SME
Hydrology
Water budgets
Use this for “A 250 km² basin gets 900 mm of rain a year, loses 550 mm to evapotranspiration and stores 20 mm. Find the runoff and mean discharge.”
Chart
Runoff ratio: r = 0.3667
This is an example. Type your own values to start a new problem.
P (mm/yr)
=
ET (mm/yr)
+
Q (mm/yr)
+
ΔS (mm/yr)
A
Basin area
example · km²
V
Runoff volume
calculated · m³
Qₘ
Mean discharge
calculated · m³/s
r
Runoff ratio
calculated
Formulas
P
=
ET
+
Q
+
ΔS
900 = 550 + 330 + 20
V
=
Q
×
A
×
1,000
8.25 ×
10
7
=
330
×
250
×
1,000
Qₘ
=
V
31,557,600
2.61
=
8.25 ×
10
7
31,557,600
r
=
Q
P
0.3667
=
330
900
Assumptions
•
A closed basin: no groundwater leaves underground, so runoff carries out what is not evaporated or stored.
•
Each term is a depth over the basin in a year, so basins of any size compare; 1 mm over 1 km² is 1,000 m³.
•
A year is 365.25 days, or 31,557,600 s.
Step-by-step
WE KNOW
P = 900 mm/yr, ET = 550 mm/yr, ΔS = +20 mm/yr, A = 250 km²
FIND
runoff (Q), runoff volume (V), mean discharge (Qₘ), runoff ratio (r)
Step 1 · Find runoff (Q)
Use P = ET + Q + ΔS
What falls and is neither evaporated nor stored runs off.
Q
=
P
−
ET
−
ΔS
Q
=
900
−
550
−
20
Q
=
330
mm/yr
Step 2 · Find runoff volume (V)
Use V = Q × A × 1,000
Each millimeter of depth over each square kilometer is 1,000 m³ of water.
V
=
330
×
250
×
1,000
V
=
82,500
×
1,000
V
=
8.25 ×
10
7
m
3
Step 3 · Find mean discharge (Qₘ)
Use Qₘ = V ÷ 31,557,600
Spread the year’s volume over the seconds in a year.
Qₘ
=
8.25 ×
10
7
31,557,600
Qₘ = 2.61 m³/s
Step 4 · Find runoff ratio (r)
Use r = Q ÷ P
The share of the precipitation that runs off.
r
=
330
900
r
=
0.3667
Check
Put the numbers back in. Both sides should match.
900 = 550 + 330 + 20 ✓
8.25 ×
10
7
=
330
×
250
×
1,000
✓
2.61
=
8.25 ×
10
7
31,557,600
✓
0.3667
=
330
900
✓
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