MODEL FLOOD PEAK DISCHARGE BASED ON THE WATERSHED SHAPE FACTOR

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1 International Journal of Civil Engineering and Technology (IJCIET) Volume 9, Issue 12, December 2018, pp , Article ID: IJCIET_09_12_094 Available online at ISSN Print: and ISSN Online: IAEME Publication Scopus Indexed MODEL FLOOD PEAK DISCHARGE BASED ON THE WATERSHED SHAPE FACTOR Dandy Ahmad Yani Doctoral Program on the Department of Water Resources, Faculty of Engineering, University of Brawijaya, Malang, Indonesia Mohammad Bisri, Lily Montarcih Limantara and Ery Suhartanto Department of Water Resources, Faculty of Engineering, University of Brawijaya, Malang, Indonesia ABSTRACT The lack of hydrograph data presentation in the hydrology field has long become the drawback of the hydraulic structure planning. Such a conditional deficiency however has respectively place the Synthetic Unit Hydrograph model becomes as a very great utility. Ideally, every watershed has the certain specific unit hydrograph. This study intends to investigate the characteristic of observed hydrograph in all of the watersheds in the river region of Jeneberang, Sulawesi-Indonesia. However, the main aim of this study is to design the model of Synthetic Unit Hydrograph, one of them is the formula of flood peak discharge (Qp) that is as the function of watershed area (A), the length of main river (L), and the watershed shape factor. The watershed shape factor is defined as the ratio between watershed periphery (K) and area (A). The result shows that the watershed shape factor has linear relation with the parameters of Synthetic Unit Hydrograph. Key words: peak flood discharge, time to reach peak, watershed area, river length Cite this Article: Dandy Ahmad Yani, Mohammad Bisri, Lily Montarcih Limantara and Ery Suhartanto, Model Flood Peak Discharge Based on the Watershed Shape Factor, International Journal of Civil Engineering and Technology, 9(12), 2018, pp INTRODUCTION A method for estimating the river flow in gauge as well as ungagged watershed is mentioned as hydrograph analysis (Safarina et.al. 2011). The main physical characteristic of watershed is the area, slope, elevation, shape, soil type, channel network, water storage capacity, and land cover (Samudro and Mangkoedihardjo, 2006). Watershed is divided into small watershed (area < 1 km 2 ), meso scale watershed (10 km 2 < area < 1,000 km 2 ), and macro watershed (area > editor@iaeme.com

2 Dandy Ahmad Yani, Mohammad Bisri, Lily Montarcih Limantara and Ery Suhartanto 1,000 km 2 ). Sosrodarsono and Kensaku (2003) and Hundecha (2004) indicate that the shape coefficient of the watershed (F) is as a comparison between area (A) and main river length (L) with the formula: F = A/L 2. The watershed shape factor gives a good hope to be further used and developed in the Synthetic Unit Hydrograph modeling. The factor of watershed shape is as the watershed physical characteristic that is defined as above and it can be built the peak discharge as the function of watershed shape factor. Ideally, it is needed to be carried out the calibration of model parameters based on the watershed characteristic (Nandakumar and Mein, 1997). The lack of hydrograph data presentation in the hydrology field has long become the drawback of the hydraulic structure planning (Limantara, 2009). Such a conditional deficiency however has respectively place the Synthetic Unit Hydrograph model becomes as a very great utility. The Synthetic Unit Hydrograph can become as the source of several important information that is needed for the reliability of hydraulic structure (Tung et.al., 1987). In practitioner part, the model application is intended to analyze the design flood with the rainfall input. However, so far the practitioner in Indonesia is still very fanatic using the Synthetic Unit Hydrograph of Nakayasu because it is seen practice actually application of the model for Java Island still needs the calibration of some parameters (Hoesein and Limantara, 1993). They almost never use the Synthetic Unit Hydrograph of Gama I (founded by Sri Harto, Indonesia) because this model needs 10 watershed physical data and it cannot be applied for watershed that only has one river, while Limantara (2006) has tried to build a Synthetic Unit Hydrograph model that is relatively simple by using the physical factors of watershed that are the length of main river (L), the area of watershed (A), the average of river slope (S), the roughness coefficient of watershed (n), the river length from the weighted point of watershed to the outlet (Lc), remembering that the Synthetic Unit Hydrograph models are researched and generated in the area with the watershed characteristics are far different from the application watershed, so it frequently produces the in-accurate analysis result. In further, it will cause the in-efficient impact in determining the dimension of water structure. The hydrology condition in every region is specific. Therefore, not all of the available manner and concept can be used for solving the hydrology problem in every watershed. This research intends to build the formula of peak discharge that is regionally fitted in each river region. In addition, this research aims to produce the specific flood peak discharge model of Synthetic Unit Hydrograph in South Sulawesi with the simple formula and without calibration in the model application. 2. MATERIALS AND METHODS This research is conducted in river region of Jeneberang (Sulawesi-Indonesia) that consists of 58 watersheds. Map of location is presented as in the Figure editor@iaeme.com

3 Model Flood Peak Discharge Based on the Watershed Shape Factor Figure 1. River region of Jeneberang 2.1. The watershed physical parameters that are influenced to the model The watershed parameter that is the easiest to be obtained and relatively does not experience change is the geographic behaviour and watershed morphology (Harto, 1993). Based on the concept of storage, if the whole watershed has contributed in the run-off form, it will reach the maximum flow that is not happened the storage change (Chow, 1988). For the watershed, the formula of peak discharge is due to the physical factors that are the watershed roughness coefficient (n), the length of main river (L), the watershed area (A), the slope of main river (S) or Qp = f(n,l,a,s) and there are strong correlation among n, L, A, and S. Therefore, there is a strategy to combine some of the watershed physical factors into a parameter like to be carried out (Mangkoedihardjo, 2010; Mulyantari, 1993). Gupta (1967) has researched to relate the peak discharge with the other watershed physical factor that is the river length from the weighted point of watershed to the outlet (Lc). Therefore, the watershed shape factor that is as the ratio between watershed periphery (K) and area (A), is necessary to be attended. The factor that is influenced the model will be formulated based on the coefficient of determination. Analysis of modeling is carried out by using regression analysis with some alternatives based on the independent variables that are used (five, four, three, two, or one independent variable) Observed unit hydrograph. The observed hydrograph is a food hydrograph or a discharge hydrograph that is as relation curve of the discharge against the time (period). This curve is obtained from the conversion of the water level hydrograph by using the general formula as follow (Soewarno, 1991): Q = c H m (1) Where: Q = discharge (m 3 /s), H = water level (m), and c, m = the constant that is obtained from the direct calibration in the location of water level recorder. However, the unit hydrograph has the base dependable and based on the concept as follow (Harto, 1995): 1) the unit hydrograph is raised by the distributed rainfall in the whole watershed editor@iaeme.com

4 Dandy Ahmad Yani, Mohammad Bisri, Lily Montarcih Limantara and Ery Suhartanto (evenly spatial distribution); 2) the unit hydrograph is raised by the distributed rainfall during the time that has been remained (constant intensity); 3) the ordinate of unit hydrograph that is comparable with the rainfall volume that is raised (linier system); 4) the watershed response is not depended on the time of rainfall input (time invariant); and 5) time to peak of the unit hydrograph until the end of direct run-off hydrograph ia always fixed (it is not due to the magnitude of the rainfall intensity level) Formulation of peak discharge model The formulation of peak discharge in this study is based on the two watershed physical characteristic that is watershed periphery (K) and area (A). Besides that, it will be analyzed the length of longest river (L) and area (A). In this analysis, the peak discharge (Qp) is as the dependent variable, however, the watershed physical characteristic (A, L, and FD) are as the independent variables. Therefore it will be produced many alternatives. The criteria of sample/ data selection for each watershed is as follow: 1) there is Automatic Water Level Recorder (AWLR) and there are Automatic Rainfall Recorder (ARR) inside or outside the watershed, watershed area < 5,000 km 2 ; 2) watershed physical factor has relatively homogeneous soil type as well as the yearly rainfall, therefore there are the similar hydrograph shape; 3) The hydrograph jays to be selected as the single peak that is due to the hourly rainfall. Time of rainfall and hydrograph has to be fitted. If there are some hydrograph that are complied with the condition, so it will be carried out the distributed hydrograph and it is noted that it is remained to represent the highest peak discharge for the watershed. The secondary data that is needed is as follow: 1) Watershed map with the minimum scale of 1: 500,000; 2) Stage hydrograph form Automatic Water Level Recorder (AWLR); 3) Hourly rainfall from Automatic Rainfall Recorder (ARR) station and daily rainfall from the manual station for the watershed that is no available the Automatic Rainfall Recorder (ARR) station; 4) Data of the river slope and forest area that is fitted with the time of observed hydrograph and rainfall data. To build the model of peak discharge, it is needed the unit hydrograph that is differentiated from the direct run-off hydrograph and it is mentioned as the observed unit hydrograph. Based on the observed unit hydrograph, there is produced the curve shape, then it can be measured the time to peak (Tp), recession time (Tr), time base (Tb), and peak discharge (Qp) 3. RESULTS AND DISCUSSION 3.1. Observed Unit Hydrograph Based on the observed discharge hydrograph for each watershed, there is analyzed the observed unit hydrograph by using the Collins method. The flood hydrograph of Automatic Water Level Recorder (AWLR) is used for differentiating the observed unit hydrograph from the selected observed discharge hydrograph that are the highest one and has the single peak. For each watershed, the time period of observed discharge hydrograph has to be the same with the time period of hourly rainfall from Automatic Rainfall Recorder (ARR). However, it is not needed the homogeneous time inter watershed because the objective of hydrograph analysis is for the high flow. Therefore, data for the analyses has to have the extreme value as optimal as possible that is by taking the flood hydrograph with the highest peak in every watershed. Table 1 until 6 and Figure 2 until 7 presents the result of Collins method in the 6 watersheds in river region of Jeneberang that has Automatic Water Level Recorder (AWLR) and Automatic Rainfall Recorder (ARR) editor@iaeme.com

5 Model Flood Peak Discharge Based on the Watershed Shape Factor Table 1. Observed unit hydrograph of Bonto Jai station No t/tp Q/Qp T Q Explanation: t = time (hour), Tp = time to peak (hour), Q = discharge (m 3 /s), Qp = time to peak (m 3 /s), T = time (hour) Figure 2. Curve of Collins method result for Bonto Jai station Table 2. Observed Unit Hydrograph of Daraha station No t/tp Q/Qp T Q editor@iaeme.com

6 Dandy Ahmad Yani, Mohammad Bisri, Lily Montarcih Limantara and Ery Suhartanto Explanation: t = time (hour), Tp = time to peak (hour), Q = discharge (m 3 /s), Qp = time to peak (m 3 /s), T = time (hour) Figure 3. Curve of Collins method result for Daraha station Table 3. Observed unit hydrograph of Jenelata station No t/tp Q/Qp T Q , editor@iaeme.com

7 Model Flood Peak Discharge Based on the Watershed Shape Factor Explanation: t = time (hour), Tp = time to peak (hour), Q = discharge (m 3 /s), Qp = time to peak (m 3 /s), T = time (hour) Figure 4. Curve of Collins method result for Jenelata station Table 4. Observed Unit Hydrograph of Jonggoa station No t/tp Q/Qp T Q Explanation: t = time (hour), Tp = time to peak (hour), Q = discharge (m 3 /s), Qp = time rto peak (m 3 /s), T = time (hour) editor@iaeme.com

8 Dandy Ahmad Yani, Mohammad Bisri, Lily Montarcih Limantara and Ery Suhartanto Figure 5. Curve of Collins method result for Jonggoa station Table 5. Observed unit Hydrograph of Kampili station No t/tp Q/Qp T Q Explanation: t = time (hour), Tp = time to peak (hour), Q = discharge (m 3 /s), Qp = time rto peak (m 3 /s), T = time (hour) Figure 6. Curve of Collins method result for Kampili station editor@iaeme.com

9 Model Flood Peak Discharge Based on the Watershed Shape Factor Table 6. Observed unit hydrograph of Maccini Sombala No t/tp Q/Qp T Q , Explanation: t = time (hour), Tp = time to peak (hour), Q = discharge (m 3 /s), Qp = time rto peak (m 3 /s), T = time (hour) editor@iaeme.com

10 Dandy Ahmad Yani, Mohammad Bisri, Lily Montarcih Limantara and Ery Suhartanto Figure 7. Curve of Collins method result Maccini Sombala station 3.2. Watershed physical parameters that are affected to the model By the peak discharge (Qp) as the independent variable and watershed area (A), length of the longest river (L), watershed shape factor (FD) that is as the ratio between periphery (K) and watershed area (A) as the dependent variables, it will produce some alternatives of regression equation. The selection of these alternatives is based on the rationalization of model and criteria as above. Asdak (1995) said that getting longer the river, the distance between the rainfall drop and outlet is getting big, so the time that is needed by the rainfall for reaching the outlet is getting longer and therefore it will decrease the peak discharge. It is due to the getting longer the river will give the chance to the rainfall to flow as the run-off. It means that the getting longer the river will produce the peak discharge is getting smaller. It is true as expressed by Asdak (1995) that the longer river will cause the water losses is getting big, however, the percentage of water losses is very small if it is compared with the peak discharge, remembering that there is high flow is to be discussed. In addition, the longer river will give the chance to the rainfall is still in the river body, it means that the possibility to overflowing is very small. Therefore, for the river that is relatively long is very possible that almost all of the rainfall that is dropped into the river will reach the outlet and it will increase the peak discharge. The getting bigger of watershed will cause the run-off reaching the outlet in a long time so the time base of hydrograph (time of run-off) becomes longer and the peak discharge will be decreasing (Harto, 1995). The getting bigger the area will cause the rainfall distribution is getting uneven. This characteristic is contradictory with the concept that is developed by Sherman (1932) (Harto, 1993) which is said that the unit hydrograph is as the direct run-off hydrograph that is produced by the even effective rainfall in the watershed. The watershed size determines the maximum standard of using the unit hydrograph. In fact, there is no certain size, however, according to Soemarto (1995) the maximum area is 5,000 km 2 as being used in this research. Therefore, if there is happened the even rainfall in a watershed, so the getting bigger of watershed will cause the run-off is getting faster to reach the outlet and it will increase the peak discharge. Table 7 presents the physical parameters that influence the peak discharge model editor@iaeme.com

11 Model Flood Peak Discharge Based on the Watershed Shape Factor Table 7. The physical parameters that influence the peak discharge model Station tp Qp A L periphery FD Daraha Jonggoa Jenelata Bonta la Kampill Maceni Sombala Explanation: tp = time to peak (hour), Qp = peak discharge (m 3 /s), A = area (km 2 ). L = river length (km), periphery (m), FD = watershed shape factor 3.3. Peak discharge modeling The watershed shape factor is defined as the ratio between the watershed periphery (K) and the watershed area (A). The watershed area can be used as one of the variables in the unit hydrograph modeling, besides the variables of watershed area (A) and the longest of river length (L). The peak discharge modeling (Qp) with one of the independent variable is the watershed shape factor (FD) is built by using the statistical technique of multiple regression. If the initial result of modeling is not too satisfied, then it is carried out to transform the data into logarithm and the data invers, and if the result is remained not to be satisfied, then it is carried out the homogeneous test or the abnormality data test which has the maximum deviation. The selection of model is carried out based on the: 1) statistical criteria: determination coefficient and minimum standard error; 2) rationalization of model; for whatever the independent variable value of A, L, and FD there does not produce the negative value for the discharge; 3) hydrology philosophy: the hydrology model is analog with the flow continuity equation that is Q V x A (according to Manning formula, V = 1/n x R 2/3 x S 1//2 ), so it is as the multiplication function. Based on the criteria, it is obtained the model of peak discharge Qp =.A0, 7086.L0, 3894.FD0, 3384 Where: Qp = peak discharge of unit hydrograph (m 3 /s/mm), A = watershed area (km 2 ). L = the length of main river (km), FD = watershed shape factor (ratio between watershed periphery and area). Determination coefficient for A = 0.874, for L = 0.954, and for FD It means that the influence of A (area) to Qp (peak discharge) is 87.4%; L (the longest river length (L) to Qp (peak discharge) is 95.4%, and FD (the watershed shape factor) tp Qp (peak discharge) is 95.4%. 4. CONCLUSION Based on the analysis as above, it can be concluded as follow: 1) The watershed factor (FD) has the directly proportional with the parameters of unit hydrograph; and 2) The model of peak discharge in the Jeneberang river area is as follow: Qp =.A 0,7086.L 0,3894.FD 0,3384 where: Qp = peak discharge of unit hydrograph (m 3 /s/mm), A = watershed area (km 2 ). L = the length of main river (km), FD = watershed shape factor (ratio between watershed periphery and area) editor@iaeme.com

12 Dandy Ahmad Yani, Mohammad Bisri, Lily Montarcih Limantara and Ery Suhartanto REFERENCES [1] Asdak C. (1995). Hidrologi dan Pengelolaan DAS (Hydrology and Watershed Management), University Press, Gajah Mada Yogyakarta. [2] Chow, V. (1988). Handbook of Applied Hydrology, Singapore: Mc. Graw Hill Book Company. [3] Harto S. (1993). Hidrologi: Teori, Soal, Penyelesaian (Hydrology: Theory, Problem, Solving), Nafiri Offset. Yogyakarta. [4] Hoesein, A.A. and Limantara L.M. (1993). Kalibrasi Parameter Hidrograf Satuan Sintetik Nakayasu di Sub DAS Lesti, Genteng, dan Amprong, Jawa Timur, Laporan Penelitian (Research Report), Fakultas Teknik Universitas Brawijaya Malang. [5] Hundecha Y, and Andreas B. (2004). Modeling of the Effect of Land Use Changes in the Runoff Generation of a River Basin Through Parameter Regionalization of a Watershed Model. Journal of Hydrology, Institute of Hydraulic Engineering, University of Stuttgart, Germany. [6] Limantara L.M. (2009). Evaluation of Roughness Constant of River in Synthetic Unit Hydrograph. World Applied Sciences Journal, Vol. 7 No.49, pp [7] Mangkoedihardjo, S. (2010). A new approach for the Surabaya sewerage and sanitation development programme Advances in Natural and Applied Sciences 4 (3): [8] Mulyantari, F. (1993). Modifikasi Hidrograf Satuan Sintetis Segitiga Untuk Small Watershed Di Wilayah Sungai Bengawan Solo, Jurnal Litbang Pengairan. No. 26, th.7- KW.IV hal. 48. [9] Nandakumar, N and Mein, R.G..(1997). Uncertainty in Rainfall-Runoff Model Simulations And The Implications for Predicting the Hydrologic Effect of Land-Use Change, Journal of Hydrology 192, pp [10] Safarina A.B., Salim H.T., Hardihardaja I.K., and M. Syahri B.K. (2011). Clysterization of Synthetic Unit Hydrograph Method Based on Watershed Characteristics, International Journal of Civil and Environmental Engineering: IJCED-IJENS, Vol. 11 No.6, pp [11] Samudro, G. and Mangkoedihardjo, S. (2006). Water equivalent method for city phytostructure of Indonesia. International Journal of Environmental Science and Technology, 3(3), [12] Soemarto C.D. (1995). Hidrologi Teknik (Engineering Hydrology), Penerbit Erlangga, Jakarta. [13] Sosrodarsono S. and Takeda K. (2003). Hidrologi untuk Pengairan (Hydrology for Watering), Pradnya Paramita, Jakarta, Indonesia. [14] Tung B.Z., Yeh Y.K., Chia K., Juang J.Y. (1987). Storm Re-sampling for Uncertainty Analysis of a Multiple Storm Unit Hydrograph, Journal Hydrology, Vol.194, editor@iaeme.com