Fluvial Geomorphology – Drainage Basin Laws “The mean basin area of successive stream orders forms a linear relationship when graphed (on appropriate axes).” This statement refers to:

Introduction / Context:
Quantitative geomorphology uses empirical “laws” to describe how properties of stream networks change with order (Strahler or Horton ordering). One such observation is that certain variables, such as mean basin area, change systematically from one stream order to the next and plot as straight lines on logarithmic or semi-logarithmic graphs.

Given Data / Assumptions:

• Variable of interest: mean basin area for each stream order.
• Observation: a linear trend appears when graphed (commonly on log scales).
• We must identify the named empirical relationship.

Concept / Approach:
Horton’s and subsequent stream-order laws include the law of basin areas, which states that mean basin area increases geometrically with stream order. When plotted as log(mean area) versus order, a linear relationship emerges. Other named laws include the law of stream numbers (geometric decrease with order) and the law of stream lengths (geometric increase). “Morphometric analysis” is a general term for the field, not this specific relationship.

Step-by-Step Solution:

Verification / Alternative check:
In many drainage basins worldwide, plotting log(mean basin area) against stream order yields straight lines whose slope reflects the area ratio between orders. This consistent behavior supports the named law.

Why Other Options Are Wrong:

• Morph metric analysis: Broad methodology; not a specific law.
• Law of drainage composition: Not the standard name for this relationship.
• None of the above: Incorrect because the law has a recognized name.

Common Pitfalls:
Confusing the three principal Horton laws (numbers, lengths, areas). Remember: numbers decrease with order; lengths and areas increase with order; the “area” version is the law of basin areas.

Final Answer:
law of basin areas