The Centre for Australian Weather and Climate Research A partnership between CSIRO and the Bureau of Meteorology The Tropical Cyclone Boundary Layer 4: Thermodynamics Jeff Kepert Head, High Impact Weather Research Oct

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.

The Centre for Australian Weather and Climate Research A partnership between CSIRO and the Bureau of Meteorology Choice of definitions of BL depth h infl : inflow layer depth z i : mixed layer depth h vmax : height of maximum wind speed Ri cr : Bulk Richardson number = 0.25From Zhang et al. (2009) Which is “correct”?

The Centre for Australian Weather and Climate Research A partnership between CSIRO and the Bureau of Meteorology Interesting questions … Why is the inflow layer so stable? SST > T s (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 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 Research A partnership between CSIRO and the Bureau of Meteorology Budget equation for θ Potential temperature budget in axisymmetric cylindrical coordinates: horizontal advection vertical advection horizontal diffusion vertical diffusion 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

The Centre for Australian Weather and Climate Research A partnership between CSIRO and the Bureau of Meteorology Budget equation for stability, ∂θ/∂z Budget equation of the lapse rate: 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

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

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

The Centre for Australian Weather and Climate Research A partnership between CSIRO and the Bureau of Meteorology Red = warming Blue = cooling Log-like scale, K s -1 Vertical diffusion Model θ-budget 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: 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 advectionVertical 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 advectionVertical 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 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)

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

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

The Centre for Australian Weather and Climate Research 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 z i 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

The Centre for Australian Weather and Climate Research A partnership between CSIRO and the Bureau of Meteorology Rainband structure Barnes and Powell (1995) Hurricane Gilbert as eye made landfall on Jamaica Based on aircraft Doppler radar and insitu data.

The Centre for Australian Weather and Climate Research A partnership between CSIRO and the Bureau of Meteorology Boundary-layer flow near a rainband Composite cross-section across a rainband. Inflow abruptly stops at rainband, strong convergence Near-surface wind maximum on outer edge of rainband Strong θ e gradient across rainband Barnes and Powell (MWR, 1995)

The Centre for Australian Weather and Climate Research A partnership between CSIRO and the Bureau of Meteorology Hurricane Earl Powell (1990a,b, MWR)

The Centre for Australian Weather and Climate Research A partnership between CSIRO and the Bureau of Meteorology Not all rainbands are alike – mid-level inflow? Left: Schematic of flow and thermodynamics in Gilbert Right: Schematic in Hurricanes Earl and Floyd Barnes and Powell (MWR, 1995)

The Centre for Australian Weather and Climate Research A partnership between CSIRO and the Bureau of Meteorology Wroe and Barnes (2003)

The Centre for Australian Weather and Climate Research A partnership between CSIRO and the Bureau of Meteorology Wroe and Barnes (2003)

The Centre for Australian Weather and Climate Research A partnership between CSIRO and the Bureau of Meteorology Air-sea temperature differences SST – TA, SST>27 o C SST – TA, SST<27 o C Observed air-sea temperature difference in hurricanes from buoy data From Cione et al (2000)

The Centre for Australian Weather and Climate Research A partnership between CSIRO and the Bureau of Meteorology Observed surface humidity in hurricanes Observed RH and q from buoy data in hurricanes. From Cione et al (2000)