Residence time distributions for hydrologic systems: Mechanistic foundations and steady-state analytical solutions

Leray, Sarah; Engdahl, Nicholas B.; Massoudieh, Arash; Bresciani, Étienne; McCallum, James L.

doi:10.1016/j.jhydrol.2016.01.068

Cited by 63 publications

(56 citation statements)

References 136 publications

(205 reference statements)

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“…Equation also can be solved analytically for a homogeneous groundwater basin with uniform thickness, recharge, and fully penetrating stream (Haitjema, ; Leray et al, )

ρ (|, a) = τ^{- 1} e^{- a / τ}

where

τ = θ H / R

, θ is porosity,

R

is recharge, and

H

is the thickness of the aquifer. This distribution applies regardless of horizontal basin shape, hydraulic conductivity, and drainage density.…”

Section: Approachmentioning

confidence: 99%

Regionalization of Groundwater Residence Time Using Metamodeling

Starn

Belitz

2018

Water Resources Research

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Groundwater residence‐time distributions (RTDs) are critical for assessing susceptibility of water resources to degradation. A novel combination of numerical modeling and statistical methods allows estimation of regional RTDs with unprecedented speed. In this method, particle RTDs are generated in 30 type locales in the northeastern glaciated U.S. by using automated generalized finite‐difference groundwater flow and advective transport models. Targets for statistical learning were created from particle RTDs by fitting Weibull, gamma, and inverse Gaussian distributions. Whole‐basin flux‐weighted RTDs were well fit by one‐component Weibull distributions. Flux‐weighted RTDs at stressed receptors such as wells often produced more complicated RTDs that required a two‐component mixture to fit. A Multitask LASSO regression was trained on the parametric RTDs using hydrogeographic features of the modeled areas as explanatory features. In this way, RTDs are regionalized with mappable physical features such as recharge and aquifer volume. The shape, location, and scale parameters of the parametric RTDs are strongly related to the mean exponential age. The shape parameter of the distribution, which controls deviation from exponential, is additionally a function of aquifer heterogeneity and hydrologic features. Regionalized RTDs provide useful metrics with respect to groundwater lag times and solute loading to streams. The lag time between input and output contained in the RTD is critical to understanding the relation between the land surface and human and ecological receptors.

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“…Equation also can be solved analytically for a homogeneous groundwater basin with uniform thickness, recharge, and fully penetrating stream (Haitjema, ; Leray et al, )

ρ (|, a) = τ^{- 1} e^{- a / τ}

where

τ = θ H / R

, θ is porosity,

R

is recharge, and

H

is the thickness of the aquifer. This distribution applies regardless of horizontal basin shape, hydraulic conductivity, and drainage density.…”

Section: Approachmentioning

confidence: 99%

Regionalization of Groundwater Residence Time Using Metamodeling

Starn

Belitz

2018

Water Resources Research

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“…Although the LPM can provide appropriate estimation of the groundwater age distribution for properly conceptualized aquifer systems, its applicability may be limited in settings with multiple and discrete groundwater flow components, such as with the perched layer in this study. Under a complex hydrogeologic setting, therefore, the use of multimodal LPMs (e.g., Green et al, ; Jurgens et al, ) on the basis of the proper conceptual model and adequate selection of the age tracers could be recommended to better characterize age mixing phenomena (Green et al, , ; Leray, Engdahl, Massoudieh, Bresciani, & McCallum, ; Marçais, Dreuzy, Ginn, Rousseau‐Gueutin, & Leray, ). Our study also demonstrates that despite potential uncertainties caused by various input parameters (i.e., aquifer geometry, hydraulic conductivity, porosity, and recharge rate), the numerical models combined and calibrated with the tracer concentration could also be an alternative method to characterize the multiple recharge pathways and multimodal age distributions.…”

Section: Discussionmentioning

confidence: 99%

Comparison of groundwater age models for assessing nitrate loading, transport pathways, and management options in a complex aquifer system

Koh

Lee

Kaown

et al. 2018

Hydrological Processes

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In an aquifer system with complex hydrogeology, mixing of groundwater with different ages could occur associated with various flow pathways. In this study, we applied different groundwater age‐estimation techniques (lumped parameter model and numerical model) to characterize groundwater age distributions and the major pathways of nitrate contamination in the Gosan agricultural field, Jeju Island. According to the lumped parameter model, groundwater age in the study area could be explained by the binary mixing of the young groundwater (4–33 years) and the old water component (>60 years). The complex hydrogeologic regimes and local heterogeneity observed in the study area (multilayered aquifer, well leakage hydraulics) were particularly well reflected in the numerical model. The numerical model predicted that the regional aquifer of Gosan responded to the fertilizer applications more rapidly (mean age: 9.7–22.3 years) than as estimated by other models. Our study results demonstrated that application and comparison of multiple age‐estimation methods can be useful to understand better the flow regimes and the mixing characteristics of groundwater with different ages (pathways), and accordingly, to reduce the risk of improper groundwater management plans arising from the aquifer heterogeneity.

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“…Overviews are given by Leray et al (2016), andMcGuire andMcDonnell (2006). Nonparametric distributions are less utilised but do appear from time to time in the literature.…”

Section: Discussionmentioning

confidence: 99%

A nonparametric approach toward upper bounds to transit time distribution functions

Bardsley

2017

Preprint

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Abstract.A nonparametric method is proposed as a possible approach to obtaining upper bounds to distribution functions of time-varying transit times for catchment environmental tracers. A discretization is employed for the tracer throughput process, with tracer input represented as a sequence of K discrete pulses over a given time period. Each input pulse is associated with a different and unknown upper-bounded nonparametric discrete transit time distribution. The model transit 10 time distribution function is therefore a K-component finite mixture of different and unknown discrete distribution functions, weighted by the relative magnitudes of the respective tracer pulses. Upper bounds to this distribution function can be obtained by linear programming to achieve a sequence of K discrete optimised transit time distributions which yield the maximum possible value of tracer fraction less than a given age, subject to a constraint of matching the catchment tracer output time series to some specified linear measure of accuracy. The individual optimised distributions do not estimate actual 15 transit time distributions and the optimisation procedure is not hydrological modelling. This is actually a strength of the methodology in that the true transit time distributions are permitted to be created as a consequence of any time-varying nonlinear catchment process with complete or partial mixing. However, a negative aspect is that the extreme flexibility of K different nonparametric distributions is likely to give transit time distribution functions upper bounds near 1.0, unless sufficient constraints can be imposed on the form of the individual optimised distributions. There is a possibility, however, 20 that optimising just a single nonparametric L-shaped distribution could yield useful distribution function upper bounds for time-varying situations. 25Hydrol. Earth Syst. Sci. Discuss., https://doi

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Residence time distributions for hydrologic systems: Mechanistic foundations and steady-state analytical solutions

Cited by 63 publications

References 136 publications

Regionalization of Groundwater Residence Time Using Metamodeling

Regionalization of Groundwater Residence Time Using Metamodeling

Comparison of groundwater age models for assessing nitrate loading, transport pathways, and management options in a complex aquifer system

A nonparametric approach toward upper bounds to transit time distribution functions

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