Reply to comment by H. Lough, Department of Civil Engineering, University of Canterbury, Christchurch, New Zealand, on the paper “Stream depletion predictions using pumping test data from a heterogeneous stream–aquifer system (a case study from the Great Plains, USA)”

1. General remark 2. The study by Kollet and Zlotnik (2003) 3. Remark on the explanation of the drawdown behavior 4. Remark on the re-analysis of the data from piezometer C2d 5. Summar

Adaptive Uncertainty Quantification for Stochastic Hyperbolic Conservation Laws

We propose a predictor-corrector adaptive method for the study of hyperbolic partial differential equations (PDEs) under uncertainty. Constructed around the framework of stochastic finite volume (SFV) methods, our approach circumvents sampling schemes or simulation ensembles while also preserving fundamental properties, in particular hyperbolicity of the resulting systems and conservation of the discrete solutions. Furthermore, we augment the existing SFV theory with a priori convergence results for statistical quantities, in particular push-forward densities, which we demonstrate through numerical experiments. By linking refinement indicators to regions of the physical and stochastic spaces, we drive anisotropic refinements of the discretizations, introducing new degrees of freedom (DoFs) where deemed profitable. To illustrate our proposed method, we consider a series of numerical examples for non-linear hyperbolic PDEs based on Burgers' and Euler's equations

Pumping-Induced Drawdown and Stream Depletion in a Leaky Aquifer System

The impact of ground water pumping on nearby streams is often estimated using analytic models of the interconnected stream-aquifer system. A common assumption of these models is that the pumped aquifer is underlain by an impermeable formation. A new semianalytic solution for drawdown and stream depletion has been developed that does not require this assumption. This solution shows that pumping-induced flow (leakage) through an underlying aquitard can be an important recharge mechanism in many stream-aquifer systems. The relative importance of this source of recharge increases with the distance between the pumping well and the stream. The distance at which leakage becomes the primary component of the pumping-induced recharge depends on the specific properties of the aquifer, aquitard, and streambed. Even when the aquitard is orders of magnitude less transmissive than the aquifer, leakage can be an important recharge mechanism because of the large surface area over which it occurs. Failure to consider aquitard leakage can lead to large overestimations of both the drawdown produced by pumping and the contribution of stream depletion to the pumping-induced recharge. The ramifications for water resources management and water rights adjudication can be significant. A hypothetical example helps illustrate these points and demonstrates that more attention should be given to estimating the properties of aquitards underlying stream-aquifer systems. The solution presented here should serve as a relatively simple but versatile tool for practical assessments of pumping-induced stream-aquifer interactions. However, this solution should not be used for such assessments without site-specific data that indicate pumping has induced leakage through the aquitard

Dynamic interpretation of slug tests in highly permeable aquifers

This is the published version. Copyright American Geophysical Union[1] Considerable progress has been made in developing a theoretical framework for modeling slug test responses in formations with high hydraulic conductivity K. However, several questions of practical significance remain unresolved. Given the rapid and often oscillatory nature of test responses, the traditional hydrostatic relationship between the water level and the transducer-measured head in the water column may not be appropriate. A general dynamic interpretation is proposed that describes the relationship between water level response and transducer-measured head. This theory is utilized to develop a procedure for transforming model-generated water level responses to transducer readings. The magnitude of the difference between the actual water level position and the apparent position based on the transducer measurement is a function of the acceleration and velocity of the water column, test geometry, and depth of the transducer. The dynamic approach explains the entire slug test response, including the often-noted discrepancy between the actual initial water level displacement and that measured by a transducer in the water column. Failure to use this approach can lead to a significant underestimation of K when the transducer is a considerable distance below the static water level. Previous investigators have noted a dependence of test responses on the magnitude of the initial water level displacement and have developed various approximate methods for analyzing such data. These methods are re-examined and their limitations clarified. Practical field guidelines are proposed on the basis of findings of this work. The soundness of the dynamic approach is demonstrated through a comparison of K profiles from a series of multilevel slug tests with those from dipole-flow tests performed in the same wells

A Model of IceWedge Polygon Drainage in Changing Arctic Terrain

As ice wedge degradation and the inundation of polygonal troughs become increasingly common processes across the Arctic, lateral export of water from polygonal soils may represent an important mechanism for the mobilization of dissolved organic carbon and other solutes. However, drainage from ice wedge polygons is poorly understood. We constructed a model which uses cross-sectional flow nets to define flow paths of meltwater through the active layer of an inundated low-centered polygon towards the trough. The model includes the eects of evaporation and simulates the depletion of ponded water in the polygon center during the thaw season. In most simulations, we discovered a strong hydrodynamic edge eect: only a small fraction of the polygon volume near the rim area is flushed by the drainage at relatively high velocities, suggesting that nearly all advective transport of solutes, heat, and soil particles is confined to this zone. Estimates of characteristic drainage times from the polygon center are consistent with published field observations

Discrete empirical interpolation for hyper-reduction of hydro-mechanical problems in groundwater flow through soil

This is the peer reviewed version of the following article: Nasika, C. [et al.]. Discrete empirical interpolation for hyper-reduction of hydro-mechanical problems in groundwater flow through soil. "International journal for numerical and analytical methods in geomechanics", 10 Abril 2023, vol. 47, núm. 5, p. 667-693, which has been published in final form at https://onlinelibrary.wiley.com/doi/10.1002/nag.3487. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Use of Self-Archived Versions. This article may not be enhanced, enriched or otherwise transformed into a derivative work, without express permission from Wiley or by statutory rights under applicable legislation. Copyright notices must not be removed, obscured or modified. The article must be linked to Wiley’s version of record on Wiley Online Library and any embedding, framing or otherwise making available the article or pages thereof by third parties from platforms, services and websites other than Wiley Online Library must be prohibited.The recent surge in the availability of sensor data and computational resources has fostered the development of technologies for optimization, control, and monitoring of large infrastructures, integrating data and numerical modeling. The major bottleneck in this type of technologies is the model response time, since repetitive solutions are typically required. To reduce the computational time, reduced order models (ROMs) are used as surrogates for expensive finite element (FE) simulations enabling the use of complex models in this type of applications. In this work, ROMs are explored for the solution of the fully coupled hydro-mechanical system of equations that governs the water flow through partially saturated soil. The POD-based Reduced Basis Method and the Discrete Empirical Interpolation Method (DEIM), as well as its localized version (LDEIM), are examined in solving a parametrized problem simulating the mechanical loading of an embankment dam. Hydraulic and mechanical soil properties are considered as parameters. It is shown that the combination of these methods results in simulations that require 1/10 to 1/100 of the FE response time. Moreover, the method is shown to yield scaling efficiency gains with increasing problem size.Peer ReviewedPostprint (published version

A Model of IceWedge Polygon Drainage in Changing Arctic Terrain

As ice wedge degradation and the inundation of polygonal troughs become increasingly common processes across the Arctic, lateral export of water from polygonal soils may represent an important mechanism for the mobilization of dissolved organic carbon and other solutes. However, drainage from ice wedge polygons is poorly understood. We constructed a model which uses cross-sectional flow nets to define flow paths of meltwater through the active layer of an inundated low-centered polygon towards the trough. The model includes the eects of evaporation and simulates the depletion of ponded water in the polygon center during the thaw season. In most simulations, we discovered a strong hydrodynamic edge eect: only a small fraction of the polygon volume near the rim area is flushed by the drainage at relatively high velocities, suggesting that nearly all advective transport of solutes, heat, and soil particles is confined to this zone. Estimates of characteristic drainage times from the polygon center are consistent with published field observations

Optimal Ensemble Control of Matter-Wave Splitting in Bose-Einstein Condensates

We present a framework for designing optimal optical pulses for the matter-wave splitting of a Bose-Einstein Condensate (BEC) under the influence of experimental inhomogeneities, so that the sample is transferred from an initial rest position into a singular higher diffraction order. To represent the evolution of the population of atoms, the Schroedinger's equation is reinterpreted as a parameterized ensemble of dynamical units that are disparately impacted by the beam light-shift potential in a continuous manner. The derived infinite-dimensional coupled Raman-Nath equations are truncated to a finite system of diffraction levels, and we suppose that the parameter that defines the inhomogeneity in the control applied to the ensemble system is restricted to a compact interval. We first design baseline square pulse sequences for the excitation of BEC beam-splitter states following a previous study, subject to dynamic constraints for either a nominal system assuming no inhomogeneity or for several samples of the uncertain parameter. We then approximate the continuum state-space of the ensemble of dynamics using a spectral approach based on Legendre moments, which is truncated at a finite order. Control functions that steer the BEC system from an equivalent rest position to a desired final excitation are designed using a constrained optimal control approach developed for handling nonlinear dynamics. This representation results in a minimal dimension of the computational problem and is shown to be highly robust to inhomogeneity in comparison to the baseline approach. Our method accomplishes the BEC-splitting state transfer for each subsystem in the ensemble, and is promising for precise excitation in experimental settings where robustness to environmental and intrinsic noise is paramount

First-order thermal correction to the quadratic response tensor and rate for second harmonic plasma emission

Three-wave interactions in plasmas are described, in the framework of kinetic theory, by the quadratic response tensor (QRT). The cold-plasma QRT is a common approximation for interactions between three fast waves. Here, the first-order thermal correction (FOTC) to the cold-plasma QRT is derived for interactions between three fast waves in a warm unmagnetized collisionless plasma, whose particles have an arbitrary isotropic distribution function. The FOTC to the cold-plasma QRT is shown to depend on the second moment of the distribution function, the phase speeds of the waves, and the interaction geometry. Previous calculations of the rate for second harmonic plasma emission (via Langmuir-wave coalescence) assume the cold-plasma QRT. The FOTC to the cold-plasma QRT is used here to calculate the FOTC to the second harmonic emission rate, and its importance is assessed in various physical situations. The FOTC significantly increases the rate when the ratio of the Langmuir phase speed to the electron thermal speed is less than about 3.Comment: 11 pages, 2 figures, submitted to Physics of Plasma

Allen Telescope Array Multi-Frequency Observations of the Sun

We present the first observations of the Sun with the Allen Telescope Array (ATA). We used up to six frequencies, from 1.43 to 6 GHz, and baselines from 6 to 300 m. To our knowledge, these are the first simultaneous multifrequency full-Sun maps obtained at microwave frequencies without mosaicing. The observations took place when the Sun was relatively quiet, although at least one active region was present each time. We present multi-frequency flux budgets for each sources on the Sun. Outside of active regions, assuming optically thin bremsstrahlung (free--free) coronal emission on top of an optically thick ~10 000 K chromosphere, the multi-frequency information can be condensed into a single, frequency-independent, "coronal bremsstrahlung contribution function" [EM/sqrt(T)] map. This technique allows the separation of the physics of emission as well as a measurement of the density structure of the corona. Deviations from this simple relationship usually indicate the presence of an additional gyroresonance-emission component, as is typical in active regions.Comment: 16 pages, 11 figures. Accepted for publication in Solar Physic