A new analytical solution for water table fluctuations in coastal aquifers with sloping beaches

The Boussinesq equation appears as the zeroth-order term in the shallow water flow expansion of the non-linear equation describing the flow of fluid in an unconfined aquifer. One-dimensional models based on the Boussinesq equation have been used to analyse tide-induced water table fluctuations in coastal aquifers. Previous analytical solutions for a sloping beach are based on the perturbation parameter, epsilon(N) = alphaepsilon cot beta (in which beta is the beach slope, alpha is the amplitude parameter and epsilon is the shallow water parameter) and are limited to tan(-1) (alphaepsilon) much less than beta less than or equal to pi/2. In this paper, a new higher-order solution to the non-linear boundary value problem is derived. The results demonstrate the significant influence of the higher-order components and beach slope on the water table fluctuations. The relative difference between the linear solution and the present solution increases as 6 and a increase, and reaches 7% of the linear solution. (C) 2003 Elsevier Ltd. All rights reserved.

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).

Swash-aquifer interaction in the vicinity of the water table exit point on a sandy beach

The coupling of sandy beach aquifers with the swash zone in the vicinity of the water table exit point is investigated through simultaneous measurements of the instantaneous shoreline (swash front) location, pore pressures and the water table exit point. The field observations reveal new insights into swash-aquifer coupling not previously gleaned from measurements of pore pressure only. In particular, for the case where the exit point is seaward of the observation point, the pore pressure response is correlated with the distance between the exit point and the shoreline in that when the distance is large the rate of pressure drop is fast and when the distance is small the rate decreases. The observations expose limitations in a simple model describing exit point dynamics which is based only on the force balance on a particle of water at the sand surface and neglects subsurface pressures. A new modified form of the model is shown to significantly improve the model-data comparison through a parameterization of the effects of capillarity into the aquifer storage coefficient. The model enables sufficiently accurate predictions of the exit point to determine when the swash uprush propagates over a saturated or a partially saturated sand surface, potentially an important factor in the morphological evolution of the beach face. Observations of the shoreward propagation of the swash-induced pore pressure waves ahead of the runup limit shows that the magnitude of the pressure fluctuation decays exponentially and that there is a linear increase in time lags, behavior similar to that of tidally induced water table waves. The location of the exit point and the intermittency of wave runup events is also shown to be significant in terms of the shore-normal energy distribution. Seaward of the mean exit point location, peak energies are small because of the saturated sand surface within the seepage face acting as a "rigid lid'' and limiting pressure fluctuations. Landward of the mean exit point the peak energies grow before decreasing landward of the maximum shoreline position.

Sugarcane water use from shallow water tables: implications for improving irrigation water use efficiency

The resource potential of shallow water tables for cropping systems has been investigated using the Australian sugar industry as a case study. Literature concerning shallow water table contributions to sugarcane crops has been summarised, and an assessment of required irrigation for water tables to depths of 2 m investigated using the SWIMv2.1 soil water balance model for three different soils. The study was undertaken because water availability is a major limitation for sugarcane and other crop production systems in Australia and knowledge on how best to incorporate upflow from water tables in irrigation scheduling is limited. Our results showed that for the three soils studied (representing a range of permeabilities as defined by near-saturated hydraulic conductivities), no irrigation would be required for static water tables within 1 m of the soil surface. Irrigation requirements when static water tables exceeded 1 m depth were dependent on the soil type and rooting characteristics (root depth and density). Our results also show that the near-saturated hydraulic conductivities are a better indicator of the ability of water tables below 1 m to supply sufficient upflow as opposed to soil textural classifications. We conclude that there is potential for reductions in irrigation and hence improvements in irrigation water use efficiency in areas where shallow water tables are a low salinity risk: either fresh, or the local hydrology results in net recharge. (C) 2003 Elsevier B.V. All rights reserved.

Response of coastal groundwater table to offshore storms

Large groundwater table fluctuations were observed in a coastal aquifer during an offshore storm. The storm induced significant changes of the mean shoreline elevation, characterized by a pulse-like oscillation. This pulse propagated in the aquifer, resulting in the water table fluctuations. A general analytical solution is derived to quantify this new mechanism of water table fluctuation. The solution is applied to field observations and is found to be able to predict reasonably well the observed storm-induced water table fluctuations. Based on the analytical solution, the damping characteristics and phase shift of the oscillation as it propagates inland are examined.

Estimating percolation and lateral water flow on sloping land in rainfed lowland rice ecosystem

Quantifying water losses in paddy fields assists estimation of water availability in rainfed lowland rice ecosystem. Little information is available on water balance in different toposequence positions of sloped rainfed lowland. Therefore, the aim of this work was to quantify percolation and the lateral water flow with special reference to the toposequential variation. Data used for the analysis was collected in Laos and northeast Thailand. Percolation and water tables were measured on a daily basis using a steel cylindrical tube with a lid and perforated PVC tubes, respectively. Percolation rate was determined using linear regression analysis of cumulative percolation. Assuming that the total amount of evaporation and transpiration was equivalent to potential evapotranspiration, the lateral water flow was estimated using the water balance equation. Separate perched water and groundwater tables were observed in paddy fields on coarse-textured soils. The percolation rate varied between 0 and 3 mm/day across locations, and the maximum water loss by lateral movement was more than 20 mm/day. Our results are in agreement with the previously reported findings, and the methodology of estimating water balance components appears reasonably acceptable. With regard to the toposequential variation, the higher the position in the topoesquence, the greater potential for water loss because of higher percolation and lateral flow rates.

Application of a coupled ground-surface water flow model to simulate periodic groundwater flow influenced by a sloping boundary, capillarity and vertical flows

Theoretical developments as well as field and laboratory data have shown the influence of the capillary fringe on water table fluctuations to increase with the fluctuation frequency. The numerical solution of a full, partially saturated flow equation can be computationally expensive. In this paper, the influence of the capillary fringe on water table fluctuations is simplified through its parameterisation into the storage coefficient of a fully-saturated groundwater flow model using the complex effective porosity concept [Nielsen, P., Perrochet, P., 2000. Water table dynamics under capillary fringes: experiments and modelling. Advances in Water Resources 23 (1), 503-515; Nielsen, P., Perrochet, P., 2000. ERRATA: water table dynamics under capillary fringes: experiments and modelling (Advances in Water Resources 23 (2000) 503-515). Advances in Water Resources 23, 907-908]. The model is applied to sand flume observations of periodic water table fluctuations induced by simple harmonic forcing across a sloping boundary, analogous to many beach groundwater systems. While not providing information on the moisture distribution within the aquifer, this approach can reasonably predict the water table fluctuations in response to periodic forcing across a sloping boundary. Furthermore, he coupled ground-surface water model accurately predicts the extent of the seepage face formed at the sloping boundary. (C) 2005 Elsevier Ltd. All rights reserved.

Characterisation of sea-water intrusion in the Pioneer Valley, Australia using hydrochemistry and three-dimensional numerical modelling

Sea-water intrusion is actively contaminating fresh groundwater reserves in the coastal aquifers of the Pioneer Valley,north-eastern Australia. A three-dimensional sea-water intrusion model has been developed using the MODHMS code to explore regional-scale processes and to aid assessment of management strategies for the system. A sea-water intrusion potential map, produced through analyses of the hydrochemistry, hydrology and hydrogeology, offsets model limitations by providing an alternative appraisal of susceptibility. Sea-water intrusion in the Pioneer Valley is not in equilibrium, and a potential exists for further landward shifts in the extent of saline groundwater. The model required consideration of tidal over-height (the additional hydraulic head at the coast produced by the action of tides), with over-height values in the range 0.5-0.9 m giving improved water-table predictions. The effect of the initial water-table condition dominated the sensitivity of the model to changes in the coastal hydraulic boundary condition. Several salination processes are probably occurring in the Pioneer Valley, rather than just simple landward sea-water advancement from modern sources of marine salts. The method of vertical discretisation (i.e. model-layer subdivision) was shown to introduce some errors in the prediction of watertable behaviour.

The water balance on sloping land in rainfed lowland rice ecosystem

Quantifying water losses in paddy fields assists estimation of water availability in rainfed lowland rice ecosystem. There is, however, no definite method for determining the water losses, and little information is available on water balance in different toposequence positions of a sloped rainfed lowland. Therefore, the aim of this work was to quantify percolation and the lateral water flow with special reference to the toposequential variation. Data used for the analysis was collected in Laos and northeast Thailand. Percolation and water tables were measured on a daily basis. The percolator is a steel cylindrical tube with a lid to prevent water loss from evapotranspiration. The water table meter is a short PVC tube for determination of perched water table and a long PVC tube for groundwater table, and the side is perforated with 5-mm diameter holes at 20-mm distance. Percolation rate was determined using linear regression analysis of cumulative percolation. Assuming that the total amount of evaporation and transpiration was equivalent to potential evapotranspiration, the lateral water flow was estimated using the water balance equation. Our results are in agreement with the previously reported findings, and the methodology of estimating water balance components appears reasonably acceptable. With regard to the toposequential variation, the higher position in the topoesquence, the greater potential of the water losses because of higher percolation and lateral flow rates.

Drying front in a sloping aquifer: Nonlinear effects

[1] The profiles for the water table height h(x, t) in a shallow sloping aquifer are reexamined with a solution of the nonlinear Boussinesq equation. We demonstrate that the previous anomaly first reported by Brutsaert [1994] that the point at which the water table h first becomes zero at x = L at time t = t(c) remains fixed at this point for all times t > t(c) is actually a result of the linearization of the Boussinesq equation and not, as previously suggested [Brutsaert, 1994; Verhoest and Troch, 2000], a result of the Dupuit assumption. Rather, by examination of the nonlinear Boussinesq equation the drying front, i.e., the point x(f) at which h is zero for times t greater than or equal to t(c), actually recedes downslope as physically expected. This points out that the linear Boussinesq equation should be used carefully when a zero depth is obtained as the concept of an average'' depth loses meaning at that time.

New approximation for free surface flow of groundwater: capillarity correction

An existing capillarity correction for free surface groundwater flow as modelled by the Boussinesq equation is re-investigated. Existing solutions, based on the shallow flow expansion, have considered only the zeroth-order approximation. Here, a second-order capillarity correction to tide-induced watertable fluctuations in a coastal aquifer adjacent to a sloping beach is derived. A new definition of the capillarity correction is proposed for small capillary fringes, and a simplified solution is derived. Comparisons of the two models show that the simplified model can be used in most cases. The significant effects of higher-order capillarity corrections on tidal fluctuations in a sloping beach are also demonstrated. (c) 2004 Elsevier Ltd. All rights reserved.

Similarity solution of axisymmetric flow in porous media

Applications of the axisymmetric Boussinesq equation to groundwater hydrology and reservoir engineering have long been recognised. An archetypal example is invasion by drilling fluid into a permeable bed where there is initially no such fluid present, a circumstance of some importance in the oil industry. It is well known that the governing Boussinesq model can be reduced to a nonlinear ordinary differential equation using a similarity variable, a transformation that is valid for a certain time-dependent flux at the origin. Here, a new analytical approximation is obtained for this case. The new solution,, which has a simple form, is demonstrated to be highly accurate. (c) 2005 Elsevier Ltd. All rights reserved.

Steepness expansion for free surface flows in coastal aquifers

Free surface flow of groundwater in aquifers has been studied since the early 1960s. Previous investigations have been based on the Boussinesq equation, derived from the non-linear kinematic boundary condition. In fact, the Boussinesq equation is the zeroth-order equation in the shallow-water expansion. A key assumption in this expansion is that the mean thickness of the aquifer is small compared with a reference length, normally taken to be the linear decay length. In this study, we re-examine the expansion scheme for free surface groundwater flows, and propose a new expansion wherein the shallow-water assumption is replaced by a steepness assumption. A comparison with experimental data shows that the new model provides a better prediction of water table levels than the conventional shallow-water expansion. The applicable ranges of the two expansions are exhibited. (c) 2004 Elsevier B.V. All rights reserved.

Dating paleochannel iron ore by (U-Th)/He analysis of supergene goethite, Hamersley province, Australia

(U-Th)/He dating of late-stage authigenic goethite, combined with corrections for diffusive loss of He-4 by the He-4/He-3 methodology, reveals strong correlation between a sample's age and its depth in ferruginized channel sediments from the Yandicoogina deposit, Western Australia. Corrected ages, ranging from ca. 18 Ma near the surface to ca. 5 Ma at the bottom of the profile, indicate that ferruginization of the aggraded channels becomes progressively younger with depth. This trend is consistent with goethite precipitation at the groundwater-atmosphere interface during water table drawdown driven by the aridification of Western Australia during the Neogene. The results demonstrate that the (U-Th)/He system is ideal for dating goethite if diffusive loss corrections are applied. The approach is suitable for dating weathering reactions on Earth and should also be suitable for dating Fe oxyhydroxides in the Martian regolith.

A numerical study of steady state evaporative conditions applied to mine tailings

The suction profile of a desiccating soil is dependent on the water table depth, the soil-water retention characteristics, and the climatic conditions. In this paper, an unsaturated flow model, which simulates both liquid and vapour flow, was used to investigate the effects of varying the water table depth and the evaporation rate on the evaporative fluxes from a desiccating tailings deposit under steady-state conditions. Results obtained showed that at a critical evaporation rate, beyond which evaporation is no longer dictated by climatic conditions, the matric suction profiles remain basically unchanged. The critical evaporation rate varies inversely with the water table depth. It is associated with the maximum evaporative flux that might be extracted from a soil at steady-state conditions. The time required to establish steady-state conditions is directly proportional to the water table depth, and it acquires a maximum value at the critical evaporation rate. A detailed investigation of the movement of the drying front demonstrated the significance of attaining a matric suction of about 3000 kPa on the contribution to flow in the vapour phase.