TY - JOUR
T1 - On the probabilistic structure of water age
AU - Porporato, Amilcare Michele M.
AU - Calabrese, Salvatore
N1 - Publisher Copyright:
© 2015. American Geophysical Union. All Rights Reserved.
Copyright:
Copyright 2015 Elsevier B.V., All rights reserved.
PY - 2015/5/1
Y1 - 2015/5/1
N2 - 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.
AB - 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.
KW - Von Foerster equation
KW - age distribution
KW - harmonic mean
KW - residence time
KW - stochastic soil moisture
KW - streamflow
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U2 - 10.1002/2015WR017027
DO - 10.1002/2015WR017027
M3 - Article
AN - SCOPUS:84932621152
SN - 0043-1397
VL - 51
SP - 3588
EP - 3600
JO - Water Resources Research
JF - Water Resources Research
IS - 5
ER -