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The Thiessen weights of 4 raingauges A, B, C and D covering a river basin are 0.15, 0.25, 0.30 and 0.30 respectively. If the average depth of rainfall for the basin is 5 cm, the rainfall recorded at B, C and D are 5 cm, 4 cm and 5 cm respectively. What is the rainfall at A?
  • a)
    5 cm
  • b)
    6 cm
  • c)
    7 cm
  • d)
    8 cm
Correct answer is option 'C'. Can you explain this answer?
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Thiessen weights method is used to calculate the average rainfall for a basin by considering the influence of neighboring raingauges. Here, we are given the Thiessen weights of 4 raingauges A, B, C and D covering a river basin as 0.15, 0.25, 0.30 and 0.30 respectively.

Given data:
- Average depth of rainfall for the basin = 5 cm
- Rainfall recorded at B, C and D are 5 cm, 4 cm and 5 cm respectively.

To calculate the rainfall at raingauge A, we can use the formula:
Rainfall at A = Average rainfall x Thiessen weight of A

Let's calculate the average rainfall first:
Average rainfall = (Rainfall at B x Thiessen weight of B) + (Rainfall at C x Thiessen weight of C) + (Rainfall at D x Thiessen weight of D)
= (5 x 0.25) + (4 x 0.30) + (5 x 0.30)
= 1.25 + 1.2 + 1.5
= 3.95 cm

Now, let's calculate the rainfall at A:
Rainfall at A = 3.95 x 0.15
= 0.5925 cm
≈ 0.59 cm

Therefore, the rainfall at A is approximately 0.59 cm, which is closest to option C (7 cm). Hence, the correct answer is option C.
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The Thiessen weights of 4 raingauges A, B, C and D covering a river basin are 0.15, 0.25, 0.30 and 0.30 respectively. If the average depth of rainfall for the basin is 5 cm, the rainfall recorded at B, C and D are 5 cm, 4 cm and 5 cm respectively. What is the rainfall at A?a)5 cmb)6 cmc)7 cmd)8 cmCorrect answer is option 'C'. Can you explain this answer?
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