Troposphere
The troposphere is the lowest atmospheric layer reaching an altitude of about 20
km. Density, pressure and temperature decline with altitude. The troposphere is
largely convective, which translates into a uniform chemical composition. Critical
component is H2O vapor from evaporation and transpiration processes. Water
vapor decreases with altitude because of condensation and cloud formation.
Temperature profile of the Troposphere
Heat transfer in air:
Q
T
 k  A
t
z
k air
W 
 0.026 
 thermal conductivity

 mK 
Heat transfer takes place by energy transfer through cross sectional area A!
Vertical convective motion takes place by moving volume of air in a reversible
adiabatic process (no heat exchange with surrounding environment Q=0!) This
is subject to energy conservation according to the first law of thermodynamics:
dU  Q  W  Q  P  dV
Heat exchange between air packet and surrounding is:
dQ  Cv  dT  P  dV
 kJ 
Cv  1.010 
 Specific heat or heat capacity of
K
kg

 an air volume element at constant
 kJ  volume or constant pressure.
CP  1.005 

K
kg


Adiabatic conditions: Q  0  Cv  dT   P  dV
For adiabatic conditions Q  0  Cv  dT   P  dV
Internal energy for V  const : dU  Cv  dT
 dU 
specific heat for V  const : Cv  

 dT V
Gas
He
Ar
N2
Cp J/mole·K Cv J/mole·K
20.79
12.52
20.79
12.45
29.12
20.8
O2
CO
CO2
29.37
29.04
36.62
20.98
20.74
28.17
H2O vapor
air
37.47
29.07
28.03
20.95
dU
Cv 
dT
 dQ 
for P  const : C P  

 dT  P
Universal gas constant
R = 8.314 J/mole·K
R  CP  Cv 
Conversion: 1 mole ≡ A g
To derive the temperature profile along the vertical atmosphere axis as function of
altitude T(z) requires differentiating the ideal gas equation P·V=R·T for Q=0:
P  dV  V  dP  R  dT  CP  Cv   dT
R  CP  Cv 
R  dT  CP  dT  Cv  dT  CP  dT  P  dV  P  dV  V  dP
 CP  dT  V  dP
for adiabatic element
Reformulating the hydrostatic equation:
dP
   g
dz
V  dP  V    g  dz  m  g  dz
C P  dT  m  g  dz

dT
m g

 
dz
CP
g  9.81 m / s 2
z
Lapse rate defines the rate at
which temperature T decreases
with increasing altitude z.
z
T
(For the troposphere a negative value)
T
Adiabatic lapse rate: =-9.7 K/km for dry air.
The adiabatic lapse rate describes the temperature change with altitude for
absolutely dry air, it serves as a normalization parameter since air is never dry.
CP increases with humidity, CP=1.88 KJ/km K for H2O vapor. An increase in
humidity decreases the temperature gradient. The actual lapse rate L
depends on humidity and is around 6-7 K/km!
dT
 g
 V 
  L  
dz
CP
K
  67
km
Higher humidity increases CP and
changes the temperature gradient
that -L < -Γ or L > Γ.
Flight height of 10 km, T=-50oC=223K
If the density ρ in an air volume element V is smaller than the density ρs
of surrounding environment, the buoyancy causes acceleration upward, if
density of air volume is larger, element will stabilize.
V   smaller  g
dT

  L  
dz
CP
Unstable situation, convection
V  larger  g
dT

  L  
dz
CP
stable situation, no convection
dTair  V 
Convective equilibrium
z
dTdry  V 
dT
 
dz
convection
T
 wet
CP
 dry  g
CP
dz   L  dz
dz    dz
m 0.8  28  0.2  32 29  amu 


V
V
V  m 3 
m 0.72  28  0.18  32  0.1 18 27.7  amu 
 

V
V
V  m 3 
 dry 
radiation
 wet  g
Clouds Rising
Cloud physics and weather
see next chapter
The stratosphere
The stratosphere is the second layer of the atmosphere above the troposphere
ranging from about 20 km to 50 km altitude. The density declines in this layer
from 100 g/m3 to 3 g/m3, the pressure drops exponentially from 100mb to 1mb.
The temperature remains constant at the lower layer of the stratosphere and
then rises with increasing altitude. At the top of the stratosphere the thin air
may reach temperatures close to 0°C (273 K).
Temperature profile of Stratosphere
~20-50km altitude
f
Temperature is dominated by radiative energy balance
f
Incoming flux must be balanced by outgoing flux.
The factor f is the fraction of transmitted radiation.
Fin    TE4  f    TS4
f
Fout  1  f     TE4  f    TS4
f
  TE4  f    TS4  1  f     TE4  f    TS4
  TE4  1  f     TE4  2 f    TS4
  T  2  T
4
E
4
S
TE
TS  1 / 4
2
TE = 255 K  TS = 215 K
This suggests that temperature in stratosphere remains constant. This is
only partially correct since ozone layer in stratosphere causes further
absorption and an increase of the stratosphere temperature up to 270K.
Chemical composition of Stratosphere
Temperature is low and constant for ~10 km,
that region is frequently called tropopause.
Towards higher altitude the temperature
increases due to the absorption of cosmic
radiation, reaching a maximum of about 0oC
(273 K) at top of stratosphere. This is
associated with the absorption of UV
radiation by Oxygen and Ozone causing
stratosphere heating in its upper layers.
UV range
Nuclear test program deposition
A total of 2057 nuclear weapon explosions since 1945
51017 Bq=500 PBq
Mesosphere
Mesosphere is the atmospheric layer above stratosphere. It is characterized by
steadily decreasing density. High altitude (~80km) location for rare kind of
clouds (noctilucent clouds) in polar zone, frequency of occurrence seems to
increase (signature for climate change, consequence of space shuttle exhaust?)
NLC formation requires a combination of
very low temperatures, a source of water
vapor, and condensation points (meteoritic
dust, volcano ashes, aerosols?)
NLC: first observed 1885 (two years
after the Krakatau eruption), increasing
appearance of noctilucent clouds is
interpreted as a consequence of a
decrease in temperature at the altitude
where the clouds form parallel with an
increase in water vapor by complex
photochemical processes. The warming
in the in the lower atmospheric layers
causes the cloud layer to cool
increasing the probability of formation.
Mesosphere is too high to be reached by balloon or aircraft and is therefore
poorly understood! New satellites such as AIM mission are launched for
more detailed exploration.
Temperature declines towards its
lowest value in the atmosphere
of about T=-80 oC (193K).
Limited absorption of the solar
radiation flux and possible
cooling by de-excitation of CO2
vibrational excitation modes by
collision with oxygen atoms,
which are in equilibrium at
higher
density
in
lower
atmospheric regions.

960
T
Q  2    e
 collision rate
This leads to the discussion of
possible enhanced cooling with
increasing CO2 budget!
Aerosol impact on stratosphere temperature
Example: Mount Pinatubo eruption in June 13, 1991 causing emission of particles
into higher atmosphere with direct impact on optical depth (·d) and temperature T.
Optical depth for
1020 nm range
F
 e  d
F0
d  40km;  0  d  0.001  v  d  0.06
F
 e  0 d  99%
F0
Fv
 e  v d  94%
F0
Impact on high altitude temperature
Heavy metal enrichment
Large numbers of meteorites are absorbed by
atmosphere, they typically evaporate in the
mesosphere, enriching the layer with about 40
tons/day of heavy metal containing dust!
FREQUENCY OF IMPACTORS:
Pea-size meteoroids - 10 per hour
Walnut-size - 1 per hour
Grapefruit-size - 1 every 10 hours
Basketball-size - 1 per month
50-m rock - 1 per 100 years
1-km asteroid - 1 per 100,000 years
2-km asteroid - 1 per 500,000 years
During the early phase of the planet
formation, the accretion rate was in
the range of more than millions /sec
from meteors to planetesimals.
N  37  D 2.7
N: number of meteorites
D: diameter of meteorites
Meteorites fragment in higher atmosphere layers and the fragments evaporate
in the mesosphere. Meteoritic material is enriched in heavy elements (iron
meteorites) which form dust particles in the high altitude layers.