If the coefficient of variation of the rainfall values of the existing rain-gauge stations is 30 and the desired error in the basin-mean rainfall estimate is 10%, the optimum number of rain-gauge stations is

Why is this the answer?

The optimum number of rain-gauge stations N = (Cv/p)², where Cv is the coefficient of variation of rainfall values at existing stations (%) and p is the desired percentage error in the mean rainfall estimate. N = (30/10)² = 3² = 9. This formula (from IS 4987) ensures the gauge network provides a mean areal rainfall estimate within ±10% of the true value. If the existing number of gauges is less than N, additional gauges must be added to meet the accuracy requirement.

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