In Figure \ref{997988}  we show three of the (infinite) curves that correspond to an instant of rainfall between \(t\ \) and \(t\ +\ \Delta t\) . For any \(t\ =t^{\bullet}\) we actually integrate over these curves, not just one of them. The procedure we followed can be used to show that any of these sections in the third dimension is actually equal to the forefront maroon curve. But this is the case because we assumed \(f=f\left(t-t_{in}\right)\), depending just on the difference between the clock and injections time. In the most general case, as seen in \cite{Rigon_2016} , any of the \(f\) is time dependent, i.e. \(f=f\left(t,t_{in}\right)\) and neglecting the right integration direction can drive to conceptual mistakes easily. 

Examples

The exponential travel time distribution

For making clearer the example let's consider first the simple case of 
and of: