621 project
Spring 2010
project
1.
The heating rate is defined as :-
dF
H  
dz
Let us assume that the effect of scattering is
small, and that in the ultraviolet region we need
only consider the effect of the incoming solar
radiation. Then at an altitude z, dF/dz due to
absorption by ozone can be written as:
dF
1.0
S  /  0

 nF e
dz
0
  N  p
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Here, σ is the ozone absorption cross section in cm2,
n is the concentration of ozone in molecules per cm3 at z, N
is the column amount of ozone in molecules per cm2 from
the top of the atmosphere to the altitude z, and FS is the solar
flux at the top of the atmosphere. p is the pressure at the
altitude z, and α is the Rayleigh scattering cross section.
You will need two data files in order to carry out the
calculations. Both are in my directory:
~hudson/METO621/m621a.dat
~hudson/METO621/m621b.dat
m621a.dat
Table of solar flux and ozone cross section versus wavelength
from 'Atmospheric Ozone, 1985' Vol 1., WMO Report #16
format of table is 2F5.0, 3F15.1
wavelength
Solar flux, Cross section Rayleigh scattering
range
photons.
cm2
Coefficient
nanometers
cm-2.sec-1
ozone
atmos -1.
per 10 nm
210 220
3.4E+13
1.2E-18
4.48
220 230
5.3E+13
3.2E-18
3.74
230 240
5.6E+13
6.9E-18
3.14
240 250
5.7E+13
1.0E-17
2.66
250 260
8.7E+13
1.1E-17
2.27
260 270
2.7E+14
9.0E-18
1.94
270 280
2.5E+14
4.7E-18
1.68
280 290
4.0E+14
1.8E-18
1.45
290 300
6.9E+14
6.2E-19
1.26
300 310
8.8E+14
1.8E-19
1.11
310 320
1.1E+15
5.1E-20
0.97
320 330
1.4E+15
6.2E-21
0.86
m621b
Alt
Ozone Ozone Atmospheric Temp
m
number Column
pressure K
density density
millibars
per cm3 per cm2
0. 7.00e+11 9.41e+18 1.0130e+03 288.
320. 6.97e+11 9.39e+18 9.7486e+02 286.
636. 6.94e+11 9.37e+18 9.3816e+02 284.
952. 6.90e+11 9.34e+18 9.0284e+02 282.
1271. 6.87e+11 9.32e+18 8.6885e+02 280.
1586. 6.84e+11 9.30e+18 8.3613e+02 277.
1903. 6.81e+11 9.28e+18 8.0465e+02 276.
2211. 6.69e+11 9.26e+18 7.7436e+02 274.
2509. 6.55e+11 9.23e+18 7.4521e+02 272.
........
69933
project
Using these files, calculate the ozone heating rate in the
atmosphere over the wavelength interval 210 to 330 nm, in
units of watts per m3 for altitudes between 10 and 62 km, for
the following three cases. Assume that the solar zenith angle
is zero, i.e. μ0=1.0.
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(1) Case A. Calculate the average cross section over the
interval 210 and 330 nm and use this to calculate the
heating rate as a function of altitude
(2) Case B. Calculate the average cross section for the
three intervals 210 to 250, 250 to 290, 290 to 330 nm
respectively. Use these average cross sections to
compute the heating rate for each wavelength interval,
and then sum the three heating rates to get the total
heating rate as a function of altitude
(3)Case C. Calculate the heating rate for all 12 intervals
given in the table. Sum these rates to get the total
heating rate as a function of altitude.
Please note that although you average the cross sections
you sum the solar flux.
Plot the results from all three cases, and discuss the
differences between the three cases.
project
The rise in temperature per unit time due to H can be
written as
2.
dT
H
 ~
dt
n Cp
where n is the density of the air (not ozone) and Cp is
the specific heat of air at constant pressure.
Note, that the sun does not shine all day, and that the
solar zenith angle changes throughout the day. The
average daily heating rate is about one quarter of the
number you have calculated. Calculate the radiative
temperature increase in degrees K per day for case
1(c) above. Compare these results with the
temperature profile and discuss the relationship.
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Now repeat the calculations in 1 and 2 for a solar zenith
angle of 60 degrees.
3.
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4. (a) The transmission, T, can be expressed by the Goody
random band model as :

T (u)  exp  Au / (1.0  Bu )

Where, u is the total mass in grams along the absorbing path
per cm2 . For the principle absorbing band of CO2 at 582 752 cm -1 , A and B have the following values:
A = 718.7 cm2 gram-1
B = 1604.24 cm2 gram-1
(b) Calculate the upwelling and downwelling intensities at
about 4, 17, and 45 km altitude, for zenith angles of 0, and
60 degrees, assuming:(1) Carbon dioxide is uniformly mixed in the troposphere
with a mixing ratio of 320 ppm.
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(2) The atmospheric parameters in Table m621b.dat
(3) No downward flux at the top of the atmosphere
(4) The temperature of the surface is at the temperature
of the atmosphere at the surface.
The intensity that you calculate at 60 degrees can be
considered as the mean intensity over all angles. The
upward and downward flux is simply π times the mean
intensity. Given this information calculate the net flux at
about 45 km, and deduce the rate of heating or cooling
at this altitude. How does this compare with the heating
due to ozone absorption? Discuss the results.
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Repeat the exercise in 3 for a doubling of the mixing
ratio of carbon dioxide, Compare the upwelling intensities
at about 17 Km with the results from 3 and discuss the
significance of any difference.
5.