Introduction
Many small coral islands exist in the Arabian Sea off the w estern coast of India. Inhabitants of these islands mostly depend upon groundw ater to meet their needs for drinking purposes. With increase in the population and developmental activities，the demand for freshw ater has also been grow ing. How ever，the fresh w ater aquifer in a small island is，generally，a fragile system occurring as a thin lens floating over saline w ater. Unregulated exploitation of groundw ater in such conditions w ould cause an irreversible deterioration of the chemical quality of groundw ater due to upconing of seaw ater. A comprehensive scheme of groundw ater exploitation consistent w ith natural constraints existing in such islands must be developed.
Figure 4. 5. 1 Location map of Kavaratti island ( Lakshadw eep)
Kavaratti is the island capital of a group of 36 coral islands called Lakshadweep( Figure 4. 5. 1) . The island is 1. 4 km w ide and 5. 5 km long. Additional groundw ater pumping from specially designed w ells fitted w ith radial pipes w as planned in order to establish a w ater supply scheme to meet drinking w ater requirements on the island. Before implementing this scheme，the impact of additional pumpage of groundw ater from these w ells must be quantified. For this purpose，a model w as prepared of vertical cross section along DD' ( Figure 4. 5. 1) . This model provided the safe rate of groundw ater pumping in order to limit the salinity at the w ater table to below 1000 mg / L or 2. 5% of seaw ater.
Hydrogeological Setting
Jacob and Madhavan Pillai in 1983，Jacob and others in 1987，and Varma and others in 1989 described salient hydrogeological conditions on the island. Coral sands，corals，and coral limestone are the main w ater-bearing formations. A w ide lagoon exists on the w estern side of the island w here hard limestone forms a ridge. Exposures of hard coral limestones occur along the beaches. The topography of the island is undulating and the elevation above the mean sea level ( m. s. l. ) ranges from a few centimeters to about 6 m. The average annual rainfall is 1500 mm and occurs mostly during June to September. Minimal drainage systems and surface w ater storage exist on the island.
Despite a high rate of percolation through very permeable coral sands，the net storage of fresh groundwater is meagre because a large percentage of the recharge flows out to sea as subsurface run-off. Several shallow open wells tap this scanty freshwater resource. The diameter of these wells varies from 1 m to about 6 m and the depth from less than 1 m to about 5 m near the coast. The depth to the water table ranges from 0. 5 m to about 4 m below land surface.
Data from the electrical conductivity ( EC) of groundw ater indicate that the salinity of the fresh w ater zone has been progressively increasing over the last decade. Also，instead of a sharp fresh w ater-sea w ater interface，a transitional saline zone exists，created by mixing w ith the underlying saline w ater caused by the pumping of groundw ater as w ell as sea tides. The consequence has been a progressive thinning of the fresh groundw ater zone.
Fluctuation of Water Table and Sea Level
The height of the w ater table above the sea level has a significant bearing on the movement of saline w ater into the fresh w ater zone. The w ater table and sea level w ere continuously monitored for 3 w eeks during January 1995 ( Figure 4. 5. 2) . Sea level w as monitored w ithin a specially designed structure to avoid the interference due to sea w aves.
The w ater table fluctuation in all the observation w ells w as correlated w ith sea tides and the magnitude of this fluctuation in the w ells is almost independent of the w ells' distance from the seashore. This implies that the influence of sea tides on the w ater table is primarily transmitted vertically except near the seashore w here the lateral flow may also be appreciable.
The w ater table does not evince any long-term variation. This is corroborated by the hydrographs for several w ells in the island. Examples are w ells No. 2 and No. 5 along section DD' monitored over a period of 5 years ( Figure 4. 5. 3) . See also w ater table data for the years 1987 and 1995 for several observation w ells given in Table 4. 5. 1.
Figure 4. 5. 2 Variation of w ater table ( at w ell No. 9) and sea level
Figure 4. 5. 3 Water table fluctuation ( w ith reference to mean sea level)
Table 4. 5. 1 Height of water table ( in m) above mean sea level during 1987 and 1995
* A negative sign implies lowering of the water table in 1995 compared to that in 1987.
Hydrogeological Parameters
Hydrogeological parameters w ere estimated by pumping tests on four selected w ells in the coral sand aquifer ( Figure 4. 5. 1) . The duration of pumping tests w as kept short to ensure that during the pumping test the effect of tidal fluctuation on hydraulic heads remained insignificant. The w ater table w as monitored at regular intervals during both pumping and recovery phases. Typical time draw dow n and recovery curves for pumping tests at tw o locations are illustrated in Figure 4. 5. 4. The details of the pumping tests are given in Table 4. 5. 2.
Figure 4. 5. 4 Time draw dow n and recovery curves for pumping tests
Table 4. 5. 2 Particulars of pumping test
Pumping test data w ere interpreted using a numerical method w herein the follow ing field conditions w ere taken into account:
1) During the initial phase of pumping，a substantial quantity of w ater is draw n from the w ell storage.
2) Wells are partially penetrating and hence the upw ard flow of groundw ater through the w ell-bottom is also appreciable.
3) The inflow into the w ell from the aquifer is caused by the decline of the w ater table as w ell as variation in fluid density w ith depth.
Groundwater Modeling
A 2-D vertical cross-section model w as constructed to simulate the hydraulic conditions and movement of the saline w ater into the fresh w ater zone. Physical Framework
The physical framew ork of the aquifer conforms to the geology as described for similar islands by Oberdorfer and others in 1990，Underw ood and others in 1992，and Griggs and Peterson in 1993. Hydrogeological information given by Jacob and others in 1987 w as also used. The top layer of coral sands reaches a depth of 8 m in the central region. This layer is underlain by carbonate rocks w hich may extend to the basaltic basement. The permeability of limestone formation near the shore w as assumed to be low.
The follow ing numerical values of the various characteristic parameters of the model w ere adopted ( Table 4. 5. 3) :
Table 4. 5. 3 Numerical values of the various characteristic parameters of the model
Boundary Conditions
All points on the vertical lines representing the island-sea boundary w ere assigned a hydrostatic pressure exerted by the column of seaw ater above that point. The fluctuation of this pressure w ith tides w as approximated by a triangular w ave function having a periodicity of 24 h and an amplitude of 0. 9 m. The solute concentration at all the nodes along the island-sea boundary w as taken to be the same as seaw ater，i. e. ，0. 0357 kg salt per kg seaw ater. The bottom of the aquifer w as considered as a no-flow boundary w hich may be an impermeable basaltic formation.
The w ater table constituted the upper boundary of the model，w hich receives natural recharge mainly during the rainy season from June to September. Different values of recharge w ere assigned to each element along the modeled section depending upon the vertical permeability for that element. Similarly，groundw ater extraction assigned to each element at the upper boundary w as varied based on the available data. Mathematical Formulation and Numerical Solution
Mathematical equations describing density-dependent flow and solute transport in the aquifer may be expressed as:
地下水科学专业英语
and
地下水科学专业英语
w here v is average fluid velocity，φ is porosity of rock matrix，k is permeability of the rock matrix，μ is fluid viscosity， p is fluid pressure， ρ is fluid density， g is gravitational acceleration，Qpis fluid mass source，c is solute concentration of fluid， C*is solute concentration of fluid source，D is dispersion tensor，I is identity tensor，and Dmis apparent molecular diffusivity.
Equation ( 4. 5. 1a) and Equation ( 4. 5. 1b) are based on the conservation of fluid mass， and the Equation ( 4. 5. 1c) also takes into account the solute mass balance. The computer softw are SUTRA w as used to solve these equations for a vertical 2 － D model. Suitable modifications w ere made to the computer code to incorporate the effect of tidal phenomenon， variable recharge in time，and w ater table conditions.
The vertical section along DD' w as divided into 24 × 42 nodes ( Figure 4. 5. 5) . Since the salinity variation near the surface needed to be estimated accurately a close nodal spacing of 0. 2 m w as taken to a depth of 3 m. How ever，for the zone from 3 m to 10 m it w as kept as 0. 5 m，and a still coarser nodal grid w as used for zones deeper than 10 m.
Figure 4. 5. 5 Nodal grid for groundw ater modeling
Various input parameters used in the model w ere progressively，but slow ly，modified until a reasonable match betw een the computed and observed values of ① w ater table above the average sea level，② salinity of groundw ater at the w ater table，and ③ tidal efficiency w ere obtained. Table 4. 5. 4 gives computed and observed values of the w ater table and salinity. Figure 4. 5. 6 show s the final input parameters of the model ( KH，KVis horizontal and vertical coefficient of permeability，respectively) .
Table 4. 5. 4 Average water table and salinity observed and computed ( field and model) values
Figure 4. 5. 6 Final input parameters for groundw ater modeling
Figure 4. 5. 7 Computed increase in salinity at the w ater table for different rates of pumping from w ater supply w ell
Results
The calibrated model was used to prognose the increase in the salinity of groundwater due to additional pumping at different rates from a new well at point A ( Figure 4. 5. 1) . Figure 4. 5. 7 depicts，from a number of prognostic runs，an increase in groundwater salinity with time for six pumping rates of 50000 L / d， 30000 L / d， 15000 L / d，13000 L / d，10000 L / d and 8000 L / d at this point. The total groundw ater pumpage in each case w as distributed over three periods each day. It can be seen that if the pumping from the w ell is less than 13000 L / d， the salinity of groundw ater stabilizes below 2. 5% that of seaw ater. This amount of groundw ater salinity is w ithin the permissible limits for drinking purposes. The salinity profile along the vertical section after 5 years of additional pumping of 13000 L / d is show n in Figure 4. 5. 8. The effect of additional groundw ater pumpage in the form of increased groundw ater salinity is felt in an area of 200-m radius. It is， therefore， imperative that in order to maintain an acceptable w ater quality， pumping from a single w ell in this situation should not exceed 13000 L / d and the distance betw een tw o w ells should be at least more than 400 m.
Figure 4. 5. 8 Change in salinity along vertical section DD’due to additional groundwater pumpage at point A
Some other measures to augment w ater supply on a small island may include rainw ater harvesting and reduction of the outflow to the sea. The techniques for rainw ater harvesting are w ell know n and are being used on the island. The outflow to the sea may be reduced if the transmissivity along the shore could be decreased. On an island w ith meagre resources，this can be conveniently achieved by drilling three row s of closely spaced 5 － cm － diameter shallow boreholes to a depth of 8 m to 10 m ( Figure 4. 5. 9a) . The boreholes may be grouted by a mixture of clay and cement. The existing 2 － D model w as used to prognose the rise in the w ater table as a result of this measure. It was seen that if the permeability of all the coastal elements ( to a depth of 8 m) is reduced from 250 m / d to 40 m / d， the w ater table w ill rise by 6 cm after 5 years ( Figure 4. 5. 9b) even after an additional pumping of 13000 L / d at the point A ( Figure 4. 5. 1) . A reduction of transmissivity all along the coast w ill，thus，help an appreciable buildup of the w ater table in the island.
Figure 4. 5. 9 ( a) Three row s of boreholes to reduce transmissivity along coast. ( b) Rise in w ater table at point A in the island after construction of a subsurface dam
Acknowledgements The work was carried out with partial support from PWD，Kavaratti ( Lakshadweep) . The Director of NGRI has kindly permitted publication of the paper. Dr. Clifford I. Voss provided very useful inputs in modeling as did Mr. Gurunadha Rao V. V. S. and Mr. Yudhaveer K. ，scientists at NGRI. Officials of PWD，Kavaratti，provided support in the field investigations. Mr. Babu G. R. ，Mr. Chandrakumar C. and Mr. Gabriel J. assisted in the preparation of the manuscript. The authors are grateful to all of them.
Words
地下水科学专业英语