Every summer you visit the same lake in Maine, and every summer the neighbor goe

Question

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 times 10^7 ft^3. There is one outlet stream. For the month of June, the total dis- charge measured at a stream gage at the lake outlet was 3.12 times 10^7 ft^3 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 ft^3 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 main influence on streamflow is precipitation runoff in the watershed. Rainfall causes rivers to rise, and a river can even rise if it only rains very far up in the watershed

- The size of a river is highly dependent on the size of its watershed. Large rivers have watersheds with lots of surface area; small rivers have smaller watersheds.

- Large rivers rise and fall slower and at a slower rate than small rivers. In a small watershed, a storm can cause 100 times as much water to flow by each minute as during base-periods, but the river will rise and fall possibly in a matter of minutes and hours.

- Large rivers may take days to rise and fall, and flooding can last for a number of days. After all, it can take days for all the water that fell hundreds of miles upstream to drain past an outflow point.

The hydrologic equations are as follows:

Basin Morphology - Volume (V) - Area (A) – Depth (h) Relation

A h2, V h3, A h0, V h1, A h2/p, V h(1+2/p)

p : parameter representing the slope ‘profile’. p = 1 for straight slope, p > 1 for convcave slope.

For normal volume: Volume (V) - Area (A) - Depth (h) Model

A = Amax (h / hmax)2/p , V = Amaxhmax / 1+2/p (h / hmax)1+2/p , where                Amax: maximum area and hmax: maximum depth.

(b) The general water balance equation, inflow = outflow ± change in volume (delta V), can be used to make accurate estimates of water use by lakes. Total water use (TWU) is the sum of all possible inflows to lakes such as precipitation (P), runoff (R), stream inflow, groundwater seepage (Si), and management additions or regulated inflows (I) whereas, consumptive water use (CWU) includes the possible outflows such as evaporation (E), seepage (So), transpiration, overflow (Of), intentional discharge or regulated discharge (D), and water in harvest biomass (about 0.75 m3/t) a negligible amount that can be ignored. In embankment aquaculture ponds, runoff is negligible and groundwater inflow is also seldom a factor. Thus the appropriate equation is: P+I = E + So + Of + D ± delta V. The water level in a lake is controlled by the balance between input and output: Qin-Qout -=A*(dh/dt)

where Qin [L3 T1] is the sum of all water inputs, Qout [L3 T1] is the sum of all outputs, A [L2] is the surface area of the lake, and dh/dt [L T1] is the rate of water-level (h) change. Note that A represents the water-covered area, which is normally dependent on h (the higher the water level, the greater the surface area). The water regime of a lake (i.e., how A and h change over time) is determined by the seasonal and interannual variability of Qin Qout. Therefore, understanding the water regime requires some knowledge.

(c) Since the weather is dry, lake levels are often low and with abundant rain, lake levels generally rise. This is due to dependence of many Florida lakes on lateral seepage from perched groundwater systems into the lake. Other lakes are highly dependent on actual rainfall and/or storm water runoff. This lake is spring fed meaning that their water supply is mostly from deep aquifer sources where water flows up and into the lake. Aside from weather patterns, there are a few other naturally occurring factors that can affect water levels. Geology can have a lot to do with a lake's ability to "hold" water. If the soil is sandy or porous are more susceptible to losing water through seepage, whereas clay soils can act as a barrier and help lakes retain water. Evaporation is another major factor. The four measurements are provided are:

- Latest Value

- High Water Levels

- Historic Norm for Month

- Historic Range

Also, it is important to remember that one should never jump to conclusions when comparing lakes, even lakes that are in close proximity.

(d) Water level data for water bodies with gaging stations may not always be accurate or available due to damage, or mechanical or electrical problems that cause instrumental errors. In some cases, water levels may even drop so low that an accurate measurement cannot be made without professionally resurveying the water body first. Be sure to check for gaps in data that might result from gaging problems before using water level data. Groundwater-surface water studies that use conventional near-shore piezometers and/or seepage meters are impractical in larger, areal extensive lakes, as they require exorbitant numbers of instruments to quantify groundwater discharge zones. In smaller lakes an electrical conductivity mapping method has proven useful in mapping groundwater discharge zones. The technique identifies groundwater discharge by measuring variations in sediment pore water electrical conductivity and reduces the number of instruments necessary to quantify inflow, thereby lowering instrumentation costs and increasing a study's efficiency. Onshore and offshore piezometers should be used to verify the presence of upward gradients and elevated electrical conductivities. The sediment probe survey provided qualitative maps of areas of elevated electrical conductivity indicative of groundwater discharge and allowed a fairly extensive shoreline to be mapped quickly and economically. Survey results will lead to guided installation of nearshore piezometers to discharge zones, eliminating the inefficiency of more conventional ``hit or miss'' point source installation approaches. This research demonstrates that the sediment probe is a valuable tool for studying groundwater inputs into large lakes.

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