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FIGURE 24.5 The approximate watersheds of the Columbia River, the Colorado River, and the Mississippi River.

Substitute the expression of Q S in terms of surplus into the equation
EXAMPLE 24.1 for Q G .
Within a watershed with a net water surplus, the flow in a stream drain- Q G = P − [AE + 70%(P − AE)]
ing that watershed is equal to the precipitation (P) minus the actual evap-
oration (AE) within the watershed. The amount of surplus precipitation Calculate Q G .
that becomes runoff determines how much of the stream flow is from P = 914 mm Q G = P − [AE + 70%(P − AE)]
groundwater discharge (Q G ) versus surface runoff (Q S ). Hence, the water-
shed budget can be expressed as precipitation equals actual evaporation AE = 686 mm Q G = 914 mm − [686 mm
+ 0.7 (914 mm − 686 mm)]
plus groundwater discharge plus surface runoff. P = AE + Q G + Q S Q G = ?
On an annual basis, the precipitation in a watershed is 914 mm, the Q G = 914 mm − (686 mm + 160 mm)
actual evapotranspiration (evaporation and transpiration) is 686 mm, Q G = 68 mm
and 70 percent of the surplus precipitation is runoff. What is the per-
centage contribution of each component of the watershed budget? Calculate Q S .
P = 914 mm Q S = 70%(P − AE)
SOLUTION AE = 686 mm = 0.7(914 mm − 686 mm)
Rearrange the watershed budget equation to derive an equation for Q S = ? = 0.7(228 mm)
each component in terms of the other components, and then write an = 160 mm
equation that expresses Q S in terms of the surplus.
The percentage is the ratio of each component to P times 100 percent.
P = AE + Q S + Q G Calculate the percentage of each component of the watershed budget.
∴ AE = P − (Q S + Q G ) _
AE

%AE = × 100%

∴ Q S = P − (AE + Q G ) P
686 mm
∴ Q G = P − (AE + Q S ) = _ × 100%

and 914 mm
Q S = 70%(P − AE) = 75.1%
24-5 CHAPTER 24 Earth’s Waters 601