Assignment 3, Due January 29

In this assignment you will use the results from the Nature paper by Koop et al.

1. Summarize the major findings in the paper (one paragraph should suffice). We will discuss these in class on Jan 29.
2. A thin isothermal cloud approximately 1 km thick exists in the upper troposphere at a temperature of -70 degrees C.
   1. For what value of aerosol activity is the nucleation rate in the cloud sufficiently high that 1.0 $\mu$m haze particles have a characteristic time for homogeneous freezing of 1 min?
   2. Do the same calculation for 0.1 $\mu$m haze particles?
   3. In general, size distributions of haze aerosol follow a -3 power law, that is, per decade increase in size, concentrations fall by a factor of 1000. Given nucleation is inherently probabilistic, for given ambient air conditions, is it more, less, or equally likely that homogenously nucleated ice crystals will originate from big as compared to small haze aerosol. 
   4. Ignoring the fact that as a parcel of air rises, it depletes its ambient supersaturation, calculate the critical saturation vapor pressure with respect to ice required to homogeneously freeze these aerosols.
3. Consider equilibrium of an ice-liquid water system. If the ice/water interface is flat, equilibirum is achieved at the triple point $T=T_{0}$.   For temperature  $T<T_{0}$ what is  Dm for a flat ice-liquid interface? At what temperature does a small sphere of ice of radius r in contact with liquid water begin to melt? Plot $T$ versus r for r ranging from 10$^{-9}$ m to 10$^{-3}$ m. What are possible implications in the atmosphere?