The optimal number of rain gauges for a watershed can be approximated using the formula:
Steps for Calculation
Calculate rainfall mean (xˉxˉ) and standard deviation (σσ) for existing gauges.
Compute coefficient of variation: Cv=(σ/xˉ)×100Cv=(σ/xˉ)×100.
Choose an allowable error (usually 5–10% for hydrological studies).
Substitute values in the formula to find the minimum required rain gauges for adequate representation.
Indian Standard Guidelines
Plain regions: 1 gauge per 520 km²
Moderate elevation (1000 m): 1 gauge per 260–390 km²
Hilly/heavy rainfall: 1 gauge per 130 km²
These densities ensure practical coverage and accuracy.
In summary, use the coefficient of variation and allowable error in the formula above, or follow terrain-specific density guidelines, to estimate the optimal number of rain gauges for your watershed.
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