Assignment 1

Due Tuesday Jan 15th

In this data set you will analyse an airborne data set of California stratocumulus cloud properties measured by the University of Washington Cloud and Aerosol Research Group in June 1994.  

1. In a parcel of moist air, the total water mass is
   
   $$Q=\chi+w$$
   
   
   where $w$ and $\chi$ are the vapor and condensed water mixing ratios, respectively. Under adiabatic transformations, $Q$ is conserved.
   1. Derive an expression for the adiabatic liquid water content ($g/m^{3}$) in a cloud as a function of height.
   2. Using boundary layer profile data from flights 1641 and 1642 plot the liquid water content (Use the PVM-100A measurements) versus altitude, together with a line showing the adiabatic liquid water content for the cloud. Here is a description for each column of the data set.
      
   3. Plot average size distributions for each profile. These should be on a log-log plot in the form $dN/d\log D$. This is calculated taking $\Delta N$ in each size bin for the FSSP-100 and 1-D cloud probe data, and dividing it by the logarithmic difference for the bin limits for each size bin for each instrument, e.g.
      
      $$d\log D=\log\frac{D_{max}}{D_{min}}$$
      
      
      One should then plot $dN/d\log D$ against the median diameter for each bin $\left(D_{max}+D_{min}\right)/2$.
2. What is the difference between these two profiles and size distributions? Is there a physical link between the size distribution and the departure from adiabaticity in the profile? Can you suggest an explanation?