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State the Formula for optimum number for rain gauges?

Derive the formula with explanations

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If there are already some raingauge stations in a catchment, the optimal number of stations that should exist to have an assigned percentage of error in the estimation of mean rainfall is obtained by statistical analysis as


Where

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http://eduladder.com/viewquestions.php?questionid=808&title=Briefly%20explain%20optimum%20number%20of%20rain%20gauge%20stations%20in%20a%20catchment.

metaphor

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