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Thiessen average rainfall, four gauges at rectangle corners

Short answer

Each corner gauge has equal area (3750 km²) due to symmetry. Mean rainfall = (1200+1300+1500+1100)/4 = 1275 mm.

There are four rain gauges at four corners of a rectangle. The two sides of the rectangle are 100 km and 150 km. The yearly rainfalls of the four gauges are 1200 mm, 1300 mm, 1500 mm and 1100 mm respectively. Calculate the average rainfall by Thiessen polygon method.

Four gauges at the corners of a rectangle are equally spaced from the centre, so the perpendicular bisectors are the two lines through the centre parallel to the sides. The rectangle divides into four equal rectangles, one for each gauge.

  G1 +--------+--------+ G2
     | A/4    | A/4    |
     +--------+--------+
     | A/4    | A/4    |
  G4 +--------+--------+ G3

Total area =100×150=15 000= 100 \times 150 = 15\,000 km²; each gauge area =3750= 3750 km² (weight 0.25).

Pˉ=∑AiPi∑Ai=3750(1200+1300+1500+1100)15 000=51004=1275 mm\bar P = \frac{\sum A_i P_i}{\sum A_i} = \frac{3750(1200+1300+1500+1100)}{15\,000} = \frac{5100}{4} = 1275\ \text{mm}

Answer: Average rainfall by Thiessen polygon method = 1275 mm (equal to the arithmetic mean).

✓ Answer checked by Claude Sonnet 5.5

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