Consider a box model for the US atmosphere with a constant source S of aerosol particles. The box is ventilated by a steady wind resulting in a residence time of 5 days for air in the box. Another pathway for removal of aerosol particles is by episodic precipitation. We assume that short rain events occur in the box every 5 days and that 100% of the aerosol is scavenged every time it rains. Find: (a) Calculate the evolution of aerosol mass in the box over a 10-day period, starting from a mass of zero at time t (b) Calculate the time-averaged aerosol mass over that period.

(c) We would like to simplify the treatment of aerosol lifetime in the box model by viewing the rain as a constant sink for aerosol with a rate constant kr = 0.2 d-1. What would be the resulting steady state mass of aerosol in the box? How does it compare to the time-averaged aerosol mass calculated in question (b)?