Lens (hydrology)

A lens is a convex-shaped layer of fresh groundwater that floats above the denser saltwater, 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 downwards until it reaches the saturated zone. The recharge rate of the lens can be summarized by the following equation:

R = P - ET

Where R is the recharge rate in meters, p is precipitation (m), and 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.^[1]

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.^[1] The equation is summarized below:

Z_max = [Y+ (Z_td -Y)R/(B+R)]*(K)(C)(T_r,s,w,y,m)

Where Z_max = maximum depth of the lens, R = annual recharge rate (m), Y and B = parameters depending on the width of the island, Z_td = depth to Thurber Discontinuity, K = hydraulic conductivity of the upper aquifer, C = confining reef plate parameter, and 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.^[2] This relationship is described in the equation below:

H = [P_f/(P_s-P_f)]*h

Where H = the depth of the lens below sea level, P_f = the density of the freshwater aquifer, P_s = density of saltwater, and h = hydraulic head.

References

^ ^a ^b Bailey, Ryan T., John W. Jenson, and Arne E. Olsen. An atoll freshwater lens algebraic model for groundwater management in the Caroline Islands. Water and Environmental Research Institute of the Western Pacific, University of Guam, 2008.
^ MCLANE, Charles. "EFFECT OF WITHDRAWALS FROM A SIMULATED ISLAND FRESHWATER LENS AQUIFER SYSTEM: AN ANALYTIC ELEMENT MODELING APPROACH." 2002 Denver Annual Meeting. 2002.

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[:0-1] Bailey, Ryan T., John W. Jenson, and Arne E. Olsen. An atoll freshwater lens algebraic model for groundwater management in the Caroline Islands. Water and Environmental Research Institute of the Western Pacific, University of Guam, 2008.

[2] MCLANE, Charles. "EFFECT OF WITHDRAWALS FROM A SIMULATED ISLAND FRESHWATER LENS AQUIFER SYSTEM: AN ANALYTIC ELEMENT MODELING APPROACH." 2002 Denver Annual Meeting. 2002.

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