ATSC 5003 Atmospheric Radiation, Lab #2
Energy deposition as a function of altitude – Chapman Layers
See also Liou (3.2.1.5) and Brasseur and Solomon (1984) (sec 4.3)
As photons enter the atmosphere they are absorbed dependent on: the frequency of photon, υ, the
molecule causing the absorption (both its abundance and absorption properties), and the solar zenith
angle, θo.
This lab, building on notes developed in class, requires you to supply some of the mathematical
development to calculate expressions for the energy deposition layers (1-5), and then to apply those
expressions to calculate atmospheric layer development (6-8). I recommend IDL used for 6-9.
Background calculations:
1) Show that no = nair(z=0) is ~ 2.7 x 1019 cm-3, where ni(z) is the molecular number concentration for
species i at z. Convince yourself that ni(z) = nair(z) MRi for the molecular concentration of species
i, where MRi is the mixing ratio of species i.
2) Derive the following expression for the atmospheric scale height, H = Rd T/g, where Rd is the gas
constant for dry air, T temperature, and g acceleration of gravity. What two laws are required?
Convince yourself that nair(z) = no exp(-z/H).
Energy deposition:
3) Show that for an overhead sun, the altitude at which the absorption optical depth reaches 1.0 is Zo
= H ln(σa nio H) where σa = absorption cross section for species i, nio = molecular density of
species i at the surface.
4) Show that q(z) = F☼ σa no exp[-(z/H + τo e-z/H)], for q(z)= rate of energy deposition as a function
of z, F☼ = irradiance at top of atmosphere, τo = σa no H sec(θo).
5) Show that the energy deposition is a maximum at Zm = Zo + H ln(sec(θo)).
6) Show that q(z)/q(Zo) = exp[1 – Z – sec(θo) e-Z], for Z = (z-Zo)/H. Reproduce the graphs of Figure
3.6 in Liou.
7) Calculate the altitudes of maximum energy deposition from Oxygen (O2) for the:
a) Schumann-Runge continuum
b) Schumann-Runge bands
c) Hertzberg continuum
d) How do these altitude compare with the altitudes of principal absorption shown in Fig.
A.9.8.c from Goody and Yung (1984)?
e) If the photolysis of O2 is required for ozone, where might you anticipate ozone layers?
Can you find confirmation of your estimates?
8) Calculate the altitudes of maximum energy deposition from Ozone for the:
a) Hartley bands
b) Huggins bands
c) How do these altitude compare with the altitudes of principal absorption shown in Fig.
A.9.8.c from Goody and Yung (1984)?
