Adjoint modeling of stream depletion in groundwater‐surface water systems

Griebling, S. A.; Neupauer, R. M.

doi:10.1002/wrcr.20385

Cited by 14 publications

(11 citation statements)

References 24 publications

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“…The gray shade corresponds to the normalized stream depletion, ∆Q r /Q p , that would result from pumping from a well at that location for 20 years in an aquifer with a K value of 5 m d −1 . For these simulations, Equation (1) was solved using the adjoint approach [39], using a homogeneous streambed with K r = 3 × 10 −3 m d −1 (Figure 4a) and K r = 4 × 10 −3 m d −1 (Figure 4b). Both of these K r values are within the sensitive K r range for Scenario (a), Figure 3a.…”

Section: Sensitivity Of Stream Depletion Estimates To Streambed Condumentioning

confidence: 99%

Effects of Streambed Conductance on Stream Depletion

Lackey

Neupauer

Pitlick

2015

Water

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Stream depletion, which is the reduction in flow rate of a stream or river due to the extraction of groundwater in a hydraulically connected stream-aquifer system, is often estimated using numerical models. The accuracy of these models depends on the appropriate parameterization of aquifer and streambed hydraulic properties. Streambed conductance is a parameter that relates the head difference between the stream and aquifer to flow across the stream channel. It is a function of streambed hydraulic conductivity and streambed geometry. In natural systems, streambed conductance varies spatially throughout the streambed; however, stream depletion modeling studies often ignore this variability. In this work, we use numerical simulations to demonstrate that stream depletion estimates are sensitive to a range of streambed conductance values depending on aquifer properties. We compare the stream depletion estimates from various spatial patterns of streambed conductance to show that modeling streambed conductance as a homogeneous property can lead to errors in stream depletion estimates. We use the results to identify feasible locations for proposed pumping wells such that the stream depletion due to pumping from a well within this feasible region would not exceed a prescribed threshold value, and we show that incorrect assumptions of the magnitude and spatial variability of streambed conductance can affect the size and shape of the feasible region.

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Section: Sensitivity Of Stream Depletion Estimates To Streambed Condumentioning

confidence: 99%

Effects of Streambed Conductance on Stream Depletion

Lackey

Neupauer

Pitlick

2015

Water

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“…The governing equation of the backward probability model can be derived by applying the adjoint method to the forward ADE. The adjoint method evaluates the sensitivity of a system state (e.g., head and concentration) with respect to changes in a system parameter (e.g., hydraulic parameters, Sykes et al, ; recharge areas, Jyrkama & Sykes, ; and river stage, Griebling & Neupauer, ). Similarly, the backward probability model solves the adjoint state of concentration,

ψ_{i}^{*}

, which corresponds to the marginal sensitivity of the concentration (or system state) to the source mass (or system parameter) (Neupauer & Wilson, ):

ψ_{i}^{*} ((),,,, x, τ, {boldx}_{obs}, τ_{obs}) = \frac{normald C_{i} ((),, {boldx}_{obs}, τ_{obs})}{normald M_{i} ((),, x, τ)},

where τ is the backward time (T) representing an amount of time prior to a contaminant detection (or observation) at τ obs ( τ = 0), which corresponds to t 3 in Figure a.…”

Section: Methodsmentioning

confidence: 99%

Backward Probability Model for Identifying Multiple Contaminant Source Zones Under Transient Variably Saturated Flow Conditions

Hwang

Jeen

Kaown

et al. 2020

Water Resources Research

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Groundwater contamination is one of the major concerns to public health and water resource management. Identification of contamination sources is essential for designing cost-effective groundwater remediation systems and minimizing risks of further contamination. Various numerical approaches have been applied to reconstruct spatiotemporal distributions of contaminant sources. Due to difficulties in obtaining source information, the backward probability model is computationally efficient; however, its applications have largely been limited to relatively simple problems such as two-dimensional or simplified three-dimensional steady-state saturated flow conditions with a single contaminant source. More importantly, the traditional backward probability model requires some a priori knowledge on the suspected source locations or source release times to quantify source area location probabilities. Here we improve the capability of the backward probability model for solving real-world problems by implementing it into a three-dimensional transient variably saturated flow model. To evaluate the applicability of the model, we apply it combined with the shift-average method to a field-scale problem for identifying multiple contaminant sources occurring in the vadose zone that release contaminants to the saturated zone through infiltration. Compared with the suspected potential sources reported through a site characterization study, the enhanced backward probability model reasonably captures most of the reported potential sources under various hydrologic/hydrogeological/dispersion conditions, which demonstrates that the approach developed here can overcome limitations of the backward probability theory previously reported in the literature.

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“…When considered individually or used to generate maps or rankings, we refer to them by the more intuitive term "depletion potential." Depletion potential (e.g., Ahlfeld et al 2016) can be calculated in a variety of ways including using Adjoint State (Neupauer and Griebling 2012;Griebling and Neupauer 2013) and reformulation of the underlying process model (Ou et al 2016).…”

Section: Depletion Potentialmentioning

confidence: 99%

Depletion Mapping and Constrained Optimization to Support Managing Groundwater Extraction

Fienen¹,

Bradbury

Kniffin

et al. 2017

Groundwater

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Groundwater models often serve as management tools to evaluate competing water uses including ecosystems, irrigated agriculture, industry, municipal supply, and others. Depletion potential mapping-showing the model-calculated potential impacts that wells have on stream baseflow-can form the basis for multiple potential management approaches in an oversubscribed basin. Specific management approaches can include scenarios proposed by stakeholders, systematic changes in well pumping based on depletion potential, and formal constrained optimization, which can be used to quantify the tradeoff between water use and stream baseflow. Variables such as the maximum amount of reduction allowed in each well and various groupings of wells using, for example, K-means clustering considering spatial proximity and depletion potential are considered. These approaches provide a potential starting point and guidance for resource managers and stakeholders to make decisions about groundwater management in a basin, spreading responsibility in different ways. We illustrate these approaches in the Little Plover River basin in central Wisconsin, United States-home to a rich agricultural tradition, with farmland and urban areas both in close proximity to a groundwater-dependent trout stream. Groundwater withdrawals have reduced baseflow supplying the Little Plover River below a legally established minimum. The techniques in this work were developed in response to engaged stakeholders with various interests and goals for the basin. They sought to develop a collaborative management plan at a watershed scale that restores the flow rate in the river in a manner that incorporates principles of shared governance and results in effective and minimally disruptive changes in groundwater extraction practices.

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Adjoint modeling of stream depletion in groundwater‐surface water systems

Cited by 14 publications

References 24 publications

Effects of Streambed Conductance on Stream Depletion

Effects of Streambed Conductance on Stream Depletion

Backward Probability Model for Identifying Multiple Contaminant Source Zones Under Transient Variably Saturated Flow Conditions

Depletion Mapping and Constrained Optimization to Support Managing Groundwater Extraction

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