Thiessen Polygons Example PDF

Preview

Summary

Thiessen polygons example for hydrology course...

Description

Thiessen Polygons Example a) Using Thiessen polygons method, obtain an expression for the average rainfall of the catchment shown in the Figure in terms of the rainfall measurements at the 6 rainfall stations. Denote the rainfall at station i as Ri. Solution 6

∑ ( A i Ri )

Average Rainfall

´R= i=1 6

Ai ∑ i=1

Where Ai is the area assigned to station i (area over which the rainfall is assumed to be equal to the rainfall recorded in station i)

b) If the daily rainfall recorded at the stations is as given below, determine the areal rainfall for the catchment. Station (i) Rainfall Ri (mm/day)

1 5

2 10

3 3

4 7

5 8

6 2

Solution The area of the catchment to be assigned to each rainfall station are obtained by using bisectors between neighbouring stations as shown below. The green lines connect neighbouring stations and the bisectors from the midpoints of these lines are then constructed in red colour. Two important things to note: i) The bisectors are constructed from the midpoints of the lines connecting neighbouring rainfall stations ii) The bisectors are perpendicular to the green lines connecting the stations Since we are simply obtaining the areas in order to apply a weighting to the rainfalls recorded at the stations, we do not need to know the actual areas and for this example, the areas are obtained using the provided grid of squares. One could apply any software for obtaining areas as well. Linear approximations of the catchment boundary could also be assumed to obtain regular shapes for which the known formulae for determining area could then be applied. T Station (i) Rainfall Ri (mm/day) Area Ai (Number of squares)

1 5 40

2 10 47

3 3 112

4 7 10

5 8 27

6 2 0

A i=¿ 236 ∑¿

200

AiRi

470

336

70

216

0

∑ Ai Ri=¿ 1292

6

∑ ( A i Ri )

Average Rainfall

´ i=1 R= 6

Ai ∑ i=1

=

1292 =5.47 mm 236...