A semi-analytical time integration for numerical solution of Boussinesq equation

A semi-analytical time integration method is proposed for the numerical simulation of transient groundwater flow in unconfined aquifers by the nonlinear Boussinesq equation. The method is based on the analytical solution of the system of ordinary differential equations with constant coefficients. While it is unconditionally stable and more accurate than the finite difference methods, the computational cost is much more expensive than (can be more than 10 times) that of the finite difference methods for a single time step. However, by partitioning the nonlinear parameters into linear and nonlinear parts, the costly computation can be performed only once. With larger and less variable time step sizes, the total computational cost can be significantly reduced. Three examples are included to illustrate the advantages and limitations of the proposed method.     

Modelling of water table variation in response to time-varying recharge from multiple basins using the linearised Boussinesq equation

A mathematical model is presented to describe the variations of the water table in an unconfined aquifer due to time-varying recharge applied from four rectangular basins. The model is developed by solving the linearised Boussinesq equation using the extended finite Fourier cosine transform. The time-varying recharge rate is approximated by a number of piecewise linear elements of different lengths and slopes depending on the nature of the variation in recharge rate. Application of this model for the prediction of water table fluctuations and in the sensitivity analysis of various controlling parameters on the aquifer response is demonstrated in an example.     

Estimating groundwater recharge from water isotope (δ2H, δ18O) depth profiles in the Densu River basin,Ghana

Abstract

Accurate estimation of groundwater recharge is essential for the proper management of aquifers. A study of water isotope (δ²H, δ¹⁸O) depth profiles was carried out to estimate groundwater recharge in the Densu River basin in Ghana, at three chosen observation sites that differ in their altitude, geology, climate and vegetation. Water isotopes and water contents were analysed with depth to determine water flow in the unsaturated zone. The measured data showed isotope enrichment in the pore water near the soil surface due to evaporation. Seasonal variations in the isotope signal of the pore water were also observed to a depth of 2.75 m. Below that depth, the seasonal variation of the isotope signal was attenuated due to diffusion/dispersion and low water flow velocities. Groundwater recharge rates were determined by numerical modelling of the unsaturated water flow and water isotope transport. Different groundwater recharge rates were computed at the three observation sites and were found to vary between 94 and 182 mm/year (± max. 7%). Further, the approximate peak-shift method was applied to give information about groundwater recharge rates. Although this simple method neglects variations in flow conditions and only considers advective transport, it yielded mean groundwater recharge rates of 110–250 mm/year (± max. 30%), which were in the same order of magnitude as computed numerical modelling values. Integrating these site-specific groundwater recharge rates to the whole catchment indicates that more water is potentially renewed than consumed nowadays. With increases in population and irrigation, more clean water is required, and knowledge about groundwater recharge rates – essential for improving the groundwater management in the Densu River basin – can be easily obtained by measuring water isotope depth profiles and applying a simple peak-shift approach.

Citation Adomako, D., Maloszewski, P., Stumpp, C., Osae, S. & Akiti, T. T. (2010) Estimating groundwater recharge from water isotope (δ²H, δ¹⁸O) depth profiles in the Densu River basin, Ghana. Hydrol. Sci. J. 55(8), 1405–1416.     

A hydrographic method to identify the groundwater net recharge,barometric effect and evapotranspiration from a complicated semidiurnal water table fluctuation

A hydrographic method was proposed to separate out the hourly scaled groundwater level changes caused by net recharge, barometric effects and evapotranspiration from a semidiurnal water table fluctuation. A characteristic midnight time, with a turning point of the barometric pressure change and high relative air humidity, which meant that neither the barometric effect nor groundwater evapotranspiration occurred, was proposed for determining the net recharge rate r_net. Then, the barometric efficiency f_bar was estimated using the other time period without evapotranspiration, and the evapotranspiration rate r_ETG was finally obtained using the remainder of the water level changes. A case example illustrated that estimation of f_bar using the proposed method was more accurate than that using the traditional error analysis method, which may result in a significant underestimation under the condition of the present water level changes. Additionally, the abnormal semidiurnal fluctuations, more specifically, two step-down fluctuations, which may be a common pattern when the groundwater level is controlled by net recharge, barometric effects and evapotranspiration, can be well understood using the three components separated out. The results also showed that nighttime groundwater evapotranspiration, accounting for an average of 23% of that during the daytime, cannot be ignored.     

三峡水库水面蒸发年内滞后效应分析

水面蒸发在季节变化上相比净辐射等气象要素的相位延迟反映了水体储热对水面蒸发的影响,量化这一对气象要素波动的滞后响应对理解和估算深水水库(湖泊)蒸发非常重要。三峡水库等河道型深水水库的水位和面积具有显著周期性变动,使得其水面蒸发的响应模式更为复杂,而目前对其认识非常薄弱。本文利用2013年8月—2020年7月三峡水库巴东站水面蒸发场和陆面蒸发场的蒸发和气象观测数据,分析了水面蒸发的季节变化及其年内滞后效应。结果表明:水面蒸发场蒸发量在年内的8和12月呈现双峰变化,与只有8月单峰值的陆面蒸发场蒸发量显著不同。水面蒸发场蒸发量相对净辐射、平均气温和水面温度分别存在4、3和2个月的滞后,而陆面蒸发场蒸发量相对滞后时间均在1个月以内;水面与陆面蒸发场相比,水温、蒸发量和水面与大气饱和差之间的滞后时间分别为1、3和4个月,而平均气温和净辐射之间不存在滞后。本文揭示出三峡水库巴东段水面蒸发年内滞后效应主要受到水库水温引起的水面与大气饱和差在季节上滞后的影响,需通过深入分析水温的时空变化来明确整个三峡水库的水面蒸发特征。     

Origin of sulphate in the unsaturated zone and groundwater of a loess aquifer

The use of the sulphate mass balance (SMB) between precipitation and soil water as a supplementary method to estimate the diffuse recharge rate assumes that the sulphate in soil water originated entirely from atmospheric deposition; however, the origin of sulphate in soil and groundwater is often unclear, especially in loess aquifers. This study analysed the sulphur (δ³⁴S-SO₄) and oxygen (δ¹⁸O-SO₄) isotopes of sulphate in precipitation, water-extractable soil water, and shallow groundwater samples and used these data along with hydrochemical data to determine the sources of sulphate in the thick unsaturated zone and groundwater of a loess aquifer. The results suggest that sulphate in groundwater mainly originated from old precipitation. When precipitation percolates through the unsaturated zone to recharge groundwater, sulphates were rarely dissolved due to the formation of CaCO₃ film on the surface of sulphate minerals. The water-extractable sulphate in the deep unsaturated zone (>10 m) was mainly derived from the dissolution of evaporite minerals and there was no oxidation of sulphide minerals during the extraction of soil water by elutriating soil samples with deionized water. The water-extractable concentration of SO₄ was not representative of the actual SO₄ concentration in mobile soil water. Therefore, the recharge rate cannot be estimated by the SMB method using the water-extractable concentration of SO₄ in the loess areas. This study is important for identifying sulphate sources and clarifying the proper method for estimating the recharge rate in loess aquifers.     

The influence of water retention curve hysteresis on the stability of unsaturated soil slopes

Hysteresis is a common feature exhibited in hydraulic properties of an unsaturated soil. The movement of wetting front and the hysteresis effect are important factors which impact the shear strength of the unsaturated soil and the mechanics of shallow landslides. These failures are mainly triggered by the deepening of the wetting front accompanied by a decrease in matric suction induced by infiltration. This research establishes a method for determining a stability analysis of unsaturated infinite soil slopes, integrating the influence of infiltration and the water retention curve hysteresis. Furthermore, the present stability analysis method including the infiltration model and the advanced Mohr–Coulomb failure criterion calculates the variations of the safety factor (FS) in accordance with different slope angle, depth and hydrological processes. The experimentally measured data on the effect of hysteresis are also carried out for comparison. Numerical analyses, employing both wetting and drying hydraulic behaviour of unsaturated soil, are performed to study the difference in soil‐water content as observed in the experiments. The simulating approximations also fully responded to the experimental data of sand box. The results suggest that the hysteresis behaviour affect the distribution of soil‐water content within the slope indeed. The hysteresis made the FS values a remarkable recovery during the period of non‐rainfall in a rainfall event. The appropriate hydraulic properties of soil (i.e. wetting or drying) should be used in accordance with the processes that unsaturated soil actually experience. This method will enable us to acquire more accurate matric suction head and the unsaturated soil‐shear strength as it changes with the hysteretic flow, in order to calculate into the stability analysis of shallow landslides. An advanced understanding of the process mechanism afforded by this method is critical to realizing a reliable and appropriate design for slope stabilization. It also offers some immediate reference information to the disaster reduction department of the government. Copyright © 2011 John Wiley & Sons, Ltd.     

Determination of upward/downward groundwater fluxes using transient variations of soil profile temperature: test of the method with Voyons (Aube,France) experimental data

The temperature variations recorded at several points of a vertical shallow‐depth profile are governed both by conductive and convective heat transfers and can be used to calculate the vertical component of the Darcy velocity and thermal diffusivity in the soil. This paper describes such calculations when transient variations over tens of days are considered and tests them using data collected at Voyons (Aube, France). The temperature was recorded during a year and a half period with a 1 h sampling time step at three different depths: 0·2, 0·4 and 0·75 m. By processing the annual variation of temperature, we obtained a value of the Darcy velocity in good agreement with the value of actual/potential evapotranspiration ratio. By processing transient variations, despite the limitation of the calculations due to the lack of sensitivity of the sensors, results obtained at Voyons were in good correlation with tensiometric data. Copyright © 2005 John Wiley & Sons, Ltd.     

Application of the water table fluctuation method to characterize groundwater recharge in the Pampa plain,Argentina

Abstract

The water table fluctuation (WTF) method is based on accepting that rises of a water table are due to recharge water reaching the groundwater. To apply the method, an estimate of the specific yield of the zone of fluctuation of the groundwater level is required. In this paper, a method for estimation of the specific yield (S_y) is proposed; it consists of a graphical procedure which relates rises in groundwater level to the precipitation from which they originated. The method presents more reliable S_y values as the number of events measured increases. Eighteen years of daily measurements were analysed to obtain a S_y value of 0.09, which was used to apply the WTF method. The obtained recharge values show consistency with values calculated by other authors for the same region.

Editor D. Koutsoyiannis

Citation Varni, M., Comas, R., Weinzettel, P., and Dietrich, S., 2013. Application of water table fluctuation method to characterize the groundwater recharge in the Pampa plain, Argentina. Hydrological Sciences Journal, 58 (7), 1445–1455.     

Effects on catchment water balance from the management of Pinus plantations on the coastal lowlands of south‐east Queensland,Australia

A paired catchment study was conducted over a 10‐year period on the hydrology of an exotic Pinus plantation in the coastal lowlands of south‐east Queensland, Australia. Each catchment was instrumented with a stream monitoring station, tipping bucket rain gauge, and a network of piezometers to monitor the shallow perched water table. After a 6‐year calibration period a harvest treatment was imposed on one catchment (Review): clearfelling approximately 90% of the catchment area, which contained a mature (44‐year‐old) Pinus elliottii plantation. This subsequently was re‐established with a second rotation plantation of a hybrid of P.elliottii × P.caribaea var. hondurensis. The control catchment (Crayfish) contained a P. elliottii plantation similar to that clearfelled at Review. The post‐harvest period was monitored for a further 4 years. Evapotranspiration was found to be the major output flux, with stream flow only a minor component of the study catchments' water budget. Areas with gleyed podzolic soils were found to remain waterlogged for periods up to 7 months following the seasonally high summer rainfall period, with other soils having water logging periods of only a few months. Little change was observed in waterlogging characteristics following harvesting, in contrast to stream flow which increased for 3 years but with evidence of a decline after 5 years. The perched‐watertable piezometric surface indicated that its lateral drainage differs from that of surface flows; the perched‐watertable drainage fluxes from the study catchments seem minor and off‐site movement of solutes (e.g. nutrients and contaminants) via them would be limited. It was identified that the interaction between the perched and deep aquifers was poorly understood, as well as the relative importance of the soil moisture storage of the aquitard clay layer between them. It was concluded that there is a need to undertake more detailed analysis using modelling, and to obtain additional field data on soil‐layer properties and piezometric levels of the deep aquifer. Copyright © 2002 John Wiley & Sons, Ltd.     

A simulation and prediction of agricultural irrigation on groundwater in well irrigation area of the piedmont of Mt. Taihang,North China

Declining groundwater levels caused by irrigation is the main problem for agricultural development in Northern China. Due to both economics and increased population, surface water has become almost non‐existent and groundwater is the only water resource left. Currently the groundwater is declining at a rate between 50 and 100 cm per year. Sustainable development in Northern China requires effective management of the groundwater resources. In this study, the effect of future irrigation patterns on the decline of the groundwater table is examined with the aid of MODFLOW. MODFLOW was calibrated for five observation wells in the county. The calibrated model fitted the observed data well over a 7‐year period. The simulated results showed that the groundwater decline would be decreased, and perhaps halted, by decreasing the use of irrigation. Copyright © 2005 John Wiley & Sons, Ltd.     

Effect of multilayered groundwater mounds on water dynamics beneath a recharge basin: Numerical simulation and assessment of surface injection

Interactions between groundwater mounds caused by a geologic layer contrast affect the efficiency of managed aquifer recharge in arid areas. However, research has rarely examined the roles of groundwater mounding size variations on soil water dynamics in a stratified vadose zone in response to a sustained infiltration source. Numerical experiments were conducted on a two-dimensional vertical-section domain using HYDRUS software to simulate the behaviours of two adjacent (upper and lower) groundwater mounds underlying an infiltration basin subjected to clay loam and sandy alternately-layered soil profiles. The model successfully predicted the volume and extent of perched water and approximated vertical travel times during events generating downward fluxes from the surface injection. The response time of the mounding width (lateral extension) to the surface injection was delayed as compared to that of the mounding height (vertical extension), especially for the lower water mound. The mounding heights and widths show a strongly positive correlation with the infiltration rates of both high- and low-permeability layers where the injected water mounded, while the water storage amounts in the high- and low-permeability layers were governed by the mounding height and width, respectively. Exploratory simulations were then employed to assess the dependence of groundwater mounding behaviours and recharge performances on surface injection strategies. Results suggest that, by reducing injection rate or shortening injection duration, the near-term fraction of the surface injection converted to deep recharge is likely to be increased due to the narrowed groundwater mounding size, which would be limited by the water-retarding effect of layer contrasts. This study has important implications for predicting and understanding multilayered groundwater mounding behaviours and associated water mass balance under the geologic stratification, and is expected to aid in optimizing the infiltration basin operation for aquifer recharge.     

Modelling the impact of extensive irrigation on the groundwater resources

Drastic groundwater resource depletion due to excessive extraction for irrigation is a major concern in many parts of India. In this study, an attempt was made to simulate the groundwater scenario of the catchment using ArcSWAT. Due to the restriction on the maximum initial storage, the deep aquifer component in ArcSWAT was found to be insufficient to represent the excessive groundwater depletion scenario. Hence, a separate water balance model was used for simulating the deep aquifer water table. This approach is demonstrated through a case study for the Malaprabha catchment in India. Multi‐site rainfall data was used to represent the spatial variation in the catchment climatology. Model parameters were calibrated using observed monthly stream flow data. Groundwater table simulation was validated using the qualitative information available from the field. The stream flow was found to be well simulated in the model. The simulated groundwater table fluctuation is also matching reasonably well with the field observations. From the model simulations, deep aquifer water table fluctuation was found very severe in the semi‐arid lower parts of the catchment, with some areas showing around 60 m depletion over a period of eight years. Copyright © 2012 John Wiley & Sons, Ltd.     

The effects of floods on the temperature of riparian groundwater

The transition area between rivers and their adjacent riparian aquifers, which may comprise the hyporheic zone, hosts important biochemical reactions, which control water quality. The rates of these reactions and metabolic processes are temperature dependent. Yet the thermal dynamics of riparian aquifers, especially during flooding and dynamic groundwater flow conditions, has seldom been studied. Thus, we investigated heat transport in riparian aquifers during 3 flood events of different magnitudes at 2 sites along the same river. River and riparian aquifer temperature and water‐level data along the Lower Colorado River in Central Texas, USA, were monitored across 2‐dimensional vertical sections perpendicular to the bank. At the downstream site, preflood temperature penetration distance into the bank suggested that advective heat transport from lateral hyporheic exchange of river water into the riparian aquifer was occurring during relatively steady low‐flow river conditions. Although a small (20‐cm stage increase) dam‐controlled flood pulse had no observable influence on groundwater temperature, larger floods (40‐cm and >3‐m stage increases) caused lateral movement of distinct heat plumes away from the river during flood stage, which then retreated back towards the river after flood recession. These plumes result from advective heat transport caused by flood waters being forced into the riparian aquifer. These flood‐induced temperature responses were controlled by the size of the flood, river water temperature during the flood, and local factors at the study sites, such as topography and local ambient water table configuration. For the intermediate and large floods, the thermal disturbance in the riparian aquifer lasted days after flood waters receded. Large floods therefore have impacts on the temperature regime of riparian aquifers lasting long beyond the flood's timescale. These persistent thermal disturbances may have a significant impact on biochemical reaction rates, nutrient cycling, and ecological niches in the river corridor.     

Overexploitation and continuous drought effects on groundwater yield and marine intrusion: considerations arising from the modelling of Mamora coastal aquifer,Morocco

This paper studies the effect of drought and pumping discharge on groundwater supplies and marine intrusion. The investigation concerns the Mamora coastal aquifer, northwest of Morocco. A large‐scale groundwater model was established to model (a) the amount of freshwater discharge towards the ocean and the sea water volumes flowing inland as a consequence of the inverse hydraulic gradient, (b) the impact of drought and pumping discharge on the water table level and, as a consequence, on marine water intrusion. In fact, the simulated submarine groundwater discharge (SGWD) would decrease from 864 m³/d/km in 1987 to 425 m³/d/km in 2000. The simulated volumes of sea water intruding the aquifer as a result of inverse hydraulic gradient would increase from 0·25 Mm³/y in 1987 to 0·3 Mm³/y in 2000. As a consequence of a negative rainfall gradient of −5 mm/y, the simulated SGWD would decline to 9 m³/d/km and the sea water intrusion (SWI) would increase to 0·35 Mm³/y since the year 2010. Due to insufficient data on the trend of pumping discharge, a hypothetical increase of this latter from 38·3 Mm³/y to 53·2 Mm³/y is simulated to induce an increase of marine water intrusion from 0·25 Mm³/y to 0·9 Mm³/y. Consequently, to optimally exploit this seemingly fragile coastal aquifer, a plan of future actions to implement is proposed. Copyright © 2005 John Wiley & Sons, Ltd.     

Propagation of seismic waves in a viscoelastic medium and the effect of topography

In this paper we have simulated the propagation of seismic waves in viscoelastic medium and calculated the effect of irregular surface topography by using finite element method. Several types of elastic and viscoelastic medium models, such as block structure, vidges and/or valley with and without a soft layer underneath have been studied. The distribution of maximum amplitude of displacement and acceleration on surface has been calculated in the case of vertically incident SH and P waves from the basement. The possible application in earthquake engineering is also discussed. The Chinese version of this paper appeared in the Chinese edition ofActa Seismologica Sinica,13, 442–449, 1991.     

Influence of soil moisture hysteresis on the functioning of capillary barriers

Previous experimental studies of capillary barriers have identified highly hysteretic soil moisture retention characteristics in the materials used. In this study, numerical modelling is used to analyse the role of soil moisture hysteresis in capillary barrier functioning. Comparisons between published experimental results and model simulations indicate that soil moisture hysteresis was a necessary inclusion in the modelling approach to adequately reproduce pore water pressure distributions and the timing of breakthrough occurrences. Under hypothetical intermittent infiltration and evaporation conditions, the predicted volumetric water content in the moisture retention layer was significantly different for hysteretic and non‐hysteretic models. The hysteresis effect was found to be dependent on the nature of infiltration–evaporation cycling, although the predicted volume of flow through the hysteretic barrier was lower than that of the non‐hysteretic case, regardless of the nature of the cyclic upper boundary conditions. For practical engineering designs, where the water leakage through the barrier is the primary concern, the inclusion of soil moisture hysteresis in numerical modelling is needed. Copyright © 2009 John Wiley & Sons, Ltd.     

Spatial and temporal variations of nutrient concentration in the groundwater of a floodplain: effect of hydrology,vegetation and substrate

Spatio‐temporal variations in nitrogen and phosphorus concentrations in groundwater were analysed and related to the variations in hydrological conditions, vegetation type and substrate in an alluvial ecosystem. This study was conducted in the Illwald forest in the Rhine Plain (eastern France) to assess the removal of nutrients from groundwater in a regularly flooded area. We compared both forest and meadow ecosystems on clayey‐silty soils with an anoxic horizon (pseudogley) at 1·5–2 m depth (eutric gley soil) and a forest ecosystem on a clayey‐silty fluviosoil rich in organic matter with a gley at 0·5 m depth (calcaric gley soil). Piezometers were used to measure the nutrient concentrations in the groundwater at 2 m depth in the root layer and at 4·5 m depth, below the root layer. Lower concentrations of nitrate and phosphate in groundwater were observed under forest than under meadow, which could be explained by more efficient plant uptake by woody species than herbaceous plants. Thus NO₃‐N inputs by river floods were reduced by 73% in the shallow groundwater of the forested ecosystem, and only by 37% in the meadow. Compared with the superficial groundwater layer, the lowest level of nitrate nitrogen (NO₃‐N) and the highest level of ammonium nitrogen (NH₄‐N) were measured in the deep layer (under the gley horizon at 2·5 m depth), which suggests that the reducing potential of the anoxic horizon in the gley soils contributes to the reduction of nitrate. Nitrate concentrations were higher in the groundwater of the parcel rich in organic matter than in the one poorer in organic matter. Phosphate (PO₄‐P) concentrations in both shallow and deep groundwater are less than 62 to 76% of those found in surface water which can be related to the retention capacity of the clay colloids of these soils. Moreover, the temporal variations in nutrient concentrations in groundwater are directly related to variations in groundwater level during an annual hydrological cycle. Our results suggest that variations in groundwater level regulate spatio‐temporal variations in nutrient concentrations in groundwater as a result of the oxidation–reduction status of soil, which creates favourable or unfavourable conditions for nutrient bioavailability. The hydrological variations are much more important than those concerning substrate and type of vegetation. Copyright © 1999 John Wiley & Sons, Ltd.     

Modelling the time-varying extent of groundwater seepage on tidal beaches

The outcrop of groundwater on tidal beaches distinguishes an upper unsaturated region from a lower saturated region of the intertidal profile. Since the 1940s, it has been recognized that the extent of groundwater seepage at the beach face is one factor determining the tendency for erosive or accretionary conditions to prevail. As a primary step towards incorporating bed saturation characteristics within cross-shore sediment transport models, this paper (and accompanying program disk) details a simple model to simulate the time-varying extent of seepage face development across tidal beaches. From a comparison with field results obtained on the macrotidal Central Queensland (Australia) coast, the model appears to provide an encouraging degree of predictive capability. The model also assists in highlighting the sensitivity of seepage face development to varying beach face, tide and wave characteristics.     

饱和土中孔列对平面快纵波的隔离效应

在Biot饱和土波动理论的基础上,用单排孔列作为屏障,对全空间饱和土中人射平面快纵波进行了隔离分析.采用波函数展开法,将人射波和散射波的势函数展开成Fourier-Bessel函数的无穷级数的形式,利用一组可以求解多散射问题的圆柱坐标系统和界面处位移连续的条件,得到问题的理论解.对影响隔离效果的孔间距和饱和土的渗透性等...