Question

Lake Waiua is Hawaii's only alpine lake.  It has (approximately) vertical sides and a 7000 m² area.  

Between 2010 and 2013, its depth declined from 3m to 0.3 m.   

e) The soil of the lake bed has a porosity of ϕ=0.5.  After the lake drained, the soil is unsaturated and has water content of θ=0.3, and a matric potential (head) of -20m.  There is a rainstorm. After 1 day, all the rainfall infiltrates over the unsaturated soils. The cumulative infiltration (F) depth is 0.96m. What is K_sat of the lake bed soil, in units of m/day?

f) Under past conditions (when there was still water in the lake), groundwater used to flow (horizontally) into the lake from an unconfined aquifer formed within one of the lake’s banks.  

You can assume that this groundwater flow was one dimensional in the x direction.  You can also assume that there is a flat, continuous impermeable layer that forms the bottom of the aquifer and lies below both the aquifer and the lake.  

Draw a 2D control volume for this flow from the aquifer into the lake.

Label all fluxes entering and leaving the control volume, show your axes, label all dimensions, and show the location of your reference elevation (datum).   

Derive an expression for the mass balance in this control volume.

In words, how would the water level in the lake provide a boundary condition for solving the equation you obtain?  What other boundary condition(s) would you need?

g) The lake is (in real life) located on top of a volcano.  The final explanation for where the water from the lake went is that a crack suddenly opened in the lake bed, water drained into a lava chamber, and then the crack closed.

The lava chamber has an air space of 20,000 m³, its temperature is 1000 ^oC, and the volume of water that drained into the crack is the same as the change in storage you computed in (a). =18900

What pressure does the added water vapor (from the lake) exert on the lava chamber walls?   

Bonus: If the “lithostatic pressure” of rock that helps prevent a volcanic eruption happening is typically 200 MPa – should we be scared?      

Answer 1

(e) Given:

Cumulative Infiltration, F = 0.96 m

Water content before infiltration started, θ0 = 0.3

Porosity, φ = 0.5

Matric potential Head, ψf = -20 m

Infiltration rate, w =    = = 0.96m/day.

From Green-Ampt’s Equation,

F =

Where , Ksat = Hydraulic Conductivity (m/day),

Substituting the values and solving the equation we get,

0.96 =

Ksat = 0.185 m/day