Reply to comment by A. G. J. Hilberts and P. A. Troch on "Influence of capillarity on a simple harmonic oscillating water table: Sand column experiments and modeling"

We thank Hilberts and Troch [2006] for their comment on our paper [Cartwright et al, 2005]. Before proceeding with our specific replies to the comments we would first like to clarify the definitions and meanings of equations (1)-(3) as presented by Hilberts and Troch [2006]. First, equation (1) is the fundamental definition of the (complex) effective porosity as derived by Nielsen and Perrochet [2000]. Equations (2) and (3), however, represent the linear frequency response function of the water table in the sand column responding to simple harmonic forcing. This function, which was validated by Nielsen and Perrochet [2000], provides an alternative method for estimating the complex effective porosity from the experimental sand column data in the absence of direct measurements of h_(tot) (which are required if equation (1) is to be used).

Beach water table fluctuations due to spring-neap tides: moving boundary effects

Tidal water table fluctuations in a coastal aquifer are driven by tides on a moving boundary that varies with the beach slope. One-dimensional models based on the Boussinesq equation are often used to analyse tidal signals in coastal aquifers. The moving boundary condition hinders analytical solutions to even the linearised Boussinesq equation. This paper presents a new perturbation approach to the problem that maintains the simplicity of the linearised one-dimensional Boussinesq model. Our method involves transforming the Boussinesq equation to an ADE (advection-diffusion equation) with an oscillating velocity. The perturbation method is applied to the propagation of spring-neap tides (a bichromatic tidal system with the fundamental frequencies wt and wt) in the aquifer. The results demonstrate analytically, for the first time, that the moving boundary induces interactions between the two primary tidal oscillations, generating a slowly damped water table fluctuation of frequency omega(1) - omega(2), i.e., the spring-neap tidal water table fluctuation. The analytical predictions are found to be consistent with recently published field observations. (C) 2000 Elsevier Science Ltd. All rights reserved.

Collapse behavior of soil in a Brazilian region affected by a rising water table

Collapsible soils are usually nonsaturated, low density, and metastable-structured soils that are known to exhibit a volume reduction following an episode of moisture increase or suction reduction. This paper describes the collapsible behavior of clayey sand based on controlled soil suction tests carried out on undisturbed samples from the city of Pereira Barreto, in the State of Sao Paulo, Brazil. Foundation settlements due to soil collapse are common in this region and occurred during the filling of the reservoir of the Tres Irmaos Dam, which induced the elevation of the groundwater table in different parts of Pereira Barreto. This paper shows that collapse strains depend on the stress and soil suction acting in the sample and that saturation is not necessary for a collapse to occur. The influence of soil suction, gradual wetting, and the wetting and drying cycle on the collapsible behavior of the soil is also shown and discussed.

Spring-neap tide-induced beach water table fluctuations in a sloping coastal aquifer

Predictions of water table fluctuations in coastal aquifers are needed for numerous coastal and water resources engineering problems. Most previous investigations have been based on the Boussinesq equation for the case of a vertical beach. In this note an analytical solution based on shallow water expansion for the spring- neap tide- induced water table fluctuations in a coastal aquifer is presented. Unlike most previous investigations, multitidal signals are considered with a sloping coastal aquifer. The new solution is verified by comparing with field observations from Ardeer, Scotland. On the basis of the analytical approximation the influences of higher- order components on water table elevation are examined first. Then, a parametric study has been performed to investigate the effects of the amplitude ratio (lambda), frequency ratio (omega), and phases (delta(1) and delta(2)) on the tide- induced water table fluctuations in a sloping sandy beach.

Numerical modelling of tide-induced beach water table fluctuations

Field studies have shown that the elevation of the beach groundwater table varies with the tide and such variations affect significantly beach erosion or accretion. In this paper, we present a BEM (Boundary Element Method) model for simulating the tidal fluctuation of the beach groundwater table. The model solves the two-dimensional flow equation subject to free and moving boundary conditions, including the seepage dynamics at the beach face. The simulated seepage faces were found to agree with the predictions of a simple model (Turner, 1993). The advantage of the present model is, however, that it can be used with little modification to simulate more complicated cases, e.g., surface recharge from rainfall and drainage in the aquifer may be included (the latter is related to beach dewatering technique). The model also simulated well the field data of Nielsen (1990). In particular, the model replicated three distinct features of local water table fluctuations: steep rising phase versus flat falling phase, amplitude attenuation and phase lagging.

Beach water table fluctuations due to wave run-up: Capillarity effects

High-frequency beach water table fluctuations due to wave run-up and rundown have been observed in the field [Waddell, 1976]. Such fluctuations affect the infiltration/exfiltration process across the beach face and the interstitial oxygenation process in the beach ecosystem. Accurate representation of high-frequency water table fluctuations is of importance in the modeling of (1) the interaction between seawater and groundwater, more important, the effects on swash sediment transport and (2) the biological activities in the beach ecosystem. Capillarity effects provide a mechanism for high-frequency water table fluctuations. Previous modeling approaches adopted the assumption of saturated flow only and failed to predict the propagation of high-frequency fluctuations in the aquifer. In this paper we develop a modified kinematic boundary condition (kbc) for the water table which incorporates capillarity effects. The application of this kbc in a boundary element model enables the simulation of high-frequency water table fluctuations due to wave run-up. Numerical tests were carried out for a rectangular domain with small-amplitude oscillations; the behavior of water table responses was found to be similar to that predicted by an analytical solution based on the one-dimensional Boussinesq equation. The model was also applied to simulate the water table response to wave run-up on a doping beach. The results showed similar features of water table fluctuations observed in the field. In particular, these fluctuations are standing wave-like with the amplitude becoming increasingly damped inland. We conclude that the modified kbc presented here is a reasonable approximation of capillarity effects on beach water table fluctuations. However, further model validation is necessary before the model can confidently be used to simulate high-frequency water table fluctuations due to wave run-up.

Tide-induced water table fluctuations in coastal aquifers bounded by rhythmic shorelines

Previous studies on tidal water table dynamics in unconfined coastal aquifers have focused on the inland propagation of oceanic tides in the cross-shore direction based on the assumption of a straight coastline. Here, two-dimensional analytical solutions are derived to study the effects of rhythmic coastlines on tidal water table fluctuations. The computational results demonstrate that the alongshore variations of the coastline can affect the water table behavior significantly, especially in areas near the centers of the headland and embayment. With the coastline shape effects ignored, traditional analytical solutions may lead to large errors in predicting coastal water table fluctuations or in estimating the aquifer's properties based on these signals. The conditions under which the coastline shape needs to be considered are derived from the new analytical solution.

Water table waves in an unconfined aquifer: Experiments and modeling

[1] Comprehensive measurements are presented of the piezometric head in an unconfined aquifer during steady, simple harmonic oscillations driven by a hydrostatic clear water reservoir through a vertical interface. The results are analyzed and used to test existing hydrostatic and nonhydrostatic, small-amplitude theories along with capillary fringe effects. As expected, the amplitude of the water table wave decays exponentially. However, the decay rates and phase lags indicate the influence of both vertical flow and capillary effects. The capillary effects are reconciled with observations of water table oscillations in a sand column with the same sand. The effects of vertical flows and the corresponding nonhydrostatic pressure are reasonably well described by small-amplitude theory for water table waves in finite depth aquifers. That includes the oscillation amplitudes being greater at the bottom than at the top and the phase lead of the bottom compared with the top. The main problems with respect to interpreting the measurements through existing theory relate to the complicated boundary condition at the interface between the driving head reservoir and the aquifer. That is, the small-amplitude, finite depth expansion solution, which matches a hydrostatic boundary condition between the bottom and the mean driving head level, is unrealistic with respect to the pressure variation above this level. Hence it cannot describe the finer details of the multiple mode behavior close to the driving head boundary. The mean water table height initially increases with distance from the forcing boundary but then decreases again, and its asymptotic value is considerably smaller than that previously predicted for finite depth aquifers without capillary effects. Just as the mean water table over-height is smaller than predicted by capillarity-free shallow aquifer models, so is the amplitude of the second harmonic. In fact, there is no indication of extra second harmonics ( in addition to that contained in the driving head) being generated at the interface or in the interior.

Evaporation from a shallow water table: Diurnal dynamics of measured and simulated water and heat regime at the vicinity of a drying sand surface

Accurate estimates of water losses by evaporation from shallow water tables are important for hydrological, agricultural, and climatic purposes. An experiment was conducted in a weighing lysimeter to characterize the diurnal dynamics of evaporation under natural conditions. Sampling revealed a completely dry surface sand layer after 5 days of evaporation. Its thickness was <1 cm early in the morning, increasing to reach 4?5 cm in the evening. This evidence points out fundamental limitations of the approaches that assume hydraulic connectivity from the water table up to the surface, as well as those that suppose monotonic drying when unsteady conditions prevail. The computed vapor phase diffusion rates from the apparent drying front based on Fick's law failed to reproduce the measured cumulative evaporation during the sampling day. We propose that two processes rule natural evaporation resulting from daily fluctuations of climatic variables: (i) evaporation of water, stored during nighttime due to redistribution and vapor condensation, directly into the atmosphere from the soil surface during the early morning hours, that could be simulated using a mass transfer approach and (ii) subsurface evaporation limited by Fickian diffusion, afterward. For the conditions prevailing during the sampling day, the amount of water stored at the vicinity of the soil surface was 0.3 mm and was depleted before 11:00. Combining evaporation from the surface before 11:00 and subsurface evaporation limited by Fickian diffusion after that time, the agreement between the estimated and measured cumulative evaporation was significantly improved.

Impact of precipitation on the water table level of different ombrotrophic raised bog complexes, central Estonia

Sadannan vaikutus vedenpinnan tasoon kohosuolla

Evaluation of a computer model to simulate water table response to subirrigation

The objective of this work was to evaluate the water flow computer model, WATABLE, using experimental field observations on water table management plots from a site located near Hastings, FL, USA. The experimental field had scale drainage systems with provisions for subirrigation with buried microirrigation and conventional seepage irrigation systems. Potato (Solanum tuberosum L.) growing seasons from years 1996 and 1997 were used to simulate the hydrology of the area. Water table levels, precipitation, irrigation and runoff volumes were continuously monitored. The model simulated the water movement from a buried microirrigation line source and the response of the water table to irrigation, precipitation, evapotranspiration, and deep percolation. The model was calibrated and verified by comparing simulated results with experimental field observations. The model performed very well in simulating seasonal runoff, irrigation volumes, and water table levels during crop growth. The two-dimensional model can be used to investigate different irrigation strategies involving water table management control. Applications of the model include optimization of the water table depth for each growth stage, and duration, frequency, and rate of irrigation.

Increased temperature sensitivity of net DOC production from ombrotrophic peat due to water table draw-down.

The production and release of dissolved organic carbon (DOC) from peat soils is thought to be sensitive to changes in climate, specifically changes in temperature and rainfall. However, little is known about the actual rates of net DOC production in response to temperature and water table draw-down, particularly in comparison to carbon dioxide (CO2) fluxes. To explore these relationships, we carried out a laboratory experiment on intact peat soil cores under controlled temperature and water table conditions to determine the impact and interaction of each of these climatic factors on net DOC production. We found a significant interaction (P < 0.001) between temperature, water table draw-down and net DOC production across the whole soil core (0 to −55 cm depth). This corresponded to an increase in the Q10 (i.e. rise in the rate of net DOC production over a 10 °C range) from 1.84 under high water tables and anaerobic conditions to 3.53 under water table draw-down and aerobic conditions between −10 and − 40 cm depth. However, increases in net DOC production were only seen after water tables recovered to the surface as secondary changes in soil water chemistry driven by sulphur redox reactions decreased DOC solubility, and therefore DOC concentrations, during periods of water table draw-down. Furthermore, net microbial consumption of DOC was also apparent at − 1 cm depth and was an additional cause of declining DOC concentrations during dry periods. Therefore, although increased temperature and decreased rainfall could have a significant effect on net DOC release from peatlands, these climatic effects could be masked by other factors controlling the biological consumption of DOC in addition to soil water chemistry and DOC solubility. These findings highlight both the sensitivity of DOC release from ombrotrophic peat to episodic changes in water table draw-down, and the need to disentangle complex and interacting controls on DOC dynamics to fully understand the impact of environmental change on this system.