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A catchment may be idealised as a rectangle. There are three rain gauges located inside the catchment at arbitrary locations. The average precipitation over the catchment is estimated by two methods: (i) Arithmetic mean (PA) and (ii) Thiessen polygon (PT).
Q. Which of the following statements is correct?
  • a)
    PA is always smaller than PT
  • b)
    There is no definite relationship between PA and PT
  • c)
    PA is always equal to PT
  • d)
    PA is always greater than PT
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
A catchment may be idealised as a rectangle. There are three rain gaug...
There is no definite relationship between arithmetic mean and Thiessen polygon method.
Only it can be says that in Thiessen polygon method average value is more uniformly distributed as compared to arithmetic mean.
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A catchment may be idealised as a rectangle. There are three rain gaug...
Explanation:

  • Arithmetic mean (PA) is a method to estimate average precipitation by calculating the sum of precipitation at all gauges and dividing it by the number of gauges.

  • Thiessen polygon (PT) is a method to estimate average precipitation by dividing the catchment into polygons based on the proximity of gauges and assigning each polygon to the nearest gauge. The average precipitation for each polygon is then calculated using the precipitation at the assigned gauge.

  • There is no definite relationship between PA and PT because they are based on different assumptions and calculations.

  • PA assumes that precipitation is uniformly distributed over the catchment, while PT assumes that precipitation varies spatially based on the location of gauges.

  • PA gives equal weightage to all gauges, while PT gives more weightage to gauges located closer to a polygon.

  • The accuracy of PA and PT depends on the number and distribution of gauges, the spatial variability of precipitation, and the shape and size of the catchment.



Therefore, the correct answer is option B, which states that there is no definite relationship between PA and PT.
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A catchment may be idealised as a rectangle. There are three rain gauges located inside the catchment at arbitrary locations. The average precipitation over the catchment is estimated by two methods: (i) Arithmetic mean (PA) and (ii) Thiessen polygon (PT).Q. Which of the following statements is correct?a)PA is always smaller than PTb)There is no definite relationship between PA and PTc)PA is always equal to PTd)PA is always greater than PTCorrect answer is option 'B'. Can you explain this answer?
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