AOM 4932 - Atmospheric Processes
From last time -Distribution of solar radiation over earth in space and time leads to an energy imbalance.
Meteorologic and hydrologic processes originate to redistribute energy. Water in both
liquid and vapor forms plays a major role in this energy redistribution from equator to
poles. 2/3 transfer of energy occurs via atmosphere (water vapor), 1/3 occurs through
oceans (liquid water).
Composition / Characteristics of Atmosphere
80% N2 ;
20% O2
-- treated as perfect gas
100 km
Thermosphere
upper
atmosphere
Mesopause
Mesosphere
Altitude (km)
Stratopause
50 km
Stratosphere
lower
atmosphere
sharp change in temp. and
pressure produce Jet
Streams
8 - 16 km
Tropopause
Troposphere
poles
equator
-80
-60
-40
-20
0
20
Temperature C
Lower atmosphere extends up to  50 km. Plays primary role in weather determination.
Upper atmosphere doesn’t play much of a role.
Lower atmosphere most active part of atmosphere where most of the mass and energy
transfer occurs. It is divided into two parts distinguished by their temperature distribution
-- the troposphere and the stratosphere.
Troposphere -- characterized by:
1.
2.
3.
4.
5.
Variable thickness (8 km poles, 16 km equator).
Decreasing temperature with elevation (linear).
Well defined pressure gradients (max. pressure at bottom). non-linear
Well defined distribution of moisture and suspended particles (max. at bottom)
Sharp air velocity gradient. At earth’s surface velocity is zero (no-slip condition) and
velocity increases over 2700 m thick boundary layer according to a logarithmic
velocity profile.
z
u(z)
Stratosphere -- no well defined profiles
Temperature Distribution
Temperature distribution follows radiation distribution both in time (i.e. daily) and space
(i.e. distribution over earth).
In time:
10
4 p.m. peak
clear day
5
0
cloudy day (clouds buffer in
and outgoing solar radiation
because H20 absorbs heat)
-5
-10
0
6
12
18
24
Air temperature rises during day and falls at night following solar radiation. Peak
temperature lags peak solar radiation (occurs at noon) by several hours due to heating
effects on earth’s back radiation which lags solar radiation.
incoming solar radiation
energy
flux
outgoing longwave radiation
from earth
6 am
noon
4 pm
mid.
Clouds absorb incoming and outgoing radiation  attenuate diurnal fluctuations.
Similarly diurnal fluctuations not as great near ocean as inland because ocean absorbs
(and distributes) heat more efficiently throughout its fluid mass than land masses -- H2O
higher heat capacity than earth (because when energy added much of it used to break H
bonds rather than increase rate of molecular vibration which increases T. This makes it
possible for warm-blooded organisms to regulate temperatures) prevents large, rapid
temperature fluctuations.
Seasonally - Temporal distribution. Air temperatures also follow cycle of incoming solar
radiation. Again peak temperature (July / August) lags peak radiation (June 22) because
of effect of earth’s back radiation. Lag is more significant near oceans.
near oceans in Northern hemisphere: max / min  Aug. / Feb.
inland in N. hemisphere: max / min  July / Jan.
In space - Spatial distribution (horizontal). Same trend in horizontal distribution of
temperatures over globe. Time averaged temperature distribution follow latitude lines
which receive equal solar radiation.
Highest temperatures just north/south of equator due to extensive cloud cover in
this region (intertropical convergence zone).
Similarly, air over oceans tends to stay warmer in winter/colder in summer than
air over land due to high heat capacity of ocean ( i.e. same change in heat energy
produces a smaller temperature change for oceans versus land)
Vertical Distribution of Temperature - Troposphere shows well-defined linear
relationship of temperature with height above earth surface (in an average sense).
T ( z)  To  z
Z (km)
ambient lapse rate
6 - 10 C/km
To
T(C)
humid cloudy conditions   6 C/km - saturated adiabatic lapse rate
dry clear conditions   10 C/km - dry adiabatic lapse rate (9.8)
Why? Under humid conditions water vapor in air condenses as it rises and cools. Heat is
released from water to surrounding air when vapor condenses. This slows the rate of
cooling.
Ambient lapse rate dictates the stability or instability of air masses. Air can only rise and
thus lead to condensation and precipitation if it is warmer than surrounding air.
Get unusually stable weather (i.e., no precipitation) when have a temperature inversion,
i.e. when temperature increases with elevation locally. Air can’t rise -- no rainfall thus
pollution problems. Most likely to happen over continental land masses after calm dry
nights with clear skies. Land cools faster than upper air.
Pressure Distribution - Horizontal
Daily pressure distribution at sea level is variable and unstable. However if looking at
average pressure distributions over long time periods semi-permanent patterns emerge:
polar easterlies
low pressure
westerlies
high pressure
NE Tradewinds
low pressure
SE Tradewinds
high pressure
westerlies
polar easterlies
low pressure

These pressure belts migrate northward in June/July and southward in Jan./Feb.
following solar radiation distribution  i.e. are of thermal origin.

Horizontal pressure gradients are the driving force for winds. Wind direction and
circulation however is also affected by:
1. The rotation of the earth which produces the apparent Coriolis force (apparent
force which causes moving object to deviate right in N. hemisphere and left in S.
hemisphere). Results from perception of observer on rotating earth looking at
unattached moving mass.
2. Friction of lower air masses with earth’s surface.
The net effects of these forces are:
1. Convergent equatorial winds of easterly origin (tradewinds or doldrums). Converge
in low pressure belt called intertropical convergence zone, ITCZ  cloudy, showery
weather.
2. Prevailing westerly winds at mid-latitudes. Associated with high pressure centers,
little precipitation.
3. Highly variable polar easterly winds (not well-characterized).
4. Poleward circulation of air masses is broken up into 3 cells forming banded structure
around the earth.
Winds shift north/south with radiation intensity.
Pressure Distribution - Vertical
Vertical pressure distribution is also highly variable and weather dependent. To obtain a
representative profile commonly assume atmosphere is hydrostatic.
pressure
gravitational constant
dP
 g
dz
Must also account for the fact that density of air is
dependent on pressure. Assume air follows the ideal gas law:
Ideal gas law for
unit mass:
pressure of
air
P 1  RT
volume air
mass air
ambient air
temp. K
dry air gas
constant
287 J/kg K =
2.88E6 cm2/s2 K
Combine these two equations to get:
T 
 P( z ) Po  o
To

g

z  R


distribution of
pressure with height in
troposphere
Non-linear due to linear
variation of temperature with
height, and ideal gas law and
hydrostatic assumption.
z
P
Distribution of Water Vapor
Water vapor (humidity) is the most variable atmospheric component and the most
important in determining climate. Most within 2 - 4 km of earth’s surface.
Water vapor - good absorber of radiation, therefore its movement and phase changes
(which absorb and release heat) play a major role in heat and energy balance.
Liquid and solid precipitation of vapor also drives land based portion of hydrologic cycle.
When air is saturated with water vapor (i.e. holding maximum amount of water vapor at
that particular temperature and evaporation and condensation are occurring at equal rates)
water vapor behaves like an ideal gas.
e   v Rv T
vapor pressure
millibars
= 100 N/m2
= 100 kg/m s2
absolute temperature of
water vapor -- assumed
same as air temp.
vapor density
(kg water/cm3
moist air)
dry air gas
constant
(cm2/s2K)
Rv is related to universal gas constant, Ro = 1.9857 cal/K mole, through the following
equation:
universal gas
constant
vapor gas
constant
R
M
Rv R
 o Ro  M
R R
vM
vM v M v M v
dry air gas
constant
molecular weight
water vapor
0.8(28) + 0.2(32) = 28.8
M
 e e  M
 v R T  161
. . v 
R TR T Vapor Pressure
v
M v M  v R T  161
v
18
0.622e
 v   0.622e Vapor density. Also
v RT
called absolute humidity.
RT
Note: This equation indicates density of water vapor is 0.622 density of dry air at that
P
e

same T and P(e).  a 
RT RT
If you have a mixture of dry air and water vapor,
Dalton’s law of partial pressure.
Total pressure of mixture =  partial pressure of constituents
pmix = pd + e
pressure dry air
P - e = pressure due to dry air
P = pressure mixture (moist air)
e = vapor pressure
vapor
pressure
  mix   d   v
vapor pressure
pressure mix
P  e 0.622e

RT
RT
P  0.378e 

1 

RT 
P 
 mix 
 mix
 Moist air is less dense than dry air at same temp. and pressure. If moist and dry air
converge moist air will rise and cool  precipitation
Some definitions:

relative humidity = Rh (r)

vapor density
v

sat ' d vapor density
s
vapor pressure
e

sat ' d vapor pressure
es
saturated vapor pressure (es) - partial pressure at which additional vapor would cause net
condensation  max amount of vapor system can hold  function of temperature
approximate empirical equation
es
Pascals (N/m2)
1b = 105 N/m2
1mb = 100 N/m2
 17.27 T 
 611 exp 

 237.3  T  C
dew point temperature (Td) - temperature to which air must be cooled to just become
saturated at a given vapor pressure/density
absolute humidity
v

specific humidity
qv


mass water
volume moist air
mass water vapor
v

unit mass moist air
 mix
0.622 e RT
0.622e

P  0.378e
P
RT
absolute humidity
density moist air
humidity - measured with a psychrometer - instrument with two thermometers, one is
wet-bulb thermometer covered by cloth saturated with water, other is dry.
Psychrometer is ventilated by rotation to induce evaporation from wet bulb. Temperature
of wet bulb lowered because during evaporation water absorbs heat from air to break H
bonds. Amount of evaporation controlled by humidity.
Dry bulb reads ambient temperature. Change between wet bulb (dew point temperature)
and dry bulb temperatures is called wet bulb depression related to relative humidity 
tabulated or empirical equations,
e.g.,
at climate station suppose
T = 20C (ambient temperature)
Twb = 16C (wet bulb temperature)
What is relative humidity?
max vapor
pressure at 20C
actual vapor
pressure at 20C
 17.27T 
es (T  20  )  611 exp 
  2339Pa
 237.3  T 
 17.27(16) 
eact  es (T  16  )  611 exp 
  1819Pa
 237.3  16 
Rh 
e act
es

1819 Pa
 78%
2339 Pa