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GATE 2025 CE (CE1) – Question 39

Hydrology · Hydrologic cycle, precipitation, evaporation, evapo-transpiration, infiltration · 2 marks · Multiple choice

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:

Rain gauge stationPQRS
Whether located inside the catchmentYesYesYesNo
Thiessen weightage factor0.250.500.100.15
Rainfall (mm)100110100125
  1. The estimate obtained from the Thiessen-mean method is greater than that obtained using the arithmetic-mean method
  2. The estimate obtained from the Thiessen-mean method is equal to that obtained using the arithmetic-mean method
  3. The estimate obtained from the Thiessen-mean method is less than that obtained using the arithmetic-mean method
  4. The Thiessen-mean method cannot be applied in this case

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Show answer and explanation

Correct answer: (A) The estimate obtained from the Thiessen-mean method is greater than that obtained using the arithmetic-mean method

Explanation

The Thiessen mean weights each gauge by its polygon area, and a gauge outside the catchment can take part when its polygon reaches into it: $0.25(100) + 0.50(110) + 0.10(100) + 0.15(125) = 108.75$ mm. The arithmetic mean uses only the gauges inside the catchment, P, Q and R: $\frac{100 + 110 + 100}{3} = 103.33$ mm. So the Thiessen mean is larger.