Homework 4

Cloud Microphysics 2

Due on Thursday, May 7, 2009.

Problem set

Read Chapter 7 of W. R. Cotton “Cloud Physics” notes. It is in the
book I emailed but also you can get it from

1. Condensation. You should understand section 7.1-7.4 but do not
worry about Qr term for now.
1.1 Equation 7.1 defines water vapor flux. Why is flux proportional
to gradient of water vapor concentration? What is the physical reason
for this?
1.2 In 7.7 we assumed that water vapor concentration is in steady
state. What does this mean? In the steady state - is the water vapor
still transported? Is there accumulation of water vapor?
1.3 Equation 7.16 is crucial. It states that there is balance of
energy between latent heat and diffusion. Why? Is temperature of
droplet warmer from its environment? Why? Is temperature of droplet
increasing with time? Why not?
1.4 In equation 7.23 we integrate CC equation. What are the limits T
and Ta? Why such integration can be converted to integration over the
temperature only?
1.5 What is Kohler relationship? Do we have to incude this effect
for large drops?
1.6 Discuss equation 7.32. How is cloud dynamics determining droplet
growth? How is environment (T,p) determining diffusion growth?
1.7 For large droplets da/dt is proportional to 1/a. Why this leads
to narrowing of condensational spectra? Discuss initial spectrum and
its subsequent change?
1.8 Close the book and all notes and derive 7.32 yourself – from the
very beginning, every step. Doable? If not what should I discuss

2. Coagulation. Read Cotton’s notes (around page 179). Discuss
continuous model of droplet growth. Consider effects of drop/droplet
sizes. Discuss stochastic model of coagulation. How can we interpret
Smoluchowski’s equation (7.44) in terms of probabilities? What are
the strengths and disadvantages of these models in global models (GCM)
with bulk microphysics vs cloud model with detailed bin microphysics?


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