Constant Recharge Research Articles

Modeling and Evaluation of PFOS Retention in the Unsaturated Zone above the Water Table

AbstractUnderstanding the retention of per‐ and polyfluoroalkyl substances (PFAS) in the vadose zone is vital to the management of impacted sites. This paper examines PFAS retention in the unsaturated zone above the water table using a mathematical model, MODFLOW‐USG‐Transport PFAS or “USGT‐PFAS.” The USGT‐PFAS model incorporates adsorption onto air‐water interfaces, providing a more comprehensive understanding of PFAS retention near the water table and release to groundwater. Modeling of a hypothetical perfluorooctane sulfonic acid (PFOS) site under various idealized site conditions illustrated that the impacts on PFOS retention from smallest to largest were water table fluctuations, low episodic recharge, constant recharge, moderate episodic recharge, constant recharge with water table fluctuations, and high episodic recharge. PFOS retention also varied by sand type, with greater retention occurring in simulations incorporating coarse sand with low capillary potential versus fine sand with high capillary potential. PFAS management strategies were also explored, including the adaptation of gas sparging, a method traditionally used for volatile organic compounds. Gas sparging can concentrate PFAS in groundwater and the vadose zone around the water table, facilitating retention or removal. Model simulations for a simplified hypothetical site demonstrated that PFAS can be substantially retained in the unsaturated zone once gas sparging results in an upward concentration of PFAS in groundwater and the unsaturated zone near the water table. Modeling can aid in understanding PFAS behavior but requires simulation of multiple interrelated processes to correctly predict PFAS fate and transport in subsurface conditions.

Simulation-optimization model for groundwater replenishment from the river: a case study in the Hutuo River alluvial fan, China

AbstractEcological water replenishment (EWR) has been widely implemented for the restoration of the groundwater resources in the North China Plain since 2018, and the Hutuo River is one of the typical rivers. Recovering the groundwater storage capacity while ensuring the safety of the existing land use is essential for groundwater management. To simulate the groundwater response to different recharge schemes, and to determine the optimal recharge strategy that has the maximum amount of water recharged into the aquifers under specific constraints, an optimization framework, which integrates a 3D transient groundwater flow model with a genetic algorithm (GA), was realized in a Python programming environment in this study. The optimization results show that the optimal amount of water recharged into aquifers is 5.36 × 109 m3 from January 2020 to December 2029, and the upper river reaches are the main recharge area, accounting for 67.58% of the total. Compared with constant recharge, optimal results indicate that the total amount of water recharged into aquifers will increase without exceeding the upper limits of the groundwater levels. However, as groundwater exploitation reduces (18.44%), the river's optimal amount of water recharged also decreases (17.23%). Therefore, the developed model can identify the optimal groundwater recharge strategy and eventually facilitate decision-making in the case of EWR.

Analytical and numerical solutions to describe water table fluctuations due to canal seepage and time-varying recharge

Abstract Hybrid finite analytic solution (HFAS), Galerkin's method based finite element solution (FES) and fully implicit finite difference solution (FIFDS) of one dimensional nonlinear Boussinesq equation and Analytical solution of Boussinesq equation linearized by Baumann's transformation (analytical solution I, AS I) as well as linearized by Werner's transformation (analytical solution II, AS II) were employed to obtain water table rise in a horizontal unconfined aquifer lying between two canals located at finite distance having different elevations and subjected to various patterns of recharge, i.e. zero recharge, constant recharge, as well as time varying recharge. Considering HFAS as benchmark solution, water table in mid region as obtained from FES followed by FIFDS was observed quite close to that obtained from HFAS and as per L2 and Tchebycheff norms computation, it was ranked at first and second place, respectively. Both AS I and AS II predicted higher water table at t = 5 days but at t = 10 days, AS I predicted lower and AS II predicted higher water table at all distances due to linearization effect. So, analytical solutions of linearized Boussinesq equation were rated lower than numerical solutions of nonlinear Boussinesq equation.

A Mountain‐Front Recharge Component Characterization Approach Combining Groundwater Age Distributions, Noble Gas Thermometry, and Fluid and Energy Transport Modeling

AbstractMountain‐front recharge (MFR), or all inflow to a basin‐fill aquifer with its source in the mountain block, is an important component of recharge to basin‐fill aquifer systems. Distinguishing and quantifying the surface from subsurface components of MFR is necessary for water resource planning and management, particularly as climate change may impact these components in distinct ways. This study tests the hypothesis that MFR components can be distinguished in long‐screened, basin‐fill production wells by (1) groundwater age and (2) the median elevation of recharge. We developed an MFR characterization approach by combining age distributions in six wells using tritium, krypton‐85, argon‐39, and radiocarbon, and median recharge elevations from noble gas thermometry combined with numerical experiments to determine recharge temperature lapse rates using flow and energy transport modeling. We found that groundwater age distributions provided valuable information for characterizing the dominant flow system behavior captured by the basin‐fill production wells. Tracers indicated the presence of old (i.e., no detectable tritium) water in a well completed in weathered bedrock located close to the mountain front. Two production wells exhibited age distributions of binary mixing between modern and a small fraction of old water, whereas the remaining wells captured predominantly modern flow paths. Noble gas thermometry provided important complementary information to the age distributions; however, assuming constant recharge temperature lapse rates produced improbable recharge elevations. Numerical experiments suggest that surface MFR, if derived from snowmelt, can locally suppress water table temperatures in the basin‐fill aquifer, with implications for recharge elevations estimated from noble gas thermometry.

Development of groundwater lens for transient recharge in strip islands

Groundwater in surficial aquifers in small islands is stored in the form of freshwater lenses floating on the seawater due to density difference. Recharge from rainfall infiltration is one of the primary mechanisms that control the lens growth and decay. Unlike previous studies either assuming steady-state groundwater lenses or relying on numerical simulations, we derive an approximate analytical solution to describe the transient change of groundwater lenses for a time-dependent, fluctuating recharge rate. The approximate analytical solution is validated by numerical simulations of variable density flow and transport. Based on this analytical solution and dimensional analysis, we investigate the impact of periodic recharge, extended drought events and random time-series recharge on the time-dependent behavior of the lens thickness and volume. Results show that only slowly changing recharge patterns with long periods such as seasonal and yearly changes can cause significant fluctuations of groundwater lenses. In specific, 10%, 50% and 100% fluctuations correspond to dimensionless periods of 200, 500 and 1300, respectively, which are 69, 174 and 451 days for our specified hydrogeological parameters. Thus, assuming an average constant recharge rate may be valid for simulating the transient lens profile and volume for recharge patterns with short periods such as daily fluctuations. We further analyze the approximate analytical solution using the method of low-pass filter. The complex physical process of the lens development is fitted by a second-order system on the frequency domain. Such a filter passes sine-wave recharge components with frequencies smaller than the break frequency and attenuates those higher than the break frequency, yielding smooth profiles of the lens thickness and volume. By analyzing the recharge rate spectrum and comparing the component frequency with the break frequency, we demonstrate how the development of a groundwater lens is affected by the transient recharge in reported laboratory and field observations.

БИОГЕННЫЕ ЭЛЕМЕНТЫ (АЗОТ И ФОСФОР) В ХАРАНОРСКОМ ВОДОХРАНИЛИЩЕ

Kharanorsk reservoir is a natural and technogenic object, the environmental condition of which is determined by the influence of natural factors and anthropogenic pressure connected with the operation of a hydroelectric power station. A change in the composition and concentration of nutrients is one of the indicators of the environmental changes in water bodies. The spatial distribution of biogenic elements (nitrogen and phosphorus) in the ecosystem of the Kharanor reservoir was analyzed by means of complex expedition studies. The content of mineral forms of nitrogen shows seasonal dynamics. At the same time, natural components of nitrogen compounds are modified by the anthropogenic impact on the ecosystem of the reservoir associated with the condition of the river Onon waters and warm water discharged from the state district power station. The highest nitrite content was registered in summer. Seasonal changes of nitrate ions concentration are also characterized by a summer increase and an almost uniform distribution of their content over the reservoir basin with only a slight increase in the area influenced by temperature factors and in the area of the pumping station. From April to October, the seasonal concentration of ammonium ions has a tendency to increase. The highest concentration of total phosphorus in the reservoir water is recorded in summer. In autumn phosphate concentration is lower than in spring. In spring, an increase in total phosphorus is associated with intra-water processes of decomposition of organic matter. The analysis of long-term data on the Kharanorsk reservoir hydrochemical regime proves a tendency of decrease in concentration of such substances as phosphates, total phosphorus, ammonium nitrogen, and increase in the content of nitrates and nitrites. Constant recharge of the Haranor reservoir by the waters of the Onon river results in an accelerated renewal of the water mass, which prevents stabilization of the ecosystem in comparison with other natural reservoirs. In this regard, the observed changes in the concentrations of nutrients are to a greater extent features of external influence than characteristics of a longstanding isolated reservoir.

Clogging process by suspended solids during groundwater artificial recharge: Evidence from lab simulations and numerical modelling

AbstractPermeability reduction of infiltration media due to suspended solid (SS) clogging is the bane of groundwater artificial recharge. To overcome the clogging problem and advance the understanding of the process‐based spatial‐temporal evolution of SS clogging, a 1D laboratory column simulation was carried out, followed by numerical modelling of the experimental data in this study. It was found that clogging caused a reduction in the hydraulic conductivity (K) in the upper layer at the beginning and extended deeper to approximately 50 cm, and no reduction in K was detected below 52 cm throughout the experimental period of 129 hr. The most clogged layer spanned from the surface to a depth of 11 cm, and the middle 11–52 cm was characterized by a slight decrease in K. The clogging rates of the different layers decreased with the depth, which was based on data analysis, with the largest value of 0.038 hr−1 in the upper 1 cm. The overall K began to decrease from the surface layer and was increasingly affected by clogging with time. A mathematical model was established to simulate the SS clogging process evolution based on considerations of the attachments and detachments of particles. Then the model was applied to perform several scenario analyses after calibration and validation using the data obtained in the experiment. The simulation results indicated that the SS concentration was much more sensitive than the groundwater depth below the land surface, and 10 days of constant recharge is recommended as the disposal cycle of the clogged layer under the given conditions.

Two-dimensional numerical modelling of the Riardo Plain aquifer (Campania, Italy) to constrain the recharge from the deep reservoir - Preliminary results

A local preliminary 2D model was built in the Riardo Plain in order to preliminary evaluate the regional hydrogeological conceptual model. The used finite element code was FeFlow 6.2 and calibration of data was performed via inverse modelling through FePEST (PEST code).A volcanic and a carbonate aquifer can be distinguished at regional scale. The multilayered volcanic aquifer presents a radial flow towards gaining streams and it is recharged by direct infiltration.Regional information about the carbonate aquifer are not available. The basement upraise and the fault systems allow the local mixing between the carbonate and volcanic aquifers. Recharge of the carbonate aquifer is likely to up-flow from the deep reservoir, but no direct information is available about rates and spatialdistribution. Therefore, the aim of the 2D numerical model was to test the reliability of the hypothesis of possible bottom recharge through the carbonate basement, proposed in previous groundwater budget research.After a first steady state calibration of the model, transient calibration was performed to fit the groundwater levels of the carbonate and the volcanic aquifer monitored in 2003. The zenithal recharge was applied daily as calculated from the thermo pluviometric data elaborated by Thornthwaite’s method, and the vertical discretization of the aquifers was set according to the stratigraphic information.A constant bottom recharge was set as upflow through the carbonate basement.The calibration, performed over conductivity and specific storage, gave good results. The obtained budget parameters show the higher amount of the zenithal recharge (around 60%) over the carbonate recharge (around 40%), preliminary confirming thesupposed recharge model.

Contribution of isotopic research techniques to characterize high-mountain-Mediterranean karst aquifers: The Port del Comte (Eastern Pyrenees) aquifer

Water resources in high mountain karst aquifers are usually characterized by high rainfall, recharge and discharge that lead to the sustainability of the downstream ecosystems. Nevertheless, these hydrological systems are vulnerable to the global change impact. The mean transit time (MTT) is a key parameter to describe the behavior of these hydrologic systems and also to assess their vulnerability. This work is focused on estimating MTT by using environmental tracers in the framework of high-mountain karst systems with a very thick unsaturated zone (USZ). To this end, it is adapted to alpine zones a methodology that combines a semi-distributed rainfall-runoff model to estimate recharge time series, and a lumped-parameter model to obtain ΜΤΤ. The methodology has been applied to the Port del Comte Massif (PCM) hydrological system (Southeastern Pyrenees, NE Spain), a karst aquifer system with an overlying 1000 m thick USZ. Six catchment areas corresponding to most important springs of the system are considered. The obtained results show that hydrologically the behavior of the system can be described by an exponential flow model (EM), with MTT ranging between 1.9 and 2.9 years. These ΜΤΤ values are shorter than those obtained by considering a constant recharge rate along time, which is the easiest and most applied aquifer recharge hypothesis when estimating ΜΤΤ through lumped-parameter models.

Early‐Time Solution of the Horizontal Unconfined Aquifer in the Buildup Phase

AbstractWe derive the early‐time solution of the Boussinesq equation for the horizontal unconfined aquifer in the buildup phase under constant recharge and zero inflow. The solution is expressed as a power series of a suitable similarity variable, which is constructed so that to satisfy the boundary conditions at both ends of the aquifer, that is, it is a polynomial approximation of the exact solution. The series turns out to be asymptotic and it is regularized by resummation techniques that are used to define divergent series. The outflow rate in this regime is linear in time, and the (dimensionless) coefficient is calculated to eight significant figures. The local error of the series is quantified by its deviation from satisfying the self‐similar Boussinesq equation at every point. The local error turns out to be everywhere positive, hence, so is the integrated error, which in turn quantifies the degree of convergence of the series to the exact solution.

The Cost of Covering Costs: A Nationwide Model for Water Pricing

This study offers a high-resolution model of nationwide water supply. The model is sufficiently detailed to represent all main water sources in an economy, the principal segments of the conveyance system, urban, industrial and agricultural demand regions, and various water types, including fresh, saline and recycled. Calibrated for Israeli 2010 data, we find that the optimal extraction of fresh water is only 2% larger than the total observed supply from those sources. However, for some specific sources, the deviation between optimal and observed quantities is significant. Assuming average constant recharge, the optimal aggregated desalination is 57% of the 2010 desalination capacity and only 33% of the present desalination capacity. Even with an assumed 40% decline in recharge (for example, due to climate change), the model uses only 50% of the present desalination capacity. This may suggest that the construction of desalination facilities in Israel, which began in 2005, could have been delayed. The model establishes a comprehensive system of pumping levies and user fees that support the optimal allocation. However, due to considerable scale economies, the average cost is almost 50% larger than the marginal cost. The implications are that the welfare cost of the recent Israeli Balanced Budget Water Economy legislation is more than 100 million USD per year, about 10% of the water economy share of the GDP.

Technical Note: Three-dimensional transient groundwater flow due to localized recharge with an arbitrary transient rate in unconfined aquifers

Abstract. Most previous solutions for groundwater flow induced by localized recharge assumed either aquifer incompressibility or two-dimensional flow in the absence of the vertical flow. This paper develops a new three-dimensional flow model for hydraulic head variation due to localized recharge in a rectangular unconfined aquifer with four boundaries under the Robin condition. A governing equation describing spatiotemporal head distributions is employed. The first-order free-surface equation with a source term defining a constant recharge rate over a rectangular area is used to depict water table movement. The solution to the model for the head is developed with the methods of Laplace transform and double-integral transform. Based on Duhamel's theorem, the present solution is applicable to flow problems accounting for arbitrary time-dependent recharge rates. The solution to depth-average head can then be obtained by integrating the head solution to elevation and dividing the result by the aquifer thickness. The use of a rectangular aquifer domain has two merits. One is that the integration for estimating the depth-average head can be analytically achieved. The other is that existing solutions based on aquifers of infinite extent can be considered as special cases of the present solution before the time when the aquifer boundary had an effect on head predictions. With the help of the present solution, the assumption of neglecting the vertical flow effect on the temporal head distribution at an observation point outside a recharge region can be assessed by a dimensionless parameter related to the aquifer horizontal and vertical hydraulic conductivities, initial aquifer thickness, and the shortest distance between the observation point and the edge of the recharge region. The validity of assuming aquifer incompressibility is dominated by the ratio of the aquifer specific yield to its storage coefficient. In addition, a sensitivity analysis is performed to investigate the head response to the change in each of the aquifer parameters.

An Ultracapacitor-Based No-Break System for Microcomputers

This work aims at presenting a no-break system for microcomputers using ultracapacitors in replacement of the conventional chemical batteries. We analyzed the most relevant data about average power consumption of microcomputers, electrical and mechanical characteristics of ultracapacitors and operation of no-break power circuits, to propose a configuration capable of working properly with a microcomputer switching mode power supply. Our solution was a sixteen-component ultracapacitor bank, with a total capacitance of 350 F and voltage of 10.8 V, adequate to integrate a low-capacity no-break system, capable of feeding a load of 180 Wh, during 75 s. Our proposed no-break increases the reliability of microcomputers by reducing the probability of user data losses, in case of a power grid failure, offering, so, a high benefit–cost ratio. The replacement of the battery by ultracapacitors allows a quick no-break recharge and low maintenance costs, since these modern components have a lifetime longer than the batteries. Moreover, this solution reduces the environmental impact and eliminates the constant recharge of the energy storage device.

Nonlinear Inversion of an Unconfined Aquifer: Simultaneous Estimation of Heterogeneous Hydraulic Conductivities, Recharge Rates, and Boundary Conditions

A new inverse method is developed to simultaneously estimate heterogeneous hydraulic conductivities, source/sink rates, and unknown boundary conditions for steady-state flow in an unconfined aquifer. Unlike objective function-based techniques, the new method does not optimize any data-model misfits. Instead, its formulation is developed by honoring physical flow principles as well as observation data at sampled locations. Under the Dupuit–Forchheimer assumption of negligible vertical flow, accuracy and stability of the new method are demonstrated using synthetic heterogeneous aquifer problems with increasingly complex flow: (1) aquifer domains without source/sink effects; (2) aquifer domains with a point sink (a pumping well operating under a constant discharge rate); (3) aquifer domains with constant or spatially variable recharge; (4) aquifer domains with constant or spatially variable recharge undergoing single-well pumping. For all problems, inversion yields stable solutions under increasing head measurement errors (up to $$\pm $$ 10 % of the total head variation in a problem), although accuracy of the estimated parameters degrades with the increasing errors. The inverse method is successfully tested on problems with high hydraulic conductivity contrasts—up to 10,000 times between the maximum and minimum values. In inverting several heterogeneous problems, if the aquifer is assumed homogeneous with a constant recharge rate, physically meaningful parameter estimates (i.e., equivalent conductivities and mean recharge rates) can be determined. Alternatively, if the inverse parameterization contains spurious parameters, inversion can identify such parameters, while the simultaneous estimation of non-spurious parameters is not affected. The method obviates the well-known issues associated with model “structure errors”, when inverse parameterization either simplifies or complexifies the true parameter field.

Analysis of groundwater-surface water interaction in horizontal unconfined aquifer bounded by a stream and groundwater divide using a non-linear numerical model

In this study, a non-linear numerical model was developed to analyse the interaction between the drainage water moving from an unconfined aquifer and a surface water body. This interaction can occur during or after a rainfall event, which can cause the groundwater table to change. At first, a laboratory-scale aquifer model with stream and groundwater divide boundaries was established to examine horizontal unconfined aquifer condition. Both steady-state and transient experiments were performed by setting the water table at a steady-state using a constant recharge rate, and then allowing the aquifer to drain. The transient water table data showed highly non-linear variations. Then the experimental data were recreated using a non-linear numerical model, which used non-linear one dimensional Boussinesq equation and Picard iteration for solving non-linear term of the Boussinesq equation. The numerical model was able to predict the observed groundwater table data. The proposed numerical model is a useful and cost effective tool for managing groundwater-surface water management problems.

Study on the Performances of Nickel Hydroxide Coated with Ytterbium Hydroxide at High-Temperature

Abstract The surface of nickel hydroxide [Ni(OH)2] coated with ytterbium hydroxide [Yb(OH)3] and cobalt hydroxide [Co(OH)2] were studied and characterized by XRD, XPS, SEM and constant current recharge technology. The results show that the structure of β-Ni(OH)2 is hexagonal, Co exists mainly in the form of Co2+ with a small amount of Co3+, and the atomic ratio of Co and Ni on the sample surface is more than 8:1. The samples coated of 2 wt% Yb(OH)3 show the maximum discharge capacity and active material utilization rate at 65 °C (0.2, 1, 3 C). After 30 charge/discharge cycles, the discharge cycling stability and the discharge capacity of Ni(OH)2 coated with different contents of Yb (OH)3 are enhanced with increasing of content of Yb(OH)3 under different charge/discharge rates at 65 °C.

Boundary Condition Effects on Maximum Groundwater Withdrawal in Coastal Aquifers

Prevention of sea water intrusion in coastal aquifers subject to groundwater withdrawal requires optimization of well pumping rates to maximize the water supply while avoiding sea water intrusion. Boundary conditions and the aquifer domain size have significant influences on simulating flow and concentration fields and estimating maximum pumping rates. In this study, an analytical solution is derived based on the potential-flow theory for evaluating maximum groundwater pumping rates in a domain with a constant hydraulic head landward boundary. An empirical correction factor, which was introduced by Pool and Carrera (2011) to account for mixing in the case with a constant recharge rate boundary condition, is found also applicable for the case with a constant hydraulic head boundary condition, and therefore greatly improves the usefulness of the sharp-interface analytical solution. Comparing with the solution for a constant recharge rate boundary, we find that a constant hydraulic head boundary often yields larger estimations of the maximum pumping rate and when the domain size is five times greater than the distance between the well and the coastline, the effect of setting different landward boundary conditions becomes insignificant with a relative difference between two solutions less than 2.5%. These findings can serve as a preliminary guidance for conducting numerical simulations and designing tank-scale laboratory experiments for studying groundwater withdrawal problems in coastal aquifers with minimized boundary condition effects.

Analysis of seepage from a pond

A semi-analytical solution has been derived for predicting the time of emptying a pond due to seepage. The time for the seeping water to reach the water table since the pond was initially filled has been calculated applying the Green-Ampt infiltration theory. The recharge rate after the wetting front joins the water table has been computed using a non-linear relationship between seepage head and recharge rate proposed by earlier investigators. The maximum rise in the water table beneath the center of the pond consequent to the time-varying recharge is calculated applying kernel coefficients obtained from solution of the linearized Boussinesq equation. It was observed that a pond with 50-m initial diameter at the water surface and 3-m maximum depth of water is dry after 168 days, where the subsoil is sandy clay. If the subsoil happens to be clay, the depth of water in the pond at the end of 9 months, i.e., after completion of the non-monsoon period, is 0.62 m. The maximum mound heights beneath the pond for constant recharge rate and uniform recharging area calculated from the present solution compare well with existing numerical as well as analytical solutions.

Response of an Unconfined Sloping Aquifer to Constant Recharge and Seepage from the Stream of Varying Water Level

This paper presents analytical solution of one-dimensional linearized Boussinesq equation characterizing unsteady groundwater flow in an unconfined aquifer, overlying an impervious downward sloping bed. At one end, the aquifer is in contact with a constant water level and at the other end; water level is rising exponentially from an adjoining stream. The aquifer also receives constant or cycle of time-varying vertical recharge. Analytical expressions for hydraulic head and flow rate in the aquifer are obtained by solving the seepage model using Laplace transform. The expressions derived here can explain sudden rise or very slow rise in the stream water related to sloping or horizontal beds and are represented under asymptotic case. Response of a short and long aquifer to the variation in bed slope, recharge rate and rise rate of the stream water is illustrated with the help of numerical examples. The sensitivity of the flow rate is also analyzed with respect to various parameters.

Hydraulics of subglacial supercooling: Theory and simulations for clear water flows

Glaciohydraulic supercooling is a mechanism for accreting ice and sediment to the base of glaciers. We extend existing models by reworking the Spring‐Hutter model for subglacial water flow in tubular conduits to allow for distributed water sheets. Our goal is to determine diagnostic features of supercooling relative to controlling variables. Results focus on along‐path water flow under time‐varying conditions, with attention to ice accretion in and along subglacial overdeepenings. We contrast simulations with constant recharge to diurnally‐varying recharge and expose behavior that cannot be inferred from simple models. For example, locations of simulated ice accretion differ from those found for steady state models, even though total ice accretion remains comparable to field estimates. Downstream accretion influences upstream effective pressures that then modify the hydraulic gradient that drives water flow. This modified gradient tends to inhibit additional accretion by increasing velocity and heat production via viscous dissipation. During diurnal cycles, accretion varies considerably: in daytime, viscous dissipation dominates the heat balance and ice melts. In morning and evening, when flow is rising or falling, viscous dissipation is lower and accretion can proceed. Over nighttime, the largest temperature depressions occur in the subglacial system, but water flux is lowest and accretion rates are negligible. We conclude by inferring that overdeepened glaciers with only clear water flows evolve toward stronger supercooling regimes rather than toward a dynamic equilibrium. Stabilizing feedbacks are unlikely to occur through glacier hydrology alone, and other processes, such as erosion, sedimentation, and sliding, must play an important role.