2078 Bhadra · 5 marks

Number of additional rain gauges required

Short answer

Coefficient of variation Cv = (100 × 31.6)/143 = 22.10%; required gauges N = (22.10/7)² = 9.97 ≈ 10. Since 7 exist, 3 additional gauges are needed for a total of at least 10.

Mean and standard deviation of annual rainfall estimated based on seven stations in a catchment are 143 mm and 31.6 mm, respectively. For a 7% error in the estimation of mean rainfall, do we need additional rain gauges in the catchment? If yes, what is the minimum number of additional rain gauges required to be established in the watershed?

The number of gauges needed for a permissible error $\varepsilon$ in the mean is

N = \left(\frac{C_v}{\varepsilon}\right)^2, \quad C_v = \frac{100\,\sigma}{\bar P}

Given: $\bar P = 143$ mm, $\sigma = 31.6$ mm, existing $n = 7$ , $\varepsilon = 7\%$ .

C_v = \frac{100 \times 31.6}{143} = 22.10\%

N = \left(\frac{22.10}{7}\right)^2 = 9.97 \approx 10

Since $N = 10 > 7$ , additional gauges are needed.

Additional gauges $= 10 - 7 = 3$ .

Answer: Yes. A minimum of 3 additional rain gauges (10 in total) must be installed.

✓ Answer checked by Claude Sonnet 5.5

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