Dynamics

1
Dynamics Ted Shepherd Department of Physics,
University of Toronto

• Zonal mean state
• Disturbances
• Wave, mean-flow interaction
• Transport and mixing
• Chemical correlations

GCC Summer School, Banff, May 23, 2004
2
Vertical temperature structure of the atmosphere
(CIRA data)
3
Globally averaged energy balance in
CMAM
Thermosphere solar heating and diffusion MLT
region very complex! Middle atmosphere solar
heating and IR cooling Troposphere solar
heating, IR cooling and vertical heat fluxes
From Fomichev et al. (2002 JGR)
4

• Why is there a tropopause?

Moist adiabatic layer is the troposphere
5
Global mean radiative-convective equilibrium
1-D calculations by Piers Forster, University of
Reading (after Manabe Strickler 1964 JAS) CO2
cools the middle atmosphere No cold point
without ozone (and barely a lapse rate tropopause)
From Shepherd (2003 Chem. Rev.)
6

• Thats just the 1-D view the tropopause has
  latitudinal structure

High in tropics, lower in extratropics
Annual mean climatology from Holton et al. (1995
Rev. Geophys.)
7
Zonal mean wind and temperature structure in
January (CIRA data)
8
The atmosphere exhibits a rich spectrum of
disturbances

• Thermal tides (t 1 day, L 1000 km)
• Convection (t 1 hour, L 10 km though can
  organize
• to much larger scale in the tropics)
• Inertia-gravity waves (IW limit has t hours, L
  1000 km
• GW limit has t 10 mins, L 50 km)
• Rossby waves (t 3 days, L 3000 km including
  
• baroclinic instability) synoptic- and
  planetary-scale
• Inertial instability (t 6 hours, L 1000 km)
  in tropics
• Equatorially trapped waves (t 1 day, L 1000
  km)
• Fronts, mesoscale structures (t 6 hours, L
  100 km)
• Hurricanes (t 1 day, L 500 km)
• These length and time scales are nominal there
  is a spectrum
• Time scales modified by Doppler shifts, e.g.
  topographic GWs

9

• Waves can propagate, parcel instabilities and
  vortices cannot
• (however the latter can generate propagating
  waves)
• Waves need to be forced instabilities arise
  spontaneously
• For the most part, instability is confined to
  the troposphere
• In the middle atmosphere, most disturbances have
  propagated
• up from the troposphere
• Due to decreasing density with altitude, these
  disturbances
• must eventually break nonlinearly (unless they
  are radiatively
• damped first)
• Breaking is ensured at a critical layer (where
  U c)
• Breaking can generate small-scale disturbances
  and turbulence

10
The propagating diurnal tide as simulated in CMAM
and as observed by UARS (WINDII and HRDI)
From Beagley et al. (2000 GRL)
11
Equatorial waves seen in OLR frequency-wavenumber
spectra
Anti-symmetric about equator
Symmetric about equator
From Wheeler Kiladis (2000 JAS)
12
The physics of baroclinic instability slantwise
convection
Parcels can rise while moving into a region with
lower potential temperature Positive buoyancy
provides a positive feedback ? Instability

• Requirement is sloping isentropes, which
  requires rotation
• Of course this is only a necessary, not a
  sufficient condition

13
Baroclinic synoptic-scale disturbances around the
tropopause
Ertel potential vorticity at ? 345 K (10
km), in PVU, for a single day in
January Tropopause is often taken to be at 2
PVU This sharp PV edge corresponds to the jet
stream Figure courtesy of Yves Rochon, MSC
From Shepherd (2003 Chem. Rev.)
14

• The dominant flow in most of the atmosphere is
  zonal
• The zonal flow meanders, because of Rossby waves
• Adiabatic flow follows isolines of potential
  vorticity (PV)
• In middle atmosphere, air parcels move
  quasi-zonally species
• of moderate lifetime are uniform in PV
  coordinates
• Leads to concept of equivalent latitude
  highly useful!
• In upper troposphere, this becomes less useful
  (except at the
• gross level of a stratosphere/troposphere
  distinction)

• Vortex coordinates in the polar vortex

• Parcels dont necessarily move quasi-zonally
• Chemical species of tropospheric origin are
  inhomogeneous

15
Temperature-ozone relationship as seen from CRISTA
August 15, 1997 (SH) Planetary wave-2
disturbance Negative in upper strat (chemistry)
Positive in lower strat (dynamics)
From Ward et al. (2000 AGU)
16
The split ozone hole of 2002 a wave-2 sudden
warming
TOMS data (smoothed), from NASA GSFC web site
17
A breaking planetary wave in the stratospheric
surf zone
Ertel PV on ? 850 K (30 km) derived from
satellite temperature measurements on December 7,
1981 After McIntyre Palmer (1984
Nature) From Houghton (1986)
18
The stratospheric surf zone in CMAM Particle
advection for 30 days in July on various
isentropic surfaces

• 450 K (17 km)
• 600 K (25 km)
• 1000 K (35 km)

A planetary wave-2 critical layer is evident
From Ngan Shepherd (1999 JAS)
19

• Instantaneous snapshot of SKYHI
• zonal winds for various altitudes,
• during a model July
• Increasing gravity-wave activity
• with increasing altitude

From Koshyk et al. (1999 JGR)
20
Horizontal wavenumber spectra (n spherical
harmonic index) of kinetic energy for SKYHI and
CMAM Straight lines show -3 and -5/3
slopes Charney-Drazin filtering is
evident Shallow spectra emerge with increasing
altitude Figure courtesy of John Koshyk
21
The wave-driven circulation

• Propagating waves transfer energy and momentum,
  and
• deposit it where they are dissipated
• The energy deposition is never dominant, and is
  generally
• negligible because radiation is overwhelming
  the energy
• budget is not closed because of cooling to
  space
• In contrast, the momentum deposition is
  extremely
• important because the momentum budget is closed
• Momentum deposition drives meridional
  circulations in the
• middle atmosphere, which are accommodated by
  radiation
• The meridional circulation in the troposphere is
  driven by
• convection (tropics) and baroclinic
  instability (extratropics)

22
Seasonal cycle of meridional (TEM) circulation in
CMAM

• Poleward motion in
• troposphere and
• stratosphere,
• strongest in winter
• hemisphere
• Summer to winter
• hemisphere motion
• in mesosphere
• From Beagley et al.
• (1997 Atmos.-Ocean)

23

• Meridional circulations induce temperature
  anomalies
• More generally, momentum deposition drives
  temperature
• anomalies through dynamical heating on all time
  scales
• Net radiative heating is driven by dynamical
  heating
• (instability in troposphere, wave drag in
  middle atmosphere)
• However Trad affects dynamics, so there is a
  coupling
• Day-to-day and month-to-month variations (not
  seasonal
• cycle) are the result of dynamics essentially,
  chaos
• Inter-annual variations are also generally the
  result of
• dynamics, but there are exceptions (solar
  variations, volcanic
• eruptions)

24
Relation between wave driving and Arctic
temperatures
Stratospheric planetary wave drag drives polar
down- welling and warming
Different models have quite different kinds of
biases
From 2002 WMO/ UNEP Ozone Assessment (see Austin
et al. 2003 ACP)
25
Wave driving vs polar temperature in the Antarctic
Note different scale compared to NH wave driving
is much weaker in the SH
From 2002 WMO/ UNEP Ozone Assessment (see Austin
et al. 2003 ACP)
26
Seasonality of dynamical variability at the two
poles
27
Seasonal variation of daily temperature from
mechanistic model forced by various topographic
amplitudes (100-year integrations)
From Yoden, Taguchi Naito (2002 JMSJ)
28
Histograms (PDFs) of monthly mean temperature at
86N, 2.6 hPa

• Mechanistic model run for 1000 years under
  different topographic forcings
• One Arctic- like, the other Antarctic-like
• The PDFs are not Gaussian

From Yoden, Taguchi Naito (2002 JMSJ)
29
Seasonal variation of histograms of monthly mean
temperature at 30 hPa
1955-2000
1979-1997
From Yoden, Taguchi Naito (2002 JMSJ)
30
Dynamical variability is part of the story of
past ozone changes
Figure courtesy of Paul Newman, NASA GSFC
31
Springtime minimum of total ozone over the
Antarctic
From various coupled chemistry-climate models,
and satellite observations (black dots)

• All models show development of ozone hole in
  line with obs

• Behaviour is
• to a large extent
• deterministic

From 2002 WMO/UNEP Ozone Assessment (see Austin
et al. 2003 ACP)
32
Springtime minimum of total ozone over the
Arctic

• Natural variability is a major
• factor

• The obs seem at the lower
• edge of the ensemble defined
• by the models

• The GISS model (Shindell
• et al. 1998 Nature) is clearly
• an outlier

From 2002 WMO/UNEP Ozone Assessment (see
Austin et al. 2003 ACP)
33

• Stratospheric Rossby wave drag raises the
  tropical
• tropopause and lowers the extratropical
  tropopause

GCM calculations by Thuburn Craig (2000 JAS)
34

• Accounts for seasonal cycle of tropical
  tropopause temperature

(Note near exact cancellation between tropics and
extratropics)
MSU Ch. 4 ( 70 hPa) temperature from Yulaeva et
al. (1994 JAS)
35
Effect of meridional circulation on temperature
Annual cycle should show an exact compensation
between the tropics and extratropics (Yulaeva
et al. 1994 JAS) Some models show rather strange
errors (but not CMAM) From Pawson et al. (2000
BAMS) SPARC GRIPS intercomparison
36
Transport and mixing of chemical species

• The meridional circulation also provides a mean
  transport
• of chemical species
• Together with mixing, this is the transport
  circulation
• In stratosphere, planetary waves lead to
  stirring
• In mesosphere, mixing is likely more diffusive

• In the stratosphere, the Brewer-Dobson
  circulation
• Vertical mean advection plus horizontal mixing
• Horizontal stirring is spatially inhomogeneous,
• leads to mixing barriers (tropical pipe,
  polar vortex)

37
Comparison of Lagrangian and TEM (residual)
vertical velocity in a mechanistic model forced
by planetary waves in the NH Isentropic levels
are indicated the columns are different runs
From Pendlebury Shepherd (2003 JAS)
38
The Brewer-Dobson circulation is evident in
long-lived species
Data from UARS (HALOE and CLAES), units of
ppmv Note structure in SH Figure courtesy
of Bill Randel, NCAR See Randel et al. (1998
JAS) From Shepherd (2003 Chem. Rev.)
39
Seasonal cycle of zonal mean total ozone
Winter buildup, springtime max in
extratropics Blocking by polar vortex barrier in
SH (also ozone hole!)
Figure courtesy of Vitali Fioletov, MSC From
Shepherd (2003 Chem. Rev.)
40
Total ozone variability is controlled by dynamics
CTM simulations from Hadjinicolaou et al. (1997
GRL)
41
Total ozone and tropopause height are correlated
on many time scales Figure shows
February monthly mean values at
Hohenpeissenberg Updated from Steinbrecht et al.
(2001 GRL) From WMO (2003)
42
Seasonal cycle of NH midlatitude ozone,
for different years Interannual anomalies tend
to persist within each year
Regression coefficients for ozone anomalies
relative to April (NH) and November (SH) shows
summertime photochemical decay From Fioletov
Shepherd (2003 GRL)
43
Normalized total ozone variations (35-60N) for
April and JuneOctober Summertime variability is
slaved to springtime variability Summertime is
quiescent
Springtime trends (1979 2001) explain the trends
in other months of the year From Fioletov
Shepherd (2003 GRL)
44
The Antarctic polar vortex barrier in CMAM
Particle advection on the 450 K surface (17 km)
for 30 days in July
Figure courtesy of Keith Ngan
From Shepherd (2000 JASTP)
45
Mixing barriers in CMAM polar vortex, tropical
pipe
From Sankey Shepherd (2003 JGR)
46
Large-scale stirring in the stratosphere 3-day
CMAM calculation
at ? 1000 K (35 km) in
January
T32 spatial resolution, 3-hour sampling T10
spatial resolution, 18-hour sampling T32 ? ?x
600 km
T32 spatial resolution, 18-hour sampling T10
spatial resolution, 18-hour sampling T10 ? ?x
2000 km
From Shepherd, Koshyk Ngan (2000 JGR)
47
The Match technique joining up measurements
separated in space
and time using trajectories
This example shows a trajectory calculated on the
475 K isentropic surface, from meteorological
analyses, matching two ozonesondes launched 5
days apart (in January 1992)
From von der Gathen et al. (1995 Nature)
48
Ozone laminae
Ozonesondes over Northern Europe and the North
Atlantic January 29, 1992 Units 10
ppmv Laminae are the vertical manifestation of
filaments arise from large-scale
stirring From Orsolini (1995 QJRMS)
49
30-day particle advection in CMAM during a model
January

• Middle stratosphere (? 1000 K,
• 35 km) exhibits large-scale stirring
• from breaking planetary waves
• Middle mesosphere (? 4000 K,
• 70 km) exhibits diffusion from
• inertia-gravity waves
• From Shepherd, Koshyk Ngan
• (2000 JGR)

50
Eulerian and Lagrangian correlation times of the
horizontal wind shear, as a function of altitude
From Shepherd, Koshyk Ngan (2000 JGR)
51
Synoptic scale wave breaking (cats eyes) in the
lower stratosphere
Figure courtesy of Dirk Offermann, Wuppertal
University
From Shepherd (2000 JASTP)
52
The tropical pipe
Mixing barrier evident in aerosol measured by
airborne lidar (Ed Browell) 4 months following Mt
Pinatubo volcanic eruption
From Grant et al. (1994 JGR)
53
The tropopause as a mixing barrier gradients in
mean (dashed) and mode (solid) of PDFs of N2O
from CMAM at 320 K
Large absolute values indicate the
tropopause After Sparling (2000 Rev.
Geophys.) Figure courtesy of Sunny
Arkani-Hamed From Shepherd (2002 JMSJ)
54
Filamentation of the extratropical tropopause
Contour advection (from PV) on 320 K isentropic
surface
Meteosat water vapour image at the same time
From Appenzeller et al. (1996 JGR)
55
Airborne lidar measurement of aerosol
distribution across a tropopause fold event
(April 20, 1984)
From Browell et al. (1987 JGR)
56

• Correlations of long-lived
• species with coincident isopleths
• are compact
• Measurements can be taken
• vertically or horizontally
• Correlations remove reversible
• variability, provide instant
• climatology
• Compactness reflects mixing,
• slope of correlation reflects
• chemistry
• From Sankey Shepherd
• (2003 JGR)

57

• Correlations of long-lived
• species with non-coincident
• isopleths are not compact
• (panel b)
• Vertical or horizontal
• profiles may give a false
• impression of compactness
• (panels c,d)
• From Sankey Shepherd
• (2003 JGR)

58
Passive tracers (initialized like O3 and N2O)
develop a linear correlation before eventually
becoming homogenized
From Sankey Shepherd (2003 JGR)
59
However a blow-up shows some structure
From Sankey Shepherd (2003 JGR)
60

• Finite lifetimes mean that
• tracer isopleths never
• exactly coincide
• Correlations therefore
• have a finite width and
• show striations
• From Sankey Shepherd
• (2003 JGR)

61
N2OCH4 correlations from CMAM and from
measurements
Single profiles give an instant climatology
(variability has no effect) CMAM agrees well
with ATMOS measurements There is structure
associated with mixing barriers From Sankey
Shepherd (2003 JGR)
Diamonds Tropics Squares Midlatitudes Triangle
s High latitudes Crosses Vortex
62
The tropics and the polar vortex show distinct
correlations
Red is 70-90S, Gray is 20-70S, Blue is 0-20S
From Sankey Shepherd (2003 JGR)
63
Comparison with MANTRA FTS measurements (August
1998)
Figure courtesy of Stella Melo, University of
Toronto
64
Sensitivity of long-lived species to vertical
diffusivity in CMAM
MAM5 has Kzz 1 m2/s MAM7 has Kzz 0.1
m2/s With smaller Kzz, stratospheric air is
older and N2O and CH4 decay more rapidly with
altitude However the CH4N2O correlation is not
substantially altered Figure courtesy of David
Sankey, University of Toronto
65

• With CMAM simulated data,
• one can assess the
• representativeness of sparse
• measurements
• Black CMAM NH
• Red1 month of obs as shown
• Yellow 1 day of obs as shown
• Even one day is useful
• Higher latitudes are better

From Sankey Shepherd (2003 JGR)
66
N2ONOy correlations from CMAM and from
measurements
Diamonds ER-2 Triangles ATMOS
From Sankey Shepherd (2003 JGR)
67

• With non-compact correlations (e.g. those
  involving ozone),
• it is difficult to compare models with
  measurements

• Or, for that
• matter,
• measurements
• with other
• measurements

Diamonds ER-2 Triangles ATMOS
From Sankey Shepherd (2003 JGR)
68
Comparison between CMAM and ATMOS when binned by
latitude
Diamonds Tropics Squares Midlatitudes Triangles
High latitudes Crosses Vortex
Sankey Shepherd (2003 JGR)
69
Inferring chemical ozone loss from ozone-methane
correlations
Measurements from HALOE within Arctic vortex
November, January
March, April
0.4 0.6 0.8
1.0 1.2 1.4
1.6
Methane (p.p.m.v.)
The idea is to use CH4 as a vertical coordinate,
to account for diabatic descent
From Müller et al. (1997 Nature)
70
Chemical ozone loss in Arctic vortex estimated
from change in profiles
Red is HALOE measurements Green is undepleted
profile based on diabatic descent of early
vortex relation (using CH4 as parcel
label) Brown is range of ozonesonde profiles in
Antarctic at a comparable time From Müller et
al. (1997 Nature)
71

• Compact correlations involving ozone can develop
  in polar
• night, for an isolated vortex, but they take
  some time to emerge

Results from CMAM Correlations cover 70-90
degrees (polar cap)
From Sankey Shepherd (2003 JGR)
72
In the polar night, ozone becomes
long-lived Chemical lifetime computed from
CMAM
From Sankey Shepherd (2003 JGR)
73
The SH polar vortex is well isolated throughout
the winter 10-day particle advection
calculations in CMAM
From Sankey Shepherd (2003 JGR)
74
The same is not true of the NH (at least in CMAM)
From Sankey Shepherd (2003 JGR)
75
This example shows that the ozone-methane
correlation is not generally compact, but limited
measurements may look compact
The coloured symbols indicate CMAM data
over 70-90 N The black symbols indicate
simulated HALOE sampling points located within
the polar vortex used by Müller et al. (1997
Nature) to diagnose chemical ozone loss From
Sankey Shepherd (2003 JGR)
76
Seasonal cycle of CO2 gives a CO2 tape recorder
in the extratropical lower stratosphere
Coloured points are from CMAM, black symbols are
in-situ data from the ER2 aircraft (Boering et
al. 1994 GRL)
From Sankey Shepherd (2003 JGR)
77
Process-oriented validation

• In order to have confidence in models, they must
  be validated

• In the middle atmosphere, the lack of long-term,
  
• comprehensive data sets (especially for
  chemical fields)
• makes this a challenge

• A way forward is process-oriented validation

• Compare with simple models at a qualitative
  level
• Compare with measurements directly (map the
  model to measurement space, rather than
  vice-versa)
• This also aids in the interpretation of the
  measurements

• Data assimilation can also help by constraining
  the model, but
• interpretation can sometimes be a challenge

78
References
Andrews, Holton Leovy Middle Atmosphere
Dynamics, Academic Press (1987) Holton An
Introduction to Atmospheric Dynamics, 4th
ed, Academic Press (2004) J.R. Holton et al.
Rev. Geophys. (1995) R.A. Plumb J. Met. Soc.
Japan (2002) J. Atmos. Sol.Terres.
Phys. (2000) T.G. Shepherd J. Met. Soc. Japan
(2002) Chem. Rev. (2003) WMO Ozone
Assessments 1998, Chapter 7 2002, Chapters
3 and 4