Homework8

NOTE. Do not email derivations.

2 stream. Read pages 386-406 of the G. Petty book and Bohren’s
article leading to equations 1-9 (i.e. p. 525)
http://clouds.wikidot.com/local--files/files/bohren87_2stream.pdf

1. In eq. 13.12 and 13.14 discuss how backscatter fraction is related
to the asymmetry parameter. Discuss its probabilistic meaning (think
‘’Monte Carlo’’).
2. Begin with equations (13.16), (13.17) and discuss microscopic
properties and macroscopic properties in these equations. For purely
absorptive case (IR) show that these 2 equations decouple. What is
the reason that these equations are, in general, coupled? Discuss
boundary conditions (known variables).
3. Derive albedo for semi-infinite cloud and discuss Fig. 13.4 (do not
email it to me, just derive).
4. Solution to 2-stream equations is (13.39) and (13.40). Show from
definition of reflectance and transmittance eqs. (13.65) and (13.66)
(do not email derivations). Reproduce Figs 13.5 and 13.6 in Matlab and
discuss the results in term of single scattering albedo (SSA same as
omega) very close to 1 and 0. What is the conservative scattering. Is
it typical for solar or infrared part of the spectrum?

Stratocumulus.
Read Lilly’s paper up to page 297
http://clouds.wikidot.com/local--files/files/Lilly_QuartJRoyMeteorSoc_1968.pdf
and pages 1-4 notes
http://clouds.wdfiles.com/local--files/files/lilly_notes1.pdf
1. What is the reason that potential temperature is constant in the
well mixed layer for the dry case?
2. What is the capping inversion and what is its physical cause?
Discuss the radiative convective equilibrium (RCE) between cooling,
subsidence, and heat flux for Sc. Is the large scale subsidence
crossing the capping inversion or not?
3. Is the air entrained from above the capping inversion towards the
mixed layer or from mixed layer towards the stable layer above? Why?
4. Air is cooled at the top of the inversion. Why? Does it cause
upward or downward convection? ? Is the heat flux constant in the
well mixed layer?
5. Discuss what are unknowns in the dry case 4 basic equations (e.g.
notes, p. 4). Discuss results of Figure 1 of Lilly’s paper. Can you
say why this solution is sometimes called "encroachment mixed layer
growth"?

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