Timescales for stratospheric transport inferred from tracers - - PowerPoint PPT Presentation

Timescales for stratospheric transport inferred from tracers

Timothy Hall NASA GISS, New York

How to diagnose large-scale transport? Long-lived tracers.

Important class: sources in troposphere lead to time-varying tropospheric mixing ratio. Signal enters stratosphere (overworld) in tropics. In stratosphere, tracers ~ inert. Observation platforms: satellite, balloon, aircraft Examples: CO2, SF6, H2O Goal is to infer tracer-independent transport timescales from tracers.

Age1

Example: steadily increasing tracers, CO2, SF6.

Stratospheric concentration lags troposphere. Call lag-time “age” G. Tempted to interpret as transit-time

• f air parcel from troposphere.

q(r,t) = qtrop(t - t(r))

Periodic tracers: e.g., H2O imprint of seasonal variations

• f tropical tropopause temperature. Propagates upward.

HALOE H2O (Mote et al, 1996; 1998)

max(r,t) = maxtrop(t -t(r))

Can define t Is t a transit-time of an air parcel?

Tracer timescales in tropics

Waugh and Hall, 2002 Lag-time of linear tracer much larger than phase lag of annually- periodic tracer. (Originally in literature would find statements that both tracers should be direct measure of tropical upwelling.)

“Age spectrum” as interpretive framework: ∂c ∂t + L(c) = 0 with inhomogeneous c(W,t) = f (t) ∂G ∂t + L(G) = 0 with G(r

W,t |W,t') = d(t - t')

c(r,t) = dt'c(W,t')G

t

Ú

(r,t |W,t')

for linear transport operator L (e.g., advection-diffusion) Linearity: c(W,t) expressed as linear combination of d(t) then c(r,t) expressed as same linear combination of G(r,t|Wt’).

c(r,t) = dt'c(W,t - t')G

• Ú

(r,W,t')

If transport in steady-state

(Hall and Plumb, 1994)

t t+dt

G(r,t)

Mass fraction of parcel at r that made last troposphere contact t to t+dt ago.

dtG(r,t) =1

• Ú

Age spectrum physical interpretation: PDF of transit-times

Narrowly-peaked early times near tropical tropopause. Broad, older, asymmetric far from tropical tropopause Variance of age spectrum is measure of mixing. e.g., I-D advection-diffusion:

D2(x) = kx u3

Easy to simulate G in a GCM. Apply d(t)-like BC on concentration at surface (stratospheric response not sensitive to details). Run 10-20 years. Time-series Response (normalized in time) at each stratospheric r is G(r,t). NCAR MACCM2 (Hall et al., 1999) Characteristic shape: early peak, long tail; well-fit by two-parameter form (next lecture).

qtrop(t) = gt

q(r,t) = dt'(t - t')G(r,t')dt'

• Ú

= t - G(r)

G(r) ≡ dtG(r,t)

• Ú

where

qtrop(t) = est

t(r) ª G(r) -sD2(r)

D2(r) ≡ dt (t - G(r))2

• Ú

G(r,t)

q(r,t) = qtrop(t - t)

if s

• 1 >> D

2 /G

then t = G

Linear tracer Lag-time of linear tracer is first-moment of G, the “mean age”, independent of tracer growth rate. How linear to get mean age? Exponential tracer define Find where In GCM studies, D2/G ~ 0.5 - 1.5 year. Anthropogenic tracers grow more slowly than that, yield mean age.

G(r,t)

Past times SF6 and CO2 (annual cycle removed) growth timescale longer than typical “width” of G (as observed in GCMs).

[SF6](r,t) = [SF6]trop(t - G)

So, Note: “trop” somewhat vague. Ideally, tropical tropopause. In practice, often some surface region. Makes 0.5-1.0 year difference.

Observations of “mean age”

Bulges up more Than N2O, CH4

CCly Cly and CBry Bry with time spent in active photolysis regions. Expect some correlation with mean age. (But imperfect, because age doesn’t provide pathway information). Total Cl and total Br are inert. Time-varying signals propagate from troposphere, so correlation with mean age limited only by weak non-linearity

• f time-variation. Signals has leveled-off late 1990s, so age-dependence weak.

Romashkin et al., 2000; SOLVE data Segue …

Cltot variation nonlinear enough to be sensitive to shape of age spectrum

G(t |G,D) = 1 2D p ˜ t 3 exp - G2(˜ t -1)2 4D2˜ t Ï Ì Ó ¸ ˝ ˛

Use 2-parameter “inverse Gaussian” form Better fit to observed for D = G than simple lag by G.

HALOE data 55 km

(But still don’t understand abruptness of turnover.)

q(r,t) =A(r)exp i2p(t - t(r))/T

( )

qtrop(t) = exp i2p t/T

( )

if T >> 2pD

2 /G ª 6years

then t = G

Periodic tracer of period T. Lag-time of annually-periodic tracer (H2O, CO2) are not mean age. To interpret periodic (and other) tracers develop and apply simple model …

∂qT ∂t + W ∂qT ∂Z

• e

Z / H ∂

∂Z KTe

• Z / H ∂qT

∂Z Ê Ë Á ˆ ¯ ˜ = -s qT - qM

( )

∂qM ∂t

• aW ∂qM

∂Z

• e

Z / H ∂

∂Z KMe

• Z / H ∂qM

∂Z Ê Ë Á ˆ ¯ ˜ = l + as

( ) qT - qM ( )

l = -ae

Z / H ∂

∂Z e

Z / HW (Z)

( )

where is tropical divergence rate

a = MT 2MM

and is measure of tropical barrier latitude.

“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.

Recirculation and weak vertical mixing:

t t t

s = 0 KT = 0 G = t = tadv s =1yr

• 1

KT = 0 G > t ª tadv s = 0 KT = 0.1m

2s

• 1

G = t ª tadv

Isolated tropics: Allow recirculation: Recirculated air averages several cycles of annually-periodic tracer, but contributions to mean age add. Plug-flow up the tropical pipe. No significant change, except that Age spectra look more “realistic.”

For small KT: t(Z) ª tadv =

dZ' W (Z')

Z

Ú

A(Z) = exp - s(Z')dZ' W (Z')

Z

Ú

Ê Ë Á ˆ ¯ ˜

Mote et al. (1998) constrain 3-parameter version of TLP (W, K, s -1) with fixed midlatitude values using H2O amplitude and phase and CH4 observations (with radiative-chemical model). Obtain best-fit parameter values as function of Z. Solutions are ~ in weak K limit. Vertical diffusion plays secondary role in transporting, attenuating signal.

What do Mote’s solutions imply for tropical-midlat exchange? Use best-fit W(Z), s(Z) in full tropical-midlatitude version of TLP. High dW/dZ means minimum in tropical mass divergence (and no large mixing to counter). Fewer “up-and-over” paths cross tropical barrier at this height. Associated transit-time with minimum probability.

Andrews et al, 2001 Empirical midlatitude age spectra: bimodal spectra best fit CO2 data.

What is relationship between path height and transit-time?

Define “maximum-path-height” distribution Z(r,t|z) such that Z(r,t|z)dz = mass fraction of parcel at (r,t) that reached maximum height z to z+dz since last tropopause contact. And, joint “maximum-path-height-transit-time” distribution P(r,t|z,x) such that P(r,t|z,x)dzdx = mass fraction of parcel at (r,t) that was last at tropopause time x to x+dx ago and reached maximum height z to z+dz.

dzP =G

r

• Ú

dtP = Z

• Ú

dz

r

• Ú

dtP =1

• Ú

Marginals: Normalized:

Age spectrum does not provide path information.

Joint distributions in lower midlatitude TLP

Minimum in MPH distribution. No tropical divergence at this height, so unlikely to have trajectory with this maximum height

Upper and lower components of MPH distribution illustrate partitioning

• f trajectories to midlatitudes into two classes: “direct” and

“up-and-over”. About 50% of air in each class.

Other topics

• Tracers with stratospheric source, tropospheric sink

(e.g., radiocarbon) and relationship to aircraft emissions.

• Tracers to infer polar vortex descent, degree of isolation.
• Interannual variability as seen in tracers

(QBO, internal variability, GHG-forced trends).

• Timescales for ultimate mixing at small-scales.

BC spatial variation

c(r,t) = dt' d2r'c(r',t')G(

W

Ú

• t

Ú

r,t | r',t')

More general case of boundary propagator: spatial variation of boundary condition and non-steady flow. Still have probabilistic interpretation: G(r,t|r’,t’)d2r’dt’ = probability that parcel at (r,t) made last W contact time t’ to t’+dt’ and made the contact on d2r’. G(r,t|r’,t’) = joint PDF in source time and space. Note: much more difficult to compute, now. Need d(t) BC for each t’ and r’ to resolve on source.

Troposphere PDF

Example: surface origins and transit-times for tropospheric air

• bservation point

Ocean illustration: simulate G(r,r’,t-t’) in North Atlantic MYCOM.

(Haine and Hall, 2002)

Tile the domain. For ith tile, tracer has BC = d(t) and zero elsewhere