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621 project. Spring 2010. project. 1. The heating rate is defined as :-.

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621 project

621 project

Spring 2010


1.The heating rate is defined as :-

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:


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:



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, 3F15.1wavelength Solar flux, Cross section Rayleigh scattering range photons. cm2 Coefficientnanometers 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 1.45290 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


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.........



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.

  • (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
  • 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.

2.The rise in temperature per unit time due to H can be written as

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.


3.Now repeat the calculations in 1 and 2 for a solar zenith angle of 60 degrees.


4. (a) The transmission, T, can be expressed by the Goody random band model as :

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.


(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.


5. 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.