Question

The Thiessen weights of 4 raingauges A, B, C, and D covering a river basin are 0.15, 0.25, 0.30, and 0.30, respectively. If the average depth of rainfall for the basin is 5 cm, and the rainfalls recorded at B, C, and D are 5 cm, 4 cm, and 5 cm respectively, what will be the rainfall at A?

• A. 5 cm
• B. 3 cm
• C. 7 cm
• D. 9 cm

Hint:

For the Thiessen polygon method: - Ensure weights sum to 1. - Use given rainfall values to calculate the missing gauge’s rainfall accurately.

Answer 1

The Correct Option is C

The average rainfall ($P$) is calculated using the Thiessen polygon method:
\[P = W_A \cdot P_A + W_B \cdot P_B + W_C \cdot P_C + W_D \cdot P_D\]
where:
$W_A, W_B, W_C, W_D$: Thiessen weights of gauges,
$P_A, P_B, P_C, P_D$: Rainfall values at gauges A, B, C, and D.
Given:
\[5 = 0.15 \cdot P_A + 0.25 \cdot 5 + 0.30 \cdot 4 + 0.30 \cdot 5\]
Simplify:
\[5 = 0.15 \cdot P_A + 1.25 + 1.2 + 1.5\]
\[5 = 0.15 \cdot P_A + 3.95\]
Solve for $P_A$:
\[0.15 \cdot P_A = 5 - 3.95 = 1.05\]
\[P_A = \frac{1.05}{0.15} = 7 \, \text{cm}\]
Thus, the rainfall at A is $7 \, \text{cm}$.