Storage in confined aquifer: Spectral analysis of groundwater in responses to Earth tides and barometric effect

Dilatation of aquifer and associated water level fluctuation in groundwater well is known to be driven periodically from lunar, solar, or other tidal forces. Time‐dependent variables in groundwater system, such as water level, can be converted to power spectra in the frequency domain using Fourier transform to evaluate significant fluctuation. The major innovation of this research is to develop spectral representation in frequency domain for the groundwater system that the storage in confined aquifer can be determined considering dilatation affected by Earth tides and barometric effect. In order to verify applicability of the evolved method, time series of Earth tides and barograph are collected; aquifer storage is then determined inversely by selecting significant semidiurnal and diurnal components in spectra computation. It suggests that to discover groundwater storage using groundwater level with barograph and tidal potential of Earth in frequency domain becomes accessible and feasible.     

深井水位的固体潮效应

本文从体应变固体潮对深井水位影响的偏微分方程出发,考虑到含水层和井孔之间相互渗流的边界条件,用叠加原理、冲量定理和分离变量法等方法得出了方程的解.通过对这个解中水井含水层参数给予一些可能的值进行数值计算,讨论了水井固体潮系数和位相滞后与水井含水层参数间的关系,较好地解释了井水位对固体潮响应的位相滞后现象.计算表明,井孔的半径、含水层的孔隙度及固体骨架的体压缩系数愈大,含水的导水系数愈小,则水井水位的固体潮系数愈小,而水位对固体潮响应的位相滞后愈大.井水对长周期的潮汐响应比对短周期的更好.      

Closed-form analytical solutions incorporating pumping and tidal effects in various coastal aquifer systems

Pumping wells are common in coastal aquifers affected by tides. Here we present analytical solutions of groundwater table or head variations during a constant rate pumping from a single, fully-penetrating well in coastal aquifer systems comprising an unconfined aquifer, a confined aquifer and semi-permeable layer between them. The unconfined aquifer terminates at the coastline (or river bank) and the other two layers extend under tidal water (sea or tidal river) for a certain distance L. Analytical solutions are derived for 11 reasonable combinations of different situations of the L-value (zero, finite, and infinite), of the middle layer’s permeability (semi-permeable and impermeable), of the boundary condition at the aquifer’s submarine terminal (Dirichlet describing direct connection with seawater and no-flow describing the existence of an impermeable capping), and of the tidal water body (sea and tidal river). Solutions are discussed with application examples in fitting field observations and parameter estimations.     

深井水位固体潮的调和分析结果

使用Venedikov调和分析方法,对8口深井各一年或两年经气压改正后的水位记录,计算了水位固体潮相对于体应变固体潮的振幅比和相位差。本文从相位差的分析结果求解了含水层的渗透率,分析结果还显示出液态地核动力学效应引起的固体潮日波振幅比的共振现象。这是对以往其它观测手段得到的相应结果的支持,同时也说明了深井水位资料中含有非常丰富的地球物理信息。文中还对环境因素和井孔条件造成的某些效应做了探讨。     

Groundwater dynamics of Fongafale Islet, Funafuti Atoll, Tuvalu

Geoelectric and hydrologic surveys during spring tides revealed the spatiotemporal distribution of groundwater quality produced by tidal forcing in Fongafale Islet, Funafuti Atoll, Tuvalu. The observed low resistivity showed that saline water largely immersed the surficial Holocene aquifer, indicating that there is no thick freshwater lens in Fongafale Islet, unlike in other atoll islands of comparable size. Half of the islet was constructed by reclaiming the original swamp with porous, highly permeable coral blocks; this reclaimed area should not be considered as part of the islet width for calculation of the expected thickness of the freshwater lens. The degree of aquifer salinization depends on the topographic characteristics and the hydrologic controls on the inland propagation of the tidal forcing. Large changes in bulk resistivity and the electrical conductivity of groundwater from wells indicate that periodic salinization in phase with the semidiurnal tides was occurring widely, especially in areas at lower elevation than the high-tide level and in reclaimed areas with high permeability. Thin sheets of nearly fresh and brackish water were observed in the surficial aquifer in areas above the high-tide level and in taro swamps, respectively. The thinness of the brackish and freshwater sheets suggests that the taro swamps and the fresh groundwater resources of the islet are highly vulnerable to salinization from anticipated sea-level rise. An understanding of the inherent geologic and topographic features of an atoll is necessary to evaluate the groundwater resources of the atoll and assess the vulnerability of its water resources to climate change.     

A two-dimensional analytical solution of groundwater responses to tidal loading in an estuary and ocean

Previous studies on tidal dynamics of coastal aquifers have focussed on the inland propagation of oceanic tides in the cross-shore direction, a configuration that is essentially one-dimensional. Aquifers at natural coasts can also be influenced by tidal waves in nearby estuaries, resulting in a more complex behaviour of head fluctuations in the aquifers. We present an analytical solution to the two-dimensional depth-averaged groundwater flow equation for a semi-infinite aquifer subject to oscillating head conditions at the boundaries. The solution describes the tidal dynamics of a coastal aquifer that is adjacent to a cross-shore estuary. Both the effects of oceanic and estuarine tides on the aquifer are included in the solution. The analytical prediction of the head fluctuations is verified by comparison with numerical solutions computed using a standard finite-difference method. An essential feature of the present analytical solution is the interaction between the cross- and along-shore tidal waves in the aquifer area near the estuary’s entry. As the distance from the estuary or coastline increases, the wave interaction is weakened and the aquifer response is reduced, respectively, to the one-dimensional solution for oceanic tides or the solution of Sun (Sun H. A two-dimensional analytical solution of groundwater response to tidal loading in an estuary, Water Resour Res 1997;33:1429–35) for two-dimensional non-interacting tidal waves.     

A semi‐analytical solution for groundwater responses to stream‐stage variations and tidal fluctuations in a coastal aquifer

A two‐dimensional semi‐analytical solution to analyse stream–aquifer interactions in a coastal aquifer where groundwater level responds to tidal effects is presented. The conceptual model considered is a two‐dimensional subsurface system with stream and coastline boundaries at right angles. The dimensional and non‐dimensional boundary value problems were solved for water level in the aquifer by successive application of Laplace and Fourier transform techniques, and the results were obtained by numerical inversion of the transformed solution. The solution was then verified by reducing the solutions to one‐dimensional known problems and comparing the results with those from previous studies. Hypothetical examples were used to examine the characteristics of water‐level variations due to the variations in stream stage and the fluctuations in tide level. Sensitivity analysis indicated that streambed leakance has no influence over the amplitude of groundwater fluctuations, but that the effect of stream stage increases with increasing leakance. Little difference was observed in the water level for different aquifer penetration ratios with narrow stream width. Increases in streambed leakance caused increases in the effect of aquifer penetration by the stream on the water level. An increased specific yield value resulted in decreased amplitude of water fluctuations and mean water level, and showed that water‐level variations due to stream and tidal boundaries are sensitive to specific yield. Copyright © 2006 John Wiley & Sons, Ltd.     

垂向和径向排水的潮汐水位振幅和位相变化研究

本文根据岩石力学和地下水动力学理论, 分析了潮汐力作用下含水层与隔水层之间垂向水流交换过程, 并提出了垂向排水条件下含水层潮汐孔压-引潮高振幅比和位相差公式。 结合Hsieh等关于潮汐力作用下井水位对含水层孔压(体应变)的振幅比和位相差响应公式, 进一步推导了垂向和径向水流条件下井水位-引潮高的振幅比和位相差公式。 在径向和垂向排水条件下, 应用M2和O1波潮汐水位-引潮高振幅比和位相差的数值关系, 可以识别影响潮汐水位振幅和位相的主要因素。     

Effect of earth tide on deep well water level

On the basis of the partial differential equations of the water level in a deep well that is affected by the bulk strain tide, the boundary conditions of permeating each other between aquifer and well are considered. The solutions of the equations have been obtained by the superposition principle, inpulse theorem and separation of the variations. Some suitable values are given to the parameters of well aquifer in the solutions. By means of the numerical calculation the relations among the well tide coefficients and phase lag phenomenon of response of the well level to earth tides is well interpreted. The parametric studies and the obtained graphs show that the more the radius of casing in a well, the porosity of an aquifer and the bulk compressibility for solid matrix of an aquifer, the less the transmissibility of an aquifer, then the less the tidal coefficient of well level, while the more the phase lag for well level to respond to the tide is. The response of the well level to the tide of longer period is better than the shorter period events. The Chinese version of this paper appeared in the Chinese edition ofActa Seismologica Sinica,13, 66–75, 1991.     

潮汐水位振幅和位相变化研究及其在地下水异常分析中的应用

将多孔介质中井-含水层-隔水层的潮汐水位振幅和位相的计算公式推广到裂隙饱水岩体潮汐分析中, 分析了裂隙含水层中井与裂隙, 裂隙与微裂隙的潮汐孔压响应原理和水流交换过程, 提取了影响裂隙含水层潮汐水位振幅和位相的主要因素, 应用井-裂隙排水产生的井水位-引潮高的振幅比A和位相差α₂主要随径向等效导水系数T同向变化, 裂隙和微裂隙(孔隙)排水产生的孔压-引潮高的振幅比D和位相差α₁主要随不排水条件下微裂隙与裂隙间振幅比E'/E反向变化的规律, 提出了潮汐井水位振幅和位相的8种不同变化类型, 分析了不同类型所反映的含水层形变, 并用于分析东川、 弥勒和西昌川03等3口井井水位振幅和位相变化的成因.      

承压井水位对地表水潮汐的响应

本文以地表水潮汐影响承压井水位的偏微分方程为基础,考虑到井孔和含水层之间相互渗流的边界条件,得出方程的解。通过对解中水井含水层参数给予一些可能的值进行数值计算,绘出了承压井水位地表潮汐荷载效率与位相滞后曲线,讨论了这个效率和位相滞后水井含水层参数之间的关系。认为这个效率主要取决于含水层的孔隙度和固体骨架压缩系数;孔隙度愈小,压缩系数愈大,则效率也愈大。而位相滞后主要取决于含水层的渗透系数和厚度;这两个参数越大,则位相滞后越小。 本文还介绍了上海地区地下水位与地表水潮汐的观测结果。把这些观测结果和本文理论结果比较分析,两者符合得较好。     

Spectral responses of water level in tidal river and groundwater

The water level of five river stages and seven groundwater wells in the Taipei Basin were analysed by spectral analysis in the frequency domain. The diurnal, semi‐diurnal and quarter‐diurnal tidal components of the Tanshui River appear to relate closely to astronomical tides as K₁, M₂ and M₄, respectively. It is also found that the diurnal component reveals a reversed phase angle in the middle section of the Tanshui River; the phase of the quarter‐diurnal component is also found to be reversed at stations upstream in the Tanshui River and Hsintien Stream. It is believed that these phenomena could be caused by local variation in the river channel topography. The autospectrum and cross‐spectrum between groundwater elevation and nearby river stage were observed to correlate highly with the frequency of the astronomical tides K₁, M₂ and M₄. From the study of the phase shift and time lag of water level fluctuations at river stages and groundwater wells, it was found that the tidal effects of diurnal, semi‐diurnal, and quarter‐diurnal components were significantly different. The relationships between phase and the fluctuated range of atmospheric pressure and water level imply that change in atmospheric pressure does not affect water level fluctuation in the river stage and groundwater well. Copyright © 1999 John Wiley & Sons, Ltd.     

深井水位对固体潮和气压的响应

本文以体应变固体潮对深井水位影响的偏微分方程为基础，考虑到含水层与井孔之间相互渗流的边界条件，用叠加原理、冲量定理的分离变量等方法得出了方程的解。把水井含水层的参量给予一些可能的值，通过数值计算讨论了水井固体潮系数、位相滞后和含水层参数之间的关系，解释了井水位对固体潮响应的位相滞后现象。结果表明，井孔的半径、含水层的孔隙度及固体骨架的体压缩系数愈大，含水层的导水系数愈小，则水井水位的固体潮系数愈小     

鲁14井数字化水位潮汐响应特性初析

以井—含水层系统潮汐理论为基础,利用Baytap-G潮汐分析程序计算鲁14井数字化水位的潮汐响应特征参数,提取井水位潮汐因子和相位差,分析远场大震前后井水位潮汐响应特征参数的变化情况,同时对固体潮和气压影响量进行分离,以期深入了解井水位微动态变化特征,为该井水位观测资料的动态评价和效能评估提供参考。结果表明：鲁14井潮汐地下水流类型以径向流为主,潮汐因子和相位差变化相对稳定,但受远场大震影响显著,其含水层渗透性随潮汐参数的增大（减小）而增大（减小）;地震波作用可使含水层渗透性发生变化,但并非导致含水层渗透性变化的主要因素。     

Variations in turbulent kinetic energy at a point source submarine groundwater discharge in a reef lagoon

The influence of sea level variations due to tides and wave setup on turbulent kinetic energy (TKE) was observed at a point source submarine groundwater discharge in a fringing coral reef lagoon. Tidal and wave setup variations modulated speed, TKE, TKE dissipation, and water temperature and salinity at the buoyant jet. The primary driver of jet TKE and speed variations was tides, while wave setup was a minor contributor. An inverse relationship between surface elevation and TKE was explained with an exponential equation based on sea level variations. During low tides, peak jet speeds (up to 0.3 m s^?1) and TKE per unit mass (up to 0.4 m² s^?2) were observed. As high tide approached, the jet produced minimum TKE of ~0.003 m² s^?2 and TKE dissipation ranged from 2 to 8×10^?4 m² s^?3. This demonstrated the sensitivity of the jet discharge to tides despite the small tidal range (<20 cm). Jet temperatures and salinities displayed semidiurnal oscillations with minimum salinity and temperature values during maximum discharge. Jet salinities increased throughout low tides while temperatures decreased. This pattern suggested the jet conduit was connected to a stratified cavity within the aquifer containing cool fresh water over cool salty water. As low tides progressed, jet outflow increased in salinity because of the mixing within the conduit, while lower jet temperatures suggested water coming from further or deeper in the aquifer. The presence of such a cavity has been recently confirmed by divers.     

Tide‐induced groundwater head fluctuation in a coastal aquifer system with a submarine outcrop covered by a thin silt layer

We present an analytical solution of groundwater head response to tidal fluctuation in a coastal multilayered aquifer system consisting of an unconfined aquifer, a leaky confined aquifer and a semi‐permeable layer between them. The submarine outcrop of the confined aquifer is covered by a thin silt layer. A mathematical model and the analytical solution of this model are given. The silt layer reduces the amplitude of the hydraulic head fluctuation by a constant factor, and shifts the phase by a positive constant (time lag), both of which depend on the leakances of the silt layer and the semi‐permeable layer. The time lag is less than 1·5 h and 3·0 h for semi‐diurnal and diurnal sea tides respectively. When the leakance of the semi‐permeable layer or the silt layer assumes certain special values, the solution becomes the existing solutions derived by previous researchers. The amplitude of the hydraulic head fluctuation in the confined aquifer increases with the leakance of the silt layer and decreases with the leakance of the semi‐permeable layer, whereas the phase shift of the fluctuation decreases with both of them. A hypothetical example shows that neglecting the silt layer may result in significant parameter estimation discrepancy between the amplitude attenuation and the time‐lag fittings. Copyright © 2007 John Wiley & Sons, Ltd.     

A simple approach to adjust tidal forcing in fjord models

To model currents in a fjord accurate tidal forcing is of extreme importance. Due to complex topography with narrow and shallow straits, the tides in the innermost parts of a fjord are both shifted in phase and altered in amplitude compared to the tides in the open water outside the fjord. Commonly, coastal tide information extracted from global or regional models is used on the boundary of the fjord model. Since tides vary over short distances in shallower waters close to the coast, the global and regional tidal forcings are usually too coarse to achieve sufficiently accurate tides in fjords. We present a straightforward method to remedy this problem by simply adjusting the tides to fit the observed tides at the entrance of the fjord. To evaluate the method, we present results from the Oslofjord, Norway. A model for the fjord is first run using raw tidal forcing on its open boundary. By comparing modelled and observed time series of water level at a tidal gauge station close to the open boundary of the model, a factor for the amplitude and a shift in phase are computed. The amplitude factor and the phase shift are then applied to produce adjusted tidal forcing at the open boundary. Next, we rerun the fjord model using the adjusted tidal forcing. The results from the two runs are then compared to independent observations inside the fjord in terms of amplitude and phases of the various tidal components, the total tidal water level, and the depth integrated tidal currents. The results show improvements in the modelled tides in both the outer, and more importantly, the inner parts of the fjord.     

Preliminary Observation of Complex Salt‐Fresh Water Mixing in a Beach Aquifer

Continuous observations of beach groundwater salinity over a 35‐d period from a monitoring well established in the intertidal zone of a coastal harbor provided intriguing data on the interaction in the intertidal zone between the salt and fresh groundwater. During the monitoring period of the study, both semidiurnal variations and longer temporal trends in groundwater salinity were observed. The semidiurnal salinity variations were observed to occur nearly synchronously, but inconsistently with the tides. However, the salinity relationship with the tides was more complex, switching back and forth from being in‐sync (higher salinities at high tide) to out‐of‐sync (higher salinities at low tide) a total of four times during the 35‐d test period. The longer temporal trends showed chloride concentration (representing salinity) varying from as low as 50 mg/L to as high as 3600 mg/L over a period of between 9 to 12 d. The observations from the monitoring well reveal a complex pattern likely resulting from a combination of tidal pumping, density‐induced convection, and changes in the terrestrial hydraulic gradient. However, these observations are based upon data from only one monitoring well, and are speculative at this point. A more thorough study of the complex fresh water‐saline water relationship in the intertidal zone seems to have merit.     

Large seasonal changes in the recharge of seawater in a subterranean estuary revealed by a radon tracer

Activities of radon (²²²Rn) in groundwater were continuously monitored in a saline aquifer from September 2010 to July 2011. The activities of ²²²Rn ranged from 200 to 4300 Bq m^?3, with a large seasonal variation. Because the activity of ²²²Rn in seawater is low, ²²²Rn in saline groundwater must be produced in the aquifer from radium (²²⁶Ra) in rocks and sediments. The ²²²Rn activities were higher in the warm‐dry seasons (September–November 2010 and April–May 2011) when the saline aquifer was stable. In contrast, the lowest ²²²Rn activities were observed in the cold‐dry season (December 2010 and January–March 2011), because of the effective exchange between groundwater and seawater. In addition, sudden decreases of ²²²Rn activities coincided with episodic drops in groundwater temperatures. These results reveal that lower seawater temperature in winter may result in density‐driven seawater intrusion. During the wet season (June–July 2011), ²²²Rn activities were more clearly affected by semi‐monthly and diurnal tidal pumping, showing higher ²²²Rn activities during low and spring tides. Such a tidal effect was not clearly observed during the warm‐dry and cold‐dry seasons. This result implies that the residence time of SGD in coastal zones is significantly affected by seasonal changes in driving forces such as tidal pumping and seawater intrusion. Copyright © 2016 John Wiley & Sons, Ltd.     

Surface water–groundwater exchange dynamics in a tidal freshwater zone

In coastal rivers, tides can propagate for tens to hundreds of kilometres inland beyond the saltwater line. Yet the influence of tides on river–aquifer connectivity and solute transport in tidal freshwater zones (TFZs) is largely unknown. We estimate that along the TFZ of White Clay Creek (Delaware, USA), 11% of river water exchanges through tidal bank storage zones. Additional hyporheic processes such as flow through bedforms likely contribute even more exchange. The turnover length associated with tidal bank storage is 150 km, on the order of turnover lengths for all hyporheic exchange processes in non‐tidal rivers of similar size. Based on measurements at a transect of piezometers located 17 km from the coast, tides exchange 0.36 m³ of water across the banks and 0.86 m³ across the bed per unit river length. Exchange fluxes range from ?1.66 to 2.26 m day^?1 across the bank and ?0.84 to 1.88 m day^?1 across the bed. During rising tide, river water infiltrates into the riparian aquifer, and the downstream transport rate in the channel is low. During falling tide, stored groundwater is released to the river, and the downstream transport rate in the channel increases. Tidal bank storage zones may remove nutrients or other contaminants from river water and attenuate nutrient loads to coasts. Alternating expansion and contraction of aerobic zones in the riparian aquifer likely influence contaminant removal along flow paths. A clear need exists to understand contaminant removal and other ecosystem services in TFZs and adopt best management practices to promote these ecosystem services. Copyright © 2015 John Wiley & Sons, Ltd.