A rainfall gauge installed with its mouth perpendicular to a hillslope will over-register rainfall; by what factor should its reading be reduced to obtain the true vertical rainfall?

Introduction:
Rainfall depth is defined with reference to a horizontal collecting area. If a gauge is tilted (e.g., mounted perpendicular to a slope), the effective mouth area normal to vertical rainfall changes, causing biased measurements.

Given Data / Assumptions:

• Gauge mouth plane is not horizontal; it is perpendicular to the local slope.
• Angle of inclination is measured with the vertical.
• Rainfall is assumed vertically incident (no wind-driven obliquity).

Concept / Approach:
If the gauge mouth is tilted by angle θ from the vertical, the projected collecting area relative to a horizontal plane is larger by a factor of 1 / cosθ. Thus the recorded depth h' on the tilted gauge exceeds the true vertical rainfall h by h' = h / cosθ. To recover h, multiply by cosθ.

Step-by-Step Solution:
Step 1: Express the relation: h' = h / cosθ (tilted mouth collects more for the same vertical rainfall).Step 2: Rearrange to h = h' * cosθ.Step 3: Therefore, reduce the measurement by multiplying with cosθ, where θ is the inclination with the vertical.

Verification / Alternative check:
Check limiting cases: θ = 0° (mouth horizontal) ⇒ cosθ = 1, no correction; θ → 90° ⇒ cosθ → 0, the reading would diverge, reflecting geometric inconsistency for near-vertical mouths.

Why Other Options Are Wrong:

• Sine: Would give zero correction at θ = 0°, which is incorrect.
• Tangent: Not dimensionally appropriate for area projection.
• Calibration coefficient: Unrelated to geometric tilt error.

Common Pitfalls:

• Using angle with the horizontal instead of with the vertical (ensure the correct reference).
• Ignoring wind-driven rainfall, which requires separate aerodynamic corrections.

Final Answer:
Multiply by cosine of the angle with vertical.