Performance assessment of reservoir storage capacity

This research intends to assess the performance of reservoir capacity. The performance of reservoir capacity indicates the reliability in guaranteeing the water supply need. However, this assessment of reservoir storage capacity is based on the variability coefficient of hydrology conditions. The methodology consists of data collecting that includes the historical discharge that is used for analyzing the variation coefficient of yearly discharge (Cv), water need based on the yearly discharge ratio (D), and storage capacity over the year (Ka). The performance of reservoir storage capacity uses the regression equation of Mc Mahon and Adeloye. The result shows that Indonesia’s reservoir storage capacity is well performing only for fulfilling the water need demand of about 0.0001 to 0.15 of yearly average discharge. However, the negative NSE value is obtained for water demand about 0.2 until 0.55 of yearly average discharge. It shows that the storage capacity observed is under-estimate if it is for supplying the water need demand with a ratio of more than 0.2 of yearly average discharge. This research result is hoped to predict the feasibility of reservoir storage capacity. In addition, it can be used as a reference in assessing the performance of multipurpose reservoir storage capacity as the base of accurate decision taking in planning reservoir storage capacity and reservoir utilization. Then, it is the base of decision taking in designing the dimensions of dam complementary buildings.


Introduction
A dam is a structure built from soil fill, rockfill, and concrete, which is for holding and storing water, waste, and mud [1].The aim of dam development can be categorized into single-purpose and multipurpose.The multipurpose dam is used for irrigation, raw water supply, flood control, hydroelectric power generation, and tourism.The dam is also utilized for saving water in the rainy season and utilizing water in the dry season.The suitability of a multipurpose reservoir necessary to be individually assessed, and its usage may not be the best solution in every case, and it is better to propose the water system well to be related by infrastructure [2].
The main aim of the reservoir is to supply the facility for arranging the surface water flow.However, the reservoir storage capacity and operation policy determine how far the river flow can be saved for release later [3].The role of reservoir capacity is to conserve water availability under the scenario of climate change [4].
Besides the active storage capacity of the reservoir, some capacities can be allocated for temporary storage of flood during a certain period in a year.The flood flow usually happens in time intervals from several hours to several days or weeks [3].The flood control system in the new era is to increase the ability to adapt to floods that often happen and to increase the resilience to extreme flood disasters [5].
The ability of river type reservoir flood control is not enough to be calculated based on the measurement of historical floods.However, it is necessary to use the simulation method of stochastic flood to find the process of flood entrance that is the most dangerous in a reservoir at a certain design frequency and to simulate the flood distribution in the reservoir through the arrangement of dynamic flood capacity [6].The matching frequency method is applied to make a pair of Cumulative Distribution functions (CDF) in evaluating the reservoir operation for flood control and the reliability of water availability [7].To integrate the reservoir flood control operation in the global flood forecasting system, it is important to accurately estimate the discharge and the other variables because the available rule of modeling operational and parameters do not reflect the actual variability because there is less data related to the modeling that can be globally applied the flood regulation [8].
The new paradigm that is related to the reservoir storage capacity is based on the important need to converse the available reservoir storage capacity because of the increasing demand that is related to population growth, the increasing hydrology variability that is related to climate change, challenge, and the cost that is related with the expansion of available capacity or decommissioning and develop the new storage capacity [9].Therefore, the realization that reservoir building needs efficient reservoir storage capacity and effective control of reservoir outflow.
During ten years (2014-2024), the Indonesian government programs 62 development dams to support food, water, and energy resilience.In 2021, the dams that have been finished are 29 dams.In 2023, dams that will be inaugurated are 9-13 dams.The new dam is hoped to have good performance of the storage capacity so it can be profitable regarding the design lifetime by reviewing the factor that affects the effectivity of flood control, which is illustrated with the small ratio of storage volume to the average of inflow [10].
The evaluation of existing dam performance is in the Circular Letter of Water Resources Director General no/SE/D/2017 about the guidance of dam performance assessment.The evaluation of reservoir operation performance is carried out for reservoirs that have been built.The assessment of reservoir operation is one of the components of the operation performance aspect and reservoir service.The component includes the normal and emergency operation that is related to the implementation and operation test.The indicator of reservoir performance can be categorized into two main indicators (implementation and reservoir operation test), the component of reservoir operation performance can be categorized into three subcomponents (normal, emergency, and dam operation), the criteria of reservoir operation assessment can be categorized into four categories (good, moderate, less, and bad) [11].
So far, there is no development model of reservoir storage capacity performance index for multipurpose reservoirs used in the design stage based on the water supply characteristics for water demand supply and flood control.The available regression equation of the reservoir storage capacity performance model is the reservoir storage capacity's performance for supplying water demand [12].The regression equation expresses the performance of reservoir storage capacity for supplying the water needs.However, the performance model of reservoir storage capacity in Malaysia, which is useful because it can be used in the initial planning stage of the reservoir system, is still not needed for detailed analysis [13].There has also been an empirical equation for analyzing the reservoir capacity based on the estimation of SPA reservoir capacity and the behavior that is allowed in Africa, Europe, North America, and the South Pacific [14].
This study aims to assess the performance of reservoir capacity, which indicates the reliability in guaranteeing the supply of water demand based on the coefficient of variation of yearly discharge (Cv), the ratio of water demand to yearly discharge (D), and storage capacity over the year (Ka).Cv, D, and Ka values represent historical discharge variability coefficients of hydrological conditions developed to predict the total performance of reservoir capacity [13], [14].Selatan regency, Nusa Tenggara Timur province-Indonesia.8. Lolak dam, located in the Pindol village, Lolak district, Bolmong regency, Sulawesi Utara province-Indonesia.9. Sukarahmat dam, located in the Suka Rahmat village, Teluk Pandan district, Kutai Timur regency, Kalimantan province-Indonesia.10.Marangkayu dam, located in the Sebuntal district, Kutai kartanegara regency, Kalimantan Timur province-Indonesia.

Performance Equation of Reservoir Storage Capacity at The Planning Stage
This research refers to the previous research for expanding and deepening the theory used in this research.The previous research can help to make the base reference in this research and become the base of developing this research.In addition, the previous research is the inspiration source and can give the disadvantages and advantages of being developed.The performance of reservoir storage capacity is expressed in the Gould-Dincer Gamma storage equation [15].Furthermore, has been had developed a regression equation to adjust the capacity in the year (K) by Adeloye and Mc Mahon [16].The equation that has been developed for predicting the yearly capacity (K) as well as over year capacity on the reservoir planning stage as the formulation, as well as the curve, is as follows: 2  (1) (3) Where KA is over year storage capacity that is as the yearly average discharge ratio (MAF); D is the demand that is expressed as the MAF ratio; and CV is the variation coefficient of yearly flow, Zf is equivalent standard gamma variation,  is the skewness coefficient of yearly discharge [16].The performance function of reservoir storage capacity without failure for 12 rivers based on the coefficient of discharge variation (Cv) has been developed by Lallemand [12].In this study, there are presented six curves of the performance of reservoir storage capacity are presented in Figure 1.Cv, as a coefficient of discharge variation, is used to assess the performance of reservoir storage capacity.It was chosen due to its ability to demonstrate the variation coefficient of yearly flow.This coefficient, Cv, was also applied in a study of reservoir storage capacity performance in some reservoirs in the USA and the UK [14], as presented in Figure 1 =  +   +  +   + = −0.222+ 0.322  + 0.6 + 1.025  ( 2 = 0.988) (6) KT is total capacity, CV is yearly average discharge variation coefficient, D is water need, and KA is over year capacity.The equation of reservoir storage capacity performance (KT) has been very good validated, with the value of R2 is close to 1 [14].

Validation Model
Root Mean Squared Error (RMSE) is one of the manners for evaluating the linear regression model by measuring the accuracy level of the estimation result of a model.RMSE is analyzed by quadrating the error (predictionobservation), divided by the number of data (n), and then rooted.RMSE is the error level of the prediction result, which is getting smaller (close to 0) than the RMSE, so the prediction result will be accurate.
NSE (Nash-Sutcliffe Efficiency) shows how good the plotting of observation value (measurable) that is compared with the prediction-simulation value regarding the line 1:1.The value is in the range from -15.169 until 0.667 (suitable with Table 1 about the classification of the Goodness of fit).The getting bigger NSE value means that the model performance is better.If the NSE value is close to 1.0, it shows that the modeled reservoir storage capacity is the same as the reservoir storage capacity in the field [17].The model validation of reservoir storage performance assessment is carried out to evaluate the level of model enforceability to the output.The validation of output is carried out by using Root Mean Square Error (RMSE) and Nash-Sutcliffe Efficiency (NSE) with the criteria as presented in Table 1 [18].

The Hydrology Characteristic
The hydrology characteristic in this research is carried out in 6 islands in Indonesia, as presented in Table 2, Figure 2, and Figure 3, with the smallest watershed area is 11.69 km2 and the biggest one is 554.21 km2; the yearly rainfall is between 1,048 mm/ year until 2,652 mm/ year.The yearly average rainfall ranges from 9 million m2 to 431 million m3.Cv is for knowing the variability of hydrology conditions in each dam location.It shows that Bali Island has the smallest variability of yearly discharge, which is 0.09 to 0.14; Sumbawa, Sulawesi, and Kalimantan islands have the biggest CV of 0.16 to 0.19.However, Lombok island and Timor island have a relatively big CV of 0.34 to 0.45.The small CV shows that the discharge difference over the year is not too big.However, the Cv > 0.3 shows a discharge difference between dry and rainy seasons.The value of Cv is very important in assessing reservoir storage capacity performance, which has been researched in Malaysia [13].The skewness value shows that all of them are in the normal curve.These research locations are assumed to have represented the hydrology condition in most of the areas in Indonesia.Table 2 presents the hydrology characteristics of 6 islands in Indonesia.Research on the reservoir storage performance equation (KT) is for seeing the suitability of the reservoir storage capacity performance equation if it is applied in 10 dams in Indonesia [19].Table 2 presents the hydrology characteristics of 6 islands in Indonesia.

Over-year Reservoir Storage Capacity (KA)
Table 3 presents the ratio between over year reservoir capacity (KO or reservoir that is not necessarily full or overflow in a year) based on the discharge variation coefficient and water demand, the ratio of mean annual flow (MAF).For the bigger CV (e.g., CV > 0.3), the value of KO is also getting bigger regarding the demand (D).It indicates that the greater discharge variation is, so the reservoir's ability to back full needs time more than one year, and the value of KA shows it is close to 1.

Total Reservoir Storage Capacity (KT)
Then, the total reservoir storage capacity is analyzed as presented in Table 4 in the MAF ratio unit and Table 4 in the million m3 unit.The total reservoir storage capacity (KT) is a number of over year capacity (KA) and year capacity (K).Table 4 and Table 5 shows the total capacity performance of reservoir storage (KT) due to the various condition of demand that is compared with the observed condition of reservoir storage capacity.The result shows that the dam performance in Indonesia is in the range from 0.1 to 0.3 towards the demand, so there is about 70% until 90% water is released or as the spill out.However, Table 5 presents the performance of reservoir storage and observation of reservoir storage capacity.

Figure 1 .
Figure 1.Performance of Reservoir Storage Capacity without Failure[12] . Adeloye, Mc Mahon, et al. developed the regression model for well predicting the equivalent yearly capacity on the reservoir design stage with the model as follows:  = (  , ,   )

Figure 5
Figure5presents the performance of observation reservoir storage in Indonesia, shown by the dotted red line.The performance of reservoir storage still utilizes the water in the range from 10% to 30% of the yearly average discharge.

Figure 5 .
Figure 5. Performance of Reservoir Storage Capacity Due to The Adeloye and Mc Mahin Method

Table 2 .
Hydrology Characteristics in 6 Islands in Indonesia

Table 3 .
The ratio of Over Year Reservoir Storage Capacity (KA)

Table 4 .
Matrix of the Ratio between Reservoir Storage Capacity Performance and Observation Reservoir Storage Capacity

Table 5 .
Performance of Reservoir Storage Capacity Performance and Observation Reservoir Storage Capacity in Million m3 Table 6, the validation of the reservoir storage capacity performance model uses the Mc Mahon and Adeloye Model.Based on the validation in Table 1, the RMSE value ranges from 0.063 to 0.444, the value with the very good category (it is suitable with Table 6 about the classification of the Goodness of fit).It indicates that the performance of reservoir storage capacity due to the Mc Mahon and Adeloye model has very good accuracy for the demand from 0.0001 until 0.55 of yearly average discharge.