On the probabilistic structure of water age

Amilcare Michele M. Porporato, Salvatore Calabrese

Research output: Contribution to journalArticlepeer-review

23 Scopus citations


The age distribution of water in hydrologic systems has received renewed interest recently, especially in relation to watershed response to rainfall inputs. The purpose of this contribution is first to draw attention to existing theories of age distributions in population dynamics, fluid mechanics and stochastic groundwater, and in particular to the McKendrick-von Foerster equation and its generalizations and solutions. A second and more important goal is to clarify that, when hydrologic fluxes are modeled by means of time-varying stochastic processes, the age distributions must themselves be treated as random functions. Once their probabilistic structure is obtained, it can be used to characterize the variability of age distributions in real systems and thus help quantify the inherent uncertainty in the field determination of water age. We illustrate these concepts with reference to a stochastic storage model, which has been used as a minimalist model of soil moisture and streamflow dynamics.

Original languageEnglish (US)
Pages (from-to)3588-3600
Number of pages13
JournalWater Resources Research
Issue number5
StatePublished - May 1 2015

All Science Journal Classification (ASJC) codes

  • Water Science and Technology


  • Von Foerster equation
  • age distribution
  • harmonic mean
  • residence time
  • stochastic soil moisture
  • streamflow


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