Continental moisture recycling as a Poisson process

On their journey over large land masses, water molecules experience a number of precipitation–evaporation cycles (recycling events). We derive analytically the frequency distributions of recycling events for the water molecules contained in a given air parcel. Given the validity of certain simplifying assumptions, the frequency distribution of recycling events is shown to develop either into a Poisson distribution or a geometric distribution. We distinguish two cases: in case (A) recycling events are counted since the water molecules were last advected across the ocean–land boundary. In case (B) recycling events are counted since the water molecules were last evaporated from the ocean. For case B we show by means of a simple scale analysis that, given the conditions on earth, realistic frequency distributions may be regarded as a mixture of a Poisson distribution and a geometric distribution. By contrast, in case A the Poisson distribution generally appears as a reasonable approximation. This conclusion is consistent with the simulation results of an earlier study where an atmospheric general circulation model equipped with water vapor tracers was used. Our results demonstrate that continental moisture recycling can be interpreted as a Poisson process.