CHAPTER 4: ATMOSPHERIC MOTIONS and TRANSPORT

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CHAPTER 4 ATMOSPHERIC MOTIONS and TRANSPORT

• WHAT ARE THE FORCES BEHIND ATMOSPHERIC
  CIRCULATION?
• Global Circulation as a Giant Sea
  Breeze.Concepts Pressure Gradient Force
  visualizing pressure with isobars
• 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

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TRANSPORT ATMOSPHERIC CHEMISTRY

• The important role of circulation for atmospheric
  chemistry
• Dilute concentrations of chemical species in a
  large volume of air
• Mix Promote oxidation by bringing various
  chemical constituents into contact
• Cloud formation promote aqueous phase chemistry

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CHAPTER 4 ATMOSPHERIC TRANSPORT

• Forces in the atmosphere
• Gravity
• Pressure-gradient
• Coriolis
• Friction

to R of direction of motion (NH) or L (SH)
Equilibrium of forces
In vertical barometric law In horizontal
geostrophic flow parallel to isobars
gp
P
v
P DP
gc
In horizontal, near surface flow tilted to
region of low pressure
gp
P
v
gf
P DP
gc
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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.
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The geometry of the earth, showing the distance
from the axis of rotation as a function of the
latitude ? .
r r the distance from the axis of rotation ?
An object on the earths surface at a high
latitude has less angular momentum (Lr x p
RcoslmvE) than an object on the surface at a
low latitude.
vE 2?Rcos( ? ) / t where t 1 day (86400
seconds). The latitude of Fort Collins is 40.6?
plugging in numbers, you will find that you are
traveling at a constant speed v 1266 km/h (800
mph!). 1667 km/hr at the equator. Note sound
speed 1440 km/hr
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• 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 parcels angular velocity is GREATER THAN
  the angular velocity of the earths surface at
  the higher latitude.

It deflects to the right of its original
trajectory relative to the earths surface. In
the Southern Hemisphere, the parcel would appear
to deflect to the left.
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The air parcel is deflected to the right.
g
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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.
Coriolis acceleration( ?c) F/m Coriolis
acceleration increases as ? (latitude)
increases, is zero at the equator.
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DEFLECTION OF AN OBJECT BY THE CORIOLIS FORCE
?y ? (?x)2 / v sin(?) (a) A snowball
traveling 10 m at 20 km/h in Fort Collins
(40.6N) 20 km/hr 5.5 m/s ? 7.5 ? 10-5 s-1
sin (l).65 Dx10 ?y (b) A missile traveling
1000 km at 2000 km/h at 40.6 N. v 555 m/s, Dx1
? 106 m ?y In Fort Collins (? 40.6?N), we
find that a snowball traveling 10 m at 20 km/h is
displaced by ?y 1 mm (negligible), but a
missile traveling 1000 km at 2000 km/h is shifted
100 km (important!). Note the importance of (?x)2
gc 2 ? v sin (l) t Dx/v ? Dy ½ gc t2
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GEOSTROPHIC FLOW
low pressure
Pressure gradient force
N
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.
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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. )
DP/DX
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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. 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.
keep high pressure on the right
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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.
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CONVERGENCE AND DIVERGENCE
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THE HADLEY CIRCULATION (1735) global sea breeze

• 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.

Problems 1. does not account for Coriolis force
correctly 2. circulation does not extend to the
poles.
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TROPICAL HADLEY CELL

• Easterly trade winds in the tropics at low
  altitudes
• Subtropical anticyclones at about 30o latitude

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CLIMATOLOGICAL SURFACE WINDS AND PRESSURES(July)
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CLIMATOLOGICAL SURFACE WINDS AND
PRESSURES(January)
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TIME SCALES FOR HORIZONTAL TRANSPORT(TROPOSPHERE)
1-2 months
2 weeks
1-2 months
1 year
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VERTICAL TRANSPORT BUOYANCY

• What is buoyancy?

Balance of forces
FP-gradient
zDz
Object (r)
Fluid (r)
z
Fg
Note Barometric law assumed a neutrally buoyant
atmosphere with T T
T
T would produce bouyant acceleration
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ATMOSPHERIC LAPSE RATE AND STABILITY
Lapse rate -dT/dz
Consider an air parcel at z lifted to zdz and
released. It cools upon lifting (expansion).
Assuming lifting to be adiabatic, the cooling
follows the adiabatic lapse rate G
z
G 9.8 K km-1
stable
z
unstable

• What happens following release depends on the
  local lapse rate dTATM/dz
• -dTATM/dz gt G e upward buoyancy amplifies
  initial perturbation atmosphere is unstable
• -dTATM/dz G e zero buoyancy does not alter
  perturbation atmosphere is neutral
• -dTATM/dz lt G e downward buoyancy relaxes
  initial perturbation atmosphere is stable
• dTATM/dz gt 0 (inversion) very stable

ATM (observed)
inversion
unstable
T
The stability of the atmosphere against vertical
mixing is solely determined by its lapse rate.
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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
z
final G
ATM G
ATM
initial
G
T
T
T
Initial equilibrium state - dT/dz G
Solar heating of surface/radiative cooling of
air unstable atmosphere
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.

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IN CLOUDY AIR PARCEL, HEAT RELEASE FROM H2O
CONDENSATION MODIFIES G
Wet adiabatic lapse rate GW 2-7 K km-1
z
RH 100
Latent heat release as H2O condenses
GW 2-7 K km-1
RH gt 100 Cloud forms
G 9.8 K km-1
If ?wlt -dT/dz lt ? ? air parcel is conditionally
unstable
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SUBSIDENCE INVERSION
typically 2 km altitude
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VERTICAL PROFILE OF TEMPERATUREMean values for
30oN, March
Radiative cooling (ch.7)
- 3 K km-1
Altitude, km
2 K km-1
Radiative heating O3 hn e O2 O O O2 M e
O3M
heat
Radiative cooling (ch.7)
Latent heat release
- 6.5 K km-1
Surface heating
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DIURNAL CYCLE OF SURFACE HEATING/COOLINGventilat
ion of urban pollution
z
Subsidence inversion
MIDDAY
1 km
G
Mixing depth
NIGHT
0
MORNING
T
NIGHT
MORNING
AFTERNOON
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EFFECT OF STABILITY ON VERTICAL STRUCTURE
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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).
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PLUME LOOPING, BALTIMORE 2pm.
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PLUME LOFTING, BEIJING 7am
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TYPICAL TIME SCALES FOR VERTICAL MIXING
How fast does air mix due to molecular diffusion?
Use Ficks Law And the Einstein Equation for
Molecular Diffusion
Flux is proportional to the spatial gradient
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)
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TYPICAL TIME SCALES FOR VERTICAL MIXING

• Define by analogy the time Dt to travel Dz by
  turbulent diffusion

tropopause
(10 km)
5 km
2 km
planetary boundary layer
0 km