Lens (hydrology)

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.