Chapter 2 Precipitation

Transcription

1 Engineering Hydrology Chapter 2 Precipitation

2 Adequacy of Rain gauge Stations N Cv 2 C P V m P 1 m Pi m 1 m 1 m 1 ( P i m 1 P) 2 N = optimal number of stations ε = allowable degree of error in the estimate of the mean rainfall Cv = coefficient of variation of the rainfall values at the existing m stations (in percent) m 1 = standard deviation, P = mean precipitation P i = precipitation magnitude in the i 4th station

3 Question_1 A catchment area has seven rain gauge stations. In a year the annual rainfall recorded by the gauge are as follows: Station P Q R S T U V Rainfall (cm) For a 5% error in the estimation of the mean rainfall, calculate the minimum number of additional stations required to be established in the catchment?

4 Question_1 Solution Station P Q R S T U V Rainfall (cm) o P= = cm o σ = o C v = 100 σ P m (Pi P) 2 1 m 1 = = (Pi ) = = 22.5 o N = ( C v ε )2 = ( ) 2 = 12 5 o 5 additional stations are required

5 Question_2

6 Estimation of Missing Data

7 Estimation of Missing Data القراءات للمحطات بعد الخطأ : Pm P1, P2 القراءات للمحطات قبل الخطأ N1, N2.. Nm عدد المحطات بدون المحطة الخطأ : M قيمة المطر عند المحطة التي حدث فيها الخطأ : Nx قيمة المطر المفقودة عند المحطة التي حدث فيها الخطأ : Px % error = {(Nx Navg)/Nx} * 100%

8 Question_3 The normal annual precipitation of five rain gauge stations P,Q,R,S and T are respectively 125, 102, 76, 113 and 137 cm. During a particular storm the precipitation recorded by stations P,Q,R and S are 13.2, 9.2, 6.8 and 10.2 cm respectively. The instrument at station T was inoperative during that storm. Estimate the rainfall at station T during that storm?

9 Question_3 Solution Navg = ( ) / 5 = % error = {( )/137}*100% = 19.27% > 10% P x cm

10 Test for Consistency of Record

11 Test for Consistency of Record Solution steps (من الجديد للقديم ( of: 1. Arrange in reverse order the data 1. The annual rainfall of station X (P x ) 2. The average rainfall of the group of base stations (P avg ) 2. Calculate the accumulated precipitation of station X ( P x ) and the accumulated values of average of the selected base group ( P avg ). 3. Plot P x againest P avg for various consecutive time periods { Double mass curve } 4. Locate the break in the slope of the resulting plot (which is the change in precipitation regime of station X) 5. Correct the precipitation values at station X beyond the period of regime change by:

12 Question_4

13 year station 8 cum. average station A cum. ann. rainfall aver age ann. rainfall for )cm( at station A )cm( stations

14 Accumulated annual rainfall at X in units of 10 3 cm Mc= Ma = = 0.6 / 0.75 = 0.8 or = /1.172= = = accumulated annual rainfall of 8 station mean in units of 10 3 cm

15 corrected value = original value * (Mc/Ma) year original value( cm) corrected value (cm)

16 Rainfall Representation 1) Mass curve 2) Hyetograph 3) IDF curve

17 Mass curve نهاية ال -1 storm ال يوجد أمطار ال يوجد أمطار i= /8=0.25c m/hr i= 2.4/8=0.3cm/ hr Slope of the curve = intensity

18 Hyetograph Every storm has its own Hyetograph Area = 0.3*8 = 2.8 cm Sum Area of Every Boxes = 10 cm area under hyetograph = total preci. in that period

19 Question_5

20 Question_5 Solution Time since start of storm (min) rainfall (cm) Intensity (cm/min) Cumulative ( cm )

21 Intensity (cm/min) Question_5 A. Hyetograph representation 0.25 Hyetograph of Storm Time (min)

22 Cumulative rainfall (cm) Question_5 b. Mass curve representation 25 Mass curve of Storm Time (min)

23 Question_6

24 Question_6 Solution

25 Question_7

26 Mean Precipitation over an Area

27 Mean Precipitation over an Area Thiessen-Mean Method هذه الطريقة تعتمد على حساب المساحة التي تمثلها كل محطة ولحساب المساحة : A. يتم وصل المحطات ببعض ليكونوا مثلثات B. يتم تنصيف أضالع المثلثات)منصف عمودي( إلى أن تلتقي األعمدة المنصفة C. يتم حساب المساحات الخاصة بكل محطة مع استبعاد المساحة التي تكوت خارج Catch.Area D. ثم حساب P بالقانون التالي :

28 Mean Precipitation over an Area لحساب المساحة بهذه الطريقة: Rainfall ارسم خطوط كنتورية بحيث يمر كل خط في النقاط التي لها نفس قيمة A. B. احسب المساحة بين كل خطين )Isohyetal( مع استثناء المساحة التي تقع خارج Catch.Area C. احسب متوسط Rainfall بين كل خطين D. ثم احسب Pمن القانون التالي :

29 Question_8

30 Question_9 The following figure shows a catchment area with six rain gauge stations. The rainfall recorded by each of these stations are indicated in the figure. Calculate 1) The mean precipitation using Thiessen-mean method. 2) The Total precipitation over the area in m3

31 Question_10

32 Frequency of Point Rainfall

33 Frequency of Point Rainfall

34 Frequency of Point Rainfall

35 Question_11

36 Question_11

37 Question_11

38 Question_12

39 Question_12

40 Question_13

41 Plotting Position

42 Plotting Position P = m/n+1 T = 1/P ترتيب تنازلي من األعلى لألصغر اذا كان هناك تكرار لقيمة معينة في أكثر من سنة نحذف التكرار الموجود

43 Question_14

44 Question_14 m N = 20

45 Question_14

46 Intensity Duration Frequency (IDF) Curve

47 IDF Curve

48 Rainfall Intensity and Corresponding Depth

49 Rainfall Intensity versus Duration

50 Interpretation of IDF curve P= 2in/hr * 90/60 = 3in

51 Interpretation of IDF curve = 4.6in/hr * 30/60 = 2.3 in

52 Development of IDF curve

53 Development of IDF curve

54 Development of IDF curve

55 Development of IDF curve

56 Development of IDF curve

57 Depth-Duration Frequency curve (DDF)

58 Intensity versus Return Period for Deferent Durations

59 Question_15 The mass curve of rainfall in a storm of a total duration of 270 minutes is given in the table: Time Cumulative Rainfall Draw the Hyetograph of the storm at 30 minutes time step 2- Plot the Maximum Intensity-Duration curve 3- Plot the Maximum Depth-Duration curve

60 Question_15 Solution

61 Question_15

62 Question_15

63 Question_15

64 Question_16

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66 Question_17

67 Question_17 Retern Period / Duration

68 Rainfall Depth Question_ Year Year Duration

69 Intensity Question_17 Return period / Duration Depth at 1-Yr Depth at 10-Yr intensity at 1-Yr Intensity at 1-Yr Intesity at 10-Yr intensity at 10-Yr Duration

70 Homework