In hydrology, a lens, also called freshwater lens or Ghyben-Herzberg lens, is a convex layer of fresh groundwater that floats above the denser saltwater and is usually found on small coral or limestone islands and atolls. This aquifer of fresh water is recharged through precipitation that infiltrates the top layer of soil and percolates downward until it reaches the saturated zone. The recharge rate of the lens can be summarized by the following equation:
R = p − E T {\displaystyle R=p-ET}
Where R {\displaystyle R} is the recharge rate in meters, p {\displaystyle p} is precipitation (m), and E T {\displaystyle ET} is evapotranspiration (m) of water. With higher amounts of recharge, the hydraulic head is increased, and a thick freshwater lens is maintained through the dry season. Lower rates of precipitation or higher rates of interception and evapotranspiration will decrease the hydraulic head, resulting in a thin lens.
Models of freshwater lenses
Algebraic model An algebraic model for estimating the thickness of a freshwater lens was developed using groundwater simulations by Bailey et al. 2008. This equation relates lens thickness to geologic and climatic factors such as island geometry, geologic composition, and recharge rate, among others. The equation is summarized below:
Z m a x = Y + ( Z t d − Y ) R B + R ⋅ K C T r , s , w , y , m {\displaystyle Z_{max}={\frac {Y+(Z_{td}-Y)R}{B+R}}\cdot KCT_{r,s,w,y,m}}
Where Z m a x {\displaystyle Z_{max}} = maximum depth of the lens, R {\displaystyle R} = annual recharge rate (m), Y {\displaystyle Y} and B {\displaystyle B} = parameters depending on the width of the island, Z t d {\displaystyle Z_{td}} = depth to Thurber Discontinuity (the transition between the upper and lower aquifers), K {\displaystyle K} = hydraulic conductivity of the upper aquifer, C {\displaystyle C} = confining reef plate parameter, and T {\displaystyle T} = time parameter depicting long-term rainfall patterns with the subscripts representing different aspects of this such as region, weather pattern, etc.
Classic Badon Ghyben-Herzberg lens Many freshwater aquifers on atolls and small rounded islands take on the form of a Badon Ghyben-Herzberg lens. This relationship is described in the equation below:
H = h ⋅ P f P s − P f {\displaystyle H=h\cdot {\frac {P_{f}}{P_{s}-P_{f}}}}
Where H {\displaystyle H} = the depth of the lens below sea level, P f {\displaystyle P_{f}} = the density of the freshwater aquifer, P s {\displaystyle P_{s}} = density of saltwater, and h {\displaystyle h} = thickness of lens above sea level.
Effects of drought Freshwater lenses rely on seasonal rainfall to recharge the underground aquifer and can drastically change in thickness following drought or heavy rainfall. A USGS report following the 1997/1998 drought in the Marshall Islands observed a noticeable decline in the thickness of the lens. After the reservoirs of the public rainfall catchment system were rapidly depleted following several months of inadequate precipitation, the islands' population began increasing the rate of groundwater pumping to the point that groundwater supplied up to 90% of the island's drinking water during the drought. A network of 36 monitoring wells at 11 sites was installed around the island to measure the amount of water depleted from the aquifer. By the end of the drought in June 1998, the maximum thickness of the freshwater lens was about 45 feet (14 m) in some wells, while one site measured a thickness as low as 18 feet (5.5 m). Following the resumption of the rainy season, the thickness of the lens increased by up to 8 feet (2.4 m) in some areas, indicating that the recharge rate of freshwater lenses on atolls and small islands responds rapidly to changes in precipitation and groundwater pumping rate.
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