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"?