Form factor – choose the correct formula The drainage-basin form factor is defined in terms of basin area and axial (maximum) length. Which expression is correct?

Introduction / Context:
Basin shape indices help anticipate runoff timing. The form factor normalizes area by length scale to compare the “roundness” or elongation of catchments of different sizes.

Given Data / Assumptions:

• Axial length is the maximum straight-line length of the basin.
• Area and length are measured at consistent map scale.
• No need for relief corrections for this planimetric index.

Concept / Approach:
The correct and widely used formula is: form factor Ff = A / L^2, where A is basin area and L is axial length. This yields a dimensionless number because the units cancel, enabling inter-basin comparison.

Step-by-Step Solution:
Identify required terms: A (area) and L (axial length).Apply the standard definition: Ff = A / L^2.Among the options, only (c) matches the formula.

Verification / Alternative check:
If two basins have the same A but one has twice the L, the longer one has one-quarter the form factor, reflecting a more elongated shape—exactly what Ff = A / L^2 captures.

Why Other Options Are Wrong:

• (a) and (b) do not square the length, so they do not provide a dimensionless, scale-normalized measure.
• (d) and (e) include incorrect components and thus are not valid definitions.

Common Pitfalls:
Using average width or perimeter in place of axial length; different indices (e.g., circularity ratio) use different inputs—do not mix them.

Final Answer:
Area of the basin divided by the square of the axial length