on Items Every summer you visit the same lake in Maine, and every summer the nei

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on Items

Every summer you visit the same lake in Maine, and every summer the neighbor goes on and on about how the lake is “spring-fed” (groundwater discharges up into the lake bottom). You got to wondering if that was true, so you collected all the information you could from the local geological survey office about the lake hydrology for the month of June:

•    The surface area of the lake is 285 acres.

•    There is one inlet stream. For the month of June, the total discharge measured at a stream gage at the lake inlet was 2.77 × 107 ft3.

•    There is one outlet stream. For the month of June, the total discharge mea- sured at a stream gage at the lake outlet was 3.12 × 107 ft3.

•    During the month of June, the total precipitation measured in a rain gage at the lakeshore was 1.63 inches.

•    Direct evaporation off the lake surface totaled 3.47 inches during the month of June.

•    The lake level dropped 4.30 inches during the month of June.

(a) List the items that contribute flow into the lake, and items that contribute flow out of the lake (there may be unknown items I have not listed above). Write a hydrologic equation for the water balance of the lake in June.
(b) Quantify each of the terms in the hydrologic equation in units of ft3 for the month of June, and solve for unknowns in the equation.
(c) What, if anything, can you conclude about the notion that the lake is “spring- fed”?

(d) What measurements would you make to prove whether or not groundwater is discharging up into the lake bottom? (Assume someone is willing to pay for it.)

Explanation / Answer

(a) The items that contribute flow into the lake are:  inlet stream, precipitation and Subsurface flow

and items that contribute flow out of the lake are: outlet stream, evaporation, tranpiration, Infiltration and Percolation

Hydrologic equation for the water balance of the lake in June =

(discharge from inlet stream+precipitation) - (discharge from outlet stream+evaporation)

(b) (2.77 × 107 ft3 + 1.63 inches* 285 acres) - (3.12 × 107 ft3 + 3.47 inches * 285 acres)

= (2.77 × 107 ft3 + 1.63*0.0833333*285*43560 ft3) - (3.12 × 107 ft3 + 3.47*0.0833333*285*43560 ft3)

(2.77 × 107 ft3 + 0.168 x107 ft3) - (3.12 × 107 ft3 + 0.357 × 107 ft3)

2.938 × 107 ft3 - 3.477 × 107 ft3

- 0.539 × 107 ft3

(c) As we have seen from the material balance equation mentioned above that the water lost is greater than the incoming water and which can be justified by the decrease in water level which is equivalent to:

4.30*0.0833333*285*43560 ft3

= 0.443 × 107 ft3

But the water lost as shown by the fall in water level is less than the water loss that is coming from water balance equation and hence there is some other source of water apart from the mentioned one which can be spring and hence the stream is “spring- fed”.

(d)

As per the above equation we are seeing that the fround water is feeding the stream

decrease in water level which is equivalent to = 4.30*0.0833333*285*43560 ft3

= 0.443 × 107 ft3

water feeded by ground water = 0.539 × 107 ft3- 0.443 × 107 ft3 = 0.106 ft3 of water in june only.

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