Source

In each $x,y$ box we put a source of pollution that may vary with time. We denote the rate at which the pollutant is added to the atmosphere by $q(x,y,t)$ in units of kg/h. So over the time interval $dt$ the quantity $q(x,y,t)dt$ gives the mass of pollutant added to the atmosphere in that square. While the pollutant is added from the ground surface, for simplicity, we assume that it is immediately dispersed to height $h$ in that square. Here is how we update the mass as a result of emissions:

$$\Delta m(x,y,t) = q(x,y,t)dt$$ (2)

so that the mass at time $t+dt$ in a given box is given by $m(x,y,t+dt) = m(x,y,t) + \Delta m(x,y,t)$.