Transcript 8/27

ATS 621 Fall 2012
Lecture 3
H2O part of constant
Chain Reaction Example
“M” is any other
molecule available
for collisions
UNITS
Mixing ratio or mole fraction CX [mol mol-1]
# moles of X
CX 
mole of air
Trace
gases
remains constant when air density changes
e robust measure of atmospheric composition
GAS
MIXING RATIO
(dry air)
[mol mol-1]
Nitrogen (N2)
0.78
Oxygen (O2)
0.21
Argon (Ar)
0.0093
Carbon dioxide (CO2)
365x10-6
Neon (Ne)
18x10-6
Ozone (O3)
(0.01-10)x10-6
Helium (He)
5.2x10-6
Methane (CH4)
1.7x10-6
Krypton (Kr)
1.1x10-6
• Air also contains variable H2O vapor
(10-6-10-2 mol mol-1) and aerosol
particles
• Trace gas concentration units:
1 ppmv = 1x10-6 mol mol-1
1 ppbv = 1x10-9 mol mol-1
1 pptv = 1x10-12 mol mol-1
Slide courtesy Colette Heald
"Perfect Gas" Law
PV = N' kT
or PV = N RT
N' = number of molecules in the air parcel
N = number of moles; N' = N x Av
k = Boltzmann constant
R = Universal Gas Constant; R = k x Av
=================================
(In meteorology texts: P = r RT - different "R“ = 287 J/kg/K)
k = 1.3806503 × 10-23 m2 kg s-2 K-1
R = 8.31 J mole-1 K-1
Slide courtesy Colette Heald
Number density nX [molecules cm-3]
nX 
Proper measure for
• reaction rates
• optical properties of atmosphere
# molecules of X
unit volume of air

Column concentration  X =  nX ( z )dz
0
nX and CX are related by the ideal gas law:
Also define the mass concentration (g cm-3):
rX 
Proper measure for absorption of radiation
by atmosphere
na = air density
Av = Avogadro’s number
P = pressure [Pa]
R = Universal gas constant
= Av k k=Boltzmann cnst
T = temperature [K]
MX= molecular weight of X [g/mol]
mass of X
unit volume of air
Slide courtesy Colette Heald
Partial pressure Px [Pa]
Dalton’s law:
PX  C X P
Proper measure for phase change
(such as condensation of water vapour)
Evaporation of liquid water from a pan:
No lid: water molecules escape from pan to
atmosphere (evaporation)
Add a lid:
• escaping water molecules collide on lid and return
to surface; collision rate measures PH2O
• eventually, flux escaping = flux returning :
saturation (PH2O,SAT)
• cloud formation in atmosphere requires
PH2O > PH2O,SAT
•T
e PH2O,SAT
Slide courtesy Colette Heald
CLAUSIUS-CLAPEYRON EQUATION
PH 2O , SAT
1 1
 A exp[ B(  )]
T0 T
A = 6.11 hPa (= Pvap at 0C)
B = 5310 K
To = 273 K
PH2O,SAT (hPa)
Vapour pressure increases sharply
with temperature, due to the large
latent heat.
T (K)
Slide courtesy Colette Heald
PHASE DIAGRAM FOR WATER
gas-liquid
metastable
equilibrium
RH (%)  100
PH 2O
PH 2O,sat (T )
triple point of water
(n=0)
Dew point: Temperature Td such that
PH2O = PH2O,SAT(Td)
Slide courtesy Colette Heald
RUNAWAY GREENHOUSE EFFECT ON VENUS
due to accumulation of water vapor from volcanic outgassing early in its history
…did not happen on Earth because farther from Sun; as water accumulated it reached
saturation and precipitated, forming the oceans
EARTH
Slide courtesy Colette Heald
VENUS
REGIONS OF THE ATMOSPHERE
Troposphere:
• generally homogeneous, characterized by strong mixing
• decreasing T with increasing altitude from heat-radiating surface
• near surface boundary layer exists (over the oceans ~1km depth), BL often cloud topped and can
trap emissions
Tropopause:
• serves as a “barrier” that causes water
vapor to condense to ice
• “tropopause folding” where strat air intrudes
into lower levels  exchange mechanism
Stratosphere:
• increasing T with altitude due to OZONE
causing heating from absorption of UV
Mesosphere:
• absence of high levels of radiation absorbing
species and thus a T decrease
• upper mesosphere and higher defines the
exosphere from which molecules and ions
can escape the atmosphere
Thermosphere:
• rarified gases reach temperatures as high as 1200C by absorption of high energy radiation
VERTICAL PROFILES OF PRESSURE AND TEMPERATURE
Mean values for 30oN, March
Stratopause
Tropopause
Pressure is the weight exerted
by the overlying atmosphere:
P
F
A
N

units :  2  Pa 
m

Average sea-level pressure (SLP):
≡101.325 kPa
≡1 atm
≡1.013 25 bar
≡1013.25 millibars (mbar, mb) or hectopascals (hPa)
≈760.001 mm-Hg, 0 °C ≡760 torr
≈1033.227 cm–H2O, 4 °C
≈14.695 948 psi
MASS ma OF THE ATMOSPHERE
P=F/A
Mean pressure at Earth's surface:
984 hPa
Radius of Earth:
6378 km
ma 
4R 2 PSurface
g
 5.129 10 kg
18
g = gravitational acceleration
= 9.80665 m/s2
Total number of moles of air in atmosphere:
ma
Na 
 1.8  1020 moles
Ma
Mol. wt. of air: 29 g mole-1 = .029 kg mole-1
PRESSURE-GRADIENT FORCE
Fp = [P(z)-P(z+dz)]A
Fg = mg
P(z+dz)
P(z)
Low Pressure
High Pressure
slab of surface area A
Pressure gradient force goes from high to low pressure
BAROMETRIC LAW
(variation of pressure with altitude)
• Consider elementary slab of atmosphere:
P(z+dz)
P(z)
[ P( z )  P( z  dz )] A  r a gAdz
unit area
PM a
ra 
RT
Ideal gas law:

dP
Mag

dz
P
RT

dP
  ra 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
Ma= .02897 kg/mole
At high altitudes (low P)
the mean free path is >>
than mfp at sea level
(e.g., 106 cm at 500 km;
10-6 cm at sea level)
Source: Ahrens,
Meteorology Today
How (where) are species transported in the atmosphere?
Planetary boundary
layer (PBL) is the
zone influenced by
frictional drag at the
surface
• lowest ~500 m of the
atmosphere
• important zone for
urban air pollution
•Includes semipermanent high and low pressure
areas that reside over oceans & continents
•Affects pollutant long-range transport
•Includes migratory high and low
pressure fronts
•Affects urban and regional
pollutant transport
•Examples: meandering & dispersion of
chimney plume, flows around a building
http://apollo.lsc.vsc.edu/classes/met130/notes/chapter9/scales.html
idealized
reality
Idealized general circulation
Midlatitudes:
• westerlies caused by
Coriolis force on winds
moving across the
subtropical latitudinal
belts, and requirement of
thermal wind balance
(equator-to-pole T
gradient)
• at low levels, semistationary subtropical
high P regions pump
anti-cyclonically moving
air into the midlatitudes
• Coriolis force pushes
air toward east,
producing westerly flow
Idealized general circulation
Midlatitudes:
• Thermal wind invigorates
westerly flow at midlats, esp
in the winter hemisphere
(equator-to-pole T gradient
largest)
• in NH, higher T in
subtropics imply higher P
and anti-cyclonic motion;
lower T at high lats imply
lower P and cyclonic motion
• converge at midlats -westerly flow strongthen -e.g. jet stream
Westerlies play large role in
re-distribution of
anthropogenic emissions
from NH mid-lats: jet
stream disperses to all parts
of hemisphere
Idealized general circulation
Idealized general circulation
Tropics:
• Hadley Cell moves warm,
moist air upwards into the
tropical upper atmospheres
and transports it across
latitudinal belts to higher lats
in both hemispheres
• Sustained by solar
input to equatorial lats results in strong,
persistent convection
• winter hemisphere is
most vigorous
• Inter-tropical
Convergence Zone (ITCZ)
is a band of low P, migrates
seasonally (NH summer:
closer to Northern midlats;
NH winter, closer to, but
somewhat north of, equator)
Idealized general circulation
• Ferrel Cell is weaker - transports
cold air upward near poles and
Ferrel
warm air downward near midlats
(opposite of natural tendency)
Hadley
• Monsoonal flow occurs in lowlatitude regions around the globe
due to T gradients bewteen land and
sea (solar heating during summer)
• drives moist flow from ocean to
land - strong convective currents
induced by hot land surface lift
air -- precipitation
• currents typically oriented
north-south - strong localized
cross-equatorial flow
•Interact with other features of
the general circ (e.g. E. Pac.
SST)
Side view
Note how species might get mixed;
mixing relatively slow between hemispheres
Characteristic mixing times
Lower stratosphere
2 years
Troposphere
50 years
1 year
Planetary boundary layer
1 month
1 hour
Surface mixed layer of ocean, 10 hours
POLE
EQUATOR
1 year
2.5 years
POLE
Mixing time scales
More detail on air motion
Geostrophic Wind
winds balanced by the Coriolis and Pressure Gradient forces
An air parcel initially at rest will move from high pressure to low pressure because of the pressure
gradient force (PGF). However, as that air parcel begins to move, it is deflected by the Coriolis force
to the right of the wind velocity in the northern hemisphere (to the left on the southern hemisphere).
This is an apparent horizontal deflection force arising from Earth’s rotation; max at poles, zero at
Equator.
As the wind gains speed, the deflection increases until the Coriolis force
equals the pressure gradient force.
At this point, the wind will be blowing parallel to the isobars (lines of constant pressure).
When this happens, the wind is referred to as geostrophic.
Northern hemisphere:
blows with lower P to
LEFT and higher P to
RIGHT
The diagram above shows the two forces balancing to produce the
geostrophic wind. Winds in nature are rarely exactly geostrophic,
but can be close, at altitudes above the PBL and away from
low or high pressure centers.
This is because winds are only considered truly geostrophic when the isobars are
straight and there are no other forces acting on it.
Vg= velocity of geostrophic wind
f = Coriolis parameter
rho = air density
delta P = pressure difference between isobars
d = spacing between isobars
Gradient wind
• Near high or low pressure centers, isobars are curved and centripetal
acceleration is important. Resulting wind is termed the gradient wind.
Line of
constant
pressure
L
Fp
Fcor
Vgradient
L
Fcentrifugal
cyclone
Cyclonic and anticyclonic flows
Near the surface, the frictional force slows wind velocity
- This decreases the Coriolis force (=f(windspeed))
- wind then turns toward low pressure until the frictional force is
sufficient to account for the decreased Coriolis force
- effect is strongest near surface (reason that wind direction
rotates with height)
L
As as result, wind in cyclonic flow converges toward low,
leading to rising motion in center.
CYCLONES and ANTICYCLONES are transient waves,
with periods of 3-7 days
Cyclone: low-P center
Divergence aloft; rising
Air flows toward the center at the surface
Produces cloudy, inclement weather
Anticyclone: high-P center
Convergence aloft; sinking (subsidence)
Air flows outward from the center at the surface
Produces sunny, dry conditions
H
Subsidence Inversion
• Subsidence associated with high-pressure systems produces stable air
aloft, which can trap pollutants near the surface
• Covers hundreds of thousands of square kms and can persist for days
• Los Angeles is at the eastern
edge of the semi-permanent
North Pacific ant-cyclone –
frequently experiences pollutant
trapping from subsidence
• Short-lived anticyclones can
lead to episodic pollution
trapping in affected areas
More detail on Earth’s energy budget
Earth’s Energy Balance
Sunlight
(Shortwave, visible
radiation)
235 Watts per square
meter (W/m2)
Perturbations to energy balance are known as “radiative forcings”
45
Heat (Longwave,
infrared radiation)
235 Watts per square
meter (W/m2)
Global energy budget
350-195 = 155+67+24+78 = 324
Extra stuff
(mostly from Prof. Heald, and in Jacob text)
Chapter 2. ATMOSPHERIC PRESSURE
“SEA LEVEL” PRESSURE MAP
http://weather.unisys.com
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)
dF  ( P( x)  P( x  dx))dydz
1 P
Acceleration   
r x
Pressure-gradient force
Vertical area
dydz
For DP = 10 hPa over Dx = 100 km,  ~ 10-2 m s-2 a 100 km/hr wind in 1 h!
Effect of wind is to transport air to area of lower pressure a dampen DP
On mountains, however, the surface pressure is lower, as the pressure-gradient
force along the Earth surface is balanced by gravity:
P(z+Dz) P-gradient
gravity
P(z)
aThis is why weather maps show “sea level” isobars;
a The fictitious “sea-level” pressure at a
mountainous site assumes an isothermal air column
to be present between the surface and sea level (at T
of surface site)
BAROMETRIC LAW: THE SEA-BREEZE EFFECT
reminder :
H
RT
Mag
~1 km
~10 km
VERTICAL TRANSPORT: BUOYANCY
Imagine object of same density as fluid:
P-gradient
r  r'
z+Dz
Fluid (r’)
FP  FG  r 'Vg
Object (r)
z
Gravity
Now look at force imbalance when
density of object differs from surrounding
fluid:
rr
FB  FP  FG  r 'Vg  rVg
B 
r ' r
g
r
If object is lighter
than fluid 
accelerate upwards
Note: Barometric law assumed a neutrally buoyant atmosphere with T = T’
T  T '  r  r '  buoyant acceleration