Analysis of factors affecting the intake gate operations of Gerokgak Reservoir for command areas of Subak Gede

Subak Gede in Gerokgak Village, Buleleng, practices traditional irrigation in Bali based on Tri Hita Karana principles. Subak sources water from Gerokgak Reservoir, where intake gate operations depend on three factors: the recent ten-day discharge (item 1), rainfall in command areas (item 2), and crop type (item 3). Quantification Analysis I simulated the intake gate from 2019 to 2022, comprising Models A to D, each using yearly data for its respective year (2019, 2020, 2021, 2022), and Model E using four years of data. Items 1 and 2 had high, moderate, and low categories; item 3 had paddy, palawija, paddy-palawija, and fallow categories. The simulation exhibited strong correlations between predicted and recorded discharge of every quantification model, with R-total > 0.6, varying for each sample year. Based on the analysis, the three items showed a different impact every year, depending on the item-category distribution and variation. Notably, due to its sample, quantification Model E excelled in predicting intake gate operations for other yearly data, including its own sample year.


Introduction
Subak is a traditional irrigation management system and organization in Bali, based on socio-religioustechnical agricultural practice [1].Subak manages water distribution, irrigation, resources, conflict resolution, and religious rituals [2].Subak's main principle, Tri Hita Karana, is a Balinese Hindu philosophy about the harmonious human relationship with God (Parahyangan), nature (Palemahan), and fellow humans (Pawongan) [3].This principle aligns agriculture and river basin management with nature, humanity, technology, and the characteristics of the landscape, soil, water sources, and rainfall [4].The Subak irrigation system follows the contours of terraced paddy fields, resulting in reducing runoff, controlling water flow direction to lower areas, and retaining water on sloping land [5].During times of abundant water (kertamasa), Subak implements the paddy-paddy.However, when water availability is limited (gadon), Subak implements paddy-palawija, using nyorog.Nyorog is applied when Subak has only one irrigation water source system, and the way of distributing water from upstream (Ngulu), midstream (Maongin), and downstream (Ngasep) tertiary blocks, allowing surplus water from upstream to be used as irrigation water in downstream (Natak Tiyis) [6].The irrigation water distribution is still in traditional way, which takes advantage of mutual agreements [7].Subak determines the allocated water amount by conducting Nabdab Yeh (activities of allocating water) during monthly meetings (paruman).Through Nabdab Yeh, Subak will determine the distribution of water discharge to ensure equitable water distribution [8].Factors considered in Nabdab Yeh vary for each Subak.Several Subaks that get water from one source (one diversion gate, or one weir) will generally form a coordination forum called Subak-gde [9].These several Subaks are then called tempekan (group), representing secondary blocks with their member called krama.One of the Subak-gde is Subak Gede in Gerokgak Village, Buleleng.Subak Gede consists of 12 tempekan and primarily uses water from Gerokgak Reservoir, which collects water from Tukad Gerokgak River.Subak Gede, employs Nabdab Yeh to determine irrigation water requirements for the upcoming month.Several items have been considered as influencing factors in Nabdab Yeh.The first item is the type of crops that were currently or planned to be planted.Farmers then assess recent rainfall and the discharge from the previous period.Once decided, Subak informs the operator of the requested water amount.The operator operates the intake accordingly.Thus, the determined water demand through Nabdab Yeh, including the items considered in the process, affects the intake operation.However, the influence of these items on the operation is still unknown.Meanwhile, irrigation management and operation itself have a significant influence on Subak continuity [10].Considering the impact of these items on Subak and operations, it becomes important to determine the influence of these items.
The procedure for operating the intake gate is static, while agriculture is dynamic [11].Human intelligence addresses this problem by using past variables to predict future possibilities.However, there are limits to weighing each item, requiring a method that could mimic human intelligence to process these items.One of these methods is Quantification Analysis I.In this study, a prediction model will be built for the years 2019-2022.The models' ability to predict the Gerokgak Reservoir intake operations are based on each category in Subak Gede's Nabdab Yeh.The objective of this study is to confirm whether the specified items have an influence on the operation of the Gerokgak Reservoir intake gate.

Research Location
This study was conducted in Subak Gede, Gerokgak, Bali, which spans an area of 414 ha.The majority of Subak Gede, covering 374 ha, receives water from Gerokgak Reservoir, located in the northern part of Bali Island, Buleleng Regency, as shown in Figure 1.As shown in Figure 1, Subak Gede is bordered by two rivers, with the western part being the Tukad Lesung River and the eastern part being the Tukad Gerokgak River.The Tukad Gerokgak River serves as the primary irrigation channel, while the Tukad Lesung River functions as the drainage system for Subak Gede.The Gerokgak Reservoir is classified as a single-purpose reservoir for Subak Gede irrigation, which consists of 12 tempekan as in Figure 2. Based on the scheme, Subak Pangkung Lesung and Renon are the two tempekan that do not use water from the Gerokgak Reservoir for their irrigation.

Figure 2. Irrigation Schemes of Subak Gede Consisting of 12 Tempekan
The sustainability of Subak schemes relies on having enough river runoff available, and it's crucial to maintain this balance from upstream to downstream [12].While Subak has their water demand determined through Nabdab Yeh, the water allocation procedure implemented in Subak Gede, based on [13], is more semi-demand rather than on-demand.The intake gate operator's allocation of water, taking reservoir water availability into account, demonstrated a semi-demand procedure employed by Subak Gede and the Gerokgak Reservoir operator for a 10-day period.

Data collection
The data in Table 1, collected from Bali-Penida River Basin Organization (BWS Bali-Penida) and Subak Gede Gerokgak, is organized into 10-day periods to match the planting schedule, resulting in 36 periods per year (I, II, and III each month), totaling 144 data samples for 2019-2022.Rainfall data is averaged per 10-day period, while discharge data is converted from daily discharge to 10-day averages.The paddy varieties cultivated in Subak Gede consist of Ciherang, IR 64, Bondoyudo, and Inpari 43.The planting schedule is typically evaluated by Subak Gede after the end of the second planting season (II) or before entering the first planting season (I) of the following year through monthly meetings.The latest cropping pattern applied in Subak Gede is the paddy-palawija, with a detailed

Analysis method
In Quantification Analysis I, data is categorized into specific items, and each item is then converted into binary values (1 for yes, 0 for no) based on field conditions.These binary values are used to calculate item-category weights, forming the foundation for unique predictive models customized for each sample's conditions.This adaptability ensures a unique model for each sample.Model suitability is assessed through calibration, which indicates the effectiveness and alignment of the model's items with the original conditions, enabling us to determine the level of each item's influence.The model's predictive accuracy is also validated against data from the other yearly sample.

Identification of item-category
Some of the factors that significantly influence irrigation management are crop type and rainfall [14].
In terms of Subak Gede, the identification was based on interviews with the operator and member of Subak Gede regarding intake gate operations and Nabdab Yeh.The factors found to have an influence are the recent ten days of discharge (item 1), Recent ten days of rainfall within the command areas (CA) (item 2), and the type of crops cultivated in Subak Gede (item 3).Categories for items 1 and 2 use Netto Field Water Requirements (NFR) as the parameter.Item 3 is based on the planting schedule.The determination of item categories can be seen in Table 3.Based on the item categories, there will be a set of "yes" and "no" that need to be converted for further analysis.

Building the simulation model
The converted set of "yes" and "no" into binary numbers, for "yes" is 1 and "no" is 0, are organized into dummy variables (Xijk).These dummy variables are organized in a matrix of size m x N. In general, the notations i, j, k are defined as follows: 1. Item (j) : m 2. Category (i) : n1, n2, …, nm 3. Sample (k) : N Based on the general equation of Quantification Analysis I by Dr. Hayashi in [15], predicted discharge (yk) was calculated using Equation 1: = weighing factor for each category    = each category for each item Modeling will be conducted using yearly samples (36 periods) and a continuous sample of 4 years (144 periods), resulting in the formation of 5 models.These models are as follows: Model A (2019), Model B (2020), Model C (2021), Model D (2022), and Model E (2019-2022).Each model will adapt to the conditions of its respective sample year.The model's predictive capability will be assessed by applying it to other years' data.The parameter used for assessment is R-total.

Correlation coefficient (R)
The correlation coefficient (R-total) can be calculated using a general equation, as shown in Equation 2. A value of R-total ≥ 0.5 is considered a moderate to strong correlation.Therefore, a model with R-total ≥ 0.5 is shown to have good accuracy with a relatively small error rate [16].This correlation is needed as we require adaptable systems or models that can effectively accommodate changes, whether they result from natural phenomena or human actions [17].The correlation between the model and intake operations is obtained through the relationship between observed discharge and predicted discharge.
After obtaining models R-total, R-partial (ρ) for each item is also calculated using Equation 3. The value of R-partial can indicate the extent of influence of each item, and it is categorized as shown in Table 4.

Result of model calibration
The distribution of item categories can vary each year, as shown in Figure 3, which also illustrates the differences in data distribution between each 1-year period with the 4-year period sample.Quantification Analysis I is conducted based on this matrix, from which the weights for each item can be determined.Therefore, the distribution of item categories will affect the obtained weights.These item categories shown in Figure 3 provide insights into the yearly conditions.For instance, in 2022, both recent 10-day discharge (item 1) and rainfall are mostly "High" with some "Moderate." The crops cultivated are mainly only Paddy or Palawija, with the longest Paddy-palawija period and shortest Fallow periods.This distribution indicates that Subak Gede received plenty amount of water from the Gerokgak Reservoir during a wet year in 2022, allowing for extended kertamasa and gadon periods with a focus on Paddy and Palawija cultivation and reduced nengin (Fallow) time.
The performance of the model is influenced by the weights within it, which vary based on the distribution of item categories.The weights will determine the R-partial and R-total obtained.The predictive capability of the model can be assessed through its R-total.
Additionally, the level of item influence is indicated by its R-partial, which in this analysis is examined for each sample year.The weights of item categories can be seen in Table 5, and the calculated results for R-total and R-partial are shown in Table 6.
Table 6.R-partial, and R-total for Each Year  In Table 6, it is shown that all models have a strong R-total.The models are able to predict discharge according to the conditions of their sample years, as shown in Figure 4.It is found to be difficult for the model to predict when the observed discharge fluctuated extremely.Among the models with a 1year R-partial values for each item in each model vary yearly.Among the four one-year sample models (Model A, B, C, and D), recent 10-day discharge (Item 1) consistently shows moderate to high R-partial values.Recent 10-day rainfall over CA (Item 2) starts with a low R-partial but gradually reaches a moderate level by 2022.Crop type (Item 3) generally has a high R-partial, except in 2020.However, this differs when calculated over a continuous four-year period in Model E. In Model E, both recent 10day discharge and crop type, typically high in R-partial, show only moderate influence.Conversely, recent 10-day rainfall over CA consistently has a low R-partial.
The varying influence for each item can be caused by the following factors: (1) The nyorog system relies on continuous water distribution aligned with planting schedules to accommodate Natak Tiyis, resulting in minimal changes in intake operation.(2) The Nabdab Yeh determines the monthly water demand, adjusted to each planting schedule and water availability period (kertamasa and gadon).When no adjustments were made by Subak, the intake will be operate based on water availability in reservoir or rainfall.(3) Crop types are regulated after Subak assesses the kertamasa and gadon periods, in addition to rainfall.This suggests that both periods can be inferred using crop types.(4) The Natak Tiyis mentioned in point (1) and the condition in point (2) lead to rainfall influence being the least significant.
(5) The regulated planting schedule causes the intake gate to be operated based on the crop type each year.However, having a similar planting schedule in general for over 4 years results in fewer variations of item categories, reducing the influence of crop types over the 4-year period.

Model verification
The predictive ability of the models in Table 6 was based on their respective sample years.Therefore, the models are applied to other years using 36 periods of data for verification of their predictive capability.7, R-total values assess model performance across the four sample years.Most models exhibit weaker R-total values in 2022 due to extreme data fluctuations.However, apart from Model A, they generally exhibit better performance in 2020 when compared to their respective sample years.This can be attributed to the similarity between the conditions in 2020, 2021, and 2022, as indicated by their corresponding kertamasa and gadon periods, resulting in similar intake operations.Overall, all models consistently demonstrate high R-total values, indicating accurate predictions for these years.
Model E, being a 4-year model, predicts discharge that closely aligns with the measured data of each year.Referring to Table 7, Model E is not only considered good for predicting the observed discharge but also achieves an R-total category mostly equivalent to each model's sample year.Model E exhibits a strong overall correlation of 0.92 between its predicted discharge and the other models'predicted discharge, as indicated by the remarkably similar patterns observed in Figure 5.This could be due to the longer data span used for Model E, that consists of samples from other models.

Conclusions
The models are built based on sample-year item categories, allowing them to adapt to those conditions, reflecting Subak Gede's considerations during Nabdab Yeh.The models' predictive ability, aligned with sample-year conditions, is shown by R-total, which may differ yearly.The influence of each item in the model, indicated by R-partial, also varies based on item category distribution.Each model had a stronger correlation for its respective sample year.Models with yearly data exhibit higher R-total than those with 4-year continuous data.Items from Nabdab Yeh indeed have an influence on the operation of the Gerokgak Reservoir intake gate, though their influence varies each year depending on current or previous conditions.Model E, with its longest data span that includes other model samples, offering a richer dataset, proves most suitable for predictions extending beyond the sample year, supported by its strong R-total.However, extreme fluctuations in observed discharge can affect predictive accuracy, reducing R-total values.

Figure 3 .
Figure 3. Distribution of Item-category for Item 1 (Recent 10 Days Discharge), Item 2 ((Recent 10 Days Rainfall Over CA), and Item 3 (The Type of Cultivated Crops in CA)

Figure 4 .
Figure 4. Comparison Between the Predicted Discharge and Observed Discharge D has the lowest R-total, consisting of an observed discharge with more extreme fluctuation than the other sample years.The number of periods (data) in the model determines the models range capability.Therefore, Model E is capable of predicting up to 144 periods (4 years), while Models A, B, C, and D are up to 36 periods (1 year).

9 Figure 5 .
Figure 5.Comparison of Model E Predicted Discharge with Each Sample Model (A, B, C, D)

Table 1 .
Research Data Collection

Table 2 .
Only the 10 tempekan that utilize water from Gerokgak Reservoir are shown in Table2.

Table 2 .
Planting Schedule and The Area of Each Tempekan Subak Gede

Table 3 .
Variable and Parameter for Item-category

Table 5 .
Weighing Factor of Item-category for Each Year

Table 7 .
Verification of Each Model for Different Data Years