Ground Water Development—The Time to Full Capture Problem

Bredehoeft, John; Durbin, Timothy J.

doi:10.1111/j.1745-6584.2008.00538.x

Cited by 70 publications

(78 citation statements)

References 14 publications

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“…We note that the expression for RT(δ) takes the form of a constant, depending on the specified tolerance δ, multiplied by the time scale L 2 /D. Therefore, in summary, we find that our approach provides a rigorous mathematical connection with the often stated claim that the response time is proportional to L 2 /D [10,18,19,24]. Some very simple formulae for specific values of the tolerance δ are listed in Table 1.…”

Section: A Rigorous Connection To Scaling Results For Flow In Homogenmentioning

confidence: 93%

“…While this kind of calculation is widespread in the literature [10,18,19,24], it is difficult to use this approach in practice because this kind of argument provides no information about the appropriate constant of proportionality. In this section we will apply our new theory to the simplified problem of flow in a homogeneous porous medium where we consider Equations (3) and (4) with constant values for the initial condition, saturated hydraulic conductivity and recharge rate:…”

Section: A Rigorous Connection To Scaling Results For Flow In Homogenmentioning

confidence: 99%

“…Since steady state flow conditions arise as the long time limit of a transient flow response [20], is it natural for us to determine an estimate of the amount of time required for a transient response to occur, after which steady state conditions will prevail and simpler steady models can be used to describe the flow process. Such a time scale is often referred to as a response time [10,13,19].…”

Section: Introductionmentioning

confidence: 99%

“…In the first approach, both the transient groundwater flow model and the steady state groundwater flow models are solved, and the response time is taken to be the amount of time taken for the difference between the transient solution and the associated steady state solution to fall below some sufficiently small tolerance [23,28,35]. In the second method a simple scaling approach is adopted whereby if groundwater flow takes place in a confined aquifer with aquifer diffusivity D, then the response time is proportional to L 2 /D, where L is a relevant length scale [10,13,19]. Both of these methods suffer from certain limitations.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Accurate and efficient calculation of response times for groundwater flow

Carr¹,

Simpson²

2018

Journal of Hydrology

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We study measures of the amount of time required for transient flow in heterogeneous porous media to effectively reach steady state, also known as the response time. Here, we develop a new approach that extends the concept of mean action time. Previous applications of the theory of mean action time to estimate the response time use the first two central moments of the probability density function associated with the transition from the initial condition, at t = 0, to the steady state condition that arises in the long time limit, as t → ∞. This previous approach leads to a computationally convenient estimation of the response time, but the accuracy can be poor. Here, we outline a powerful extension using the first k raw moments, showing how to produce an extremely accurate estimate by making use of asymptotic properties of the cumulative distribution function. Results are validated using an existing laboratory-scale data set describing flow in a homogeneous porous medium. In addition, we demonstrate how the results also apply to flow in heterogeneous porous media. Overall, the new method is: (i) extremely accurate; and (ii) computationally inexpensive. In fact, the computational cost of the new method is orders of magnitude less than the computational effort required to study the response time by solving the transient flow equation. Furthermore, the approach provides a rigorous mathematical connection with the heuristic argument that the response time for flow in a homogeneous porous medium is proportional to L 2 /D, where L is a relevant length scale, and D is the aquifer diffusivity. Here, we extend such heuristic arguments by providing a clear mathematical definition of the proportionality constant.

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Section: A Rigorous Connection To Scaling Results For Flow In Homogenmentioning

confidence: 93%

Section: A Rigorous Connection To Scaling Results For Flow In Homogenmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Accurate and efficient calculation of response times for groundwater flow

Carr¹,

Simpson²

2018

Journal of Hydrology

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“…More recent studies have called into question both the value and the sustainability of safe yield [80][81][82]. Evaluations of groundwater development sustainability account for natural groundwater recharge rates, as well as capture which includes induced recharge and decreases in natural discharge [5,83,84]. Advances in numerical and statistical models are improving our estimates and projections of groundwater use sustainability.…”

Section: Evaluation Tools and Modelsmentioning

confidence: 99%

Sustainable Water Management in Urban, Agricultural, and Natural Systems

Russo

Alfredo

Fisher

2014

Water

104

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Sustainable water management (SWM) requires allocating between competing water sector demands, and balancing the financial and social resources required to support necessary water systems. The objective of this review is to assess SWM in three sectors: urban, agricultural, and natural systems. This review explores the following questions: (1) How is SWM defined and evaluated? (2) What are the challenges associated with sustainable development in each sector? (3) What are the areas of greatest potential improvement in urban and agricultural water management systems? And (4) What role does country development status have in SWM practices? The methods for evaluating water management practices range from relatively simple indicator methods to integration of multiple models, depending on the complexity of the problem and resources of the investigators. The two key findings and recommendations for meeting SWM objectives are:(1) all forms of water must be considered usable, and reusable, water resources; and (2) increasing agricultural crop water production represents the largest opportunity for reducing total water consumption, and will be required to meet global food security needs. The level of regional development should not dictate sustainability objectives, however local OPEN ACCESSWater 2014, 6 3935 infrastructure conditions and financial capabilities should inform the details of water system design and evaluation.

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Global change and the groundwater management challenge

Gorelick

Chen

2015

Water Resources Research

350

142

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With rivers in critical regions already exploited to capacity throughout the world and groundwater overdraft as well as large-scale contamination occurring in many areas, we have entered an era in which multiple simultaneous stresses will drive water management. Increasingly, groundwater resources are taking a more prominent role in providing freshwater supplies. We discuss the competing fresh groundwater needs for human consumption, food production, energy, and the environment, as well as physical hazards, and conflicts due to transboundary overexploitation. During the past 50 years, groundwater management modeling has focused on combining simulation with optimization methods to inspect important problems ranging from contaminant remediation to agricultural irrigation management. The compound challenges now faced by water planners require a new generation of aquifer management models that address the broad impacts of global change on aquifer storage and depletion trajectory management, land subsidence, groundwater-dependent ecosystems, seawater intrusion, anthropogenic and geogenic contamination, supply vulnerability, and long-term sustainability. The scope of research efforts is only beginning to address complex interactions using multiagent system models that are not readily formulated as optimization problems and that consider a suite of human behavioral responses.

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Ground Water Development—The Time to Full Capture Problem

Cited by 70 publications

References 14 publications

Accurate and efficient calculation of response times for groundwater flow

Accurate and efficient calculation of response times for groundwater flow

Sustainable Water Management in Urban, Agricultural, and Natural Systems

Global change and the groundwater management challenge

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