Dam water conservation equation index using AHP and cluster analysis methods: a study on selected dams in Java

This research, which was conducted on 12 selected existing dams, focuses on the application of the Analytical Hierarchy Process method for determining the “Dam Conservation Equation Index” based on three main issues for water conservation: namely, dam contribution to reservoir water quality (DO, pH, TDS), groundwater (DO, TDS, pH) and local climate (min temperature, max temperature, precipitation). It is a new approach to indexing existing dams’ effect on water conservation. The result from the AHP method shows correlations between dams and water condition, with groundwater being affected, shown by a 70% effect on the priority scale, followed by local climate and reservoir water quality with approximately 20% and 10%, respectively. There is also the effect of ‘unknown parameters’ affected by dams, albeit not significantly. Meanwhile, the results from cluster analysis are: there are three clusters of dams in the research areas: cluster 1 (Cipancuh and Delingan dam), cluster 2 (Cacaban, Wadas Lintang, Sermo, Pondok, Lahor, Sampean Baru and Wonorejo dam) and cluster 3 (Darma, Malahayu). Cluster 1 and 3 are dams with the lowest water quality in the research area.


Introduction
Uneven water distributions and availability are why dams are essential to support and fulfill water demands, especially in monsoon seasons [1] [2].Due to its water retention capacity, dams could also be used for flood control and hydropower generation [3].
Like many other nations, the dam is one of Indonesia's most important water infrastructures, mainly used as an irrigation water source [4].Up until 2023, there are 220 operational dams in Indonesia, in addition to 38 dams that are still in the construction phase [5].Approximately 1/3 of operational dams are located in Nusa Tenggara Barat Province (58), followed by Central and East Java, with 44 and 34 operational dams, respectively [6].
Each dam has its unique characteristics and conditions.These conditions are affected by but are not limited to, catchment conditions, climate, and groundwater.Due to its uniqueness, the water conditions in individual dam needs to be analyzed separately.
According to previous research, the needs indexation for the dam needs because of each dam's complexities and different conditions.Thus, we need a new approach to indexing existing dam's effect on water conservation.To achieve this, one of the most widely used and cost-effective methods is the statistical approach.Many fields, including landslide susceptibility mapping [7], [8] and water 1311 (2024) 012050 IOP Publishing doi:10.1088/1755-1315/1311/1/012050 2 vulnerability analysis [9], widely use the Analytical Hierarchy Process (AHP) to support decisionmaking.This approach is complemented by cluster analysis for further analysis of dam indexation.

Dam Effect on Reservoir Water Quality
The presence of reservoir has two main effects on water quality [10]: a.The change of the reservoir in the horizontal direction is hampered b.Sediment concentration changes as water and sediment are deflected.
Reservoir management works, such as meander canals and construction of cribs or embankment protection, will also affect the motion of the reservoir bed.These works will generally cause degradation of the reservoir bed due to increased carrying capacity.The reservoir bed in the lower reaches will consist of medium to fine sand, possibly with layers of silt and clay.When a river flows into a dam, the base slope is slight, and depending on the amount of sediment carried by the river, a delta in the reservoir of dams may form.The formation of a delta is a sure sign that the lower segment of the river is in a state of aggradation that would influence water quality.
If the reservoir embankment consists of rock, cemented conglomerate, or boulders, then it can be assumed that the dam reservoir is stable with its present bed.If the bed is full of rocks and gravel, the course of the reservoir will not be fixed, and the trough will move at a high level, which would also influence water quality.

Dam Effect on Groundwater Quality
Water in the reservoir always looks for a way out through the weakest channel, which could be the body of the dam, the foundation, or around the pedestal [11].The process of flowing water into the soil's pores is called seepage.Soil below the groundwater table is usually in complete saturation with a saturation level close to 100%.Permeability or water permeability depends on the average size of soil particles that are controlled by the distribution of soil grains, particle shape, and soil structure.
In general, two main types of seepage occur in artificial reservoirs: horizontal seepage and vertical seepage.The amount of vertical seepage depends on the soil's texture and the soil's structure at the bottom of the reservoir.In horizontal seepage, water escapes through the reservoir walls due to higher permeability caused by the materials used to build the walls, water pressure, and slope.
Various factors affect the seepage rate, for example, the material used in the construction and the type of soil at the bottom of the reservoir.Seepage loss rates in millim eters per day from various types of soil are listed in Table 1.To calculate the amount of seepage, the following equation could be used: Global warming causes disruption of various air circulations in the atmosphere, which causes an increase in the intensity of extreme climate events and seasonal irregularities.Global climate change is expected to increase the frequency and intensity of extreme climate events [14].The shift in the rainy season could cause: a.An earlier dry season with a more extended period and less rainfall b.The start of the rainy season is reversed with shorter periods with high rainfall intensity c.The Madden Jullien Oscillation (MJO) phenomenon occurs more frequently, which causes dry periods during the rainy season or wet periods during the dry season.Changes in the amount and intensity of rain affect the discharge of reservoirs and rivers.Bodies of water cannot accommodate rainwater that falls with high intensity, so it flows quickly into the sea, and the relatively longer dry season causes drought.
The increase in air temperature due to climate change significantly impacts the environment.One of the consequences of this temperature rise is the heightened evaporation process, which, in turn, reduces the amount of rainfall.As a result of increased evaporation and decreased precipitation, there will be a notable decrease in the availability of water resources, which could have far-reaching consequences for various aspects of ecosystems and human activities that depend on these water sources.
To simulate the impact of climate change on river discharge, one requires two main components: a model capable of describing the projected climate in the future and the simulation of rain into flowing water.
The IPCC commonly uses the General Circulation Models (GCMs) ensemble model for climate projections [15].This model has been agreed upon by climate scientists worldwide to project a variety of climate factors, including atmospheric and ocean temperatures, precipitation, wind, clouds, ocean currents, and the extent of sea ice.Direct use of GCM outputs in hydrological impact studies is still challenging because GCM outputs usually exhibit errors and uncertainties with observational data [16].Therefore, the GCM model must be corrected to reduce systematic bias between simulated data and observations to increase the precision and accuracy of the model.The Quantile Mapping (QM) correction bias method is a relatively simple method and has been successfully used in hydrological and climate impact studies, for example, Cayan et al. 2008;Hayhoe et al. 2004; Maurer and Hidalgo 2008; Broca et al. 2011a [17].QM showed the best results in annual maximum hydrological simulations compared to other bias correction methods [18].

Research Locations
Dams all over Java will be investigated in this research (Table 2 and Figure 1).There are 12 dams spread all over Java, with East Java having the most dams (5) as opposed to Jogjakarta, which only has one dam investigated.2.5.1 AHP Analysis.AHP analysis is one of the best methods for decision-making.AHP analysis involves simplifying and accelerating the decision-making process to find the best alternative in many possibilities.There are several advantages and disadvantages to using the AHP method: Pros of the AHP method: 1. Unity, AHP transforms the general and unstructured problem into a flexible and simple model.2. Complexity AHP solves complex problems by doing a systemic approach and deductive integration.3. Inter-dependence AHP could be used on independent system elements and does not need a linear relationship.

Cons of the AHP method:
1.The people involved should be familiar with the AHP method 2. AHP is a mathematical method without statistical testing.Hence, the reliability of the model is unproven.
3. AHP is highly reliant on its main input.The main input is very subjective, depending on the perception of the expert.Incorrect determination of the main input could produce a wrong result.In order to implement the AHP method, several steps that will be explained in the following subsubsection need to be carried out.

Comparative judgment between two parameters and comparison matrix.
The comparisons are expressed using the Saat scale.The parameters must be arranged in a comparison matrix for analytical purposes.

3
A1 is a little bit more important than A2. 5 A1 is more important than A2.7 A1 is a little bit more important compared to A2. 9 A1 is much more important compared to A2. 2,4,6,8 *) mean value.

Priority Determination.
The priority needs to be determined by assigning the weight in each cell in the range of 0-1, with the total weight for each column being 1.This priority will be determined based on the inputs from experts.

Consistency Measurement.
Consistency is an essential factor in an assessment to ensure that the result can be consistent for future use.The consistency will be checked using the Consistency Ratio (CR).CR is the result of comparing the Consistency Index (CI) with the Random Index (RI).The consistency ratio needs to be less than 10% to be acceptable.

𝐶𝑅 = 𝐶𝐼 𝑅𝐼
(2) 2.5.5 Cluster Analysis Method.Cluster analysis was performed using R with a single linkage method, which grouped items based on the smallest distance.Hierarchical agglomerative clustering starts with treating each observation as an individual cluster and then merges clusters iteratively until all the data points are merged into a single cluster.Clusters are merged based on the distance between them to calculate the distance between the clusters.Dendrograms are used to represent hierarchical clustering results.

AHP Result for Formulating Conservation Equation Index Measured Parameters
The dam water conservation index is greatly affected by three main parameters: reservoir water quality, groundwater quality, and local climate.Furthermore, the priority parameters are organized into a comparison matrix for analysis, with the priority comparisons arranged in a reverse matrix comparison.Hence, the priority comparison between rows and columns will be reversed.This condition is following the mathematical equation, which states that if A: B = X, then B: A = 1/X.For example: if priority A1 (row) : A2 (column) = 5, then priority A2 (row) : A1 (column) = 1/5.The following is a priority comparison matrix for all Dam Water Conservation Index parameters (Table 5).
AHP uses a ratio calculation scale.The scale compares the ratio between two parameters.The assessment of pairwise comparisons (weighting) in each hierarchy is based on the level of relative importance as stated in the comparison matrix in AHP and may be inconsistent.There are ways to measure the consistency of these assessments.For each parameter, pairwise comparisons need to be carried out.The relative comparison values are then processed to determine the alternative ranking of all alternatives.Qualitative and quantitative criteria can be compared to predetermined assessments to produce weights and priorities.Weights or priorities are calculated by matrix manipulation or through solving mathematical equations.The weights are normalized so that the total sum is one.Normalized weights can be used as a reference for the level of importance between parameters.The criterion weight results of this calculation are as follows: 0.024 for A1 (DO of reservoir water), 0.038 for A2 (pH of reservoir water), 0.017 for reservoir water TDS, 0.153 for DO of groundwater, 0.213 for Groundwater TDS, 0.327 for groundwater pH, 0.083 and 0.062 for the local climate minimum and maximum temperature respectively, and 0.083 for precipitation.The conservation equation index is as follows: 0.024 A1 + 0.038 A2 + 0.017 A3 + 0.153 B1 + 0.213 B2 + 0.327 B3 + 0.083 C1 + 0.062 C2 + 0.083 C3 = 100% (3) Based on the formula in Equation 1, the consistency ratio for the analysis is less than 0.1, showing that the result is consistent.The addition operation needs to be done on each quadratic data on every single element to get normalized alternative data.It should be emphasized that pH and TDS negatively affect the water quality, meaning that a neutral pH will result in better water quality than a pH value of more than seven and less than 7.In addition to that, the TDS value will be converted inversely by the deficit of value with the maximum TDS value in the same column.The next step in normalizing the data involves dividing the alternative data by the square root result.The final step is multiplying the criterion weight vector with the matrix above to determine the ranking for each location (Table 6).The higher the rank, the better the water conditions in the field.Location 10 (Lahor Dam) has the best water quality compared to other dams.In addition to known parameters affecting water conditions in the field, there are also unknown (unanalyzed) parameters affecting water conditions (Table 7).These unknown parameters will simply be called 'others' and will be used to verify the calculations done in the previous sub-chapter using the exact procedure.Compared to the analysis result with all known parameters, the 'others' parameter yields approximately the same results (Table 8 -9).Unlike scenario 1 (without 'others' parameters), the best water quality from this analysis is location 11 (Sampean Baru Dam).The consistency ratio is less than 0.1, so the result is consistent:

Cluster Analysis method for Clustering Dams according to Conservation Index
Overall, there are three groups of water qualities for the first scenario, called cluster 1 (location 7), cluster 2 (locations 4 and 10), and cluster 3 (the rest) (Figure 2 and Table 10).The same could be said about scenario two, albeit with a different group composition.Dams with the same group composition for locations 4 and 10 scenarios.Also, locations 2, 3, and 9 are grouped in both scenarios (Figure 3).For scenario 2, the three groups are: cluster 1 (location 2, 3 and 9), cluster 2 (location 8, 11, 4, 10, 12, 5) and cluster 3 (location 1 and 7).Cluster 1 and Cluster three consist of locations with dams with the lowest water quality.
The clustering method used for scenarios one and 2 shows the similarity in each group's dam water conservation index.Dam Water Conservation Index in all clusters has a relatively high dependence on Reservoir Water Quality TDS (A3), groundwater DO (B1), Maximum Temperature (C2), and Precipitation (C3).On the other hand, groundwater TDS (B2) and Groundwater pH (B3) for cluster 1 are the lowest among other clusters.Comparatively, cluster 2 also has a high value for Reservoir Water Quality DO (A1) and TDS (A3), groundwater DO (B1), Maximum Temperature (C2), and Precipitation (C3).

Conclusions
This research found a new approach to indexing existing dams' effect on water conservation.This condition concluded that dam conservation equation index could be based on three main issues for water conservation: namely dam contribution to reservoir water quality (DO, pH, TDS), groundwater (DO, TDS, pH) and local climate (min temperature, max temperature, precipitation) could be explained by the following formula with 0.024 for A1 (DO of reservoir water), 0.038 for A2 (pH of reservoir water), 0.017 for reservoir water TDS, 0.153 for DO of groundwater, 0.213 for Groundwater TDS, 0.327 for The clustering method used for scenarios one and 2 shows each group's similarity in the Dam Water Conservation Index.Dam Water Conservation Index in all clusters has a relatively high dependence on Reservoir Water Quality TDS (A3), groundwater DO (B1), Maximum Temperature (C2), and Precipitation (C3).On the other hand, groundwater TDS (B2) and Groundwater pH (B3) for cluster 1 are the lowest among other clusters.Comparatively, cluster 2 also has a high value for Reservoir Water Quality DO (A1) and TDS (A3), groundwater DO (B1), Maximum Temperature (C2), and Precipitation (C3).Overall, there are three groups of water qualities for the first scenario, called cluster 1 (location 7), cluster 2 (locations 4 and 10), and cluster 3 (the rest).

Figure 1 .
Figure 1.Dam Locations 2.5 Analysis Method This study involves combining the Analytical Hierarchy Process with a field survey.The parameter is as follows: Table 3. Parameters determining water quality Parameter Code Reservoir Water Quality (A) DO A1 pH A2 TDS A3 Groundwater (B) DO B1 TDS B2 pH B3 Local Climate (C) Minimum Temperature (°C) C1 Maximum Temperature (°C) C2 Precipitation (mm) C3

Table 2 .
Dam Research Location

Table 5 .
Comparison Matrix for Dam Water Conservation Index

Table 6 .
Normalized Data Weighting

Table 7 .
The effect of the 'others' parameter on water quality

Table 8 .
Comparison Matrix for Dam Water Conservation Index

Table 9 .
Normalized Data Weighting