An Analytical Study And Application Of Groundwater Head Fluctuation With Dual Tide In An Island Aquifer

Island resource is one of the most important parts in the nature wealth which has a great impact on the development of society both in the developing and developed countries. Its key status is irreplaceable. The coastal environmental degradation, seawater intrusion, the frequent disaters and the other similar problems are emerging endlessly with the social and economic development in coastal areas and worsening the frangibile island ecology. In order to understand and solve these problems and to make sustainable use of the island resource, the coastal hydrogeological conditions need to be identified including the aquifer parameters and the interaction processes between groundwater and seawater. The traditional and standard methods for identifying coastal hydrogeological conditions, such as pumping test or slug-test data analysis, numerical modeling, Guelph permeameter test and floodwave-response technique, are well-documented in many text books. However, some of them are expensive and the others are very site-specific. Pumping-test, for example, is very popular and is deemed as the standard method to date, but it is very costly, time-consuming and not always advisable for coastal aquifer systems. In addition, it may cause seawater intrusion and/or aggravate intrusion problems, and the conventional analysis of pumping-test data is cumbersome and difficult due to the complex interations between seawater and groundwater.Ocean tides are a high-frequency natural forcing which induces the periodical fluctuation of the groundwater head in coastal aquifers. This nature phenomenon provides us a kind of convenient, economic, and reliable method, namely tidal effect method, which may be used to figure out the coastal hydraulic parameters in large scale via the analysis of the tidal effect data from observation wells in coastal areas.Islands are bounded by seawater around them. This special geological situation makes the fresh groundwater in islands particularly precious. The groundwater fluctuation in the island aquifer will be influenced by the tides from all directions. Understanding of the groundwater movement will ensure its proper utilization.This paper presents an analytical solution and an application of groundwater head response to dual-tide fluctuation in a transect of an island leaky aquifer system. The main contents and results of the study are as follows. 1. The conceptual and methmetical models for the island leaky aquifer system were given.The model considered comprises a confined aquifer and. its overlying semipermeableconfining layer. Both layers terminate at the coastallines on two sides of the island. The dual-tide fluctuation in the transect of the island and the semipermeable layer's leakage are taken into account. Tide-induced water table fluctuations in the semipermeable layer, the elastic storages of the semipermeable layer and the density difference between the fresh water and the seawater are neglected.2. An analytical solution to describe the tide-induced groundwater head fluctuation in the leaky confined aquifer system was derived.Based on above-mentioned assumptions, a mathematical model is setup to consider the dual-tide fluctuation and the leakage effect. The analytical solution was derived using the theories of Fourier transform and complex variable functions. For aquifers with infinite length, or/and with impermeable roof, existing solutions in the literature are obtained, indicating that the solutions by many previous researchers are the special cases of our new solution.3. Threshold value of the island aquifer length was discussed.The groundwater head fluctuates in the island aquifer was influenced by the tides from both sides of the transect. With the increasing of the aquifer's length, the groundwater head was less affected by the tides. This paper made a quantitative study about this phenomenon, and a formula of the threshold value of the aquifer's length was found to be less than 5 km for typical coastal aquifer systems. For an aquifer with its length greater than this threshold, it can be regarded as an aquifer influenced from only one tide, although the groundwater in the island is connected to the tidal seawater on both sides of the transect.4. The boundary conditions on both sides of the island transect are discussed.For an aquifer with two different opposite tidal boundary conditions, the island has an asymmetrical boundary condition. The change of the amplitude of groundwater head at the middle line of the aquifer with the phase shift difference was discussed when the amplitudes from the two opposite tide are the same, whereas the phase shifts are different. When the two tides from the opposite side of the island are totally the same, the island has a symmetrical boundary. In this case, the middle line of the island aquifer can be regarded as an unpermeable boundary.5. The impact of the parameters on the groundwater fluctuation was analyzed.The impact of the dual-tide on the groundwater head fluctuation decreases as the distance from the considered point in the aquifer to the nearest boundary increases. So at the middle line of the aquifer (the points have an equal distance to the two boundaries), the influence of the dual-tide on the groundwater head is minimum. The influences of the dimensionless length of the aquifer aL and semipermeable layer's leakage u on the groundwater head fluctuation in middle line of the island were discussed. The analyses show that the dimensionless length aL has a decreasing effect on the groundwater head, and the phase shift is non-negative (time-lag) and increases with aL for any fixed u; the leakage has a decreasing effect on the groundwater head fluctuation and the phase shift, i.e. the large lekage may result in very small time lag in the island aquifers near the coastline, which is meaningful when analysing the observed "propagation bias"at the coastal area.6. A case study was conducted in Garden Island in Western Australia.The new analytical solution was used to analyze the observed tidal amplitudes and time lags in the eight wells during 57 days with the least-squres method. The aquifer parameters such as diffusion and leakage were obtained, the "propagation bias" reported by Trefry and Bekele [2004] was well explained by the new solution.In summary, this paper considered an island aquifer system and derived a new analytical solution. The solution agreed well with the observations in eight piezometes in Garden Island reported by Trefry and Bekele [2004] . Finally, some shortages were discussed in point of this model and case study.