When estimating average precipitation over a catchment, which method(s) give weighted importance to individual rain-gauge stations?

Introduction / Context:
Average areal precipitation is central to hydrologic design, flood estimation, and water-balance studies. Different methods assign different weights to gauge data depending on spatial representativeness.

Given Data / Assumptions:

• A catchment has multiple rain gauges with nonuniform spatial distribution.
• We compare common averaging methods used in India and worldwide.
• Goal: identify which methods weight individual gauges.

Concept / Approach:
Arithmetical mean method: simple average, equal weight to each gauge.Thiessen’s mean method: divides the basin into Thiessen polygons; each gauge is weighted by its polygon area.Isohyetal method: draws isohyets (contours of equal rainfall) and integrates areas between isohyets, yielding area-weighted averages, implicitly weighting nearby gauges.
Thus, methods that explicitly or implicitly weight stations are Thiessen’s and Isohyetal methods.

Step-by-Step Solution:

Verification / Alternative check:
Textbook definitions confirm that only Thiessen’s and Isohyetal use spatial weights; arithmetic mean does not.

Why Other Options Are Wrong:

• Arithmetical mean only: No weighting—just simple average.
• Thiessen only / Isohyetal only: Incomplete; both methods weight gauges.
• Both (a) and (b): Includes arithmetic mean, which is unweighted.

Common Pitfalls:

• Applying arithmetic mean in mountainous terrain with sparse gauges.
• Misconstructing Thiessen polygons leading to wrong weights.
• Drawing coarse isohyets that ignore orography or storm tracks.

Final Answer:
Both (b) and (c)