 Open Access
 Authors : Tina Moni Boruah , Neha Tiwari , Pompy Chutia , Senchumbeni . M. Patton, Shyamoly Phukan
 Paper ID : IJERTV10IS070074
 Volume & Issue : Volume 10, Issue 07 (July 2021)
 Published (First Online): 19072021
 ISSN (Online) : 22780181
 Publisher Name : IJERT
 License: This work is licensed under a Creative Commons Attribution 4.0 International License
Development of Intensity Duration Frequency Curves for Precipitation in North Lakhimpur (ASSAM)
Tina Moni Boruah*, Senchumbeni. M. Patton**, Shyamoly Phukan***, Neha Tiwari****, Pompy Chutia*****
Department of Civil Engineering
Royal School of Engineering & Technology, Ghy35, Assam
Abstract: An Intensity Duration Frequency (IDF) curves is the graphical representation of the probability that a given average rainfall intensity will occur in a particular region for a given duration of storm having desired frequency of occurrence. The intensity of rainfall is the rate of precipitation, i.e., depth of precipitation per unit time. This can be either instantaneous intensity or average intensity over the duration of rainfall. Here, in this project we have considered average intensity of rainfall. The Intensity Duration Frequency (IDF) relationship of rainfall amounts is considered as one of the most commonly used tools in water resource engineering for planning, design and operation of water resources project, or for various engineering projects against design floods. The objective of this research is to derive IDF relationship of rainfall for watershed of North Lakhimpur, Assam. These relationships are useful in design of urban drainage works, for example storm sewer, culverts and other hydraulic structure. In this study, rainfall depth for 11 years viz. 2006 to 2016 has been collected from the Regional Meteorological centre, Guwahati. Gumbles frequency analysis technique has been used to calculate the return periods for a period of 2yrs, 5yrs, 10yrs, 50yrs and 100yrs from the maximum intensity. Finally, regression analysis has been to develop the Intensity Duration Frequency (IDF) curve.
Keywords: IDF, Return Period, Regression Analysis, North Lakhimpur

INTRODUCTION
In many parts of the world, flooding is probably the most severe hazard among the natural hazards occurring due to change in rainfall pattern. Development of rainfall IntensityDurationFrequency (IDF) relationship is a primary basic input for the design of the storm water drainage system for cities. IntensityDurationFrequency (IDF) relationship of rainfall amounts is one of the most commonly used tools in water resources engineering for planning, design, and operation of water resources projects. Rainfall IntensityDurationFrequency IDF curves are graphical representations of the amount of water that falls within a given period of time in catchment areas. IDF curves are used to aid the engineers while designing urban drainage works. A design flood is the flood magnitude selected for the use as a criterion in designing flood control works. The objective of the rainfall IDF curves is to estimate the maximum intensity of rainfall for any duration and return period. This frequency analysis uses annual or seasonal maximum intensity of rainfall for any duration and return period. This frequency analysis uses annual or seasonal maximum series, or independent values above a high threshold selected for different durations. IDF analysis takes into account the different durations in a single study, and prevents curves intersecting.

STUDY AREA
Lakhimpur is an administrative district in the state of Assam in India. It is situated at 27Â°13'60 N and 94Â°7'0 E.The district headquarters are located at North Lakhimpur. The district is bounded on the north by Siang and Papump are District of Arunachal and on the east by Dhemaji District and Subansiri River. Majuli Sub Division of Jorhat District stands on the southern side and Gohpur sub division of Sonitpur District is on the West. The Brahmaputra is navigable for steamers in all seasons as far as Dibrugarh, in the rainy season as far as Sadiya; its navigable tributaries within the district are the Subansiri, Ranganadi and Dikrong. Lakhimpur's climate is classified as warm and temperate. The summers here have a good deal of rainfall, while the winters have very little. In Lakhimpur, the average annual temperature is 25.0 Â°C. The rainfall here averages 1200 mm.
Fig 1.1: Study Area Map of North Lakhimpur district (Source: Ground water booklet of Lakhimpur district)

Objectives of the study

To collect the data of rainfall depth of North Lakhimpur for 11 years from Regional Meteorological centre, Guwahati. The data of 24 hours rainfall was obtained from the year 20062016.

To calculate the return period for the period of 2yr, 5yr, 10yr, 50yr and 100yr from the maximum intensity using Gumbels distribution.

To establishment of IntensityDurationFrequency curves for several purpose :

The estimation of extreme rainfall for design purposes.

The assessment of the rarity of observed rainfalls.

Comparison of methods to estimate design rainfall.




METHODOLOGY
The classical approach for building IDF curves has three steps. In the first step, a probability distribution function is fitted to each duration sample. In a second step, the quantities of several return periods T are calculated using the estimated distribution function from step1. Lastly, the parameters of the IDF equations and coefficient of different return periods are calculated by using nonlinear multiple regression method. The results obtained showed that in all the cases the correlation coefficient is very high indicating the goodness of fit of the formulae to estimate IDF curves in the region of interest.
3.1 IntensityDurationAnalysis
It is observed that the most intense storms last for every short durations. As the duration of storm increases, the maximum average intensity of storm decreases. If the observed maximum rainfall intensities at a place for various durations such as 10min, 15min, 1hr, 3hr, 5hr, 7hr, etc are plotted against respective durations, a graph known as intensityduration graph is obtained.
3.1.1 Empirical IDF Equations
The IDF formulae are the empirical equations representing a relationship among maximum rainfall intensity (as dependent variable) and other parameters of interest such as rainfall duration and frequency (as independent variable). There are several commonly used functions found in the literature of hydrology applications, four basic forms of equations used to describe the rainfall intensity duration relationship are summarized as follows:
Talbot equations:
I=
+
Bernard equations:
I=
Kimijima equation:
I=
. (3.1)
. (3.2)
. (3.3)
Sherman equation:
I= (+)
. (3.4)
Where I is the rainfall intensity (mm/hr); d is the duration (minutes); a, b and c are the constant parameters related to the meteorological conditions. These empirical equations show rainfall intensity decreases with rainfall duration for a given return period. All functions have been widely used for hydrology practical applications.
3.1.2 Calculation of Recurrence Period by Gumbels method
The extreme value distribution was introduced by Gumbel and is commonly known as Gumbels distribution. The estimate of rainfall intensity of given duration for different return period is obtained by this method. It is one of the most widely used probabilitydistribution functions for extreme values in hydrologic and meteorological studies for protection of flood peaks, maximum rainfalls, maximum wind speeds, etc. It was confirmed that the Gumbel distribution well describes the variation of annual series of maximum rainfall intensity. According to this theory of extreme vents, the probability of occurrence of an event equal to or larger than a value of Xo is,
o
o
P(Xx ) =1 .(3.5)
In which y is a dimensionless variable given by
y=(xa)
a=x0.45005X
=1.2825/X
Thus, y=1.2825() + 0.577 . (3.6)
Where, =mean and X=standard deviation of the variable X
In practice it is the value of X for a given P that is required and as such equation 3.5 is transposed as, Yp=ln[ln(1P)]
. (3.7)
Noting that the return period T=1/Pand designating y1= the value of y, commonly called the reduced variable, for a given T Y1 = [ln.ln ] . (3.8) Or
1
Y1= [0.834 + 2.303log log
1
. (3.8 a)
Now by rearranging equation 3.6, the variable X with a return period T is, Xt=x+k
Where, K=0.577
1.2825
Gumbels Equation For Practical Use are as follows
(3.10)
Equation 3.9 gives the value of the variable X with a recurrence interval T is used as XT = + Kn1
Where, n1 =standard deviation of the sample of size N K = frequency factor expressed as K=
In which y=2 reduced variable, a function of T and is given by, YT = [. ] Or
1
YT = – [0.834 + 2.303 log ]
1
= reduced mean,a function of sample size N
Sn = reduced standard deviation, a function of the sample size

IntensityDuration Frequency Analysis
Every storm in a year is analyzed to find the maximum intensities for various duration. Thus each storm gives one value of maximum intensity for duration. The largest of all such values is taken to be the maximum intensity in that year for that duration. Likewise the annual maximum intensity is obtained for all the duration. Similar analysis yields the annual maximum intensities for various durations in different years. It will then be observed that the annual maximum intensity for any given duration is not the same every year but varies from year to year. In other words it behaves as a random variable.

Regression Analysis
Regression analysis tries find out the average relationship between the variables. It refers to the methods by which estimates are made of the values of one variable from the knowledge of the values of one or more other variables. In regression analysis however one variable is taken as the dependent variable and the other taken as the independent variables, thus making it possible to study the cause and effect relationship. However, the maximum intensity varies inversely with the duration and
generally an equation of the for, I=
(+)
4.1 Calculation of Return Period:
.(3.14)


RESULTS AND CALCULATIONS
The calculation of return period is done according to Gumbels distribution method. The return period for 2 years, 5 years, 10 years, 50 years, 100 years are found out.
Table 4.1 : For 1 day, the return period of 2yr, 5yr, 10yr, 50yr, and 100yr :
Order No.
INTENSITY
SUM
AVERAGE
XXavg
(XXavg)2
S=(X
Xavg)2
S/(N1)
n1=S/(n1)
(X)
(Xavg)
mm/day
1
103.8
436.7
39.7
64.1
4108.81
8354.87
835.48
28.9
2
67.6
39.7
27.9
778.41
3
66
39.7
26.8
718.24
4
40
39.7
0.3
0.09
5
38.9
39.7
0.8
0.64
6
34.1
39.7
5.6
31.36
7
28.6
39.7
11.9
141.61
8
17.7
39.7
22
484
9
14.8
39.7
24.9
620.01
10
13.8
39.7
25.9
670.81
11
11.4
39.7
28.3
800.89
For N= 11, Yn= 0.4996, Sn= 0.9676
T
T1
T/T1
ln(T/T1)
ln(ln(T/T1))
Y= ln(ln(T/T1))
2
1
2
0.6931
0.3666
0.3666
5
4
1.25
0.2231
1.5001
1.5001
10
9
1.1111
0.1053
2.2509
2.2509
50
49
1.0204
0.0202
3.9021
3.9021
100
99
1.0101
0.01
4.6052
4.6052
Y
Yn
YYn
Sn
K=(YYn)/Sn
0.3666
0.4996
0.1333
0.9676
0.137
1.5001
0.4996
1.0005
0.9676
1.034
2.2509
0.4996
1.7513
0.9676
1.809
3.9021
0.4996
3.4025
0.9676
3.516
4.6052
0.4996
4.1056
0.9676
4.243
Return Period
Xavg
K
n1
K*n1
Xt=Xavg+K*n1
2
39.7
0.137
28.9
3.959
35.741
5
39.7
1.034
28.9
29.882
69.582
10
39.7
1.809
28.9
52.28
91.98
50
39.7
3.516
28.9
101.612
141.312
100
39.7
4.243
28.9
122.622
162.322
Table 4.2 : For 3 day, the return period of 2yr, 5yr, 10yr, 50yr, and 100yr :
Order No.
INTENSITY (X)
mm/day
SUM
AVERAGE
(Xavg)
XXavg
(XXavg)2
S=(X
Xavg)2
S/(N1)
n1=S/(n1)
1
164.4
1003.9
6
91.27
73.13
5347.99
21753.1
2175.3
14.75
2
138.7
91.27
47.43
2249.6
3
136.1
91.27
44.83
p>2009.72 4
112.6
91.27
21.33
454.96
5
109.8
91.27
18.53
343.36
6
85.1
91.27
6.17
33.06
7
74.8
91.27
16.47
271.26
8
74.8
91.27
16.47
271.26
9
68.2
91.27
23.07
532.22
10
21.1
91.27
70.17
4923.83
11
18.36
91.27
72.91
5315.86
For N= 11 ,Yn= 0.4996,
Sn=0.9676
T
T1
T/T1
ln(T/T1)
ln(ln(T/T1))
Y= – ln(ln(T/T1))
2
1
2
0.6931
0.3666
0.3666
5
4
1.25
0.2231
1.5001
1.5001
10
9
1.1111
0.1053
2.2509
2.2509
50
49
1.0204
0.0202
3.9021
3.9021
100
99
1.0101
0.01
4.6052
4.6052
Y
Yn
YYn
Sn
K=(YYn)/Sn
0.3666
0.4996
0.1333
0.9676
0.137
1.5001
0.4996
1.0005
0.9676
1.034
2.2509
0.4996
1.7513
0.9676
1.809
3.9021
0.4996
3.4025
0.9676
3.516
4.6052
0.4996
4.1056
0.9676
4.243
Return Period
Xavg
K
n1
K*n1
Xt=Xavg+K*n1
2
91.27
0.137
14.75
2.02
89.25
5
91.27
1.034
14.75
15.25
106.52
10
91.27
1.809
14.75
26.68
117.95
50
91.27
3.516
14.75
51.86
143.13
Table 4.3 : For 5 day, the return period of 2yr, 5yr, 10yr, 50yr, and 100yr :
Order No.
INTENSITY
(X) mm/day
SUM
AVERAGE
(Xavg)
XXavg
(XXavg)2
S=(X
Xavg)2
S/(N1)
n1=S/(n 1)
1
341.7
1541.7
140.15
201.55
40622.4
85608.13
8560.81
92.52
2
219.4
140.15
79.25
6280.56
3
194.4
140.15
54.25
2943.06
4
185.3
140.15
45.15
2038.52
5
161.9
140.15
21.75
473.06
6
120.8
140.15
19.35
374.42
7
102.1
140.15
20.05
402
8
96.6
140.15
43.55
1896.61
9
55.9
140.15
84.25
7098.06
10
31.8
140.15
108.35
11739.72
11
31.8
140.15
108.35
11739.72
For N= 11 ,Yn= 0.4996,
Sn= 0.9676
T
T1
T/T1
ln(T/T1)
ln(ln(T/T1))
Y= – ln(ln(T/T1))
2
1
2
0.6931
0.3666
0.3666
5
4
1.25
0.2231
1.5001
1.5001
10
9
1.1111
0.1053
2.2509
2.2509
50
49
1.0204
0.0202
3.9021
3.9021
100
99
1.0101
0.01
4.6052
4.6052
Y
Yn
YYn
Sn
K=(YYn)/Sn
0.3666
0.4996
0.1333
0.9676
0.137
1.5001
0.4996
1.0005
0.9676
1.034
2.2509
0.4996
1.7513
0.9676
1.809
3.9021
0.4996
3.4025
0.9676
3.516
4.6052
0.4996
4.1056
0.9676
4.243
Return Period
Xavg
K
n1
K*n1
Xt=Xavg+K*n1
2
140.15
0.137
92.52
12.67
127.48
5
140.15
1.034
92.52
95.66
235.81
10
140.15
1.809
92.52
167.37
307.52
50
140.15
3.516
92.52
325.3
465.45
100
140.15
4.243
92.52
392.56
532.71
Table 4.4 : For 6 day, the return period of 2yr, 5yr, 10yr, 50yr, and 100yr :
Order No.
INTENSITY
(X) mm/day
SUM
AVERAGE
XXavg
(XXavg)2
S=(X
Xavg)2
S/(N1)
n
1=S/(n
1)
1
294.3
1976.5
179.68
114.62
13137.74
89135.91
8913.59
94.41
2
256.8
179.68
77.12
5947.49
3
256.8
179.68
77.12
5947.49
4
241.7
179.68
62.02
3846.48
5
225.7
179.68
46.02
2117.84
6
199
179.68
19.32
373.26
7
167.9
179.68
11.78
138.76
8
158.8
179.68
20.88
435.97
9
151.1
179.68
28.18
794.11
10
24.4
179.68
155.28
24111.87
11
0
179.68
179.68
32284.9
For N= 11 ,Yn= 0.4996,
Sn= 0.9676
T
T1
T/T1
ln(T/T1)
ln(ln(T/T1))
Y= ln(ln(T/T1))
2
1
2
0.6931
0.3666
0.3666
5
4
1.25
0.2231
1.5001
1.5001
10
9
1.1111
0.1053
2.2509
2.2509
50
49
1.0204
0.0202
3.9021
3.9021
100
99
1.0101
0.01
4.6052
4.6052
Y
Yn
YYn
Sn
K=(YYn)/Sn
0.3666
0.4996
0.1333
0.9676
0.137
1.5001
0.4996
1.0005
0.9676
1.034
2.2509
0.4996
1.7513
0.9676
1.809
3.9021
0.4996
3.4025
0.9676
3.516
4.6052
0.4996
4.1056
0.9676
4.243
Return Period
Xavg
K
n1
K*n1
Xt=Xavg+K*n1
2
179.68
0.137
94.41
12.93
166.75
5
179.68
1.034
94.41
97.61
277.29
10
179.68
1.809
94.41
170.78
350.46
50
179.68
3.516
94.41
331.94
511.62
100
179.68
4.243
94.41
400.58
580.26
B. Construction of IntensityDurationFrequency Curves:

Intensity frequency curve
The frequency analysis and the maximum intensity of rainfall for various return period can be obtained. Then from the result of these analysis graphsof maximum rainfall intensity against the return period for various durations are plotted.
Maximum rainfall intensity
(mm/hr)
Maximum rainfall intensity
(mm/hr)
Table 45 : For 1 day Maximum Intensity
Return Period
Xavg
K
n1
K*n1
Xt=Xavg+K*n1
2
39.7
0.137
28.9
3.959
35.741
5
39.7
1.034
28.9
29.882
69.582
10
39.7
1.809
28.9
52.28
91.98
50
39.7
3.516
28.9
101.612
141.312
100
39.7
4.243
28.9
122.622
162.322
250
200
150
100
50
Series1
Expon. (Series1)
250
200
150
100
50
Series1
Expon. (Series1)
0
20
60
Return Period(yr)
100
120
0
20
60
Return Period(yr)
100
120
0
0
40
40
80
80
Fig 4.1 Intensity frequency curve for 1 day
Table 4.6: For 3 day Maximum Intensity
Return Period
Xavg
K
n1
K*n1
Xt=Xavg+K*n1
2
91.27
0.137
14.75
2.02
89.25
5
91.27
1.034
14.75
15.25
106.52
10
91.27
1.809
14.75
26.68
117.95
50
91.27
3.516
14.75
51.86
143.13
100
91.27
4.243
14.75
62.58
153.85
180
160
140
120
100
80
60
40
20
0
Series1
Expon. (Series1)
180
160
140
120
100
80
60
40
20
0
Series1
Expon. (Series1)
0 20 40 60 80 100 120
Return Period (yr)
0 20 40 60 80 100 120
Return Period (yr)
Maximum rainfall intensity
(mm/hr)
Maximum rainfall intensity
(mm/hr)
Fig 4.2 Intensity frequency curve for 3 day
Table 4.7 : For 5 day Maximum Intensity
Return Period Xavg K n1 K*n1 Xt=Xavg+K*n1
532.71
2
140.15
0.137
92.52
12.67
127.48
5
140.15
1.034
92.52
95.66
235.81
10
140.15
1.809
92.52
167.37
307.52
50
140.15
3.516
92.52
325.3
465.45
100
140.15
4.243
92.52
392.56
700
600
500
400
300
200
100
0
Series1
Expon. (Series1)
700
600
500
400
300
200
100
0
Series1
Expon. (Series1)
0 20 40 60 80 100 120
Return period(yr)
0 20 40 60 80 100 120
Return period(yr)
Maximum rainfall intensity
(mm/hr)
Maximum rainfall intensity
(mm/hr)
Fig 4.3 Intensity frequency curve for 5 day
Table 4.8: For 6 day Maixmum Intensity
Return Period
Xavg
K
n1
K*n1
Xt=Xavg+K*n1
2
179.68
0.137
94.41
12.93
166.75
5
179.68
1.034
94.41
97.61
277.29
10
179.68
1.809
94.41
170.78
350.46
50
179.68
3.516
94.41
331.94
511.62
100
179.68
4.243
94.41
400.58
580.26
700
600
500
400
300
200
100
0
Series1
Expon. (Series1)
700
600
500
400
300
200
100
0
Series1
Expon. (Series1)
0 20 40
60
Return period(yr)
80
100
120
0 20 40
60
Return period(yr)
80
100
120
Maximum rainfall intensity
(mm/hr)
Maximum rainfall intensity
(mm/hr)
Fig 4.4 Intensity frequency curve for 6 day

Intensity frequency duration curve
Table 4.9: Return period 2, 5, 10, 50,100 years maximum Intensity duration
Maximum rainfall intensity
Maximum rainfall intensity
Return Period Intensity for duration (mm/hr)
years
1day
3day
5day
6day
2
35.741
89.25
127.48
166.75
5
69.582
106.52
235.81
277.29
10
91.98
117.95
117.95
350.46
50
141.312
143.13
143.13
511.62
100
162.332
153.85
153.85
580.26
700
600
500
400
300
200
100
0
700
600
500
400
300
200
100
0
0
50
100
Return Period
150
200
0
50
100
Return Period
150
200
Fig 4.5 Return period 2, 5, 10, 50,100 years Intensity


CONCLUSION
This study had been conducted for the formulation and construction of IDF curves using rainfall data for the year 2006 to 2016 for North Lakhimpur area, Assam. The rainfall intensity is found to be nonuniform throughout the area. The actual method to construct IDF curves involves three main steps. The first step is to obtain the annual maximum intensity for each interval length. Then for each time interval, a statistical analysis has to be done to compute the quantiles for different return periods. In the third
step, the IDF curves are usually determined by fitting a specified parametric equation for each return period to the quantiles estimates, using regression techniques. Using this method the same can be found out for other cities as well as by collecting the rainfall data for the respective day. From this study, the following conclusions are made:

The gradual exponential decrease of IDF curves for different return periods reveal that the conclusion of maximum intensity for all the years is satisfactory.

The value of a for which the sum of the squared deviation is minimum is found out and when the corresponding value of c and b for the maximum squared deviation of a is put in the equation (3.14) and is back calculated, the values of intensity for the corresponding time interval is found out to be approximately same.

The values of a, b and c are found to be 34, 0.97, and 12.133 respectively.
ACKNOWLEDGEMENT
At the very outset, we are pleased and highly honored to express our sincere and heartfelt gratitude to Mr. Priyanjit Purkaystha, Assistant Professor, Department of Civil Engineering, Royal School of Engineering & Technology, Betkuchi, Guwahati35, for his constant guidance, support, inspiration and full cooperation throughout the project work.
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