A morphometric quantitative analysis of a river basin using Strahler's stream ordering met… — JAMB UTME

A morphometric quantitative analysis of a river basin using Strahler's stream ordering method yields the following stream segment counts:
- $N_1$ (1st-order streams) = $40$
- $N_2$ (2nd-order streams) = $10$
- $N_3$ (3rd-order streams) = $4$
- $N_4$ (4th-order streams) = $1$

Based on these morphometric data, what is the mean bifurcation ratio ( $R_b$ ) of this drainage basin?

Answer: 3.5

Answer

The mean bifurcation ratio (

R_b

) of the drainage basin is 3.5.

The mean bifurcation ratio (

R_b

) is obtained by computing the ratio of stream segments between successive orders:

N_1/N_2 = 4.0

N_2/N_3 = 2.5

, and

N_3/N_4 = 4.0

. Averaging these three values gives

(4.0 + 2.5 + 4.0) / 3 = 3.5

Step-by-Step Solution

Calculate the individual bifurcation ratios (

R_b

) between consecutive stream orders using the formula

R_b = \frac{N_u}{N_{u+1}}

R_{b(1-2)} = \frac{40}{10} = 4.0

R_{b(2-3)} = \frac{10}{4} = 2.5

, and

R_{b(3-4)} = \frac{4}{1} = 4.0

Bifurcation ratio measures the ratio of the number of stream segments of a given order to the number of segments of the next higher order.

Sum the calculated individual bifurcation ratios.

Sum

= 4.0 + 2.5 + 4.0 = 10.5

To find the average across all order transitions, the sum of all calculated ratios must first be determined.

Divide the total sum by the number of order transitions (

k = 3

Mean

R_b = \frac{10.5}{3} = 3.5

There are 3 transitions between the 4 stream orders, so dividing the sum by 3 gives the arithmetic mean bifurcation ratio.

Key Concept

Bifurcation Ratio and Stream Order Analysis in River Basins

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