The mean rainfall over a catchment has to be estimated. The data for four rain gauges located in and around the catchment is listed in the table. Which one of the following statements is correct:
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The Thiessen polygon method provides a weighted average based on the relative area of influence of each rain gauge, which can give a more accurate estimate of the mean rainfall in a catchment area compared to the arithmetic mean method.
The estimate obtained from the Thiessen-mean method is greater than that obtained using the arithmetic-mean method.
The estimate obtained from the Thiessen-mean method is equal to that obtained using the arithmetic-mean method.
The estimate obtained from the Thiessen-mean method is less than that obtained using the arithmetic-mean method.
The Thiessen-mean method cannot be applied in this case.
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The Correct Option isA
Solution and Explanation
By the Arithmetic mean method, the mean rainfall is calculated as:
\[
\bar{P}_A = \frac{P_A + P_Q + P_R}{3} = \frac{100 + 110 + 100}{3} = 103.33 \, {mm}.
\]
By the Thiessen polygon method, the mean rainfall is calculated as:
\[
\bar{P}_T = \frac{\sum P_i x_i}{\sum x_i} = \frac{100 \times 0.25 + 110 \times 0.5 + 100 \times 0.1 + 125 \times 0.15}{1} = 108.75 \, {mm}.
\]
Clearly, \( \bar{P}_T>\bar{P}_A \), which means the estimate obtained from the Thiessen-mean method is greater than that obtained using the arithmetic-mean method. Hence, the correct answer is option (A).
