Application of A Tank Model to Assess the Performance of Rotiklot Reservoir Initial Filling

ABSTRACT Rotiklot dam is located in Belu Regency that has the tropic climate, with very short wet season (4-5 months) and a very long dry season (7-8 months). The average monthly rainfall in December – April of approximately 300 – 500 mm/month, while in another month only ranges 3060 mm/month. During the rainy season, rainwater will overflow as surface water and collect in the river as a flood toward the sea. The construction of a dam is one alternative to overcome the water needs of the community during the dry season. The Rotiklot dam retains the flow of water in the Motamuru River and its reservoir can accommodate 2.9 million m3. Impounding is a process carried out once a dam has been constructed. It is a comprehensive process involving filling time and water inflow. The purpose of this study was to determine the first filling time and the inflow volume in Rotiklot Reservoir in the years of dry, low, normal and sufficient water using the Tank method. It aimed to simulate the initial filling of the reservoir. Also, the study is expected to evaluate the most suitable Tank model, with parameters calibrated using the Genetic Algorithm optimization approach. The determination coefficient using a four series tank is 0.531 greater than the coefficient obtained from 3 series tank simulation, which was 0.506. The total inflow volume in Rotiklot Reservoir for dry, low, normal and sufficient were 1.946, 7.289, 9.699, 13.822 million m3 respectively. Based on the calculation result of the inflow volume of the year of the low water, the filling time is around three months, starting from mid-December to mid-March.


INTRODUCTION
Belu Regency of East Nusa Tenggara Province has a dry climate with very short rainy and long dry seasons ranging from December-March and April-November, respectively. The rainy days per year amounts to 40. The region experiences relatively short wet season with mountainous topography and rare vegetation. Consequently, there is a small rainfall average of ± 1.500 mm/year, leading to water deficiency. This affects food-crops production, such as palawija/rice (BPS Kab.Belu, 2018). The government needs to address the issue of water deficiency with concrete and long-term plans. In response to this problem, the Rotiklot Dam in the Fatuketi Village of Kakuluk Mesak District was constructed. The dam retains the flow of water in the Motamuru River, which has a length of 6.6 km, with 11.69 km 2 watershed area. It was designed with a storage capacity of 2.9 million m 3 and expected to provide several benefits, including irrigation to an area of 139 hectares and a secondary crop of 500 hectares. It is also supposed to control floods in flood-prone areas, apart from providing domestic water to the people of Belu Regency especially the Fatuketi Village community (Balai Besar Wilayah Sungai NT II, 2012).
The construction of the dam involved several stages, including preparation, development planning, as well as construction and impounding. The initial filling is carried out after construction work is completed and it is the most critical phase (Regulation 37,2010). In this stage, the amount of inflow into the inundation area is very essential. If the inflow is small, the initial filling time is long and can cause drought downstream (Amaral and Biligardo, 2018).

Location Research
As shown in Figure 1, Rotiklot Dam is located in Fatuketi Village, Kakuluk Mesak District, Belu Regency, on the 9°4'1.82"S and 124°50'11.33"E coordinates. It is an earth-fill dam, approximately 8.74 km from the center of Atambua and the river length of 6.6 km with an area of 11.69 km 2 (Balai Besar Wilayah Sungai NT II, 2012).. The study was conducted for approximately 1 (one) year, starting from May 2018 to April 2019.

Procedures and Analysis
This study uses quantitative methods, which involve developing mathematical models. This requires linking a natural phenomenon in observation with calculations that represent the data as follows ( Figure 2).  (1994)(1995)(1996) Data Analysis Analysis observation discharge data (1994)(1995)(1996) Recap the amount annual rainfall at the Atambua rain station

Rainfall Data Analysis
Rainfall data in BMKG Lasiana Station was processed half-monthly from 1992-2016. The data was from the Atambua rain station since it is closer to the location of the reservoir and still within the Motamuru River Basin. According to data from 1992-2016 shown in Figure 3, the maximum annual rainfall value in Atambua was recorded in 2008, specifically 3,029 mm, while the minimum was in 2007 which was 956 mm.

Evapotranspiration Data Analysis
Potential evapotranspiration is critical in determining the discharge of the Tank model. It was calculated using CROPWAT 8.0 program. This is a decision support system developed by the FAO Division of Land and Water Development based on the Penman-Monteith method to plan and regulate irrigation.  1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008  In Figure 4, the maximum monthly evapotranspiration was recorded in the second part (II) of August, precisely 90.0 mm. The minimum was in the first part (I) of December with 58.4 mm and the average of evapotranspiration in the Motamuru watershed was 72.7 mm.

The Tank Model Structure
The Tank model is one of the rainfall-runoff simulations that introduced by Sugawara and Funiyuki (1956) and is widely used in Indonesia. The tank model is a simple structure but an efficient and powerful tool in rainfall-runoff simulation and verification.

Equation of original tank model
Tank Model is grouped into two parameters, including 1) outlet hole coefficient parameter on the side of the wall and the bottom of the tank and 2) groundwater storage parameters (Kuok, et al., 2011). The total outflow from the outlet on the side (Q) shows the accumulation of water flow from the system in the watershed based on Equation (1).
Where Qa1(t) and Qa2 (t) are the run-off value at the first and second outlet in tank 1 respectively.

Qb(t) and
Qc(t) are the run-off value at tank outlet 2 and 3 respectively.
The tank model simulates rainfall at a time P(t) which then fills up tank I. The collected water flows through holes in the right wall or seeps through holes in the bottom, filling tank II. Similarly, Water collected in tank II flow through holes in the right wall and enter the tank III. The downward infiltrated water stabilizes the groundwater and flows slowly out of the aquifer (Suryoputro and Nugroho, 2018). This process repeats until the last tank is filled (Figure 5, 6).
In Equation (2) Ha (t + 1) is the reservoir in tank 1, Ha(t) is the initial storage in tank 1, Qa1(t) and Qa2(t) are run-offs at the first and second outlet in tank 1 respectively, while Ia(t) is the infiltration. In Equation (3), Hb (t + 1) is a basin in tank 2, Hb(t) is the initial storage, Qb(t) is run-off at outlet 2, and Ib(t) is the infiltration. In Equation (4), Hc(t + 1) is reservoir in tank 3, Hc(t) is Initial storage, Qc(t) is run-off at outlet 3, and Ic(t) is infiltration. In Equation (5), Hd(t + 1) is reservoir in tank 4, Hd(t) is initial storage value, and Qd(t) is runoff value. In this study, two tank models were used, specifically 3 and 4 series.

The 3-series arranged tank model
This model consists of 3 tanks arranged vertically. The row of tanks is shown in Figure 5. In Figure 5, ET0 is evapotranspiration, Cia, Cib, and Cic are the Infiltration coefficients in Tank 1,2, and 3, respectively. Da1and Da2 is the height of surface flow outlet 1 and 2, respectively. Db1 and Db2 are heights of intermediate outlet-1 and 2, while Dc1 and Dc2 are the heights of sub-base flow outlets 1 and 2 respectively.  I II I II I II I II I II I II I II I II I II I II I II I   In the previous calculation, the determination coefficient (r 2 ) has not fulfilled the requirements of 0.50 ≤ r 2 ≤ 1.00 for satisfying r 2 values (Silva, et al., 2015). Therefore, a Genetic Algorithm Optimization for Excel software is used as shown in Figure 6. The software uses an excel spreadsheet as a link to display results. In the function section, the optimization is selected from the drop-down in the design variable. It is then entered into the cell excel link which displays the new parameters and provides realistic boundaries between the lower and upper limits. This is in line with Setiawan and Rudiyanto (2003) and JICA (2003). The constraints section is selected as the boundary used for the new parameters to be searched ("less or equal ≤", "greater or equal ≥" or "exactly equal ="). Once all the settings are filled, the Run GA tab is selected before clicking Run. The software runs an iterative process to determine new and more optimal parameters. In this study the search for new parameters is conducted twice, for 3 and 4 Series Arranged tank models. Table 2 shows the results of GA optimization for 3-series arranged tank models. Once the parameters are re-calibrated using the GA Optimization for Excel software, the new determination coefficient of r 2 is 0.506. It is acceptable in case 0.50 ≤ r 2 ≤ 1.00. Optimization for Excel software, the new determination coefficient of r 2 is obtained at 0.531. The value of r 2 determination coefficient for the 4-series tank model is much larger than the tank model arranged in 3-series. Therefore, for the next calculation, a 4-tank model is used series.  Based on Table 4, the volume annual error has a significant deviation (1994 = 20%, 1995 = -41.7%, 1996 = -52.7%). This is because the data of observed discharge from Oesao River is located quite far from the catchment area. The unavailability of observation discharge data leads to the use of discharge data from another river with similar characteristics catchment area.

DISCUSSION
The recapitulation of monthly inflow volume probabilities in the watershed of the Rotiklot Reservoir is divided into 4 season criteria (Sosrodarsono, et al., 1980). This includes the year of: 1). dry water with the total inflow into the reservoir annually, amounting to 1.9461 a reliability of 97.30% is obtained; 2). low water with the reliability of 75.34% is obtained, having a total inflow into the reservoir annually at 7.2898 million m 3 ; 3). normal water with the reliability of 50.68% is obtained by the total inflow into the reservoir annually at 9.6991 million m 3 ; 4). Sufficient water with the reliability of 26.02%. The total inflow into the reservoir per year is 13.8217 million m 3 ( Table 5).
The initial filling was carried out in mid-December as shown in Table 6. Therefore, the amount of inflow volume in the Rotiklot Reservoir is counted since then. As shown in Table 7, the time needed for initial filling in Rotiklot Reservoir is 3 months until it exceeds the capacity of the Rotiklot Reservoir, which is 2.9 million m 3 . The time needed for initial filling is shown in Figure 7 Figure 7 shows that in the first part (I) of December, the inflow volume is still zero (0). In the second part (II) it is 0.308 million m 3 . There is an increase in volume in the subsequent months up to the first part of March (I). The total volume of water collected is 2.929 million m 3 , which means that the planned storage of 2.9 million m 3 at an elevation of +54.8 masl was attained. The excess water specifically 0.29 million m 3 pass through the spillway at the beginning of March.

CONCLUSION
The amount of inflow simulation volume on the Motamuru river calculated using the 4-series arranged tank model is 21.56 million m 3 while the minimum is 2.23 million m 3 . The average volume inflow of the Rotiklot Reservoir is 10.40 million m 3 . The probability calculations are divided into four criteria, including the year of a). dry water with the reliability of 97.30%, which is obtained by the annual inflow into the reservoir, amounting to 1.9461 million m 3 , b). low water with the reliability of 75.34%, obtained by the total inflow into the reservoir annually at 7.2898 million m 3 , c). normal water with the reliability of 50.68%, obtained by the annual inflow into the reservoir at 9.6991 million m 3 ; and d). sufficient water with the reliability of 26.02%. The total inflow into the reservoir per year is 13.8217 million m 3 . The filling time needed to reach a planned pool of 2.9 million m 3 three and a half months, from the middle of December to March. The determination value of r 2 produced by the tank model composed of 3-series is 0.506. The 4series tank model of the determination value of r 2 produced is equal to 0.531. Therefore, based on the determination value of r 2 from the two tank models, the 4-series tank model is the most suitable to be used in the Rotiklot Reservoir watershed.

DISCLAIMER
The authors declare no conflict of interest.