LECTURE 2
METO/CHEM 637
ATMOSPHERIC CHEMISTRY
Russell R. Dickerson

Outline
I. B. Atmospheric Stability and Circulation (F-P & P., Ch. 2; S&P Ch. 1, 14)
   1. Pressure and temp. profiles
   2. Thermo diagram and stability
   3. Geostrophic winds and General Circulation

I. C. Electromagnetic Radiation

The motion of the atmosphere is caused by differential heating.  That is, some parts of the
atmosphere receive more radiation than others, and become unstable.

1. PRESSURE AND TEMPERATURE PROFILES
 
(Figure)

1A  Derive Hydrostatic Equation.

    START:  Ideal Gas Law

PV = nRT or
P = R'T or
P = R'T

Where R' = R/Mwt
	Mwt = Mole weight of air
	 = Density of air (g/l)
	 = Specific Volume of air = 1/

      The pressure at any given altitude is due to the weight of the atmosphere above it.
Weight is the mass times the acceleration.
 
W = mg
BUT  m = V or
m = Z

weight per unit area is pressure

P = W = gZ

For a second layer, the difference in pressure can be written:

dP = - (Pg/R'T) dZ

For an isothermal atmosphere, g/R'T is a constant.  By integrating both sides of the above equation, from the ground (Z = 0) to some height Z we find:

ln (P/Po) = - Z/Ho

WHERE

Ho  = R'T/g

or

HYDROSTATIC EQUATION:        Pz = Po exp(-Z/Ho)

NOTE, for T = 280 K:     Ho  8 km

Pz (atm)  e (-Z/8)
 
Scale height:  For each 8 km, the pressure decreases by a factor of e-1 or by one "e-fold".

Useful problems left to the student:
1. Calculate the altitude at which the pressure drops by a factor of ten and two.
2. Derive an expression for the pressure as a function of altitude for an atmosphere with a temperature that varies linearly with altitude.
3. Calculate the depth of a constant density atmosphere.
4. Calculate the fraction of the mass of the atmosphere between 200 and 700 mb.

1B. TEMPERATURE LAPSE RATE 
 
(Figure)

NOTE: This is a little different from the version on the viewgraph.

As a parcel of air rises in the atmosphere it will expand and cool.  If it exchanges no heat with its surroundings, it will cool "adiabatically".

CALC. ADIABATIC LAPSE RATE:

  First law thermodynamics:

dE = DQ -  DW

Where  E = Energy
Q = Heat across boundaries
W = Work done

Assume: all work PdV work
Internal energy = CvdT
Adiabatic i.e. DQ = 0

From the Ideal Gas Law
PV = nRT
d(PV) = nRdT
= PdV + VdP
PdV = nRdT - VdP

The First Law is now:
CvdT = VdP - nRdT

= (nRT/P) dP - nRdT
     
Rearranging
 
dT/dP = (nRT/P)/(Cv + nR)
 
Remember the Hydrostatic Equation
 
dP/dZ = -gP/nRT

dT/dZ = (-gP/nRT)(nRT/P)/(Cv +nR)

= -g/(Cv + nR)

dT/dZ = -g/Cp

This quantity, -g/Cp, is a constant in a dry atmosphere.  It is called the dry adiabatic lapse rate and is given the symbol gamma.
 
 = -9.8 K/km
 
It is a general thermodynamic property of the atmosphere, and always expresses the way a dry parcel of air will cool on rising or warm on sinking if there is no interaction with the surroundings - a good  assumption for most cloud-sized air parcels.

This equation is easily corrected for a wet air parcel.  The heat capacity must be modified: Cp' = (1-a)Cp + aCp(water), where "a" is the mass of water per mass of dry air.  If the parcel becomes saturated, then the process is no longer adiabatic.  Condensation adds heat.
 
DQ = -Lda
 
Where L is the latent heat of condensation
 
-dT/dZ = g/Cp + (L/Cp) da/dZ

Because the amount of water decreases with altitude the last term is negative, and the rate of cooling with altitude is slower in a wet parcel.  The lapse rate becomes the wet adiabat or the pseudoadiabat.

STABILITY AND THERMODYNAMIC DIAGRAMS
 
(Figure)

 Solid lines - thermodynamic  properties
 Colored lines - measurements or soundings                               

DAY
 A    <  o unstable
 B    =  o neutrally stable
 C    >  o stable
(for absolute values)

On day A parcel will cool more slowly than surroundings - air will be warmer and rise. On day B parcel will always have same temperature as surroundings - no force of buoyancy.  On day C parcel will cool more quickly than surroundings - air will be cooler and return to original altitude.

 (handout)
  
Very important for air pollution and mixing of emissions with free troposphere.
 
FORMATION OF THERMAL INVERSIONS
 
(viewgraphs, 2)
 
In stratosphere the temperature increases with altitude, thus stable or stratified.
 
Dfn. Potential temperature  as the temperature a parcel of air would have if it were brought
adiabatically to the 1000 mb (hPa) level.

  = T + Zo 

ATMOSPHERIC CIRCULATION - WINDS
 
GENERAL CIRCULATION - GLOBAL WINDS
 
small assumptions - 
      no continents
      no rotation
      no seasons
 
(Figure)
 
 Heating of Equator - cooling at poles
 Hadley cells - 18th century 
 Rising air storms at Equator - stop at tropopause                  
 Descending air over poles - dry

 Add rotation of earth

C = 2 v {sin}
 = rate of spin
v = velocity of object
 = latitude
 
Maximum at poles  -   zero at Equator

MOTION
 Toward right in Northern Hemisphere
 Toward left  in Southern Hemisphere

Now we see three cells.   High winds go north get bent to right (E) and we have west winds.  Low (surface) winds go south get bent to right (W) and we have east winds, the  Trades.  At the Equator surface winds are out of the east, without a north-south component.   Intertropical convergence zone - ITCZ - wind can not cross ITCZ.   Mixing within Northern Hemisphere takes about 1 yr.   Global mixing requires about 5 yr.   See sharp gradient of trace gases at ITCZ

SYNOPTIC AND MESOSCALE MOTIONS

Synoptic area approx 1000's km, highs and lows.   Meso area approx 100's km, the size of a city or thunderstorm.  Micro refers to scales on the order of 1000's of meters, such as the planetary boundary layer (PBL).
 
(Figure)
 
Winds follow isobars

RADIATION

The sun produces essentially all the energy we receive
 It powers atmospheric chemistry
 Energy decreases with wavelength
 Most chemical bonds broken only by UV 

 Sun emits over almost whole spectrum
 Black body radiation - photosphere at about 6000 K

 Only a fraction reaches surface
 Atmosphere controls amount reaching the surface
 
 e   = energy of a photon
 Et = total energy emitted
 h   = Planck's const.
   = freq.
 c   = speed of light
  = Stefan Boltzman const.
  = wavelength
 k = Boltzman const.
 
 Planck's law gives other two laws
 Other form of Planck's law E = f (,T)
 Differentiate and find max., get: Wien's Law
 Integrate and get: Stefan Boltzman Law

 Atmospheric O2 and O3 absorb most of UV 
 while H2O and CO2 absorb most of the IR.
 Small fraction of atmospheric gases do most of the absorbing
 Visible window 
 IR window at 8 to 10 m (note ozone)
                                                  
 Note UV absorption spectrum of ozone sets solar intensity received.

 Transitions only at quantum mechanically allowed energy levels.

Greenhouse effect: Ts  > Te where Ts is the surface temperature and Te is the effective temperature, that is the temperature of the earth as perceived from outside the atmosphere, based on black body emission.   is the optical depth.

Ts4 = (1 +  )Te4