SME
Physical Geography · Problem type
Drainage density and bifurcation ratio
Use this for “A 75 km² basin has 180 km of streams: 40 of order 1, 9 of order 2 and 2 of order 3. Find its drainage density, bifurcation ratios and stream frequency.”
Table
Order
N
Rb
1
40
4.444
2
9
4.5
3
2
—
This is an example. Type your own values to start a new problem.
L
Total stream length
example · km
A
Basin area
example · km²
Dd
Drainage density
calculated · km/km²
N₁
Order-1 streams
example
N₂
Order-2 streams
example
N₃
Order-3 streams
example
Rb12
Bifurcation ratio, orders 1 to 2
calculated
Rb23
Bifurcation ratio, orders 2 to 3
calculated
F
Stream frequency
calculated · km⁻²
Formulas
Dd
=
L
A
2.4
=
180
75
Rb12
=
N₁
N₂
4.4444
=
40
9
Rb23
=
N₂
N₃
4.5
=
9
2
F
=
N₁
+
N₂
+
N₃
A
0.68
=
40 + 9 + 2
75
Assumptions
•
Streams are ordered by Strahler’s rule: two streams of one order join to make the next order, so each ratio is at least 2.
•
High drainage density means impermeable ground, steep slopes or little plant cover; low density means permeable ground.
•
Bifurcation ratios near 3 to 5 are usual; much higher ones suggest the rock steers the streams.
Step-by-step
WE KNOW
L = 180 km, A = 75 km², N₁ = 40, N₂ = 9, N₃ = 2
FIND
drainage density (Dd), bifurcation ratio, orders 1 to 2 (Rb12), bifurcation ratio, orders 2 to 3 (Rb23), stream frequency (F)
Step 1 · Find drainage density (Dd)
Use Dd = L ÷ A
Kilometres of stream for each square kilometre of the basin.
Dd
=
180
75
Dd = 2.4 km/km²
Step 2 · Find bifurcation ratio, orders 1 to 2 (Rb12)
Use Rb12 = N₁ ÷ N₂
How many order-1 streams there are for each order-2 stream.
Rb12
=
40
9
Rb12 = 4.4444
Step 3 · Find bifurcation ratio, orders 2 to 3 (Rb23)
Use Rb23 = N₂ ÷ N₃
How many order-2 streams there are for each order-3 stream.
Rb23
=
9
2
Rb23 = 4.5
Step 4 · Find stream frequency (F)
Use F = (N₁ + N₂ + N₃) ÷ A
Count the streams of every order, then share them over the basin’s area.
F
=
40 + 9 + 2
75
F
=
51
75
F
=
0.68
km⁻²
Check
Put the numbers back in. Both sides should match.
2.4
=
180
75
✓
4.4444
=
40
9
✓
4.5
=
9
2
✓
0.68
=
40 + 9 + 2
75
✓
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