Hydrological Evaluation Using the Generalized Extreme Value (GEV) Distribution Method at Tamblang Dam, Bali

The purpose of a dam is to control the water flow in a river, stream, sea, or lake. However, the water storage capacity of the dam can decrease over time due to the sediment that settles in the reservoir. Therefore, it is important to manage the water resources well and prevent problems like floods. The frequency analysis shows that the Pearson III and Gumbel Log probability distributions are the best methods to analyze the data because they have the smallest deviation values. The Generalized Extreme Value (GEV) probability distribution is the second-best method and can also be used. The GEV distribution method gives higher results for the maximum discharge in 50-, 00- and 1000-year return periods with percentages of 0.10%, 3.04% and 12.35%.


Introduction
One of the most important resources to support the needs of living things is water, by looking at the facts, good and orderly management of water resources is needed which can overcome water problems such as flood problems [1].One way to overcome the problem of flooding is to build a dam.According to PUPR Ministerial Regulation No. 27 of 2015 concerning dams Article 1 No. 1 explained that a dam is a building in the form of earth, stone and concrete piled up, which is built, in addition to holding and storing water, it can also be built to hold and accommodate mining waste or accommodate mud to form a reservoir.Dams are included in heavy construction so that they have a very large potential for danger and have a risk of malfunction and physical damage.Increasing the number of water reservoirs in a sustainable manner for raw water supply and irrigation of rice fields is a mission of food security and national water availability by the Ministry of PUPR through the Directorate General of Water Resources with a target of building 13 dams to be completed by the end of 2022.
The positive impact of the construction of this dam is to minimize water problems in Indonesia, one of which is the Tamblang Dam in Buleleng Regency, North Bali Island which is in the Tukad Daya Watershed.The Tamblang Dam was built to meet the needs for irrigation and raw water in Sawan District and Kubutamban District, Buleleng Regency, this reservoir is in the Tukad Daya River and is planned to have a total reservoir of 6,137,228 m 3 while the effective reservoir capacity is 4,199,646 m 3 .The function of the Tamblang Reservoir is for irrigation of 584 Ha and provision of raw water of 306 liters/second.The Tamblang Reservoir operation simulation uses a reliable discharge alternative of 80% and 90% [2].Over time, the dam's reservoir will decrease due to the accumulation of sediment carried by river water that enters the Tamblang Dam and then settles which results in reduced dam capacity.Because of these problems, the dam needs to be evaluated within a certain return period to find out whether the dam is still able to accommodate the return period flood discharge at the Tamblang Dam [1].Rainfall in Indonesia is very high so that it often has a negative impact on life, which, if you know the pattern of change, can reduce the risk of the extreme climate impacts that are caused [5].
The data analysis method that is commonly used among hydrologists to identify extreme value movements in the Extreme Value Theory (EVT), namely Generalized Extreme Value (GEV).GEV is a family of continuous distributions built into EVT to combine the Gumbel, Frechet, and Weibull distributions [3].The three distributions have different distribution tips, making it difficult to determine the pattern of distribution of extreme values, the Weibull distribution has finite distribution ends, while the Gumbel and Frechet distribution has infinite distribution ends.In this study, the HEC-HMS software was used to help model the Tamblang Dam by simulating the planned rainfall for a certain return period to become a simulated discharge using predetermined parameters [4].
So that it can evaluate the Tamblang Dam catchment when receiving flood discharge from the Tukad Daya DAS.In addition, if the Tamblang Dam reservoir is no longer able to receive a certain return period flood discharge, HEC-HMS can also simulate the amount of flood discharge that overflows from the Tamblang Dam.Based on the description above, in this study a simulation study of maximum rainfall data was carried out to determine the performance of the GEV distribution by comparing three distributions of frequency analysis, namely the distribution of GEV, Gumbel and Log Pearson III so that the level of effectiveness of the distribution of GEV in the Tamblang Dam can be determined.

Study Locations
In this study it is located at Tamblang Dam, Buleleng Regency, Bali Province which is geographically located at 8° 03' 40" -8° 23' 00" South Latitude and 114° 25' 55" -115° 27' 28" East Longitude.This dam is located on the Tukad Jaya River with a watershed area of 78.63 km and a river length of 22.7 km.

Methods
In this research, the Tamblang Dam's behavior was studied using the HEC-HMS software.The software simulated a specific period of rainfall and its impact on discharge, based on predetermined parameters.This allowed an assessment of the dam's capacity to handle flood discharge from the Tukad Daya Watershed [4].If the dam's catchment is unable to manage a flood of a certain return period, HEC-HMS can also predict the amount of overflow.The study further involved a simulation of maximum rainfall data to evaluate the performance of the GEV distribution.Three frequency analysis distributions -GEV, Gumbel, and Log Pearson IIIwere compared to determine the effectiveness of the GEV distribution for the Tamblang Dam.

Data Screening
Before the rainfall data is used in the hydrological analysis of the Tamblang Dam, it is necessary to test the reliability of the data first to evaluate whether the rainfall data is reliable for analysis.This reliability test includes outlier tests, trend tests, and independence tests.The table below shows that the data from the Sawan and Kahang-kahang rain stations are not independent, and both stations have upper outliers, so that the Sawan and Kahang station data cannot be used.While the TRMM 3 and TRMM 4 data are all independent or stand-alone, so for further research this uses TRMM 3 and TRMM 4 data.The full result is in Table 1.From the results of the division of the data area, it will be known that regional rainfall data from the two-satellite data are calculated based on the percentage ratio of the area that influences.

Frequency Analysis
To determine the magnitude of the design rainfall at the study site, it is necessary to carry out a frequency analysis with the help of an Excel Macro to calculate the design rainfall with various return periods using the Normal Distribution, Gumbel Distribution, Pearson III Distribution, Pearson III Log Distribution, and with the Generalized Extreme Value (GEV) Distribution.In the analysis of rainfall using the GEV probability distribution, several parameters are used for the rain data used as shown in Table 2.The results of frequency analysis of TRMM3 maximum daily rainfall data (Table 3.) show that the design rainfall value with the GEV distribution is the highest at the 100-, 500-, and 1000-year return periods.Whereas for TRMM4 (Table 4.) it shows that the design rain value with the Gumbel distribution is the highest at the return period of 5 to 500 years.At the 1000year return period, the design rain value with the GEV distribution shows the highest value.

Distribution Test
The distribution suitability test was used using two methods, namely the Smirnov-Kolmogorov Test and the Chi-Square Test.Table 5 shows that the results of the Smirnov -Kolmogorov and Chi-Square tests for the GEV distribution are accepted as are the Log Pearson III and Gumbel distributions.

Rain Analysis of Various Areas of Distribution
The regional rainfall recapitulation results in Table 6 show that the GEV distribution has less rainfall than the Gumbel distribution, but for the 500 and 1000 return periods the rainfall values for the GEV distribution area are the largest.7 shows the value of rainfall for return periods from 2 to 100 years with a smaller GEV distribution when compared to the Gumbel distribution, but for return periods of 500 and 1000 years the rainfall value of the GEV distribution is the largest compared to Gumbel and Log Pearson III.

Peak Flow
Table 8 shows the highest peak discharge values with the GEV distribution only occurring at the 2year return period, for the 5-to-1000-year return period the highest peak discharge values occur at the Gumbel distribution.From the analysis of the 5 (five) tables with the GEV distribution, it can be concluded that the simulation results show that the Gumbel distribution is better than the GEV, but there are return periods of 500 and 1000 in regional rainfall and the highest rainfall is in the best GEV distribution.This resulting higher value of flood hydrograph as seen in Figure 3.

Table 1 .
Data Reliability Test Results

Table 2 .
GEV Parameters for TRMM Stations

Table 5 .
Results of the Third Probability Test Distribution.

Table 6 .
Precipitation Regions Various Distributions

Table 7 .
The Highest Rainfall Various Distributions

Table 8 .
Peak Discharge Various Distributions Peak Time Table9shows the peak times of various distributions, with the Gumbel distribution showing the best values at each return period.

Table 9 .
Peak Time of Each Distribution