Technical note: Transit time distributions are not L-shaped

Abstract. A probability density function f(t) with origin at t = 0 is defined here as being "L-shaped" if f'(t) ≤ 0 for t ≥ 0. L-shaped probability density functions, especially exponential distributions, are often assumed as transit time distributions in hydrological studies. However, L-shaped transit time distributions are not possible. This is because the transit time of a particle must always be with reference to a store, the transit time being some finite duration of time between particle entry and exit. Tracer particles cannot transit through any part of a store in zero time so transit time distributions have the property f(0) = 0, which is incompatible with L-shaped probability density functions. This is a fundamental constraint on the form of transit time distributions, which must possess at least one mode at t > 0. Some L-shaped probability density functions may well approximate actual transit time distributions, but they are of different form to the true distributions. A call is therefore made for L-shaped probability density functions to be no longer employed in transit time modelling.