1. The Centre for Australian Weather and Climate Research A partnership between CSIRO and the Bureau of Meteorology The Tropical Cyclone Boundary Layer 2: Dynamics Jeff Kepert Head, High Impact Weather Research Oct 2013 www.cawcr.gov.au

2. The Centre for Australian Weather and Climate Research A partnership between CSIRO and the Bureau of Meteorology Turbulence time scales are short (< 1 hour) Cyclone evolves slowly (~ 10 hours to days) Assume that boundary layer flow in tropical cyclones is the response to Conditions above the boundary layer (gradient wind, stability structure) Surface conditions (roughness, fluxes) One side of two-way interaction Approach successful for marine boundary layer theory except for strong horizontal advection needs modification over land where diurnal effects are strong

3. The Centre for Australian Weather and Climate Research A partnership between CSIRO and the Bureau of Meteorology Theoretical framework BL affects the TC: distribution of updraft thermodynamic properties of updraft dynamic properties of updraft TC affects the BL: distribution of gradient wind / pressure large-scale divergence asymmetry turbulent fluxes through top convective downdrafts IgnoreKeep (some of)

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

5. Types of models Full nonlinear equations, asymmetric (Kepert and Wang 2001) Linearised equations, asymmetric (Rosenthal 1962, Kepert 2001) Depth-averaged equations, nonlinear, asymmetric (Shapiro 1983, Smith 2003, Smith and Vogl 2008) Depth-averaged equations, nonlinear, symmetric (Smith 2003, Smith and Vogl 2008) Depth-averaged equations, linear, symmetric (Ooyama 1969, Emanuel 1986) Prescribed vertical structure, symmetric (Smith 1968, Kuo 1971, Kepert 2010) One-dimensional (Moss and Rosenthal 1975, Powell 1980) Most of these models study the response to an imposed, steady, tropical cyclone-like pressure field. See Kepert (2010, QJRMS) for additional references.

6. The Centre for Australian Weather and Climate Research A partnership between CSIRO and the Bureau of Meteorology Angular momentum axisymmetric inviscid Absolute angular momentum is conserved for inviscid flow

7. The Centre for Australian Weather and Climate Research A partnership between CSIRO and the Bureau of Meteorology The full BL model Solves the thermodynamic and momentum budget equations over a domain that is hundreds of km across and a few km deep Upper boundary conditions represent all the effects of the TC on the BL Prescribed pressure / gradient wind Storm motion Convection Turbulent transfer Asymmetries (including environmental) Lower boundary condition has sophisticated air-sea interaction, etc Includes suitable turbulence closure, other parameterisations Model described in Kepert and Wang (2001, JAS) and Kepert (2012, MWR)

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

9. The Centre for Australian Weather and Climate Research A partnership between CSIRO and the Bureau of Meteorology Symmetric structure Radial Azimuthal Vertical

10. The Centre for Australian Weather and Climate Research A partnership between CSIRO and the Bureau of Meteorology Symmetric structure Radial Azimuthal Vertical

11. The Centre for Australian Weather and Climate Research A partnership between CSIRO and the Bureau of Meteorology Comparison to observations Obs in H. Isabel (Bell 2010) Typical model run

12. The Centre for Australian Weather and Climate Research A partnership between CSIRO and the Bureau of Meteorology Flow summary diagram v gr 10 4 ζ 100w -u 10 v 10

13. The Centre for Australian Weather and Climate Research A partnership between CSIRO and the Bureau of Meteorology Supergradient flow fig Black contours: v Shading: v – v gr, zero contour white Vectors u-w

14. The Centre for Australian Weather and Climate Research A partnership between CSIRO and the Bureau of Meteorology Supergradient flow Inflow produces an azimuthal acceleration (by conservation of angular momentum) Supergradient flow implies that there is an outwards acceleration Centrifugal force (outwards) + Coriolis (outwards) > pressure gradient (inwards) The jet maximum occurs within the inflow layer What maintains the inflow in the presence of this outwards acceleration?

15. The Centre for Australian Weather and Climate Research A partnership between CSIRO and the Bureau of Meteorology u gradient wind residual friction vertical advection radial advection v angular momentum advection friction vertical advection Contours: 0, +/-{1,2,3…128}*1e -4 m s -2

16. The Centre for Australian Weather and Climate Research A partnership between CSIRO and the Bureau of Meteorology Supergradient flow Inflow produces an azimuthal acceleration (by conservation of angular momentum) Supergradient flow implies that there is an outwards acceleration Centrifugal force (outwards) > Coriolis (inwards) + pressure gradient (inwards) The jet maximum occurs within the inflow layer What maintains the inflow in the presence of this outwards acceleration? Diffusion and advection of inflow from below, plus self-advection of inflow (less important)

17. The Centre for Australian Weather and Climate Research A partnership between CSIRO and the Bureau of Meteorology Radial wind Azimuthal wind Inside RMW Outside RMW Same above BL Large Variation in Nearby Wind Profiles

18. The Centre for Australian Weather and Climate Research A partnership between CSIRO and the Bureau of Meteorology Hurricane Guillermo (1997)

19. The Centre for Australian Weather and Climate Research A partnership between CSIRO and the Bureau of Meteorology Radial FlowAzimuthal Flow Strongest winds in right forward quadrant Strongest inflow to right 5 m/s Near-Surface Earth-Relative Flow

20. The Centre for Australian Weather and Climate Research A partnership between CSIRO and the Bureau of Meteorology Surface winds Powell (1982, MWR)

21. The Centre for Australian Weather and Climate Research A partnership between CSIRO and the Bureau of Meteorology Asymmetries (earth-relative) Total flow Asymmetric Wavenumber-1 Radial (10 m) Azimuthal (10 m)Vertical (400 m)

22. The Centre for Australian Weather and Climate Research A partnership between CSIRO and the Bureau of Meteorology Asymmetries (storm-relative) Total flow Asymmetric Wavenumber-1 Radial (10 m) Azimuthal (10 m)Vertical (400 m)

23. The Centre for Australian Weather and Climate Research A partnership between CSIRO and the Bureau of Meteorology 5 m/s Surface wind factor is 0.6 to 0.8 in outer part of storm. It increases towards the centre and is 0.8 to 1.0 near the RMW. It is larger on the left than on the right (in the NH). Surface Wind Reduction Factor - Ratio of surface wind speed to gradient wind

24. The Centre for Australian Weather and Climate Research A partnership between CSIRO and the Bureau of Meteorology Objective analysis, observations plotted as percentage, black ring shows RMW. No shading => not enough data for analysis. |V 50 | / |V 1500 | Largest values (~1) in left eye-wall. Smallest values to right. Secondary max associated with outer rainband. |V 50 | / |V 2500 | H. Georges: Observed Surface Wind Factor

25. The Centre for Australian Weather and Climate Research A partnership between CSIRO and the Bureau of Meteorology Track of Andrew at landfall over Miami in 1992, with positions of surface wind observations for which co-located aircraft data (at altitude ~ 3 km) were available. Hurricane Andrew

26. The Centre for Australian Weather and Climate Research A partnership between CSIRO and the Bureau of Meteorology From tabulated aircraft-surface wind speed comparison in Powell and Houston (Weather & Forecasting, 1996) Hurricane Andrew

27. The Centre for Australian Weather and Climate Research A partnership between CSIRO and the Bureau of Meteorology Hurricane Mitch (1998)

28. The Centre for Australian Weather and Climate Research A partnership between CSIRO and the Bureau of Meteorology Convection biased towards left rear of slowly moving storm. Data courtesy of NOAA/HRD Hurricane Mitch

29. The Centre for Australian Weather and Climate Research A partnership between CSIRO and the Bureau of Meteorology Hurricane Mitch - Comparison of gradient and observed winds GPS dropsonde data from NOAA/HRD Pressure profiles were fitted to observations at 100, 200 … 3000 m (left). Black = Holland Red = Willoughby Gradient wind compared to observed storm-relative azimuthal flow (right) Super-gradient near eye-wall from about 500 m to 2 km. 100 m 3 km 1.5 km 500 m

30. The Centre for Australian Weather and Climate Research A partnership between CSIRO and the Bureau of Meteorology Best track from NOAA/NHC Hurricane Georges

31. The Centre for Australian Weather and Climate Research A partnership between CSIRO and the Bureau of Meteorology Hurricane Georges From NOAA/NHC reconnaissance aircraft.

32. The Centre for Australian Weather and Climate Research A partnership between CSIRO and the Bureau of Meteorology Data from NOAA/HRD H. Georges – Observed eyewall wind profiles

33. The Centre for Australian Weather and Climate Research A partnership between CSIRO and the Bureau of Meteorology Georges : Observations and model wind speed

34. The Centre for Australian Weather and Climate Research A partnership between CSIRO and the Bureau of Meteorology Nonlinear model predicts Supergradient flow in upper boundary layer Inflow layer becomes shallower towards centre Surface wind factor increases towards centre, higher on left Strongest surface winds in right front quadrant Wind profile variation between storms Observational evidence for all of this Conclusions