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Intensity-Duration-Frequency (IDF) Curve and the Most Suitable Method to Determine Flood Peak Discharge in Upper Werba Sub-Watershed.

Introduction

Information of design flood is one of important factors for flood risk assessment and water infrastructures planning and development in a certain location [1]. Many approaches have been used to estimate it including flood frequency statistics and the design storm method [2]. Rogger et al. [2] mentioned that geological information on the catchments is important to identify the mismatch of flood discharge estimation and flood discharge observed.

Flood frequency analysis is a well-established approach which has been applied in decades [1,3-5]. This analysis is still commonly used until recently. Hailegeorgis and Alfredsen [6] used L-moments method and annual maximum series for flood quantiles prediction ungauged basins in mid-Norway and Ozga-Zielinski et al. [7] used two-dimensional (2D) normal distribution and copula-based 2D probability distribution to estimate flood peak and flood volume in Narew River, Poland. Other method such as modelling of rainfall-runoff process presented in flood hydrograph can be used for flood discharge estimation.

Flood hydrograph can be derived from unit hydrograph at certain location. In order to develop a unit hydrograph for a certain location, specifically a watershed, detailed and complete historical data of rainfall and streamflow are needed. However, such data would not available in every watershed [1]. Therefore, Synthetic Unit Hydrograph can be generated.

Unit Hydrograph (UH) and Synthetic Unit Hydrograph (SUH) are the common methods applied to estimate flood discharge. Swain et al. [8] used Geomorphologic Instantaneous Unit Hydrograph (GIUH) and SUH to estimate streamflow in Koel River basin of India. Kusumastuti et al. [9] developed Soil Conservation Service Synthetic Unit Hydrograph (SCS SUH) in Ambon, Indonesia, to estimate peak of flood discharge and evaluate drainage channels capacity. Procedure of development of various SUHs have been discussed in detail in many hydrology handbooks, e.g. Snyder's SUH and SCS Dimensionless Hydrograph [1,3,4]; SCS Triangular Hydrograph [1]; GAMA I SUH and Nakayasu [4].

Indonesia is an archipelago country. It consists of more than 16,000 islands [10]. Papua Island is the biggest island located in the easternmost territorial of Republic of Indonesia. In the last few years, infrastructures planning in the area became important issue including water infrastructures. This paper aims to present the intensity-duration-frequency (IDF) curve for a certain watershed in West Papua Province as well as to compare several methods which provide the closest magnitude of the estimated flood peak discharge to the observed stream flow.

Study Area and Rainfall Data

Study Area

The study area of the research is Upper Werba Sub-Watershed. Werba River is flowing in Werba District, Fakfak Regency, West Papua Province, Indonesia, as can be seen in Figure 1. Fakfak Regency is located between 131[degrees]30' - 138[degrees]40' East Longitude and 2[degrees]25' - 4[degrees] South Latitude [11]. Werba River flows from Onin Mountain to Laut Seram (Seram Sea). Specifically, the watershed map in presented in Figure 2. The length of the river which is analyzed in this paper is 12.50 km with 28.02 [km.sup.2] catchment area.

Rainfall Data

Average number of rain day in Fakfak Regency is 269 days [11]. Daily rainfall data from 2009-2018 and hourly rainfall data in 2018 were collected from a meteorological station in Torea Airport, Fakfak Regency. The maximum daily rainfall from 2009-2018 is analyzed from those data and presented in Table 1.

The frequency analysis of maximum daily rainfall data is conducted to observe the type of extreme value distribution. The coefficient of skewness and coefficient of kurtosis of the maximum daily rainfall data are 0.329 and 3.16, respectively. At those numbers, the distribution of the data is close to the characteristic of Log Normal distribution. Goodness of fit test, i.e. Chi-square test [3], is then conducted as a validation step. At 5% significant level and three degree of freedom, the value of Chi-suare, [X.sup.2], is obtained as much as 3. This calculated [X.sup.2] is lower than the critical value of chi-square distribution ([X.sup.2]Cr = 7.815), therefore statistical distribution of maximum daily rainfall data in Fakfak Regency follows Log Normal distribution.

Development of Intensity-Duration-Frequency (IDF) Curve

To develop intensity-duration-frequency (IDF) curve, rainfall intensity is transformed from daily rainfall data using Mononobe method [4] in Equation 1. The formula requires the information of time of concentration to transform rainfall depth into rainfall intensity (I).

[mathematical expression not reproducible] (1)

for:

I : rainfall intensity (mm/hour)

[R.sub.24] : maximum daily rainfall at certain return period (mm)

t : time of concentration (hour)

In this research, the time of concentration is determined based on the average duration of rain in a day recorded in meteorological station in Torea Airport, Fakfak Regency in 2018. Based on one-year data of hourly rainfall in 2018, the average duration of rain in a day in Fakfak Regency is 3 (three) hours. The second component of Mononobe formula is [R.sub.24]. By using Log Normal distribution function in Equation 2 [4], the design rainfall for 2, 10, 25, and 50-year return period is estimated and presented in Table 2. The result of conversion of design rainfall depth to design rainfall intensity using Mononobe formula is presented in Table 2.

[x.sub.T] = antilog ([z.sub.T]) (2)

for:

[Z.sub.T] = [bar.z] + [K.sub.z][[sigma].sub.z]

z = logx

[x.sub.T] : hydrologic parameter value at certain return period, T

[[sigma].sub.z] : standard deviation of the Z variate sample

[K.sub.z] : frequency factor of Log Normal distribution

IDF curve represents the information of intensity, duration, and frequency of rainfall. The frequency in this curve is shown by the return period of design rainfall. The IDF curves for Upper Werba Sub-Watershed at 2, 10, 25, and 50-year return period are presented in Figure 3.

The IDF curves in Figure 3 provide the important information of rainfall intensity which can be used to estimate flood discharge using Rational Method [1] in Upper Werba Sub-Watershed. Rational Method has been used previously by Kusumastuti et al. [12,], to estimate peak of flood discharge in several watersheds in Probolinggo Regency, Indonesia and Kusumastuti et al. [13] to estimate surface runoff volume for designing eco-drainage system in Mojokerto Municipality, Indonesia.

Flood Discharge Estimation

Flood frequency analysis is the main method to estimate flood discharge in Upper Werba Sub-Watershed in this research. There are three methods chosen, i.e. Soil Conservation Service SUH, Nakayasu SUH, and Rational Method. The estimated peak of flood discharge obtained through those methods is then compared with observed streamflow in Upper Werba River.

Soil Conservation Service SUH

To develop Soil Conservation Service (SCS) SUH, several data of river and rainfall characteristic, i.e. time of concentration, duration of effective rainfall, and catchment area are needed. Those data is used to estimate the peak of flood discharge using Equation 3 [3].

[q.sub.p] = [CA/T.sub.p] (3)

for:

[T.sub.p] = [t.sub.r]/2 + [t.sub.p]

C : 2.08

A : catchment area ([km.sup.2])

[T.sub.p] : time to peak (hour)

[t.sub.p] : lag time (hour)

[T.sub.c] : time of concentration (hour)

By using 3-hour time of concentration, the time to peak of flood discharge is 3.3 hours and the magnitude of peak of flood discharge in upper Werba River is as much as 1.778 [m.sup.3]/s.cm. 1-hourly magnitude flood discharge is presented in Figure 4. For 2-year return period of design rainfall which is presented in Table 2., the estimated peak of flood discharge in Upper Werba Sub-Watershed by using SCS SUH is 25.06 [m.sup.3]/s.

Nakayasu SUH

The second synthetic unit hydrograph (SUH) which is developed for Upper Werba Sub-Watershed is Nakayasu SUH. Information of length of the river and time of concentration are needed to develop Nakayasu SUH. The peak of flood discharge is estimated by using Equation. (4).

[Q.sub.p] = A*[R.sub.e]/3.6(0.3[T.sub.p] + [T.sub.0.3]) (4)

for:

[T.sub.p] = [T.sub.g] + 0.8[T.sub.r]

[T.sub.g] = 0.21 [L.sup.0.7] for L < 15 km

[T.sub.g] = 0.4 + 0.058 L for L > 15 km

[T.sub.r] = 0.5 [T.sub.g] up to [T.sub.g]

[T.sub.0.3] = [alpha][T.sub.g]

[Q.sub.p] : peak of flood disharge ([m.sup.3]/s)

[T.sub.p] : time to peak (hour)

L : river length (km)

A : catchment area ([km.sup.2])

[R.sub.e] : effective rainfall (mm)

[alpha] : watershed characteristic coefficient = 2

For 2-year return period of design rainfall in Table 2., the estimated peak of flood discharge by using Nakayasu SUH in the sub-watershed is 391.3 [m.sup.3]/s. Unlike SCS SUH, the ordinate of rising limb (eq. 5) and falling limb of the unit hydrograph (eq. 6, 7, 8) of Nakayasu SUH are defined specifically [4].

For period of time of 0 < t < [T.sub.p], the ordinate of rising limb ([Q.sub.n]) is calculated using Equation (5).

[mathematical expression not reproducible] (5)

For period of time [T.sub.p] < t < ([T.sub.p]+[T.sub.0.3]), the ordinate of falling limb ([Q.sub.t]) is calculated using Equation (6).

[mathematical expression not reproducible] (6)

For period of time ([T.sub.p]+[T.sub.0.3]) < t < ([T.sub.p] +[T.sub.0.3]+1.5[T.sub.0.3]), the ordinate of falling limb ([Q.sub.t]) is calculated using Equation (7).

[mathematical expression not reproducible] (7)

For period of time t > ([T.sub.p] +[T.sub.0.3]+1.5[T.sub.0.3]), the ordinate of falling limb ([Q.sub.t]) is calculated using Equation (8).

[mathematical expression not reproducible] (8)

The first development of Nakayasu USH using 28.2 [km.sup.2] of catchment area, 12.50 km river length, and one-hour time of concentration produced the one-hour Nakayasu SUH which is presented in Figure 5(a). Due to the estimated time of concentration in Upper Werba River is 3 (three) hours, therefore, the one-hour Nakayasu SUH is transformed into three-hour SUH by using superposition method [4] and presented in Figure 5(b).

The 3-hour Nakayasu SUH shows that with three times longer of time of concentration in Upper Werba River, the time to peak occurred two hours late and the magnitude of peak of flood discharge is about 67% lower.

Rational Method

Rational method is commonly used in sewer design to estimate the peak of flood discharge using Equation (9). The information to be known for estimating peak of flood discharge using Rational method are runoff coefficient, rainfall intensity, and catchment area [1].

[Q.sub.p] = 1/3.6 C ([i.sub.tc,p])A (9)

for:

[Q.sub.p] : peak discharge ([m.sup.3]/s)

C : runoff coefficient

([i.sub.tc,p]) : intensity of precipitation (mm/h) for a duration equal to tc and an exceedence probability P

A : catchment area ([km.sup.2])

Runoff coefficient is determined based on the land use of the catchment area. In this research, the percentage of land area and its utilization, as well as runoff coefficient for each land use in Upper Werba River in 2014-2018 is presented in Table 3. The C value which used in the Rational Formula is the composite value of runoff coefficient for all land utilization in the research area. Based on the presented data in Table 3, the composite runoff coefficient for Upper Werba Sub- is 0.353.

Streamflow Measurement

The verification step in the research is done by comparing the estimated peak of flood disharge by using SCS SUH, Nakayasu SUH, and Rational Method at 2-year return period to the measured streamflow in upper Werba River which is presented in Table 4. The measurement of streamflow was conducted for 100 m length of river at 10 m-upstream of Intake 2 (Figure 2).

The streamflow measurement was done in May 2019. It covered the measurement of average velocity and depth of flow. The measured average velocity in the location of measurement is 1.38 m/s and the depth of flow is presented in Figure 6. By multiplying the average velocity and average cross sectional area of the river, the measured streamflow is obtained as much as 66.19 [m.sup.3]/s.

The expected result of estimated peak of flood discharge at 2-year return period by using certain method is close to the measured streamflow. The results presented in Table 4 show that the Rational method provides the closest magnitude to the measured discharge at 1.8% difference.

Conclusions

The research has developed 4 (four) IDF curves at 2, 10, 25, and 50-year return period for Upper Werba Sub-watershed. It is expected that the IDF curves could be used for further water infrastructures planning and development in the area. The research also has presented 3 (three) methods to estimate peak of flood discharge, i.e. SCH SUH, Nakayasu SUH, and Rational method. From those three methods to estimate the peak of flood discharge, Rational method provides the closest magnitude to the measured streamflow in Upper Werba River. Therefore, it is suggested that the Rational method can be used for other purposes in water infrastructures planning and development in the sub-watershed.

References

[1.] Subramanya, K., Engineering Hydrology, Tata McGraw-Hill Publishing Company Limited, New Delhi, 2008.

[2.] Roger, M., Kohl, B., Pirk, H., Viglione, A., Komma, J., Kirnbauer, R., et al., Runoff Models and Flood Frequency Statistics for Design Flood Estimation In Austria-Do They Tell a Consistent Story?, Journal of Hydrology, 456-457, 2012, pp. 30-43.

[3.] Chow, V.T., Maidment, D.R., and Mays, L.W., Applied Hydrology, McGraw-Hill Book Company, Singapore, 1988.

[4.] Triatmodjo, T., Hidrologi Terapan, Beta Offset, Yogyakarta, 2008.

[5.] Dalrymple, T., Flood-Frequency Analysis (Manual of Hydrology: Part 3. Flood-flow Techniques), United States Government Printing Office, Washington, 1960.

[6.] Hailegeorgis, T.T. and Alfredsen, K., Regional Flood Frequency Analysis and Prediction in Ungauged Basins Including Estimation of Major Uncertainties for mid-Norway, Journal of Hydrology: Regional Studies, 9, 2017, pp. 104-126.

[7.] Ozga-Zielinski, B, Ciupak, M., Adamowski, J., Khalil, B., and Malard, J., Snow-melt Flood Frequency Analysis by Means of Copula Based 2D Probability Distributions for the Narew River in Poland, Journal of Hydrology: Regional Studies, 6, 2016, pp. 26-51.

[8.] Swain, J.B., Jha, R., and Patra, K.C., Stream Flow Prediction in a Typical Ungauged Catchment using GIUH Approach, Aquatic Procedia 4, 2015, pp. 993-1000.

[9.] Kusumastuti, C., Djajadi, R., and Rumihin, A., Evaluation of Drainage Channels Capacity in Ambon City: A case Study on Wai Batu Merah Watershed Flooding, Procedia Engineering, 125, 2015, pp. 263-269

[10.] BPS-Statistics Indonesia, Statistical Yearbook of Indonesia, BPS-Statistics Indonesia, 2018.

[11.] Statistics of Fakfak Regency, Fakfak Regency in Figures, Statistics of Fakfak Regency, Fakfak, 2019.

[12.] Kusumastuti, C., Djajadi, R., Winarko, E.A., and Richard, E.A., Dampak Perubahan Tata Guna Lahan terhadap Besarnya Debit banjir di Kabupaten Probolinggo, Proceeding of the 35th Scientific Annual Meeting (Pertemuan Ilmiah Tahunan 35) of Indonesian Hydraulics Engineers, Medan, Indonesia, 2018.

[13.] Kusumastuti, C., Chandra, H.P., Wibisono, K., and Hartono, A.C., Eco Drainage System for Surface Runoff Reduction in Indonesia, Civil Engineering Dimension, 21(1), 2019, pp 29-35.

[14.] Department of Public Works and Public Housing Fakfak Regency, Tata Guna Lahan Kabupaten Fakfak, 2019.

Kusumastuti, C. (1*), Sudjarwo, P. (1), Christhie, M. (1), and Krisna, T. (1)

(1) Department of Civil Engineering, Petra Christian University, Jl. Siwalankerto 121-131, Surabaya 60236, INDONESIA

(*) Corresponding author; email: cilcia.k@petra.ac.id

Note: Discussion is expected before November, 1st 2019, and will be published in the "Civil Engineering Dimension", volume 22, number 1, March 2020.

Received 13 September 2019; revised 16 September 2019; accepted 16 September 2019.

DOI: 10.9744/CED.21.2.70-75
Table 1. Maximum Daily Rainfall in Fakfak Regency

No.  Year  Rainfall Depth (mm)

 1   2009  184.0
 2   2010  113.0
 3   2011  184.0
 4   2012  112.8
 5   2013  144.2
 6   2014  140.2
 7   2015  154.0
 8   2016  122.3
 9   2017  136.3
10   2018  136.6

Table 2. Design Rainfall at Various Return Period for Fak-fak Regency

Return Period,  Design Rainfall  Rainfall Intensity
T (year)        (mm)             (mm/h)

 2              140.9            23.5
10              151.6            25.3
25              155.9            25.9
50              158.5            26.4

Table 3. Land use of Upper Werba Watershed 2014-2018

Land Use[11]               Area (%) (*)[14]  Runoff
                                             Coefficient (*)[4]

Productive forest          44.42             0.38
Conversion productive      22.02             0.35
forest
Limited production forest  14.00             0.36
Protected forest            3.98             0.38
Nature conservation area    6.26             0.30
Others                      9.22             0.25
Water Body                  0.11             -

Note: (*) estimated value

Table 4. Discharge Comparison in Upper Werba River using Various Method

               Qmeasured  Qp        Qp SCS  Qp
                          Nakayasu          Rational

([m.sup.3]/s)  66.19      391.30    25.06   65.00
% different    -          491.2     62.1     1.8
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Author:Kusumastuti, C.; Sudjarwo, P.; Christhie, M.; Krisna, T.
Publication:Civil Engineering Dimension
Geographic Code:9INDO
Date:Sep 1, 2019
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