Question

Difficulty: HardDrainage Patterns and River Basin Analysis

A morphometric analysis of a river basin provides the quantitative data shown below:

Morphometric ParameterValue
Total Basin Surface Area (AA)50 km250\text{ km}^2
Cumulative Stream Length (LL)125 km125\text{ km}

Based on these hydrological parameters, what is the drainage density of the basin, and what does its magnitude imply about the basin's surface runoff response?

  1. 2.5 km/km22.5\text{ km/km}^2, indicating a high drainage density associated with rapid surface runoff and high flood potential.Answer
  2. B
    0.4 km/km20.4\text{ km/km}^2, indicating a low drainage density associated with slow surface runoff and dominant groundwater recharge.
  3. C
    2.5 km/km22.5\text{ km/km}^2, indicating a low drainage density because stream channels are widely spaced over highly permeable terrain.
  4. D
    6,250 km/km26,250\text{ km/km}^2, indicating an ultra-dense drainage network resulting from extreme vertical relief mismatch.

Answer

The drainage density of the basin is 2.5 km/km22.5\text{ km/km}^2, which indicates a high drainage density characterized by rapid surface runoff and high peak flood potential.
The correct answer properly calculates drainage density (DdD_d) as the total stream length divided by basin area (125 km/50 km2=2.5 km/km2125\text{ km} / 50\text{ km}^2 = 2.5\text{ km/km}^2). Hydrologically, a high drainage density (2.5 km/km22.5\text{ km/km}^2) signifies a closely knit stream network that collects and transmits storm runoff rapidly, resulting in swift hydrological response and high flood potential.

Step-by-Step Solution

1
Identify the formula for drainage density (DdD_d).
Dd=Total Cumulative Stream Length (L)Total Basin Surface Area (A)D_d = \frac{\text{Total Cumulative Stream Length } (L)}{\text{Total Basin Surface Area } (A)}
Drainage density measures the total length of stream channels per unit area of a drainage basin.
2
Substitute the given values into the formula.
Dd=125 km50 km2=2.5 km/km2D_d = \frac{125\text{ km}}{50\text{ km}^2} = 2.5\text{ km/km}^2
Dividing 125 km125\text{ km} by 50 km250\text{ km}^2 yields the linear stream length per square kilometer of basin area.
3
Interpret the hydrological significance of the calculated drainage density value.
A drainage density of 2.5 km/km22.5\text{ km/km}^2 represents a relatively high density, implying impermeable surface rocks/soils, steep slopes, minimal infiltration, rapid runoff delivery into main channels, and high flood responsiveness.
Higher drainage density values mean precipitation reaches stream channels quickly, increasing surface runoff rates.

Key Concept

Drainage Density (DdD_d) and Basin Hydrological Response
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