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- Fatemeh Mostofi (091617071) Estimation of the mean annual areal rainfall(D28HA_2010-2011) 2010

P a g e PROJECT NAME

Fatemeh Mostofi

ID: 091617071

Associated Prof.: Dr.Abdullah Yilmaz

Heriot Watt (Dubai)

26/Sep/2010

Estimationthemeanareal

rainfallforthe catchment


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- Fat M t i (091617071) Esti ati oft mean annual areal rainfall

(D28HA_2010-2011) 2010

P a g e

Tabl of Contents

Table of contents --------------------------------------------------------- 2

INTR DUCTION-------------------------------------------------------- 3

1stMet od: Arit metic Average---------------------------------------- 4

2nd Met od: Thiessen Diagram----------------------------------------- 6

3rd Method: Isohyetal method------------------------------------------- 9


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- Fatemeh Mostofi (091617071) Estimation ofthe mean annual areal rainfall

(D28HA_2010-2011) 2010

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INTRODUCTION

Water received by a catchment, is mostly comes about as rainfall measures over the basin. As

the depth is changing across the basin, so itis expected to have different quantity, from the total rainfall

within the catchment, considering one rainfall duration. So for finding the mean annual area rainfall,

rainfall of different points within the basin needs to be measured.

Climatologist takes different approaches in order to use these data, according to their situation

and available equipments. In this article,three different methods of calculating the perception overthe

short period of time, is going to be presented and then difference between the result as well as causes

forthese differences needs to be taken into consideration.

The first method is using simple Arithmetic Average; this method is dealing with simple

mathematical operations. The other method, which is more precise than the earlier, is the methods

known as Thiessen diagram. For using this method, the catchment needs to be divided by Thisen

polygons. Atthe end,the other method is going to be used to calculate the mean annual areal rainfall,

which is called as Isohyetal method; this method has the different way of sorting outthe basin area,

and using rainfall statistics.


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1st Method: Arithmetic Average

In this method, according to the basement map, rainfall measurements are taken from various

points within the basement, and then the average of this information will be represented as the mean

annual areal rainfall.

By considering the map Figure I,the rainfallin 12 different places across the catchmentis to be

recorded as Table I.

Figure I (Catchment Plan with the rainfall measurements)

A

rea

Number

Rai

nfall(mm)

1 35

2 30

3

41.

4

4

45.

8

5

33.

4

6

28.

6

7

27.

3

8

25.

9

9

21.

9

1 14.


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0 8

1

1

25

2

1

2

28

2Tabl

I -

atchm

t Rai

all mm

So by using the arithmetic average formula and table data of 12 different stations the average

rainfall can be recorded. The final average as is shown in Figure II is 29.8 mm.

Fi II A ithmatic Av age Method)

The above result its not very precise as there were just 12 arbitrary station points without

considering the area which each point is covered. so by using this method an equal importance were

given to not equal area; as the third method will show later on the area of some stations points are

much wider in relation to the others.

As a final point arithmetic average method is easy to use but as mentioned before in case of

non-consistence station portions within the catchment its not as reliable as the other methods.


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2nd Method:Thiessen Diagram

As mentioned in the first method in case of having uneven distribution of area the other

approach is preferred by the scientists called as Thiessen Polygons. In this method information on

the gauges is applying to their relevant area. In the other word this method is concentrating on

weighing both rainfall readings as well as its related area. So the proportion of each area derived from

Thisen polygons (Figure III) with its gauge number represent more accurate insight of the mean areal

rainfall within the particular catchment.

Figure III atchmentdividedbyThiessen polygons)

As Figure III shows the above catchment is divided into 18 sections with different area

measurements in a way that each section is represented by one gauge number.

So according the Thiessen formula Table II can be derived.

A

Nub

inf

ll*A

P

olygon

A

(Unit2

Rai

nfall(mm)

1 4 29

2 540

1

8 30

3 515 1 30


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7 3

4 641

1

4

45.

8

5 140 4 35

6 233.6 8

29.

2

7 254.7 9

27.

3

8 95.2 4

23.

8

9 262.8

1

2

21.

9

1

0 192.4

1

3

14.

8

1

1 224 7 32

1

2 479.4

1

7

28.

2

1

3 554.4

2

2

25.

2

1

4 284.9

1

1

25.

9

1

5 715

2

5

28.

6

1

6 634.6

1

9

33.

4

1

7

1117.

8

2

7

41.

4

1

8 455

1

3 35

T

otal 7447

2

44

Table II( Thiessen ! ethod data)

So after applying Thiessen method and formula as shown in the Figure IV, 30.52mm is derived

as the result.


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Figure IV"Thiessen methodcalculations)

The difference between this result and the one that achieved by using the arithmetic method is

0.72mm; this is a considerable amount for measuring the basin average rainfall.

So as a scientist it is more reliable to publish 30.52mm for the outcome.


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3rd Method: Isohyetal method

This method is outlining boundaries overthe same isohyets (rainfall), by considering differences

between the rainfall ranges. So recording each gauge value, and using the same formula as used earlier

in Thiessen method, other kind of area is being applied for calculation. So atthe end, range of rainfallis

being place in one area (figure V).


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Figure V# Isohyets Method $ alculationandcatchmentdivision)

According to the above calculations the mean areal rainfall by using the third method is

30.14mm which is 0.38 mm less than the number derived by using the second method.


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As this method similarto the Thiessen method is considered the relevant area of each rainfall

station point, so it s again more acute than the arithmetic method; butin compare to the second method,

the reason thatit s more precise is that, by using polygons, estimations and following that errors are

involved in calculating the relevant areas. But using the third method, help us to estimate more accurate

assumption of area, with the basis of available rainfallinformation. So by having the evidence that

similar rainfall data can be achieved from the particular area in the basin,then it s logicalto assume that

certain rainfall data are in an almost uniform area. The following table (table III) shows,the information

which gathered for calculating the present basin average rainfall by the help ofthe 3rd

method.

C

olumn1

a

i(unit2)

p

i(min)

p

i(max)

pi

(av%

)(mm)

a

i*pi

1 7

t

en

1

5

12.

5

8

7.5

2

1

4.5

1

5

2

0

17.

5

2

53.75

3

2

0

2

0

2

5

22.

5

4

50

4

8

8.5

2

5

3

0

27.

5

2

433.75

5

6

1.5

3

0

3

5

32.

5

1

998.75

6

2

9

3

5

4

0

37.

5

1

087.5

7

1

8.5

4

0

4

5

42.

5

7

86.25

8 5

4

5

5

0

47.

5

2

37.5

T

otal

2

44

7

335Table III(Isohyets & ethod Data)


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