# 100 km Dz - Atmospheric Chemistry Modeling Group

```EPS200: Atmospheric Chemistry
Instructors: Daniel J. Jacob and Steven C. Wofsy
Teaching Fellow: Helen M. Amos
EPS 200 is intended as a “core” graduate course in atmospheric chemistry
• Assumes no prior knowledge of atm chem
• Suitable as “breadth” for students in other fields
• complements other core course EPS208 (Physics of Climate)
• broad survey of field, prepares for + complements more advanced courses:
-EPS 236 Environmental Modeling
-EPS 238 Spectroscopy and Radiative Transfer of Planetary Atmospheres
-ES 267 Aerosol Science and Technology
-ES 268 Environmental Chemical Kinetics
BIG PROBLEMS IN ATMOSPHERIC CHEMISTRY
Disasters
Visibility
Ozone
layer
Urban smog
Regional smog
Climate
Point source
Acid rain
Biogeochemical cycles
LOCAL
< 100 km
REGIONAL
100-1000 km
GLOBAL
> 1000 km
GLOBAL OBSERVING SYSTEM FOR TROPOSPHERIC COMPOSITION
Satellites
Surface
networks
Chemical transport
models (CTMs)
Aircraft,
ships
CTMs solve coupled continuity equations for chemicals on global 3-D Eulerian grid:
Emissions
Transport
Ci
 U  Ci  Pi (C)  Li (C)
Chemistry
t
Aerosol processes
Deposition
Dx ~100 km
Dz ~ 1 km
ATMOSPHERIC STRUCTURE AND TRANSPORT
“SEA LEVEL” PRESSURE MAP (9/2/10, 23Z)
SEA-LEVEL PRESSURE CAN’T VARY OVER MORE
THAN A NARROW RANGE: 1013 ± 50 hPa
Consider a pressure gradient at sea level operating on an elementary air
parcel dxdydz:
P(x) P(x+dx)
Vertical area
dydz
Acceleration
dF  ( P( x)  P( x  dx))dydz
 
1 dP
 dx
For DP = 10 hPa over Dx = 100 km,  ~ 10-2 m s-2 a 100 km/h wind in 3 h!
Effect of wind is to transport air to area of lower pressure a dampen DP
On mountains, however, the surface pressure is lower, and the pressure-gradient
force along the Earth surface is balanced by gravity:
gravity
P(z)
aThis is why weather maps show “sea level” isobars;
a The fictitious “sea-level” pressure at a mountain
site assumes an air column to be present between the
surface and sea level
MASS ma OF THE ATMOSPHERE
Mean pressure at Earth's surface:
984 hPa
6380 km
ma 
4 R2 PSurface
g
 5.13 10 kg
18
Total number of moles of air in atmosphere:
ma
Na 
 1.8  1020 moles
Ma
Mol. wt. of air: 29 g mole-1 = 0.029 kg mole-1
VERTICAL PROFILES OF PRESSURE AND TEMPERATURE
Mean values for 30oN, March
Stratopause
Tropopause
Barometric law (variation of pressure with altitude)
• Consider elementary slab of atmosphere:
P(z+dz)
P(z)
P( z )  P( z  dz )   a gdz

unit area
PM a
a 
RT
Ideal gas law:

dP
Mag

dz
P
RT
dP
  a g
dz
hydrostatic
equation
Assume T = constant, integrate:
P( z )  P(0)e
z / H
RT
with scale height H 
 7.4 km (T  250 K)
Mag
Barometric law
na ( z)  na (0)e
z / H
P( z )
P( z  H ) 
;
e
P( z )
P( z  5km) 
2
Application of barometric law: the sea-breeze effect
ATMOSPHERIC TRANSPORT
Forces in the atmosphere:
• Gravity g
• Pressure-gradient γp   1/  P
• Coriolis  c  2v sin  to R of direction of motion (NH) or L (SH)
• Friction γ f  kv


Equilibrium of forces:
In vertical: barometric law
p
P
In horizontal: geostrophic flow parallel to isobars
v
c
P + DP
In horizontal, near surface: flow tilted to region of low pressure
p
f
v
c
P
P + DP
Air converges near
the surface in low
pressure centers, due
to the modification of
geostrophic flow under
the influence of
friction. Air diverges
from high pressure
centers. At altitude, the
flows are reversed:
divergence and
convergence are
associated with lows
and highs respectively
THE HADLEY CIRCULATION (1735): global sea breeze
COLD
HOT
COLD
Explains:
• Intertropical Convergence
Zone (ITCZ)
• Wet tropics, dry poles
•General direction of winds,
easterly in the tropics and
westerly at higher latitudes
parcels would tend to keep
a constant angular velocity.
Meridional transport of air
between Equator and poles
results in strong winds in
the longitudinal direction.
…but this does not account
for the Coriolis force
correctly.
TODAY’S GLOBAL INFRARED CLOUD MAP (intellicast.com)
shows Intertropical Convergence Zone (ITCZ) as longitudinal band near Equator
Today
Bright colors indicate high cloud tops (low temperatures)
• Easterly “trade winds” in the tropics at low altitudes
• Subtropical anticyclones at about 30o latitude
CLIMATOLOGICAL SURFACE WINDS AND PRESSURES
(January)
CLIMATOLOGICAL SURFACE WINDS AND PRESSURES
(July)
500 hPa (~6 km) CLIMATOLOGICAL WINDS IN JANUARY:
strong mid-latitude westerlies
500 hPa (~5 km) CLIMATOLOGICAL WINDS IN JULY
mid-latitude westerlies are weaker in summer than winter
ZONAL GEOSTROPHIC FLOW AND THERMAL WIND RELATION
  gz geopotential height
1 P

1 
p 


 y
y
a 
 = latitude
 = angular vel. of Earth
P
u
f = 2sin (Coriolis parameter)
z*   H ln( p / po ) log-P coordinate
H
P + DP
 c  2u sin   fu
RTo
scale height
Mg
fu  
Geostrophic balance:
Thermal wind relation:
f
1 
a 
u
R T

z*
aH 
y
x
ZONAL WIND: VARIATION WITH ALTITUDE
follows thermal wind relation
TIME SCALES FOR HORIZONTAL TRANSPORT
(TROPOSPHERE)
1-2 months
2 weeks
1-2 months
1 year
Illustrates long time scale for interhemispheric exchange
Dust transport over the Pacific, April 21-25, 1998
•
What is buoyancy?
R. Husar
TRANSPORT OF ASIAN DUST TO NORTH AMERICA
Clear day
Glen
Canyon,
AZ
Mean April 2001
PM concentrations
measured by MODIS
April 16, 2001: Asian dust!
GLOBAL TRANSPORT OF CARBON MONOXIDE (CO)
Sources of CO: Incomplete combustion (fossil fuel, biofuel, biomass burning),
oxidation of VOCs
Sink of CO: atmospheric oxidation by OH radical (lifetime ~ 2 months)
MOPITT satellite
observations of
CO concentrations at
500 hPa (~6 km)
OBSERVATION OF CO FROM AIRS SATELLITE INSTRUMENT
AIRS CO data at 500 hPa (W.W. McMillan)
Averaging kernels
for AIRS retrieval
ATMOSPHERIC LAPSE RATE AND STABILITY
“Lapse rate” = -dT/dz
Consider an air parcel at z lifted to z+dz and released.
It cools upon lifting (expansion). Assuming lifting to be
z
stable
G = 9.8 K km-1
g
G  dT / dz 
 9.8 K km-1
Cp
z
unstable
inversion
unstable
What happens following release depends on the
local lapse rate –dTATM/dz:
ATM
• -dTATM/dz > G e upward buoyancy amplifies
(observed) initial perturbation: atmosphere is unstable
• -dTATM/dz = G e zero buoyancy does not alter
perturbation: atmosphere is neutral
• -dTATM/dz < G e downward buoyancy relaxes
T
initial perturbation: atmosphere is stable
• dTATM/dz > 0 (“inversion”): very stable
The stability of the atmosphere against vertical mixing is solely determined
by its lapse rate.
WHAT DETERMINES THE LAPSE RATE OF THE
ATMOSPHERE?
•
•
An atmosphere left to evolve adiabatically from an initial state would
eventually tend to neutral conditions (-dT/dz = G  at equilibrium
Solar heating of surface and radiative cooling from the atmosphere
disrupts that equilibrium and produces an unstable atmosphere:
z
z
ATM
G
z
final
G
ATM
T
Initial equilibrium
state: - dT/dz = G
G
initial
T
Solar heating of
cooling of air:
unstable atmosphere
T
buoyant motions relax
unstable atmosphere
back towards –dT/dz = G
• Fast vertical mixing in an unstable atmosphere maintains the lapse rate to G.
Observation of -dT/dz = G is sure indicator of an unstable atmosphere.
IN CLOUDY AIR PARCEL, HEAT RELEASE FROM
H2O CONDENSATION MODIFIES G
Wet adiabatic lapse rate GW = 2-7 K km-1
z
T
RH
“Latent” heat release
as H2O condenses
RH > 100%:
Cloud forms
GW  2-7 K km-1
G  9.8 K
km-1
100%
GW
G
4
Altitude, km
3
cloud
2
boundary
layer
1
0
-20
-10
0
10
Temperature, oC
20
30
SUBSIDENCE INVERSION
typically
2 km altitude
DIURNAL CYCLE OF SURFACE HEATING/COOLING:
ventilation of urban pollution
z
PBL
depth
Subsidence
inversion
MIDDAY
1 km
G
Mixing
depth
0
NIGHT
MORNING
T
NIGHT
MORNING AFTERNOON
VERTICAL PROFILE OF TEMPERATURE
Mean values for 30oN, March
Altitude, km
cooling (ch.7)
- 3 K km-1
2 K km-1
O3 + hn e O2 + O
O + O2 + M e O3+M
heat
cooling (ch.7)
- 6.5 K km-1
Latent heat release
Surface heating
LATITUDINAL STRUCTURE OF TROPOPAUSE REGION
BAROCLINIC INSTABILITY
q3 >
z
q2 >
q1
Buoyant vertical motion
Is possible even when
q / z  0
0
latitude
Dominant mechanism for vertical motion in extratropics
FIRST-ORDER PARAMETERIZATION OF TURBULENT FLUX
•
Observed mean turbulent dispersion of pollutants is nearGaussian eparameterize it by analogy with molecular diffusion:
Instantaneous
plume
Time-averaged
envelope
z
Near-Gaussian
profile
Source
Turbulent flux =  K z na
 C 
z
<C>
Turbulent diffusion
coefficient
• Typical values of Kz: 102 cm2s-1 (very stable) to 107 cm2 s-1 (very unstable);
mean value for troposphere is ~ 105 cm2 s-1
• Same parameterization (with different Kx, Ky) is also applicable in
horizontal direction but is less important (mean winds are stronger)
TYPICAL TIME SCALES FOR VERTICAL MIXING
•
Estimate time Dt to travel Dz by turbulent diffusion:
Dz 

Dt 
2
2K z
with K z
105 cm2s-1
tropopause
(10 km)
10 years
5 km
“planetary 2 km
boundary layer”
0 km
1 month
1 week
1 day
```