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<Sourcebook of Alternative Technologies for Freshwater Augumentation
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Annex 4

Groundwater Assesment Technologies


This section provides an overview of some techniques that have been found useful in assessing the extent and sustainable yield of freshwater lenses on small coral islands. More detailed discussion of this topic is available in Dale et al. (1986) and UNESCO (1991).

To estimate the sustainable yield of a freshwater lens it is necessary to know the extent (location, width, depth) and behaviour (response to external influences) of the lens; and, the rate of recharge to the lens. These parameters provide information about the storage characteristics of the groundwater and the input (from rainfall) to the groundwater. There are a number of techniques which can be used to assess the location and size of freshwater lenses. Some are relatively inexpensive methods and can be used for preliminary reconnaissance, while more intensive (and expensive) methods are suited to more detailed investigations and for ongoing monitoring.

Preliminary Methods

On low-lying coral atolls, an initial ground survey combined, where possible, with aerial photography will provide a reasonable idea of potential freshwater lens areas and areas where freshwater is unlikely to occur. The latter areas can be identified by signs of seawater inundation or by elevations that are close to the high tide level. Exposed water surfaces (e.g., wells and ponds) can also be identified by these means, and, if tested with an electrical conductivity (EC) meter, can form the basis of a surface-salinity map which will give a reasonable indication of the extent of a freshwater lens on a small island. In addition, measurements of water table movements can be useful in determining the mean height of the water table above mean sea level. These data are useful in setting the levels the mid-depth of the transition zone for infiltration gallery conduits and pumping facilities (they cannot be used to determine the thickness of the freshwater lens using the Ghyben-Herzberg ratio, approximately 40:1, as the sharp interface assumption of this model does not apply to small islands). Water table measurements taken close to pumping facilities can be used to identify the relative influences of natural phenomena on pumping regimes (e.g., the cyclical response to the tidal signal, hydrograph response to major recharge events, etc.). They can also be used to determine tidal efficiencies and lags within the freshwater lenses. Depending on availability of resources, either manual or automatic recordings can be made. The advent of relatively cheap electronic data loggers makes this an effective method of recording, particularly since the data is in digital format. Electronic data loggers have been successfully used in the Cocos (Keeling) Islands (Falkland, 1988) and more recently on Aitutaki in the Cook Islands (Falkland, 1995a).

In the absence of other data, the likely thickness of a freshwater lens can be estimated using empirical methods. Oberdorfer and Buddemeier (1988) developed a relationship between freshwater lens thickness (to mid-point of the transition zone), annual rainfall, and island width:

H/P = 6.94 log a B 14.38 (3)

H = depth from watertable to mid-point of transition zone (m);
P = annual rainfall (m); and
a = island width (m).

Equation (3) is based on observations from nine coral islands (atolls and raised limestone islands) and indicates that no permanent freshwater lens can occur regardless of rainfall where the island width is less than about 120 m. For instance, using the mean annual rainfall of 1 950 mm of the Cocos (Keeling) Islands, the minimum island width for a small freshwater lens (say 5 m thick) to occur is about 280 m. This prediction is in reasonable agreement with observed freshwater lenses. Nevertheless, it should be noted that other factors which are not accounted for in equation (3) may also have an effect on the occurrence of freshwater lenses (e.g., the permeability of the coral sediments, the density of vegetation, etc.). Recent salinity monitoring studies in the Cocos (Keeling) Islands (Falkland, 1992, 1995b) showed that a freshwater lens on West Island, with a thickness of 11 m to the mid-point of the transition zone, occurs in a location where the island is only 270 m wide. Thus, empirical relationships should be used only as a preliminary means of estimation. Further, given the availability of additional and more detailed data, the development of an updated equation should be considered. Should such a model be developed, it would be preferable to develop one for atolls and one for limestone islands, owing to major differences in permeability and, hence, freshwater lens thickness between the two island types.

More recently, Underwood et al. (1992) carried out modeling simulations using the SUTRA groundwater model (Voss, 1984) to derive diagrammatic relationships for atoll islands between freshwater lens thickness (depth from mean sea level), annual recharge, and island width (Figure 50). These relationships are more realistic, predicting thicker freshwater lenses for a given width and rate of recharge (assumed to be approximately 0.3 x rainfall) than equation (3), but should still be treated as preliminary estimates as they do not always match with observed behaviour.

Detailed Investigations

Geophysical methods (mainly, electrical resistivity (ER) and electromagnetics (EM)) are useful for providing relatively quick and cheap assessments of freshwater lens locations and thicknesses. However, the results from ER and EM surveys are subject to differing interpretations and require independent calibration to be used with confidence. This can best be provided by vertical salinity profiles obtained from appropriately drilled and constructed boreholes (see below). Combined with a drilling program, geophysical techniques offer a particularly suitable means of assessing freshwater lenses.

Figure 50

Figure 50. Relationship between island width and simulated depth of portable water at the centre of an atoll island for four steady recharge rates (after Underwood et al, 1992)

ER surveys are normally conducted, in conjunction with a drilling program, to assess freshwater lens locations and thicknesses on atolls and sand islands, including Tarawa (Jacobson and Taylor, 1981) and Kiritimati (Falkland; 1983a, 1983b, 1984); Pingelap, Federated States of Micronesia (Ayers and Vacher, 1986); the Cocos (Keeling) Islands (Falkland, 1988; 1992); and, Warraber and Yorke Islands in Torres Strait, Australia (Falkland, 1990). Careful site selection is required to avoid known metal cables and pipes, and to orient soundings parallel to the coastline to minimise violation of the horizontal layering principle on which the ER method is based (Mooney, 1980).

EM surveys (see Stewart, 1988) have been used successfully on Majuro Atoll, Marshall Islands (Kauahikaua, 1987); the atolls of Mwoakkilloa, Pingelap and Sapwuahfik of the Pohnpei State, Federated States of Micronesia (Anthony, 1992); and, the limestone islands of Tonga (Furness and Helu, 1993). In general, EM surveys are more rapid than ER surveys but provide less information. The choice of method is dependent on the availability of time and funds and the degree of accuracy required.

Freshwater lens thicknesses, based on salinity profiles, and ER soundings at borehole sites generally indicate close correlation. Exceptions are found in areas where buried objects are present or where freshwater lenses are relatively thin. For example, on Kiritimati Island, Kiribati, the correlation was not good where the lens was thinner than about 5 m. This was partly due to the relatively thick, unsaturated zone (typically about 2.5 m to 3 m) which tended to mask the freshwater zone (i.e., the principle of suppression; Mooney, 1980). In contrast, on South Keeling, where one lens was found to be relatively thin (maximum thickness of 8 m), the correlation was generally good for thicknesses less than 5 m. This was mainly due to a thin unsaturated zone, typically 1 m to 1.5 m thick, which reduced the suppression effect. Thus, an important feature of ER soundings is not to rely on any one result, but, rather, to build up an overall picture from the combined results since individual readings are susceptible to anomalies. The ratio of ER soundings to the total number of boreholes should be maximised to reduce the cost of a freshwater lens assessment programme, and have ranged from 4:1 on South Keeling Atoll (Home and West Islands), to 10:1 on Tarawa, Kiribati, to 16:1 on South Keeling Atoll (South Island), to 18:1 on Kiritimati Island, Kiribati. The combined results of ER soundings and salinity profiles, and, if available, surface conductivity measurements can be used to derive freshwater lens boundaries and contour plans of their thicknesses.

Seismic surveys have been used to analyse the subsurface geology of a number of atolls including Pingelap (Ayers and Vacher, 1986) and Nukuoro (Ayers, 1990), Micronesia; and, the Cocos (Keeling) Islands (Creighton, 1988). Depths to water table and the unconformity between the upper and lower sediments can be determined by such surveys. However, they do not provide estimates of freshwater lens thickness, and, therefore, are not as useful as ER and EM methods in the conduct of groundwater studies.

The lower surface of the freshwater zone can only be accurately determined by establishing a recognisable salinity limit for freshwater. To do this, it is necessary to drill through the lens to find where the limit occurs. Drilling through to seawater will provide additional data on the thickness of the transition zone. Apart from providing accurate data about the variation of salinity with depth (salinity profiles) in freshwater lenses, a drilling and testing programme can provide control data for geophysical soundings; and, information about permeability, porosity, and depth to major hydrogeological features such as solution channels and unconformities. Such programmes can also facilitate the installation of permanent monitoring systems. If drilling is done in conjunction with a geophysical survey, the holes should ideally be drilled after some idea of the configuration of the freshwater lens is known. Some holes should be placed adjacent to pumping installations to determine the effects of pumping on lens configuration.

Drilling of 75 mm diameter holes up to 30 m below ground surface for groundwater investigations has been successfully undertaken with rotary rigs on Tarawa (Murphy, 1981), Kiritimati (Murphy, 1982), Cocos (Keeling) Islands (Murphy, 1988; Murphy and Falkland, 1992), and the islands in the Torres Strait (Falkland, 1990). An alternative to drilling holes is the driving of suitable pipes. Steel pipes have been successfully driven to 15 m below ground surface on coral atolls. On Kwajalein, 80 mm diameter pipes were driven to depths of up to 15 m using an air hammer (Hunt and Peterson, 1980). Additional monitoring holes have more recently been drilled on Kwajalein using rotary methods (Hunt et al., 1995). On Majuro, 30 mm diameter pipes were driven with a manually operated drop hammer to similar depths (Hamlin and Anthony, 1987). Boreholes should be sited to provide a wide coverage of known and likely freshwater lens areas. A line of holes from the ocean side to lagoon side of an island enables cross sectional information on freshwater and transition zones to be determined (cf., Figure 43). In particularly vulnerable lenses, such as that on Home Island, Cocos (Keeling) Islands, additional data may be required to effectively map and monitor the behaviour of the lens.

Coring or inspection of drill cuttings provides useful information about the subsurface geology including the depth to the unconformity between upper and lower sediments. Permeability estimates at selected depths in a number of bores can be effectively obtained using either in-situ falling head or constant head tests (Hvorslev, 1951). This information is essential for groundwater modelling work and, hence, these tests or similar should be conducted if detailed investigations are required. Typical permeability values obtained for the upper sediments on a number of coral atolls are 5 to 10 m/day, while the lower sediments have yielded values from about 50 to greater than 1 000 m/day. Permeability tests on core samples are not considered suitable as cores are not of sufficient size to be representative of the aquifer. Also, during drilling, water samples should be obtained from the base of the hole at depth intervals of typically 1 m to 3 m, and tested for salinity. Vertical salinity profiles (salinity versus depth) can then be plotted.

Figure 51
Figure 51. Permanent salinity monitoring system used for measuring water salinity in freshwater lenses on Cocos (Keeling) Islands, Warraber and Yoke Islands in Torre Strait. Similar types have been installed on Tarawa and Kirimati.

Salinity-monitoring systems enable long term data on the behaviour of freshwater lenses to be collected and used for the calibration of numerical models. On coral atolls, open holes or continuously perforated casings in holes are not considered suitable for the accurate determination of salinity profiles since the mixing of freshwater and seawater can easily occur in the hole. This problem is known in mainland aquifers (Rushton, 1980; Kohout, 1980) and has been demonstrated in coral atolls (e.g., Enewetak in the Marshall Islands; Buddemeier and Holladay, 1977). Also, contamination of the freshwater zone by underlying saline water can be introduced if this approach is used. Hence, two types of salinity-monitoring systems for coral atolls are commonly used, including the use of multiple holes at each location, terminated at different depths with the bottom of each hole left open, and the use of single boreholes with multiple tubes or pipes terminated at a number of pre-determined depths, between which bentonite (sealing) layers are inserted and gravel is used to fill the spaces (Figure 51). The multiple hole techniques has been used on the atolls of Kwajalein (Hunt and Peterson, 1980) and Majuro (Hamlin and Anthony, 1987), while the single hole technique has been used on Tarawa and Kiritimati in Kiribati (Murphy, 1981, 1982); Cocos (Keeling) Islands, Warraber and Yorke Islands in Torres Strait (Falkland, 1990); and, Diego Garcia in the Chagos Archipelago, Indian Ocean (Surface and Lau, 1986). Samples can be obtained by bailing or pumping from the bottom of each hole, or, alternatively, a salinity probe can be lowered to the base of each hole to obtain measurements; water samples may be pumped to the surface using a small electric or hand-operated diaphragm pump. Testing is done, as during drilling, with a conductivity meter and repeated until readings stabilise. Vertical salinity profiles obtained at different times can be plotted on the same graph to observe trends (Figure 52). For example, the differences in salinity profiles between Home and West Islands are evident by a simple comparison of these graphs.

Figure 52

Figure 52. Variation of salinity with depth over the period from late
1987 to early 1995 at borehole H11, Home Island, Cocos (Keeling)
Islands. The limit of the freshwater zone is shown by the 2500 uS/cm
line and the mid-point of the transition zone by the 25,000 uS/cm line.

Reliable estimates of recharge are required as input to groundwater models in order to estimate sustainable yields of groundwater resources. Preliminary estimates can be obtained using the relationship between mean annual rainfall and mean annual recharge developed by Chapman (1985) based upon the results of a number of studies of recharge to small low-lying islands. The graphic form of this relationship has since been further extended using the results of other studies and is shown in Figure 53. This Figure shows that a non-linear relationship best fits the data available, which suggests that, as the mean annual rainfall increases, the percentage recharge also increases. In contrast, the influence of vegetation is inversely related to recharge rate on South Keeling Atoll, Cocos (Keeling) Islands, and Kiritimati (Christmas Island), Kiribati, with thinner vegetation resulting in a greater rate of recharge. The influence of climate is also shown in Figure 52. For example, Warraber and Yorke Islands, located within the Torres Strait between Cape York peninsula, Australia and Papua New Guinea, have very seasonal rainfall, with about 90% falling during the six-month monsoonal or wet season between the months of December and May (Falkland, 1990). Hence, these two islands receive a greater recharge for a given annual rainfall than would be forecast from the curve because the rainfall effectively occurs for only one-half of a year (the data for Warraber and Yorke Islands was not used in developing the curve). This seasonal rainfall effect suggests that two curves should be developed; one relevant to those islands with marked seasonal rainfall, and another, as shown, for those islands where rainfall is more evenly distributed.

Results of work by Nullet (1987), using the Priestley-Taylor method of determining actual evapotranspiration and a water balance procedure, are shown on an areal basis in Figure 54. The analysis assumed vegetated areas on atolls with a rooting depth for coconut trees of 1 m. It is not known whether similar analyses have been done for other islands outside the region shown.

Preliminary estimates of recharge can also be made using a solute balance approach (e.g., chloride ion). Recharge from rainfall contains a small concentration of chloride due to airborne sprays from the ocean. Evapotranspiration subsequently removes some of the water leaving the chlorides behind in the groundwater. The ratio of the chloride ion concentration in rainwater to the chloride ion concentration in shallow groundwater provides an approximation of the ratio of recharge to rainfall. Ayers (1981) used this approach for estimating recharge on Guam. However, due to the facts that sea spray may affect samples of rainwater used for chloride balances, and the groundwater may be more saline than the recharging water due to saltwater intrusion where there is a thick transition zone, this method should be considered very approximate and may not be valid for use on small islands. Notwithstanding, Chapman (1985) suggests that samples for use in chloride ion balances be obtained from just below the land surface and just above the water table; although, a further problem with this method is that, in low-lying areas, the top phreatic water, which can more easily be sampled than water from the unsaturated zone, may not have originated locally but may have originated from the island's interior, where there is generally lower salinity than the local recharge.

For a more detailed assessment of recharge rates, continuous groundwater level records can be analysed in conjunction with rainfall, sea level, and barometric pressure records. This method was used by Furness and Gingerich (1993) on the island of Tongatapu, Tonga. If the effects of sea level and pressure changes are removed from the water level hydrograph, recharge can be estimated from the residual trace and knowledge of the aquifer specific yield. The water balance method of recharge estimation has often been used for estimating recharge on small islands. For example, Falkland (1992) used this method to determine recharge for the island of Bonriki in the atoll of Tarawa, Kiribati (Figures 35 and 43). This island is the location of the international airport and is partly cleared, while the rest of the island is covered by coconut trees and other vegetation. There is a relatively large and robust freshwater lens underlying the island. Extensive infiltration galleries have been constructed to enable groundwater extraction to occur (Figure 43).

The water-balance equation for the surface of a small island, used for estimating groundwater recharge, can be expressed generally as

P = ETa + SR + R + dV (4)

P = precipitation (most commonly rainfall),
ETa = actual evapotranspiration (including interception),
SR = surface runoff,
R = recharge to groundwater, and
dV = change in soil moisture storage.

Interception by vegetation and other surfaces can be treated as a separate term in the water balance, but here it has been included with ETa since the intercepted water is evaporated.

On low islands with permeable soils and subsurface geology (typically, coral atolls and small limestone islands), there is no surface runoff, and equation (4) reduces to:

R = P B ETa + dV (5)

Figure 54 shows a water balance model used for estimating recharge on a typical low coral island with a shallow water table.

As shown in Figure 54, actual evapotranspiration (ETa) is comprised of three terms:

ETa = EI + ES + TL (6)

EI = evaporation from interception storage,
ES = evapotranspiration from soil moisture storage, and
TL = transpiration by deep-rooted vegetation directly from groundwater.

Figure 54

Figure 54. Water-balance model to estimate recharge for a typical coral island.

From equations (5) and (6), the water-balance equation can be expressed in terms of groundwater recharge as follows:

R = P B (EI + ES + TL) + dV (7)

Normally, it is assumed that rainfall first fills the interception storage (to a maximum value ISMAX), with the residual (or overflow) entering the soil moisture zone. Typical values of ISMAX are 1 mm for predominantly grassed areas and 3 mm for areas consisting predominantly of trees (particularly coconut trees). Evaporation is assumed to occur from this zone at the potential rate.

Roots of shallow-rooted vegetation (grasses, bushes) and the shallow roots of trees can obtain water from within the soil moisture zone (SMZ), which is typically 0.3 m to 0.5 m thick. Water requirements of vegetation from this zone are assumed to be met before any excess drains to the water table. A maximum soil moisture limit (SMCMAX, which occurs at field capacity, FC) and a minimum soil moisture limit (SMCMIN, which occurs at wilting point, WP) are set. Above the field capacity, water is assumed to drain to the water table; below the wilting point, no further evaporation is assumed to occur and the shallow rooted vegetation wilts and possibly dies. The amount of evaporation from the SMZ is normally assumed to be linearly related to the available soil moisture content. At WP, evaporation is assumed to be nil from the SMZ. Potential evaporation is assumed to reach full potential when the SMZ is at FC. Thus, the evaporation rate is half that of the potential rate at a soil moisture content midway between FC and WP.

Vegetation types are assigned "crop factors" (Doorenbos and Pruitt, 1977). Crop factors of 1.0 and 0.8 were assumed in water-balance studies for shallow-rooted vegetation and coconut trees respectively (Falkland, 1983a, 1988a, 1992b). Thus, ETp for coconut trees is taken as 80% of that for shallow-rooted vegetation which is in turn assumed to be equal to ETp of a reference crop (Doorenbos and Pruitt, 1977). The proportions of freshwater lens areas covered by deep rooted vegetation can be estimated from ground observations or aerial photographs. On islands with a thick coverage of coconut trees, this proportion is 100%; on islands where limited clearing for houses and possibly airstrips, the proportion is generally between about 70% and 90%; while in urban areas with few trees, the proportion is typically less than 30% and may, in extreme cases, be zero.

Excess water remaining after evaporative losses, EI and ES, enters the water table. This water is assumed in the model to be gross recharge to the freshwater lens. A further evaporative loss (TL) is experienced due to transpiration by trees whose roots penetrate to the water table. Net recharge is that water remaining after TL is deducted from gross recharge. Observations in pits on a number of atolls reveal that a considerable number of roots penetrate to the capillary fringe just above the water table at typical depths of about 1 m to 2 m below ground level. It is estimated that between 25% and 50% of the roots of mature coconut trees penetrate to the water table. Because the movement of the water table is relatively small, even during drought periods, these roots enable transpiration when the soil moisture storage has been depleted. Thus, coconut trees are able to survive prolonged drought periods on coral atolls where other shallow rooted vegetation has wilted and died.

The water-balance procedure is more complex for raised atolls and limestone islands. Typical depths to water table on these islands are 10 m to 100 m, and extensive karstic formations often occur. These islands may have soils of variable thicknesses, unlike low coral islands, and roots of trees may penetrate through fissures and reach pockets of water at different levels. Flow paths from the surface to the water table may have major horizontal components due to karstic formations (solution channels), in contrast to the essentially vertical flow paths with low coral islands.

The time step for the surface water balance should not exceed one day, because the turnover time in the soil zone is measurable on this time scale (Chapman, 1985). Thus, the use of either mean or actual monthly rainfall data, rather than actual daily rainfall data, will underestimate recharge. Two coral atoll studies (Kwajalein, Hunt and Peterson, 1980; Cocos (Keeling) Islands, Falkland, 1988a) have shown that the assessed recharge is decreased by between 6% and 10% of the rainfall volume if actual monthly (rather than actual daily) rainfall data are used. The latter study showed that the use of mean monthly evaporation estimates rather than daily evaporation data, however, was acceptable. In this study, a computer program was written to simulate the water balance and derive a monthly time series of recharge rates using recorded daily rainfall and estimated monthly potential evapotranspiration (ETp) volumes. Computations were made using a daily time interval.

Water Balance for Tarawa

The ETp estimates were derived from mean monthly pan evaporation data for the period 1981 to 1991, using a pan coefficient of 0.8. Water balance simulations for the Cocos (Keeling) Islands showed that similar recharge estimates were obtained from data sets using either actual monthly values of ETp or mean monthly values of ETp (Falkland, 1994). This result is consistent with the generally low interannual variation in potential evaporation for particular months in humid tropical environments, such as that of Tarawa. For simplicity, therefore, mean monthly ETp estimates were used for the Tarawa water-balance studies. The SMZ is typically 300 mm to 500 mm thick, based on observations from shallow pits and wells. FC was assumed to be 0.15 based on observations of local soil type and typical values for this type of soil, and WP was assumed to be 0.05 based on typical values for sand-type soils (e.g., Linsley and Franzini, 1973). The operating range of soil moisture was assumed to be from 25 mm to 75 mm. The amount of evaporation from the SMZ was assumed to be linearly related to the available soil moisture content. The predominant vegetation types on the island are coconut trees and a variety of grasses and other shallow-rooted vegetation. Crop factors of 1.0 and 0.8 were assumed for grasses and shallow-rooted vegetation, and coconut trees, respectively, based upon values in Doorenbos and Pruitt (1977). Thus, the potential evaporation rate for coconut trees is taken to be 80% of ETp while that for grasses or other shallow rooted vegetation is assumed to be equal to ETp.

Table 15 shows sample water balance calculations using daily rainfall data for the island of Bonriki. The results are summarised in monthly segments over the two years, 1989 and 1990, and are part of a 44-year water balance simulation starting in 1948 and ending in 1991. Input data were: ISMAX, 3 mm; SMZ, 500 mm; FC, 0.15; WP, 0.05; ratio of deep-rooted vegetation to shallow-rooted vegetation, 0.8 (i.e., 80% tree cover); proportion of roots of deep-rooted vegetation reaching water table, 0.5; proportion of roots reaching the water table, 50%; crop factor for shallow-rooted vegetation, 1.0; and, crop factor for trees (predominantly coconut trees): 0.8. Initial values (in 1948) of water in interception storage and soil-moisture storage were assumed to be 1 mm and 50 mm (these initial values make very little difference to the results, particularly for long sequences of data such as the 44-year period used in this example and summarized in Figure 55 for an estimated tree coverage of 80 percent). The results in Table 19 show the effects of a dry year (1989) and a wet year (1990) on recharge. The total rainfall in 1989 (916 mm) was only 45% of the long-term mean annual rainfall; by comparison, the rainfall in 1990 (3 605 mm) was about 80% greater than the mean.

As shown in Table 20 and Figure 55, the recharge in 1989 was negative, since there was a net loss of groundwater of about 170 mm. Heavy rainfall in November and December of that year prevented this loss from being even greater. In 1990, the recharge was estimated to be 2 130 mm or 59% of the total rainfall. Over the period from 1948 to 1991, the mean annual recharge was calculated to be 735 mm or 36% of mean annual rainfall.

TABLE 19. Water Balance (in mm) for Tarawa, 1989 and 1990
TABLE 20. Water Balance (in mm) for Tarawa, 1989 and 1990


(larger image)

Figure 55. Annual rainfall and recharge for Tarawa, Kiribati, 1948-1991. Recharge is for the condition of 80% tree cover, which approximates current tree desity.

From Figure 55, years with high-annual rainfall generally result in high-annual recharge and vice versa. The relationship is not linear as recharge is dependent not only on total rainfall but on the distribution of daily rainfall. The most critical times for freshwater lenses are where there are a succession of low-recharge years. Recharge is even more variable at a monthly scale than at an annual scale. Annual values of the three evapotranspiration components and corresponding recharge values are shown in Figure 56 for the same period. The relative proportions of the four sets of annual components, which when summed equal the annual rainfall values, can be clearly seen. The effect of deep-rooted vegetation, primarily coconut trees, on the water balance is very significant. This effect can be analysed with the model. The percentage area covered by deep-rooted trees as a proportion of the total freshwater lens area was varied from 80% to 0%, and the water balance model was run for the full period of 44 years. The effects of different percentages of trees are summarised in Figure 57. If all trees were removed, the mean annual recharge would increase to about 1 020 mm or about 50% of mean annual rainfall. Evapotranspiration losses would be restricted to the soil moisture zone and average about 1 000 mm. Assuming Bonriki had been totally cleared of trees, the recharge estimates for 1989 and 1990 were 268 and 2 264 mm, respectively, which are equivalent to 29% and 63% of the respective annual rainfalls. The differences between rainfall and recharge in the two years (71% and 27%, respectively) represent evapotranspiration from the soil moisture zone.

Once the location and volume of a freshwater lens is known, and the recharge conditions have been estimated, the flow through the lens and the sustainable yield of the lens can be estimated. Sustainable (or safe) yield estimates are required to enable groundwater extraction systems to be properly planned and managed. Flow through freshwater lenses is influenced by hydrological (variable recharge) and geological (variable permeabilities with depth and distance) factors, as well as by tidal movements and human influences such as water abstraction. The sustainable yield of an aquifer is the rate at which water can be extracted without causing adverse effects. For non-coastal mainland aquifers, the sustainable yield can be approximated by the long-term recharge rate. For freshwater lenses on small island and some coastal-mainland aquifers, such an approximation is not valid as only a small portion of the recharge is available as sustainable yield; most of the recharge is required for maintenance of the lens by literally flushing away salt at the top of the transition zone. To avoid adverse effects from extraction (i.e., to avoid an increase in the salinity of extracted water), the pumping rate from the lens should not exceed the sustainable yield. An additional requirement is that pumping be distributed over the surface of the lens to avoid local upconing of saline water. Methods for estimating sustainable yield range from simple empirical approaches to complex numerical models. Whatever method is chosen for a particular situation, it is important that the effects on the lens of any recommended pumping scheme be monitored. Ideally, this should involve regular monitoring of salinity profiles in monitoring boreholes.

Figure 56
Figure 56. Variations in annual evapotranspiration components (EI, ES, and TI) and annual recharge for Bonriki, Tarawa for the period 1948-1991. YEAR: 1990.

Empirical methods generally assume that a proportion of average recharge can be safely extracted. They also assume that there is sufficient freshwater stored in the lens to allow for dry or drought periods when recharge is low or nil.

Figure 57
Figure 57. Relationship between recharge and coconut-tree coverage for the Bonriki freshwater lens, Tarawa.

Mather Procedure: Mather (1975) developed a procedure which enabled an estimate of yield to be made by reducing recharge and analysing the effect on the thickness of the lens. His analysis is based on an equation by Henry (1964) that relates the thickness of the lens (assuming a sharp interface) to permeability, distance from shore, and recharge. Mather's method includes consideration of extended drought periods. As the method assumes a sharp interface, it can only be used for thick freshwater lenses wherein the transition zone tends to be thin. This method was used by Jacobson (1976) in a study of the freshwater lens on Home Island, Cocos (Keeling) Islands. Based on an estimated freshwater lens thickness of 15 m (based on head measurements), he concluded that the sustainable yield was 200 m3/day. Subsequent investigations (Falkland, 1988, 1992) showed that, although the freshwater lens was much thinner (approximately 2 m to 6 m), the aquifer has been able to sustain a pumping rate of about 115 m3/day. More recent monitoring indicates that this rate may be able to be increased to about 150 m3/day (Falkland, 1994).

Maximum Unit Pumping Rate: Another approach is to use an estimate of the maximum allowable pumping rate per unit area, or per unit length for a freshwater lens, derived from detailed studies for similar hydrogeological environments. The water balance within a small island groundwater system can be expressed in its simplest form as:

R = O + Q + dV (8)

R = recharge into the lens after all evapotranspiration losses have been taken into account, including transpiration directly from the lens by deep-rooted vegetation,
O = flow through the lens (or 'flux') which either flows out at the edge of the lens or mixes with the transition zone at the base of the lens,
Q = total amount of water pumped from the lens, and
dV = change in freshwater volume.

Equation (8) is particularly applicable to relatively simple groundwater systems such as freshwater lenses on small coral islands and atolls. In equation (8), the value of R is estimated from either a water balance at the surface or other method. Further, due to a longer turnover time within the groundwater system, a monthly time step for the groundwater balance is acceptable; often the turnover time of the fresh groundwater on a small island is a number of years (even for relatively small freshwater lenses on a coral atoll, the turnover time is generally greater than 12 months). Thus, in the long term, dV tends to be negligible and equation (8) can be rewritten as:

R = O + Q (9)

Mink (1976), in a study of a freshwater lens on Guam, suggested an extraction rate equal to 25% of flux (or flow) through the lens as a good first approximation of the sustainable yield. This approach was used as a guide in estimating sustainable yields on the atolls of Kwajalein (Hunt and Peterson, 1980) and Kiritimati (Falkland, 1983). In the latter study, this preliminary estimate was used in conjunction with a sharp interface model to analyse the effects on a number of freshwater lenses on that island.

Equation (8) implies that pumping, Q, should be less than 20% of the recharge based on the condition that pumping should be less than 25% of flow through the lens. Given that recharge on many small islands is in the order of 25% to 50% of the rainfall volume in the long term, the allowable pumping rate (or sustainable yield) translates to about 5% to 10% of mean rainfall. However, in relatively large and stable lenses, the sustainable yields may approximate 30% or even 40% of the average recharge, while, for thin and fragile lenses as on Home Island, Cocos (Keeling) Islands, it is considered prudent to maintain the pumping at less than 20% (currently 17%) of average recharge, at least until further monitoring data has been collected.

Modelling: Modelling of freshwater lenses can provide more exact estimations of sustainable yields provided that there are sufficient data to justify their use. Early conceptual models and solution techniques for freshwater lens flow assumed a sharp interface between freshwater and seawater based on the Ghyben-Herzberg theory (Badon Ghijben, 1889; Herzberg, 1901) and the Dupuit assumption of horizontal flow. Observations have shown that this is not the case on atolls, where wide transition zones are the norm, and where these types of models tend to overestimate the freshwater resource. A more realistic, conceptual freshwater lens flow model has evolved (Buddemeier and Holladay, 1977; Wheatcraft and Buddemeier, 1981; Oberdorfer et al., 1990; Underwood et al., 1992) based upon detailed observations on atolls. The conceptual model accounts for vertical and horizontal tidal propagation through a dual aquifer system consisting of the upper (Holocene) coral sediments and lower (Pleistocene) limestone layer (Figures 58 and 59). This conceptual model is supported by observations on a number of atolls in the Pacific (Hunt and Peterson, 1980; Ayers and Vacher, 1986; Anthony et al., 1989) and on the Cocos (Keeling) Islands (Falkland, 1988). These studies have shown that tidal lags and efficiencies at water level monitoring locations within atolls are largely independent of their horizontal distance from the shore. Tidal lags and efficiencies (or the time difference between, and amplitude ratio of, water table movement to tidal movement) are, in fact, greatly influenced by the depth of the holes used for water level monitoring. Vertical propagation of tidal signals tends to be dominant in the middle of the island whereas both horizontal and vertical propagation are significant near the edges.

Figure 58. Cross section through a small coral island showing main features of a freshwater lens (exaggerated vertical scale) and location of an infiltration gallery.

Using this conceptual model, the numerical solution of freshwater lens flow problems can more realistically be computed using dispersion (variable-density) models rather than sharp interface models. Dispersion models are available which account for a two-layered hydrogeologic system with flows of variable density water, and mixing of freshwater and seawater. Dispersion models are inherently more complex, requiring additional parameters to be evaluated or estimated, than sharp interface models. However, both types of models can be run on personal computers, although dispersion models take much longer to run.

Figure 59

Figure 59. Conceptual flow model of a freshwater lens with a two-layer (dual aquifer) system (after Underwood et al., 1992)

One such dispersion model, SUTRA, developed by the United States Geological Survey (Voss, 1984), was applied to the study of freshwater lenses and coastal aquifers on a number of islands. This model uses finite elements to solve the equations, rather than the finite difference method used in the sharp interface models. Case studies of atolls and small carbonate islands using the SUTRA model include Enewetak Atoll, Marshall Islands (Oberdorfer and Buddemeier, 1988; Oberdorfer et al., 1990), Majuro Atoll, Marshall Islands (Griggs and Peterson; 1989, 1993), and Nauru, a raised atoll (Ghassemi et al., 1990). A generic atoll was analysed for different conditions by Underwood et al. (1992). Griggs and Peterson (1989, 1993) modelled the freshwater lens on Laura, an island of the Majuro Atoll in the Marshall Islands, Pacific Ocean, using the SUTRA model. They showed that the effects of pumping at 20% of mean annual recharge were minor, while pumping at 40% and 60% of mean annual recharge caused major upconing and destruction of the lens, respectively.

Other methods and examples of recharge estimation for small islands are described in UNESCO (1991).

Information Sources


Tony Falkland, ACTEW Corporation, Australia


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