Section 4: Soil and Water Conservation Engineering
Precipitation Analysis & Rain Gauges
Subtopic: Optimum number of rain gauges
Question Statement:
A catchment has a coefficient of variation of annual precipitation of $C_v = 40\%$. For an allowable percentage error in the estimation of mean precipitation of $\epsilon = 10\%$, the optimum number of rain gauge stations required in the catchment is ________.
Answer Key:
16
Step-by-Step Solution & Explanation
The optimum number of rain gauge stations $N$ is given by:
$N = \left( \frac{C_v}{\epsilon} \right)^2$
Given $C_v = 40\%$ and allowable error $\epsilon = 10\%$:
$N = \left( \frac{40}{10} \right)^2 = (4.00)^2 = 16$.