and Climate ResearchA partnership between CSIRO and the Bureau of Meteorology Budget equation of the lapse rate:

13. Terms in model ∂θ/∂z-budget Differential horizontal advection Vertical stretching • 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. • Tends to erode the stability structure near the surface where ∂w/∂z > 0. Red = stabilising Blue = destabilising The Centre for Australian Weather and Climate ResearchA partnership between CSIRO and the Bureau of Meteorology

14. Terms in model ∂θ/∂z-budget Vertical diffusion Diabatic term • Tends to erode the stability structure, because it mixes towards constant θ. Red = stabilising Blue = destabilising The Centre for Australian Weather and Climate ResearchA partnership between CSIRO and the Bureau of Meteorology

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

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

17. The Centre for Australian Weather and Climate ResearchA partnership between CSIRO and the Bureau of Meteorology Hurricane Boundary Layer at 60 m

18. Flux measurements in outer rainbands • Zhang et al (2009, JAS) The Centre for Australian Weather and Climate ResearchA partnership between CSIRO and the Bureau of Meteorology

19. Heat and moisture fluxes • Zhang et al (2009, JAS) The Centre for Australian Weather and Climate ResearchA partnership between CSIRO and the Bureau of Meteorology

20. 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 ResearchA partnership between CSIRO and the Bureau of Meteorology

21. 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 ResearchA partnership between CSIRO and the Bureau of Meteorology

22. 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 ResearchA partnership between CSIRO and the Bureau of Meteorology