$3\mathrm{.}2$ Ventilation of Pollution from the United States

We model the lower atmosphere over the United States as a well$-$mixed box

extending horizontally $5000km$ in the west$-$east direction. The box is venti$-$

lated by a westerly wind of speed $U=10m{s}^{-1}.$

What is the residence time ${}_{\text{o}\text{u}\text{t}}($in days$)$ of air in the lower atmosphere

over the United States?

Consider a pollutant emitted in the United States and having a lifetime

${}_{\text{c}\text{h}\text{e}\text{m}}$ against chemical loss. Calculate the fraction $f$ of the pollutant

exported out of the United States box as a function of the ratio $\frac{{}_{\text{o}\text{u}\text{t}}}{{}_{\text{c}\text{h}\text{e}\text{r}\text{n}}}.$

Plot your result. Comment on the potential for different pollutants emitted

in the United States to affect the global atmosphere.