Variable analysis for supporting reservoir impounding modeling

The impounding stage of the reservoir is a stage after the implementation of dam construction is finished. The process of reservoir impounding is started by closing the tunnel diversion gate and the elevation of the water level will be moving up slowly. The speed of the increasing reservoir water level elevation is affected by the dry season or rainy season, so it is arranged in such a way for obtaining the daily increase is not more than 1.0 m/day, due to dam safety. This research intends to build this modeling, at first by studying which variables are affecting in order to get the safe period of impounding. The methodology consists of a correlation analysis of inflow, outflow, and the ratio between storage volume and inflow volume to the optimal impounding equation. The statistical hydrology approach is used in this modeling that will assess the 7 observed reservoir impounding which is started from base elevation until Full Supply Level (FSL). This modeling will help in decision-making about the selection of the safe and optimal period of reservoir impounding. At the end of impounding, the reservoir will be full and it starts to be allocated regarding the utilization that has been designed.


Introduction
The process of reservoir impounding is started by closing the diversion tunnel gate and the water level elevation will be moving up gradually.The increasing velocity of the reservoir water level is affected by initial impounding, whether dry season or rainy season, so it is arranged in such a way that the daily increase is not more than 1.0 m/ day because of the safety reason for the dam body.The condition that will be modeled in this analysis is by studying the affected variable so there is obtained the safe initial impounding.Inflow, outflow, ratio between storage and inflow volume, and reservoir storage form are the variables that will be studied in their correlation for formulating the optimal initial impounding.
Therefore, the accuracy in predicting the increase of reservoir water level elevation will be arranged in the model by using the statistical analysis approach.The analysis result of the water level increasing is a reference in the analysis of the other aspect of dam observation as an analysis of deformation and implementation of plugging.According to Tchemutter et.al [1], they said that during the impounding time, there is needed an understanding of the impact of load and deformation behavior at the dam body and core.
The researcher who carried out the impounding observation at the dam of Three Georges Reservoir in Chongqing municipality, Hubei province-China said that the change of water level elevation in the 1311 (2024) 012052 IOP Publishing doi:10.1088/1755-1315/1311/1/012052 2 reservoir had an impact on the hydrology condition and operation arrangement at reservoirs under it.The research is carried out by analyzing the relation between the gradient hydraulic and discharge ratio at downstream rivers [2].
The experience of impounding at a small reservoir (309,000 m3) in Qionglin reservoir on Kinmen Island, Taiwan that is written by Hung et.al [3] concluded that rainfall is the factor that influenced the impounding of Qionglin reservoir mainly in the climate which the evaporation is relatively higher than rainfall depth.The research plan is to investigate time and increase in water level elevation during reservoir impounding by studying the affected variable so there is obtained the supporting system model formulation of initial impounding.

Research Location
To obtain the formulation of the initial impounding model, there is used the observation data of elevation at the reservoir initial impounding time that is taken at several dams as presented in Tables 1, 2, and 3.

Relation Analysis Among Variables
This research began by studying the observation data of initial impounding elevation at several dams that have been observed.This is carried out to select the field data so there is used the recording of elevation that is started from bed elevation until spillway (full) elevation continuously.In several cases, there is the scenario of impounding gradually which is caused by the land problem that has not been free or there is part of the building that is needed improvement.However, this research is carried out the analysis of the dam that experiences 1 stage of impounding.
The assessment among variables is carried out to know the effect of the increasing reservoir water level at an initial impounding time.
Based on the observation of reservoir water level elevation at initial impounding, so it is obtained the parabolic equation with polynomial one dominates the relation between elevation and initial impounding time.The relation analysis among variables includes: 1.The relation between independent and dependent variable 2. The relation between independent and dependent variables that is moderated by moderating variables.3. The relation between independent and dependent variables that is mediated by intervening variables.

Theory of Reservoir Simulation
According to [4], [5], [6], a reservoir is operated according to a set of rules or guidelines for storing and releasing water depending upon the purposes it, is required to serve.The decisions are made regarding releases in different time periods in accordance with the demands.One type of management frequently used for reservoir operation is based on the rule curves.The following formula is used.One of the manners that is often used for the simulation of reservoir operation is by using the rule curve and the formula as follows: The equation is used when analyzing the increasing reservoir water level during impounding, there is the condition that initial storage V0 = 0, and sometimes the outflow demand = 0 or the outflow demand does not flow first until the reservoir water level elevation reaches full elevation regarding the design.
Meanwhile, Linsley et.al [4] said that the change of water level elevation in the natural scheme is based on the continuity principle that is applied to the river with the formulation as follows: with  ̅ is the average inflow during Δ,  ̅ is the average inflow during Δ, Δ is water volume change in the channel that is located between the section of inflow and outflow during Δ.If  ̅ is outflow that can be measured through the flow meter structure or peilschaal, so  ̅ can be calculated through the result of Δ analysis.The value of Δ can be approached by using the reservoir capacity curve.If the average of flow during a certain time is the same as the average of flow at the beginning and ending of the time, so equation-2 becomes as:

Result and Discussion
This research will present the influenced variable to the duration of impounding and carry out the determination of the variable that will be arranged to become a model.The variables and the explanations are as follows: i.Independent variables: watershed area, reservoir volume, reservoir capacity curve, storage depth.The reservoir volume is the target volume during the first stage of impounding.
ii. Dependent variables that become the independent ones in this context are daily inflow discharge, and outflow discharge (it is calculated based on the demand or percentage (%) to the inflow).The average inflow as well as outflow, and rainfall are as the observation during the implementation of impounding.iii.Dependent variables: duration (y1) of water level increasing from bed elevation until reaching the design storage volume, and design elevation (y2t) during t.Data of each variable from the observation of 8 dams are presented in Table 1.At the initial stage, the assessment of the average inflow and outflow data to the duration of impounding.The duration of impounding is expressed as a Y variable, so every variable of x1 until x7 is evaluated about the effect on the Y, and in this stage, the r2 (correlation) coefficient from each variable.It is known that watershed area (x1), reservoir volume (x2), average of inflow (x4), average of outflow (x5), and rainfall (x6) indicate a good correlation to the duration of impounding (Y).Meanwhile, the ratio of Vi/Vt (x7) is the comparison between the volume of inflow and volume of storage, which does not give a significant correlation, likewise, the variable of water level depth (x3) shows a relatively small r2 correlation [7], [8].
Based on the initial assessment of the average value, the influenced variables to the duration of reservoir impounding are as follows: watershed area (x1), volume of reservoir storage (x2), average of inflow (x4), and average of outflow (x5), and rainfall (x6).Rainfall is an independent variable that will influence the inflow (x4) and outflow (x5), and outflow is a fixed flow that is obtained from water demand during the impounding process, so x4 and x5 are calculated as the independent variables [9].Therefore, during the development of the model, it will be used the dimensionless equation approach.
Then, there is carried out the evaluation of variables to the daily observed data series.Figures 1 until 8 present the impounding observed curve to the 8 dams that the rhythm can be approached with the parabolic equation by the polynomial equation.Based on the curve, there is carried out the evaluation of the correlation between the daily elevation (y2) and daily inflow variable (x4), daily outflow (x5), and rainfall (x6).According to [6], [9], due to the model development, the regulation of reservoir impounding operation can be made formularized through the algorithm approach, and the initial period of impounding can be further developed.Based on the argument above, the increasing water level elevation is influenced by inflow discharge to the reservoir (in a stochastic context) and outflow discharge of the reservoir.Table 5 presents the correlation between daily elevation and x4, x5, x6.According to the discussion above, there is arranged the resume of analysis results between daily elevation (y) and variables of inflow, outflow, and rainfall which the daily data of inflow variable (x4) and outflow variable (x5) is more significant influencing to the reservoir elevation change such as the daily rainfall (x6).

Conclusion
Based on the analysis and discussion above, it is concluded as follows: a.The process of impounding by closing the tunnel diversion gate and the water level elevation will be moving up gradually.From the observation of reservoir water level elevation at initial impounding, it is obtained that the parabolic equation with the polynomial equation dominates the relation between elevation and implementation period of reservoir initial impounding.b.From the statistical approach, the influenced variable to the duration of impounding is watershed area (x1), volume of storage reservoir (x2), average of inflow (x4), and average of outflow (x5), and rainfall (x6).c.However, in the study of daily data, the daily data of the inflow variable (x4) and outflow variable (x5) is more significantly influencing the reservoir elevation change than daily rainfall (x6).

Table 1 .
Locations that are used for Model Calibration and Simulation

Table 2 .
Locations that are used for Model Verification

Table 3 .
Locations that are used for Model Simulation (alternative)

Table 4 .
Assessment Variable of Impounding Duration