Abstract
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.
Highlights
Since the pioneering studies on the isotopic composition of precipitation and moisture recycling in the Amazon basin in the late 1970s (Salati et al, 1979; Lettau et al, 1979), it has become conventional wisdom that tropical forests maintain a substantial fraction of their precipitation by their own evaporation
The goal of the following derivations is to find simple analytical expressions for the frequency distribution of n, where n is the number of continental recycling events the water molecules contained in an air parcel have experienced either (A) since they were last advected across an ocean– land boundary, or (B) since they last evaporated from the ocean
In contrast to case A, in case B there is no moment in time at which the frequency distribution of n is set to an initial Poisson distribution; a parcel crossing the ocean–land boundary contains water molecules with n > 0
Summary
Since the pioneering studies on the isotopic composition of precipitation and moisture recycling in the Amazon basin in the late 1970s (Salati et al, 1979; Lettau et al, 1979), it has become conventional wisdom that tropical forests maintain a substantial fraction of their precipitation by their own evaporation (including plant transpiration). Brubaker et al, 1993; Eltahir and Bras, 1994; Numaguti, 1999; van der Ent et al, 2010; Goessling and Reick, 2013) It has been shown by means of climate model simulations that reduced continental evaporation rates, for example, due to deforestation, result in less continental precipitation Most studies dealing with continental moisture recycling focussed on determining the evaporative source regions of precipitation, for example, the fraction of continental moisture in precipitation, using either atmospheric general circulation models equipped with passive water vapour tracers (Numaguti, 1999; Bosilovich et al, 2002; Goessling and Reick, 2013), or using reanalysis data together with diagnostic moisture tracing algorithms (Yoshimura et al, 2004; van der Ent et al, 2010). Reick: Continental moisture recycling as a Poisson process assumptions, the frequency distribution of continental recycling events for the water molecules contained in a given air parcel attains either a Poisson distribution or a geometric distribution, depending on the assumptions
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