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Title: On the probabilistic structure of water age: Probabilistic Water Age

Journal Article · · Water Resources Research
DOI:https://doi.org/10.1002/2015WR017027· OSTI ID:1454928
 [1];  [1]
  1. Duke Univ., Durham, NC (United States). Department of Civil and Environmental Engineering
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We report 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. Finally, 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.

Research Organization:
Duke Univ., Durham, NC (United States)
Sponsoring Organization:
USDOE Office of Science (SC), Biological and Environmental Research (BER)
Grant/Contract Number:
SC0006967
OSTI ID:
1454928
Journal Information:
Water Resources Research, Vol. 51, Issue 5; ISSN 0043-1397
Publisher:
American Geophysical Union (AGU)Copyright Statement
Country of Publication:
United States
Language:
English
Citation Metrics:
Cited by: 22 works
Citation information provided by
Web of Science

References (42)

Mathematical models for cellular systems the von Foerster equation. Part I journal September 1965
Some simple models for nonlinear age-dependent population dynamics journal April 1979
The McKendrick partial differential equation and its uses in epidemiology and population study journal September 1997
Residence Time Theory journal May 2008
Theory of population transport journal November 1972
Quantifying catchment-scale mixing and its effect on time-varying travel time distributions: QUANTIFYING CATCHMENT-SCALE MIXING journal June 2012
Superstatistics journal May 2003
Superstatistics of hydro-climatic fluctuations and interannual ecosystem productivity journal January 2006
Transit Times for Water in a Small Till Catchment from a Step Shift in the Oxygen 18 Content of the Water Input journal December 1996
Debates-The future of hydrological sciences: A (common) path forward? A call to action aimed at understanding velocities, celerities and residence time distributions of the headwater hydrograph journal June 2014
Applications of Mathematics to Medical Problems journal February 1925
On the distribution of multicomponent mixtures over generalized exposure time in subsurface flow and reactive transport: Foundations, and formulations for groundwater age, chemical heterogeneity, and biodegradation journal May 1999
Residence time distribution theory for unsteady stirred tank reactors journal September 1969
Simulation of groundwater age distributions journal December 1998
Basin-scale soil moisture dynamics and the probabilistic characterization of carrier hydrologic flows: Slow, leaching-prone components of the hydrologic response: STOCHASTIC BASE FLOWS IN RIVER BASINS journal February 2007
Analysis of soil carbon transit times and age distributions using network theories journal January 2009
Dose-structured population dynamics journal July 2007
Direct Simulation of Groundwater Age journal February 1996
Representation of space–time variability of soil moisture
  • Isham, V.; Cox, D. R.; Rodríguez-Iturbe, I.
  • Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 461, Issue 2064 https://doi.org/10.1098/rspa.2005.1568
journal September 2005
On a first-passage problem for a cumulative process with exponential decay journal January 1976
Shot noise models for the generation of synthetic streamflow data journal February 1977
State-dependent fire models and related renewal processes journal October 2006
Effect of different jump distributions on the dynamics of jump processes journal June 2010
Toward a general theory of the age in ocean modelling journal January 1999
Catchment residence and travel time distributions: The master equation: CATCHMENT RESIDENCE TIMES journal June 2011
Impact of hydroclimatic fluctuations on the soil water balance: HYDROCLIMATIC FLUCTUATIONS AND SOIL WATER BALANCE journal June 2006
Prescription-induced jump distributions in multiplicative Poisson processes journal June 2011
Transient soil-moisture dynamics and climate change in Mediterranean ecosystems: TRANSIENT SOIL-MOISTURE DYNAMICS journal November 2008
Kinematics of age mixing in advection-dispersion models: AGE MIXING IN ADVECTION-DISPERSION MODELS journal December 2013
A review and evaluation of catchment transit time modeling journal November 2006
Non-linear age-dependent population dynamics journal September 1974
Turbulent Flows book July 2012
Hydrology book January 2012
Compartment Models and Reservoir Theory journal November 1971
Residence time distributions of variable flow processes journal October 1977
Stochastic modeling of soil salinity: STOCHASTIC SOIL SALINITY journal April 2010
Dynamical modelling of concentration-age-discharge in watersheds journal May 2010
Time-variable transit time distributions and transport: Theory and application to storage-dependent transport of chloride in a watershed journal January 2015
A note on the relation between average age and average transit time in natural reservoirs journal January 1978
A note on the concepts of age distribution and transit time in natural reservoirs journal January 1973
Transport of kinetically sorbing solute by steady random velocity in heterogeneous porous formations journal April 1994
Fractal stream chemistry and its implications for contaminant transport in catchments journal February 2000

Cited By (8)

Fifty years of Water Resources Research : Legacy and perspectives for the science of hydrology: FIFTY YEARS OF WATER RESOURCES RESEARCH journal September 2015
Using high resolution tracer data to constrain water storage, flux and age estimates in a spatially distributed rainfall-runoff model: Tracers to Constrain Stores, Fluxes and Ages in Distributed Model journal June 2016
Characterization of mean transit time at large springs in the Upper Colorado River Basin, USA: a tool for assessing groundwater discharge vulnerability journal July 2016
Transit-time and age distributions for nonlinear time-dependent compartmental systems journal January 2018
Age distribution dynamics with stochastic jumps in mortality
  • Calabrese, Salvatore; Porporato, Amilcare; Laio, Francesco
  • Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 473, Issue 2207 https://doi.org/10.1098/rspa.2017.0451
journal November 2017
The muddle of ages, turnover, transit, and residence times in the carbon cycle journal November 2016
Spatially distributed characterization of soil-moisture dynamics using travel-time distributions journal January 2017
The Demographics of Water: A Review of Water Ages in the Critical Zone text January 2019

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54 ENVIRONMENTAL SCIENCES
58 GEOSCIENCES
age distribution
residence time
stochastic soil moisture
streamflow
Von Foerster equation
harmonic mean