Frictional Damping of Baroclinic Waves HHH, 26th May 2006 Bob Plant With thanks to Stephen Belcher, Brian Hoskins, Dan Adamson
Motivation Control simulation, T+60 Simulation with no boundary layer turbulence, T+60. 950mb 930mb Simulations with and without boundary layer processes active for T+60 of storm on 12Z 31/10/00. Frictional Damping of Baroclinic Waves p.1/24
Surface Roughness Accounting for orographic and ocean wave effects has produced increased roughness in NWP The increased roughness has increased NWP skill. But how and why? (How much roughness should be there?) Has become a real issue in deciding between competing (but very different) parameterizations of orographic effects. Frictional Damping of Baroclinic Waves p.2/24
Some Context Potential vorticity framework Baroclinic wave studies with IGCM: LC1 and LC2 Added simple (but realistic) boundary layer scheme Three cyclones in UM (different forcing mechanisms) with careful diagnosis of PV generation by model physics Here, focus will be on LC1, with friction but no boundary layer heat fluxes Frictional Damping of Baroclinic Waves p.3/24
Bulk Effect of Friction 100 90 80 R0 2 ) Eddy kinetic energy (J/m 70 60 50 40 30 Rd 20 10 0 0 2 4 6 8 10 12 Time (days) Frictional Damping of Baroclinic Waves p.4/24
Mechanisms for Frictional PV Generation Frictional Damping of Baroclinic Waves p.5/24
PV Generation (1) Average over boundary layer: DP Dt = G 1 ρ F θ, (2) D[P] Dt = [G] w hp h h + small terms. Frictional Damping of Baroclinic Waves p.6/24
Contributions to [G] Ekman term: (3) [G E ] = 1 ρ 2 h 2 θˆk τ s = f θ ρh 2 w E Baroclinic term: (4) [G B ] = 1 ρ 2 h 2 ˆk τ s ( H θ) h v s v T and some small terms. Frictional Damping of Baroclinic Waves p.7/24
Ekman Pumping Convergence over low ascent vortex-tube squashing spindown of barotropic vortex tropopause ξ 2 free troposphere ξ 1 ξ > ξ 1 2 boundary layer surface Reduces PV over the low Frictional Damping of Baroclinic Waves p.8/24
Baroclinic Term a) N H L H v T dθ dy Basic-state temperature gradient Perturbation surface zonal wind Frictional Damping of Baroclinic Waves p.9/24
Baroclinic Term For a neutral wave: b) N v T v T H L H v min v max θ min dθ dx max θ max dθ dx min Perturbation zonal temperature gradient Perturbation meridional zonal wind Frictional Damping of Baroclinic Waves p.10/24 θ min
Baroclinic Term Combine these and account for wave growth and frictional turning of the wind: c) N v T v T H L H v T v T v T v T Frictional Damping of Baroclinic Waves p.11/24
Low-level PV Evolution of the Wave Frictional Damping of Baroclinic Waves p.12/24
Near-Surface PV 70N 60N 50N H L P1 40N 30N 20N 105W 90W 75W 60W 45W PV at σ = 0.98 after 4 days Frictional Damping of Baroclinic Waves p.13/24
Where Does This Come From? 70N a) 70N b) 60N L 60N L 50N H 50N H 40N 40N 30N 30N 20N 20N 105W 90W 75W 60W 45W 105W 90W 75W Ekman (left) and baroclinic (right) generation terms 60W 45W Frictional Damping of Baroclinic Waves p.14/24
Comparison with the Theory 70N c) 60N L 10 m/s 50N H 40N 30N 20N 105W Near surface winds and angle between v s and v T 90W 75W 60W 45W Frictional Damping of Baroclinic Waves p.15/24
Transport of Generated PV 70N a) 70N b) 70N c) 60N N L 60N L P1 60N P1 L 50N P1 H 50N H 50N H 40N 40N 40N 30N 30N 30N 20N 75W 60W 45W 30W 15W 20N 75W 60W 45W 30W 15W 20N 75W 60W 45W 30W 15W PV at σ = 0.98 (left), σ = 0.955 (left) and σ = 0.92 (right) after 6 days Frictional Damping of Baroclinic Waves p.16/24
Transport of Generated PV Negative low-level PV in vicinty of low Generated by Ekman mechanism close to low Remains localized Positive PV to north and east Generated by baroclinic mechanism Advected out of boundary layer by warm conveyor belt Frictional Damping of Baroclinic Waves p.17/24
How Does This Damp the Wave? Frictional Damping of Baroclinic Waves p.18/24
Cross Section 0.7 a) 0.8 Sigma 0.9 1.0 75W L 60W 45W 30W 15W PV and θ after 6 days Frictional Damping of Baroclinic Waves p.19/24
Stability 0.6 0.7 Sigma 0.8 0.9 1.0 0N 20N 40N 60N 80N Zonal-mean stability after 7 days (P1 dθ ) Frictional Damping of Baroclinic Waves p.20/24
Estimated Stability Effects Effect on linear growth rate of Eady wave: Using resulting N 25% reduction directly from increased N 15% reduction because Rossby radius increases so that wavenumber 6 is no longer optimal Frictional Damping of Baroclinic Waves p.21/24
Case Study (FASTEX IOP15) PV attributed to barotropic frictional effects, T+24, 900mb Frictional Damping of Baroclinic Waves p.22/24
Case Study PV attributed to baroclinic frictional effects, T+24, 950 and 850mb Frictional Damping of Baroclinic Waves p.23/24
Conclusions Ekman pumping spins down a barotropic vortex PV is generated baroclinically on the NE of a low (robust mechanism) Positive PV carried out of boundary layer Associated static stability anomaly Case studies suggest 1/3 of PV generation from friction Frictional Damping of Baroclinic Waves p.24/24