If N is the optimum number of rain gauge stations, C v is the coefficient of variation of the rainfall values of the existing rain gauge stations and P is the desired degree of percentage error in the estimate of the basin mean rainfall, then how N, C v and P are connected?
- AN = (Cv/P)²Correct
- BN = (P/Cv)²
- CN = Cv/P
- DN = P/Cv
Solution
Concept
Optimum number of rain gauge stations formula
Formula
N = (Cv / P)2
Step-by-step solution
1. The formula for calculating optimum rain gauge density balances the spatial variation of precipitation with allowable estimation error. 2. Mathematically, the required number of stations N is given by N = (Cv/P)², where Cv is the coefficient of variation and P is the allowable percentage error. Answer: A
Explanation
In hydrological studies, the optimum number of rain gauge stations required for a catchment area depends on the spatial variability of rainfall and the permissible error limit. The statistical formula relates the optimum number of stations N to the coefficient of variation Cv of rainfall data and the allowable percentage error P as N equals the square of Cv divided by P. Therefore, option A gives the correct mathematical formula.
Why the other options are wrong
B) The ratio is inverted; error P should be in the denominator. C) The ratio must be squared to determine the optimum number of rain gauge stations. D) The expression lacks the required squaring operation and has inverted terms.
Shortcut
Optimum rain gauges formula: N = (Cv / P)².
Common mistake
Selecting option B instead of A by inverting the ratio of the coefficient of variation and allowable error in the formula N = (Cv/P)².
Correct answer: A) N = (Cv/P)²