SME
Hydrology · Problem type
Storm runoff by the curve number
Use this for “A basin with curve number 80 gets 75 mm of rain in a storm. How much runs off?”, or the curve number from a storm’s rain and runoff.
Table
Storm rain (P)
(mm)
Runoff depth (Q)
(mm)
This is an example. Type your own values to start a new problem.
CN
Curve number
example
S
Potential retention
calculated · mm
Iₐ
Initial abstraction
calculated · mm
P
Storm rain
example · mm
Q
Runoff depth
calculated · mm
Formulas
S
=
25,400
CN
−
254
63.5
=
25,400
80
−
254
Iₐ
=
0.2
×
S
12.7 = 0.2 × 63.5
Q
=
(
P
− Iₐ)
2
÷
(
P
+
0.8
×
S
)
30.9
=
(75 − 12.7)
2
÷
(75
+
0.8
×
63.5)
S
=
5
×
(
P
+
2
×
Q
−
√
4 ×
Q
2
+ 5 ×
P
×
Q
)
63.5
=
5
×
(75
+
2
×
30.9
−
√
4 ×
30.9
2
+ 5 × 75 × 30.9
)
Assumptions
•
Depths are in millimeters over the basin; the 25,400 and 254 of the curve number hold only in mm.
•
The first rain, the initial abstraction Iₐ = 0.2S, wets leaves and fills hollows; nothing runs off until it is filled.
•
CN near 98 for pavement, 60 to 80 for farmland and lawns, near 30 for loose sandy woods.
Step-by-step
WE KNOW
CN = 80, P = 75 mm
FIND
potential retention (S), initial abstraction (Iₐ), runoff depth (Q)
Step 1 · Find potential retention (S)
Use S = 25,400 ÷ CN − 254
The curve number turned into the most water the ground could still hold, in mm.
S
=
25,400
80
−
254
S
=
317.5
−
254
S
=
63.5
mm
Step 2 · Find initial abstraction (Iₐ)
Use Iₐ = 0.2 × S
The
rain
caught
before
any
runs
off
is
taken
as
a
fifth
of
S
.
Iₐ = 0.2 × 63.5
Iₐ = 12.7 mm
Step 3 · Find runoff depth (Q)
Use Q = (P − Iₐ)² ÷ (P + 0.8 × S)
The
rain
past
Iₐ,
squared,
over
the
rain
plus
0.8
S
:
more
of
each
extra
mm
runs
off
as
the
ground
fills.
75 > 12.7: some runs off
Q
=
(75 − 12.7)
2
÷
(75
+
0.8
×
63.5)
Q
=
62.3
2
75 + 50.8
Q
=
62.3
2
125.8
Q
=
3,881.29
125.8
Q
=
30.9
mm
Check
Put the numbers back in. Both sides should match.
63.5
=
25,400
80
−
254
✓
12.7 = 0.2 × 63.5 ✓
30.9
=
(75 − 12.7)
2
÷
(75
+
0.8
×
63.5)
✓
63.5
=
5
×
(75
+
2
×
30.85
−
√
4 ×
30.85
2
+ 5 × 75 × 30.85
)
✓
Topic check
See what you know: 5 questions on this topic
New questions each time. Pass to mark it complete.
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