Stratospheric Transport An incomplete review of various and sundry - PowerPoint PPT Presentation

Stratospheric Transport An incomplete review of various and sundry topics Timothy Hall NASA Goddard Institute for Space Studies New York

Stratospheric “middle-world” Stratospheric “over-world” in q contact with troposphere . dT/dz > 0; d q /dz >> 0 Tropospheric “middle-world” “Under-world” in frictional dT/dz < 0; d q /dz ~ 0. contact with surface

Brewer, 1949 (H 2 O) Dobson, 1956 (O 3 )

UARS (HALOE) observations

Brewer-Dobson circulation originally thought to be driven by heating. Work since 1970s* shows driving force to be mechanical (heating responds to maintain consistency). Surfaces of total angular momentum density ~ vertical Meridional motion must Entail change in parcel’s angular Momentum. Provided by force. ∂ m ∂ t + v •— m = a (cos j ) F F = wave-drag: eddy-correlation divergence due to breaking waves. *e.g., Dickinson, 1971; Held and Hou, 1980; Haynes et al, 1991

Wave drag Circulation induced by wave-drag theory in winter hemisphere. Circulation below drag region: “downward control” (Haynes et al., 1991). Note: it’s a mass circulation. Not the same as Eulerian mean. Important details remain: How to reach into tropics?

In q coordinates, vertical velocity is heating rate d q /dt. Compute from radiative calculations and composition. Rosenlof et al, 1995 Eluszkiewicz et al., 1999

Low-wave number planetary waves dominate winter stratosphere. Waves can break, forcing mean-flow and mixing trace gases. 12-day contour advection at 50hPa analysis 480K (Waugh & Plumb, JAS, 1994.)

vortex midlatitude “surf zone” entrained tropical air

What are consequences for long-lived tracer transport? (Andrews et al. 1987) Dq Linear disturbances to zonal flow q = q + q ' Dt = S Effect of zonal-mean state to second order: ∂ q ∂ t + v ∂ q ∂ y + w ∂ q ( ) ∂ z = S - r - 1 — • r v ' q ' q ' = ( x ', y ', z ') •— q Write (x’,y’,z’) is parcel displacement ∂ q † ∂ q † ∂ q ∂ z = S + r - 1 — • r K •— q ( ) ∂ t + v ∂ y + w Two effects: 1. Diffusive-like Ê ˆ Ê ˆ K = K yy K yz y ' 2 ˜ = 1 ∂ y ' z ' Á ˜ Á Á ˜ K yz K zz z ' 2 2 ∂ t y ' z ' Ë ¯ Ë ¯

∂ q † ∂ q † ∂ q ∂ z = S + r - 1 — • r K •— q ( ) ∂ t + v ∂ y + w Advective-like effect: Stoke’s drift terms. Ê ˆ Ê ˆ - 1 ∂ † = w - ∂ † = v + r 1 1 ( ) ( ) v r v ' z ' - w ' y ' w v ' z ' - w ' y ' Á ˜ Á ˜ ∂ z Ë ¯ ∂ y Ë ¯ 2 2 Generally, zonal-mean and Stoke’s drift oppose each other. Net flow (“residual circulation”) small difference of large terms. z

Impact on long-lived tracers: “slope equilibrium” (Mahlman et al., 1986; Plumb and Mahlman, 1987; Plumb and Ko, 1992) Ê ˆ * = ∂c ∂ q ∂ q ∂ y + c ∂ q ∂ t = ∂ w ∂ y K yy ˜ + S where Á ∂ z ∂ y Ë ¯ Steady-state and S slow compared to circulation (long-lived) isopleth slope = - ∂ q / ∂ y ∂ q / ∂ z = - c independent of tracer. K yy If wave-mixing globally-rapid compared to circulation … slope-steepening global mixing surface slope-flattening

UARS (HALOE) observations

Parcels undergo random-walk in latitude on mixing surface. Sample regions of up and down residual circulation. 1-D effective flux gradient relationship across mixing surface: F ( Z ) = K ( Z ) dq dZ = F = S 1 ( Z ) dq 1 ( Z ) 1 ( Z ) = lifetime tracer 2 above Z F 2 ( Z ) dq 2 ( Z ) S 2 ( Z ) lifetime tracer1above Z Know chemical lifetime of one tracer, measure slope of tracer-tracer curve (locally!), have estimate of lifetime of other tracer.

c 1 z c 2 mixing ratio

But tropics look different… Kawa et al., 1993 Murphy et al, 1993

“Transport barriers” visible directly in tracer PDF data (Neu et al, 2003).

Quantifying “surf-zone” mixing: Effective diffusivity (Nakamura, 1996) Transport across tracer contours Must be diffusive. Ê ˆ ∂ t q ( A , t ) = ∂ ∂ 2 ∂ ∂ A k L e ∂ A q ˜ + S Á Ë ¯ Effecive diffusivity proportional to “equivalent length” L e 2 , defined by ∂ A = — q ∂ q L e L e close to length of q contour. More mixing, more convoluted countours, greater effective diffusivity.

Nakamura effective diffusivity from idealized tracers transported by met. data. (Haynes and Shuckburgh, 2000.) Ê ˆ ∂ t q ( A , t ) = ∂ ∂ 2 ∂ ∂ A k L e ∂ A q ˜ + S Á Ë ¯ “Transport barriers” in tropics and polar vortex.

“Tropical leaky pipe” model (Plumb, 1996; Neu and Plumb, 1999) Limit of rapid surf-zone mixing, midlatitudes are vertical 1D, with tropical entrainment/detrainment. Result: coupled 1D advection-diffusion. Analytic solutions in certain limits. Ê ˆ ∂ q T + W ∂ q T - Z / H ∂ q T Z / H ∂ ( ) - e K T e ˜ = - s q T - q M Á ∂ t ∂ Z ∂ Z Ë ∂ Z ¯ Ê ˆ ∂ q M - a W ∂ q M - Z / H ∂ q M Z / H ∂ ( ) q T - q M ( ) - e K M e ˜ = l + as Á ∂ t ∂ Z ∂ Z Ë ∂ Z ¯ Z / H ∂ where ( ) Z / H W ( Z ) is tropical divergence rate l = - a e e ∂ Z a = M T and is measure of tropical barrier latitude. 2 M M

Stratosphere-Troposphere Exchange in Midlatitudes Downward flux into lowermost stratosphere is diabatic, driven by large-scale resididual circulation. Peaks in winter, with wave-forcing. Flux into troposphere net downward, but is two-way, isentropic, driven by complex, synoptic events. Fluxes not necessarily in phase. Can compute flux from overworld By radiative calculation of residual circulation. But across tropopause More dificult to estimate directly.

PV on 320K isentrope crossing climatoligical tropopause. Driven by upper-tropospheric cyclones … can lead to cut-off cyclones which radiate, convect, mix turbulently for final incorporation by troposphere. Contour advection illustrating filaments formed by flow features.

Appenzeller et al., 1996 F out = d dt M + F in M = mass between 380K and 2PV from UKMO data F in = net diabatic heating rate (vertical velocity in q coords)

Other topics in stratospheric transport • Quasi-biennial oscillation: dominant variability after annual. visible in tracers, particularly in tropics. • Tropical-transition layer: details of how tropospheric air enters the stratosphere. • Stability--instability of polar vortex; sudden warmings. • Modeling of stratospheric tracers.