Journal cover Journal topic
Hydrology and Earth System Sciences An interactive open-access journal of the European Geosciences Union
Hydrol. Earth Syst. Sci., 17, 4133-4142, 2013
© Author(s) 2013. This work is distributed under
the Creative Commons Attribution 3.0 License.
Research article
23 Oct 2013
Continental moisture recycling as a Poisson process
H. F. Goessling1,2,* and C. H. Reick1 1Max Planck Institute for Meteorology, Hamburg, Germany
2International Max Planck Research School on Earth System Modelling, Hamburg, Germany
*now at: Alfred Wegener Institute, Helmholtz Centre for Polar and Marine Research, Bremerhaven, Germany
Abstract. 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.

Citation: Goessling, H. F. and Reick, C. H.: Continental moisture recycling as a Poisson process, Hydrol. Earth Syst. Sci., 17, 4133-4142,, 2013.
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