The water budget is a method for balancing the input and output of a system. The system can represent a basin, stream, and groundwater reservoir. In this section you will look at an example of an annual water budget. We will use data from the Palmer River Watershed for this example. The values employed are estimated from data collected by the United States Geological Survey (USGS) summarized in the reference under Ries (1990), and Johnston and Baer (1987) listed in the Sources. (The example is based on a problem from C.W. Fetter's Applied Hydrogeology, which is cited in the "Sources" link. However, the actual data used here are based specifically on the Palmer River Watershed -- with some lterary license on the part of the author, DW.)
Given :
- Regional precipitation, 46.4 in/y (from Ries; 1990);
- Evapotranspiration, 25.5 in/y (a generic value based on 55% of precipitation; see Johnston and Baer, 1987);
- Overland flow, 9 in/y (a generic value not actually assessed for the specific watershed);
- Baseflow, 9.9 in/y (a generic value);
- Runoff, 18.9 in/y (a generic value);
- Subsea outflow, 2 in/y (a generic value).
For purposes of this watershed, you may assume there is no streamflow or ground-water flow into the basin. (Although not measured directly, Reis (1990; Table 6, p. 26) estimated an annual mean runoff of the watershed of 80.2 ft3/s based on comparisons with other similar watersheds. Is this a reasonable number, based on the parameters assumed here?)
Find :
A. Annual Water Budget for the Basin
B. Annual Water Budget for the Streams
C. Annual Water Budget for the Groundwater Reservoir
D. Annual Streamflow from the Basin
E. Average Rate of Groundwater Recharge
A. Annual Water Budget for the Basin
| |
Input |
Output |
| Precipitation |
46.4 in/y |
|
| Evapotranspiration |
|
25.5 in/y |
| Overland flow |
|
|
| Baseflow |
|
|
| Infiltration |
|
|
| Runoff |
|
18.9 in/y |
| Subsea outflow |
|
2 in/y |
| Total |
46.4 in/y |
46.4 in/y |
For the basin as a whole, the input into the basin comes from precipitation only. For the output, water leaves by evapotranspiration, subsea outflow, or runoff. In this case runoff pertains to any water above the surface that leaves the system, including water discharging from the streams. Overland flow and baseflow are not included because those are internal changes within the system.
B. Annual Water Budget for the Streams
| |
Input |
Output |
| Precipitation |
|
|
| Evapotranspiration |
|
|
| Overland flow |
9 in/y |
|
| Infiltration |
|
_ |
| Baseflow |
9.9 in/y |
|
| Runoff |
|
18.9 in/y |
| Subsea outflow |
|
|
| Total |
18.9 in/y |
18.9 in/y |
When calculating the budget for the stream, we must consider the internal changes within the watershed. The streams receive their water supply from either the surface or the ground, which are overland flow and baseflow respectively. The output of the streams, as explained above, is the runoff. All other components are not within the scope of the stream. It is also important to note that the surface area of the streams are minimal when compared to the ground, and therefore precipitation and evapotranspiration effects are not considered.
C. Annual Water Budget for the Groundwater Reservoir
This represents the partitioning of water that penetrates below the earth's surface. Accordingly, "infiltration" is the difference between precipitation (46.4 in/y) and overland flow (9 in/y).
| |
Input |
Output |
| Precipitation |
_ |
|
| Evapotranspiration |
|
25.5 in/y |
| Overland flow |
_ |
|
| Infiltration |
37.4 in/y |
_ |
| Baseflow |
|
9.9 in/y |
| Runoff |
|
|
| Subsea outflow |
|
2 in/y |
| Total |
37.4 in/y |
37.4 in/y |
For the groundwater budget, water that enters the ground is the precipitation minus the overland flow. Water leaves by evapotranspiration, baseflow and subsea outflow. Baseflow leaves the ground and enters into the streams, and subsea outflow leaves the ground and enters a larger body of water at a distant location.
D. Annual Streamflow from the Basin
The flow-rate is expressed in units of volume per unit time - typically, cubic feet per second (cfs). In this case assume that the total streamflow leaving the basin is the sum of overland flow and baseflow: 18.9 in/y. This value multiplied by the drainage area gives the discharge. Using this relation, and converting units leads to
(18.9 in/y)(1 ft/12 in)(1 y/31536000 s)(30.9 mi2)(2.79E7 ft2/mi2) = 43.1 cfs
E. Average Rate of Groundwater Recharge
Groundwater recharge is the amount of water actually entering the watertable. This is often expressed in units of millions of gallons per day per square mile of surface area (mgd/mi2). By examining question C, the water that enters this system is the precipitation minus the overland flow and evapotranspiration.
46.4 in/y - 9 in/y - 25.5 in/y = 11.9 in/y
(11.9 in/y)(1/12 ft/in)(1/31536000 y/s)(30.9 mi2)(2.79E7 ft2/mi2) = 27.1 cfs
(27.1 cfs)(0.646 mgd/cfs) / (30.9 mi2) = 0.567 mgd/mi2
Quiz: Let's see what you've learned. Click here to take the quiz.
* Footnote: With editorial changes by J. F. Hermance. The principal watershed parameters that are employed here are from Ries; 1990, along with generic estimates. See "Sources".
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