## 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

http://clouds.wikidot.com/local--files/files/chapter7_dropletgrowth.pdf

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

again?

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?

++Answers