Accurate and efficient calculation of response times for groundwater flow

Carr, Elliot J.; Simpson, Matthew J.

doi:10.1016/j.jhydrol.2017.12.023

Cited by 18 publications

(23 citation statements)

References 35 publications

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“…() used a groundwater flow model to relate spring discharge with the storage in the aquifer. Carr and Simpson () used a linearized version of the Dupuit–Forchheimer model to estimate the response time of the groundwater flow. Su et al.…”

Section: Introductionmentioning

confidence: 99%

Aquifer Responses to Rainfall through Spectral and Correlation Analysis

Gómez¹,

Melo²,

Rodrigues

et al. 2018

J American Water Resour Assoc

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The response time of hydrological components is an important feature for establishing the connections within a hydrological system and for characterizing it. This study proposes a quantitative and qualitative assessment on the response times of river discharge components, especially the baseflow, regarding the impulse provided by precipitation, using time series analyses of time and frequency domains. To this end, a set of complementary methods including correlation and spectral approaches was used, which are: autocorrelation, cross correlation, continuous wavelet transform, and cross wavelet transform. Such framework was applied in multiple and nested basin scales (53, 1,867, and 3,519 km2), located in the Jacaré‐Guaçu River Basin (Southeastern Brazil). Based on a digital filtering technique, it was found the baseflow contributes more than 80% of the annual streamflow, revealing a major role of the aquifer in regulating the river discharge in all three studied basins. In addition, we found baseflow represents a range of 24%–27% of the annual precipitation. The uniform results are mainly due to the similar physical characteristics found in those areas. Overall, our framework indicates a baseflow response time for a precipitation of approximately two years for the smaller basins and three years for the biggest one. Such results can support the water allocation in conjunctive water management, by providing estimates of future surface water availability.

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Section: Introductionmentioning

confidence: 99%

Aquifer Responses to Rainfall through Spectral and Correlation Analysis

Gómez¹,

Melo²,

Rodrigues

et al. 2018

J American Water Resour Assoc

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Section: Results Of Standard Time Series Analysismentioning

confidence: 99%

“…The three first moments are considered here and evaluated by numerical integration of the solution of Bruggeman. Alternatively, the moments can be obtained by solving the differential equation for the moments of the response function (e.g., Bakker et al 2007;Carr and Simpson 2018). The moments are recombined and expressed as the mean response time μ and the standard deviationσ of the response function (Weisstein 2018b):…”

Section: Physical Explanationmentioning

confidence: 99%

Identification and Explanation of a Change in the Groundwater Regime using Time Series Analysis

Obergfell¹,

Bakker

Maas³

2019

Groundwater

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Time series analysis is applied to identify and analyze a transition in the groundwater regime in the aquifer below the sand ridge of Salland in the Netherlands, where groundwater regime refers to the range of head variations throughout the seasons. Standard time series analysis revealed a discrepancy between modeled and observed heads in several piezometers indicating a possible change in the groundwater regime. A new time series modeling approach is developed to simulate the transition from the initial regime to the altered regime. The transition is modeled as a weighted sum of two responses, one representing the initial state of the system, the other representing the altered state. The inferred timing and magnitude of the change provided strong evidence that the transition was the result of significant dredging works that increased the river bed conductance of the main river draining the aquifer. The plausibility of this explanation is corroborated by an analytical model. This case study and the developed approach to identify a change in the groundwater regime are meant to stimulate a more systematic application of time series analysis to detect and understand changes in groundwater systems which may easily go unnoticed in groundwater flow modeling.

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“…In the discrete case, provided t N is large enough (see, e.g. [20,21], for how to estimate steady state times), the integral I T appearing in the thermal diffusivity formulas, Eqs (17)- (19) and (44)-(47), can be approximated using the trapezoidal rule [11]. For example, for the homogeneous sample:…”

Section: Verification Of Formulasmentioning

confidence: 99%

“…Each estimate of the thermal diffusivity is compared to the target value in Table 1 by calculating the signed relative errors ε = (α − α)/α (homogeneous) and ε k = (α k − α k )/α k for k = 1, 2 (twolayer) with the tilde used to indicate the estimated value produced from the rear-surface integral method. In Table 2, results for both the homogeneous and twolayer samples are presented for the rectangular (20), triangular (21) and exponential (22) pulses with τ = 0.005 s, β = 0.001 s, Q∞ = 7000 J m −2 , N = 1000 temperature rise values, ∆t = 10 −4 s, t N = 0.1 s and n = 500 nodes. In all cases, the estimate agrees with the target values of the thermal diffusivity in Table 1 to 4-5 significant digits with a relative error of approximately 10 −4 .…”

Section: Verification Of Formulasmentioning

confidence: 99%

Rear-surface integral method for calculating thermal diffusivity: Finite pulse time correction and two-layer samples

Carr

Wood

2019

International Journal of Heat and Mass Transfer

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We study methods for calculating the thermal diffusivity of solids from laser flash experiments. This experiment involves subjecting the front surface of a small sample of the material to a heat pulse and recording the resulting temperature rise on the opposite (rear) surface. Recently, a method was developed for calculating the thermal diffusivity from the rear-surface temperature rise, which was shown to produce improved estimates compared with the commonly used halftime approach. This so-called rear-surface integral method produced a formula for calculating the thermal diffusivity of homogeneous samples under the assumption that the heat pulse is instantaneously absorbed uniformly into a thin layer at the front surface. In this paper, we show how the rear-surface integral method can be applied to a more physically realistic heat flow model involving the actual heat pulse shape from the laser flash experiment. New thermal diffusivity formulas are derived for handling arbitrary pulse shapes for either a homogeneous sample or a heterogeneous sample comprising two layers of different materials. Presented numerical experiments confirm the accuracy of the new formulas and demonstrate how they can be applied to the kinds of experimental data arising from the laser flash experiment.

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Accurate and efficient calculation of response times for groundwater flow

Cited by 18 publications

References 35 publications

Aquifer Responses to Rainfall through Spectral and Correlation Analysis

Aquifer Responses to Rainfall through Spectral and Correlation Analysis

Identification and Explanation of a Change in the Groundwater Regime using Time Series Analysis

Rear-surface integral method for calculating thermal diffusivity: Finite pulse time correction and two-layer samples

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