QUESTIONS
1. Atmospheric CO2 has a lifetime (turnover time) of 5 years against
photosynthesis and a lifetime of 10 years against dissolution in the
oceans. What is its overall atmospheric lifetime?
2. Are the following loss processes first-order (linear with concentration)?
A. Uptake of CO2 by the biosphere
B. Photolysis of gases in the stratosphere
C. Scavenging of aerosol particles by precipitation
3. Consider a 2-box model for the atmosphere where one box is the
troposphere (1000-150 hPa) and the other the stratosphere
(150-1 hPa). The lifetime of air in the stratosphere is 2 years. What is
the lifetime of air in the troposphere?
4. Of the simple models we discussed in chapter 3, which one would be best suited
for addressing the following problems?
a. Is the observed rise of atmospheric CO2 concentrations consistent with the
known rate of CO2 emission from fossil fuel combustion?
b. Large amounts of radioactive particles are released to the atmosphere in a
nuclear power plant accident. Which areas will be affected by this radioactive
plume?
c. An air pollution monitoring station in Fort Collins suddenly detects high
concentrations of a toxic gas. Where is this gas coming from?
CHAPTER 4: ATMOSPHERIC MOTIONS and TRANSPORT
WHAT ARE THE FORCES BEHIND ATMOSPHERIC CIRCULATION?
1. Global Circulation as a Giant Sea Breeze.
Concepts: Pressure Gradient Force; visualizing pressure with isobars
2. Introduction to the Coriolis Force (with a supporting role played by
angular momentum).
We want to explain circulation patterns like these, which take place over
large enough scales that the rotation of the earth has an effect on moving
air parcels:
TRANSPORT & ATMOSPHERIC CHEMISTRY
The important role of circulation for atmospheric chemistry:
1. Dilute: concentrations of chemical species in a large volume of air
2. Transport: emissions away from sources
3. Mix: Promote oxidation by bringing various chemical constituents into
contact
4. Cloud formation: promote aqueous phase chemistry
CHAPTER 4: ATMOSPHERIC TRANSPORT
Forces in the atmosphere:
• Gravity g
• Pressure-gradient γ p   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
CORIOLIS FORCE
An observer sitting on the axis of rotation (North Pole) launches a projectile at the target.
The curved arrow indicates the direction of rotation of the earth. The projectile follows a
straight-line trajectory, when viewed by an observer in space, directed towards the
original position of the target. However, observers and target are rotating together with
the earth, and the target moves to a new position as the projectile travels from launch to
target. Since observers on earth are not conscious of the fact that they and the target
are rotating with the planet; they see the projectile initially heading for the target, then
veering to the right. The Coriolis force is a fictitious force introduced to the equations
of motion for objects on a rotating planet, sufficient to account for the apparent pull to the
right in the Northern hemisphere or to the left in the southern hemisphere.
The geometry of the earth, showing the distance from the axis of
rotation as a function of the latitude  .
r = R cos 
(R=6370 km)
r =the distance from the axis
of rotation
R cos 
R

R
 An object on the earth’s
surface at a high latitude has
less angular momentum
(L=r x p = RcosmvE) than an
object on the surface at a low
latitude.
Translational speed:
vE = 2Rcos(  ) / t
Rotation axis
Coriolis Force (Northern Hemisphere):
• An air parcel (mass) begins to move from the Equator toward North
Pole along the surface of the earth.
• The parcel moves closer to the axis of rotation: r decreases
• The parcel’s angular velocity is GREATER THAN the angular
velocity of the earth’s surface at the higher latitude.
It deflects to the right of it’s
original trajectory relative to
the earth’s surface.
In the Southern Hemisphere,
the parcel would appear to
deflect to the left.
The air
parcel is
deflected to
the right.
We thus find in all cases that the Coriolis force is exerted
perpendicular to the direction of motion, to the RIGHT in
the Northern Hemisphere and to the LEFT in the Southern
Hemisphere.
Angular velocity of the Earth=2π/day
Coriolis acceleration( c) = F/m = 2v sin(  ).
Coriolis acceleration increases as  (latitude) increases, is zero
at the equator.
DEFLECTION OF AN OBJECT BY THE CORIOLIS FORCE
Dy = [  (Dx)2 / v ] sin()
(a) A snowball traveling 10 m at 20 km/h in Fort Collins (40.6°N):
v = 20 km/hr = 5.5 m/s;  =7.5  10-5 s-1 ; sin ()=.65; Dx=10
Dy = 8.9  10-4 m
(b) A missile traveling 1000 km at 2000 km/h at 40.6°N.
v = 555 m/s, Dx=1  106 m; Dy = 8.8  104 m.
In Fort Collins ( = 40.6N), we find that a snowball traveling 10 m at 20
km/h is displaced by Dy = 1 mm (negligible), but a missile traveling 1000 km
at 2000 km/h is shifted 100 km (important!). Note the importance of (Dx)2
c = 2  v sin () ; t = Dx/v  Dy = ½ c t2
GEOSTROPHIC FLOW
low pressure
Pressure
gradient
force
N
1
P    P

high pressure
S
Motion of an air subjected to a north/south pressure gradient. Pt. A1, initially at
rest; Pt. A3, geostrophic flow. The motion approaches geostrophic balance in
a simple manner because atmospheric mass will be redistributed to
establish a pressure force balanced by the Coriolis force, and motion
parallel to the isobars.
GEOSTROPHY
For air in motion, not on the equator,
•Coriolis Force  Pressure gradient force
•Air motion is parallel to isobars
The geostrophic approximation is a simplification of very complicated
atmospheric motions. This approximation is applied to synoptic scale
systems and circulations, roughly 1000 km. (It is easiest to think about
measuring the pressure gradient at a constant altitude, although other definitions
are more rigorous. )
Vgeostrophic=
1
P
2 sin( ) X
DP/DX
Vg


Dx
DP
geostrophic wind (m/s)
7.29 10-5 radian/s
latitude
distance (m)
pressure diff. (N/m2)
Circulation of air around regions of
high and low pressures in the Northern
Hemisphere. Upper panel: A region of
high pressure produces a pressure
force directed away from the high. Air
starting to move in response to this
force is deflected to the right (in the
Northern Hemisphere), giving a
clockwise circulation pattern.
keep high pressure on the right
Lower panel: A region of low pressure
produces a pressure force directed
from the outside towards the low. Air
starting to move in response to this
force is also deflected to the right,
rotating counter-clockwise.
Directions of rotation of the wind about
high or low centers are reversed in the
Southern Hemisphere, as explained
earlier in this chapter.
THE EFFECT OF FRICTION
Friction: loss of air momentum
to surface obstacles such as
trees, buildings… exerted in
opposite direction to the motion
Friction slows the wind
relative to its geostrophic
velocity. This slowdown
decreases the Coriolis
acceleration so that air is
deflected towards the low
pressure region.
CONVERGENCE AND DIVERGENCE
THE HADLEY CIRCULATION (1735): global sea breeze
COLD
HOT
Explains:
• Intertropical Convergence
Zone (ITCZ)
• Wet tropics, dry poles
•General direction of winds,
easterly in the tropics and
westerly at higher latitudes
Hadley thought that air
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.
COLD
Problems: 1. does not
account for Coriolis force
correctly; 2. circulation does
not extend to the poles.
TROPICAL HADLEY CELL
• Easterly “trade winds” in the tropics at low altitudes
• Subtropical anticyclones at about 30o latitude
CLIMATOLOGICAL SURFACE WINDS AND PRESSURES
(July)
CLIMATOLOGICAL SURFACE WINDS AND PRESSURES
(January)
TIME SCALES FOR HORIZONTAL TRANSPORT
(TROPOSPHERE)
1-2 months
2 weeks
1-2 months
1 year
IMPORTANCE OF MID-LATITUDE CYCLONES FOR US
VENTILATION
• Cold fronts associated with cyclones tracking across southern Canada are
the principal ventilation mechanism for the eastern US
• The frequency of these cyclones has decreased in past 50 years, likely due
to greenhouse warming
Leibensperger et al. [2008]
GLOBAL DISTRIBUTION OF AEROSOL OPTICAL DEPTH
NASA/MODIS satellite instrument (April 2001)
Notice sharp boundary at ITCZ!
VERTICAL TRANSPORT: BUOYANCY
• What is buoyancy?
Balance of forces:
FP-gradient
 buoyancy   P  gradient   gravity
  

g

z+Dz
Fluid (’)
Object (
z
Fg
Note: Barometric law assumed a neutrally buoyant atmosphere with T = T’

T

P  gradient

gravity

T’ would produce bouyant acceleration
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
adiabatic, the cooling follows the adiabatic lapse rate G :
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
surface/radiative
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
T
If Gw< -dT/dz < G  air parcel is conditionally unstable
SUBSIDENCE INVERSION
typically
2 km altitude
VERTICAL PROFILE OF TEMPERATURE
Mean values for 30oN, March
Altitude, km
Radiative
cooling (ch.7)
- 3 K km-1
2 K km-1
Radiative heating:
O3 + hn e O2 + O
O + O2 + M e O3+M
heat
Radiative
cooling (ch.7)
- 6.5 K km-1
Latent heat release
Surface heating
DIURNAL CYCLE OF SURFACE
HEATING/COOLING:
ventilation of urban pollution
z
Subsidence
inversion
MIDDAY
1 km
G
Mixing
depth
0
NIGHT
MORNING
T
NIGHT
MORNING AFTERNOON
EFFECT OF STABILITY ON VERTICAL STRUCTURE
What you see…
Puffy little clouds, called fair weather cumulus,
occurring over land on a typical afternoon. The
lapse rate in the mixed layer is approximately
adiabatic, and air parcels heated near the ground
are buoyant. Each little cloud represents the
top of a buoyant plume. (Photograph courtesy
University of Illinois Cloud Catalog).
PLUME LOOPING, BALTIMORE ~2pm.
z
T
PLUME LOFTING, BEIJING ~7am
z
T
TYPICAL TIME SCALES FOR VERTICAL MIXING
How fast does air mix due to molecular diffusion?
Use Fick’s Law:
C
F  naD
z
Flux is proportional to the
spatial gradient
And the Einstein Equation for Molecular Diffusion:
Dx 

Dt 
2D
2
with D
2 -1
0.2cm s
Find that will take 6.9 hrs to travel 1 m!
 molecular diffusion is unimportant as a means of transport and mixing
at sea level (becomes important above 100 km)
TYPICAL TIME SCALES FOR VERTICAL MIXING
Define by analogy the time Dt to travel Dz by turbulent diffusion:
Dz 

Dt 
2
2K z
with K z
~
5
2 -1
10 cm s
tropopause
(10 km)
10 years
5 km
“planetary 2 km
boundary layer”
0 km
1 month
1 week
1 day