Volume 2, No. 5 May 2024 p-ISSN 3032-3037| e-ISSN 3031-5786
Estimation of Groundwater River Availability in Leang
Lonrong Cave Using ARIMA Model and Econophysics Valuation Approach
Nur Azizah Jaya, Muhammad Arsyad, Pariabti
Palloan
Makassar State University, Makassar, Indonesia
Email : nurazizahjaya02@gmail.com, m_arsyad288@unm.ac.id
Abstract
This
quantitative descriptive study uses the ARIMA model approach to predict
groundwater river water availability. It assesses its valuation with an
econophysics orientation in the Leang Lonrong Cave area of TN Bantimurung
Bulusaraung. Secondary data from 2010-2023, including Water Discharge and Water
Level data from the River Basin Center of Pompengan Jeneberang (BBWS) and
primary data on the Valuation of Willingness to Pay, were utilized. The
analysis reveals that water discharge predictions (2024-2030) in the Gua Leang
Lonrong area indicate consistent annual water availability, with the highest
discharge projected in December 2030 (5.08 m3/s) and the lowest in
September 2024 (1.12 m3/s). Valuation of utilizing Leang Lonrong River
water through willingness to pay showed residents willing to pay Rp
42,142.85/month for clean water management. At the same time, visitors are
willing to contribute Rp 21,596.77/visit to enhance water quality management.
Elasticity analysis modeling water discharge with willingness to pay suggests a
relatively elastic relationship, with a minor impact, indicating
unresponsiveness to changes in water discharge percentages. Statistical and economic
methods were employed to analyze daily water discharge patterns and evaluate
residents' willingness to pay for underground river water utilization. The ARIMA
model (0,1,1) forecasted future water discharge patterns with a mean absolute
percentage error (MAPE) of 33.7%. The study surveyed 62 respondents, finding an
average willingness to pay approximately IDR 21,596.77 per visit to maintain
Leang Lonrong River water quality management.
Keywords: ARIMA,
Leang Lonrong Cave, Water Discharge, WTP
Introduction
Karst mountains are found throughout the Indonesian
archipelago, with an area of approximately 15.4 million hectares. Karst areas
are often important water sources, including underground rivers, which strategically
meet human water needs and local ecosystems (Sari et al., 2019). The Maros-Pangkep Bantimurung Bulusaraung Karst area
has a high limestone (CaCO3) content and is spread throughout the region (Soma et al., 2021). The epikarst and endokarst characteristics of this
region indicate its richness. The presence of subsurface water discharge
characterized by the presence of caves is known as spring density (Noperissa & Waspodo, 2018).
The underground river inside the Leang Lonrong cave flows
through the mouth of the cave and has a stable water discharge throughout the
year (Hayati, 2019). The availability of
underground river water in Leang Lonrong Cave is the focus of research because
of the importance of access to sustainable and good quality water sources for
the local community and the sustainability of the karst ecosystem in Babul
National Park. Estimating the availability of underground river water is an
important step in sustainable water resource management (Agniy et al., 2017).
River flow discharge is one of the hydrological parameters
that is very important for water resources management. Data and forecasting of
river flow discharge is very important for the future, assuming the
characteristics of the process remain the same. Because it is impossible for a
river to have discharge population data that includes discharge data from start
to finish. The processed discharge data is a periodic series, which is
long-term data whose value shows movement over a long period of time and has an
upward and downward tendency (Mayasari, D. 2017).
Autoregressive Integrated Moving Average (ARIMA) is a method
introduced in 1970 by Box and Jenkins. ARIMA is a data analysis method that
looks at past patterns and then creates a forecasting model (Nurissaidah et
al., 2018). Time series forecasting
analysis will be used to forecast this water availability. This forecasting is
based on past data behavior, where the amount of data taken over several
periods is used as a basis for making forecasts for future periods. Therefore,
this analysis requires a large amount of information or data collected over a
relatively long period of time. Autoregressive Integrated Moving Average
(ARIMA), also known as Box-Jenkins, is a technique often used to perform time
series forecasting analysis (Mboso, 2022).
The purpose of ARIMA is to generate time series
processes (data) in which each event correlates with each other. Time series
analysis is a statistical
technique used to find data patterns in the past and use them to forecast future
data patterns. The statistical software used for data processing in this study
is Eviews software (econometrics views). As for the application of this water
discharge, it can be analyzed with a partial differential equation model with
different methods to provide insight into decision-making related to water
resources management in the karst area, precisely in the Leang Lonrong Cave
Area (Rifandi & Abdy, 2023). Water resources management of the community generally needs
water to meet their daily needs, not only for domestic needs but also for the
needs of the agricultural industry and animal husbandry. However, in karst
areas, there is a limit on the amount of clean water that can be used to meet
the needs of the population, and unstable water availability throughout the
year is part of the problem.
To achieve this, the valuation of Leang Lonrong River water
utilization for water availability involves the application of economic
principles in analyzing the use, allocation, and management of water resources.
This can involve a study of the willingness to pay and the ability of the
community to pay for water supply services to maintain and improve the water
quality of the Leang Lonrong River by analyzing the preferences and payment
desires of residents and tourist visitors by estimating the economic value they
provide to the Leang Lonrong River water (Matondang & Suseno, 2020). There are several
approaches that integrate economic principles with physics in order to
understand and explain economic systems holistically. In this context,
econophysical approaches are used to identify and model complex interactions
between economic and physical variables that affect the availability of
underground river water in karst caves (Ali, 2017).
The literature review underscores the significance of this
topic by underscoring the importance of comprehending water discharge trends
and the willingness to pay for water usage within environmental economic
evaluations. For instance, (Hossain et al., 2022) stress the influence of
precipitation on underground river water flow, while (Utami et al., 2024) delve into the impact of soil infiltration and
alterations in soil physical characteristics on water discharge. Similarly, (NATH, n.d.) accentuates the necessity of non-market valuation
methodologies, such as willingness to pay, in gauging the economic worth of
environmental assets like water. The imperative to apply the study's findings
stems from the necessity for efficient water resource management in the Leang
Lonrong Cave Area. Insights into water discharge trends and the willingness to
pay for water usage gleaned from the research can guide policy formulation and
management tactics that strike a balance between the needs of tourists and
local inhabitants while safeguarding the environment and upholding water
quality.
Therefore, this study aims to estimate the availability of
underground river water using the ARIMA Model Approach in the Leang Lonrong
Karst Pangkep Cave Area of Bantimurung Bulusaraung National Park, as well as
valuing the utilization of underground river water availability with an
econophysical orientation at the location. It is hoped that the results of this
study can help the government in planning effective water resources management
and provide relevant information related to the economic value of underground
river water utilization, which can be used in determining water tariff policies
for sustainable management in the Leang Lonrong Cave area. The theoretical
basis for the topic of daily water discharge analysis and valuation of
underground river water utilization in the Leang Lonrong Cave Area lies in the
principles of econophysics, which combines economic and physical concepts to
analyze complex systems. This approach is particularly relevant in the context
of water resource management, where understanding the dynamics of water
discharge and the willingness of local residents to pay for its utilization is
crucial for the sustainable management of these resources.
Research Methods
This study employs a quantitative
descriptive survey research method to investigate water discharge patterns and
the valuation of underground river water utilization in the Leang Lonrong
Bantimurung Bulusaraung Tourism Area. Data collection was conducted in
Panaikang Village, Minasatene District, Pangkajene Regency, and Islands. Daily
water discharge data from 2010 to 2023 was obtained from the Pompengan
Jeneberang River Basin Center (BBWS) as secondary data, while primary data on
willingness to pay for underground river water usage was collected through
research questionnaires distributed to respondents.
Data analysis involved several steps.
For water discharge analysis, the data underwent stationary testing, followed
by identification of appropriate ARIMA models, ARIMA testing, forecasting, and
calculation of the mean absolute percentage error (MAPE). Valuation data
analysis of underground river water utilization in Leang Lonrong Cave included
calculating the elasticity coefficient, ratio value, and percentage elasticity.
To conduct the analyses, Microsoft
Excel and Eviews 9 software were utilized for water discharge data analysis,
while Microsoft Excel was employed for valuation data analysis of underground
river water utilization in Leang Lonrong Cave. The research instruments were
meticulously designed to ensure validity and reliability in capturing the
necessary data for the study's objectives.
Results and Discussion
Estimated
Availability of Underground River Water in Leang Lonrong Cave Area
Characteristics
of Leang Lonrong Cave Area Based on Water Discharge
Leang Lonrong
River Water Discharge Profile 2010-2023
Based on The figure shows that for 14 years
(2010-2023), the lowest water discharge occurred in September, which wa around
0.33
Tabel 1. Water Discharge Availability in 2010-2023
|
Bulan |
Debit ( |
|
||||||||||||
|
2010 |
2011 |
2012 |
2013 |
2014 |
2015 |
2016 |
2017 |
2018 |
2019 |
2020 |
2021 |
2022 |
2023 |
|
|
January |
9.14 |
14.02 |
6.84 |
4.8 |
3.49 |
2.51 |
1.03 |
2.41 |
0.99 |
19.3 |
5.5 |
6.2 |
4.17 |
9.8 |
|
February |
3.99 |
11.3 |
4.13 |
1.77 |
1.26 |
2.7 |
1.71 |
1.75 |
0.91 |
4.2 |
4.5 |
0.8 |
1.46 |
14.8 |
|
March |
2.7 |
6.99 |
2.69 |
3.37 |
1.42 |
4.22 |
1.31 |
1.74 |
0.82 |
4 |
2.3 |
2.4 |
1.07 |
2.6 |
|
April |
2.24 |
4.4 |
1.99 |
4.76 |
1.14 |
2.49 |
1.08 |
2.32 |
1.59 |
1.7 |
2 |
1.6 |
0.83 |
3.7 |
|
May |
1.28 |
2.06 |
0.87 |
1.17 |
0.55 |
0.81 |
0.78 |
2.19 |
1.53 |
0.9 |
1.3 |
0.7 |
0.63 |
1 |
|
June |
1.28 |
0.76 |
0.53 |
0.82 |
0.37 |
0.35 |
0.21 |
1.56 |
1.6 |
0.7 |
1.5 |
0.6 |
0.45 |
0.3 |
|
July |
1.47 |
0.22 |
0.18 |
0.78 |
0.18 |
0.17 |
0.17 |
0.83 |
1.61 |
0.7 |
0.6 |
0.3 |
0.48 |
0.7 |
|
August |
1.75 |
0.2 |
0.16 |
0.41 |
0.09 |
0.13 |
0.07 |
0.34 |
1.25 |
0.2 |
0.4 |
0 |
0.52 |
0.1 |
|
September |
2.1 |
0.19 |
0.15 |
0.16 |
0.07 |
0.09 |
0.06 |
0.2 |
1.02 |
0 |
0.1 |
0.1 |
0.33 |
0.1 |
|
October |
3.36 |
0.18 |
0.14 |
0.15 |
0.08 |
0.08 |
0.35 |
0.37 |
1.13 |
0 |
0.1 |
0.1 |
1.34 |
0.1 |
|
November |
6.91 |
0.19 |
0.15 |
0.32 |
0.09 |
0.08 |
1.01 |
0.11 |
1.52 |
0 |
0.3 |
1.2 |
1.04 |
0.2 |
|
Desember |
9.07 |
1.14 |
1.02 |
2.04 |
1.01 |
0.49 |
0.72 |
0.82 |
0.99 |
1.6 |
13.4 |
5 |
3.9 |
0.6 |
Prediction of Leang Lonrong River Water Discharge Availability
Prediction using the ARIMA Model Approach
Prediction of Leang Lonrong River Water Discharge Data
with ARIMA Method. The first step to predicting water discharge with the ARIMA
model is the data stationary test and the determination of the best ARIMA
model. According to (Rosita. et al, 2019) stationary assumptions are
assumptions that must be met in predicting data. In this study, the data was
stationary (probability lower than 0.05) with a differencing process of 1,
which means shape, so the prediction model used is the ARIMA model
In this study, temporary
testing was carried out on the ARIMA model, namely the ARIMA model (1,1,1),
(1,1,0), (0,1,1), (0,1,10). This came from assumptions that can be seen at the
PAC and AC levels, which have at least 2 (two) stars read. Some of these
models, which carry out significance tests, are feasible to use for prediction.
The following are the results of the significance test of the provisional ARIMA
model shown in the table, namely:
Table 2. Comparison of Probability Values in the ARIMA Model
|
No. |
Model |
Component |
Probability |
|
1 |
ARIMA (1,1,1) |
AR 1 |
0,0000 |
|
MA 1 |
0,9979 |
||
|
2 |
ARIMA (1,1,0) |
AR 1 |
0,0610 |
|
3 |
ARIMA (0,1,1) |
MA 1 |
0,0000 |
|
4 |
ARIMA (0,1,10) |
MA 10 |
0,4392 |
The ARIMA model that is
feasible to use has the lowest significant AR and MA terms (probability values
smaller than 0.05). Based on the above data, a feasible ARIMA model is the
ARIMA model (0,1,1) with a probability value of AR and MA terms smaller than 0.05.
The ARIMA model (0,1,1) is then used to predict water discharge in the Leang
Lonrong Cave Area in 2020-2023.
Comparison Graph of Prediction Results with
Observation Data for 2020-2023
Based
on Figure 4.2, a comparison of prediction results with observation data for
2020-2023 shows that the ARIMA model (0,1,1) is able to predict the observation
data for 2020-2023 well. Although, in general, there is a difference in value
between the prediction results and the observation data, the predicted value
tends to follow the pattern of movement of reality that occurs. Furthermore,
the ARIMA model (0,1,1) is used to predict 7-year water discharge, namely from 2024
to 2030. To evaluate the suitability between the
results of the observation discharge and the prediction results, a Mean
Absolute Percentage Error (MAPE) analysis was obtained:
Table
3. MAPE
forecasting results for 2024-2030
|
Month |
Water Debit |
|||||||||||
|
2020 |
2021 |
2022 |
2023 |
|||||||||
|
Actual |
Prediksi |
MAPE |
Actual
|
Prediksi |
MAPE |
Actual |
Prediksi |
MAPE |
Actual |
Prediksi |
MAPE |
|
|
1 |
5,5 |
4,17 |
0,24 |
6,2 |
3,42 |
0,45 |
4,17 |
3,17 |
0,24 |
9,8 |
3,07 |
0,69 |
|
2 |
4,5 |
3,93 |
0,13 |
3,8 |
2,39 |
0,37 |
2,46 |
3,15 |
-0,28 |
14,8 |
1,19 |
0,92 |
|
3 |
2,3 |
1,78 |
0,23 |
2,4 |
1,38 |
0,43 |
1,07 |
0,13 |
0,88 |
2,6 |
0,95 |
0,63 |
|
4 |
2,0 |
1,69 |
0,16 |
1,6 |
1,36 |
0,15 |
0,83 |
0,10 |
0,88 |
3,7 |
0,13 |
0,96 |
|
5 |
1,3 |
1,63 |
-0,25 |
0,7 |
0,34 |
0,51 |
0,63 |
0,08 |
0,87 |
1,0 |
0,16 |
0,84 |
|
6 |
1,5 |
1,29 |
0,14 |
0,6 |
0,32 |
0,47 |
0,45 |
0,06 |
0,87 |
0,3 |
0,17 |
0,43 |
|
7 |
1,2 |
0,96 |
0,20 |
0,3 |
0,29 |
0,03 |
0,48 |
0,04 |
0,92 |
0,7 |
0,10 |
0,86 |
|
8 |
0,9 |
0,53 |
0,41 |
0,2 |
0,17 |
0,15 |
0,52 |
0,03 |
0,94 |
0,1 |
0,13 |
-0,30 |
|
9 |
0,4 |
0,51 |
-0,28 |
0,1 |
0,15 |
-0,50 |
0,33 |
0,02 |
0,94 |
0,1 |
0,11 |
-0,10 |
|
10 |
0,6 |
0,48 |
0,20 |
0,1 |
0,13 |
-0,30 |
1,34 |
1,01 |
0,25 |
0,1 |
0,15 |
-0,50 |
|
11 |
1,2 |
0,46 |
0,62 |
1,2 |
1,21 |
-0,01 |
1,04 |
0,93 |
0,11 |
0,2 |
0,28 |
-0,40 |
|
12 |
9,4 |
1,44 |
0,85 |
5,0 |
4,19 |
0,16 |
3,9 |
1,05 |
0,73 |
0,6 |
0,43 |
0,28 |
|
Total |
2,65 |
|
1,91 |
|
7,35 |
|
4,31 |
|||||
|
MAPE |
0,337 |
|||||||||||
|
MAPE (%) |
33,7% |
|||||||||||
Table
4.3 explains that the results obtained using MAPE in this study amounted to
33.7%; it can be interpreted as the result of a reduction between the actual
value and the prediction that has been absolute, then divided by the actual
value per each period, then summation of these results. The lower the MAPE
value, the ability of the forecasting model used can be said to be good, and
for MAPE, there is a range of values that can be used as measurement material
about the ability of a forecasting model; the range of values can be seen in
table 3.1. The results obtained from the MAPE method are 33.7% for evaluation
calculations that are calculated using equations (3.1), and because of these
results, the MAPE range ranges from 20-50%. It can be said that the MAPE
results are good enough to have decent forecasting model capabilities, so the
method used can be a reference to find predictions for several future time
periods in water discharge in 2024-2030.
Tabel
4. Hasil Prediksi Debit air
tahun 2024-2030
|
Months |
Debit ( |
Average |
||||||
|
2024 |
2025 |
2026 |
2027 |
2028 |
2029 |
2030 |
||
|
Januari |
1,28 |
1,30 |
1,33 |
1,33 |
1,36 |
1,37 |
1,39 |
1,34 |
|
February |
1,26 |
1,28 |
1,30 |
1,31 |
1,33 |
1,35 |
1,37 |
1,31 |
|
March |
1,22 |
1,24 |
1,25 |
1,29 |
1,30 |
1,31 |
1,34 |
1,28 |
|
April |
1,20 |
1,23 |
1,24 |
1,25 |
1,28 |
1,30 |
1,32 |
1,26 |
|
May |
1,17 |
1,20 |
1,22 |
1,22 |
1,26 |
1,28 |
1,30 |
1,24 |
|
June |
1,15 |
1,19 |
1,20 |
1,21 |
1,24 |
1,25 |
1,27 |
1,22 |
|
July |
1,11 |
1,17 |
1,19 |
1,20 |
1,22 |
1,24 |
1,25 |
1,20 |
|
August |
1,10 |
1,16 |
1,17 |
1,19 |
1,20 |
1,22 |
1,23 |
1,18 |
|
September |
1,08 |
1,13 |
1,15 |
1,17 |
1,19 |
1,21 |
1,22 |
1,16 |
|
October |
1,14 |
1,20 |
1,23 |
1,25 |
1,26 |
1,28 |
1,30 |
1,24 |
|
November |
1,19 |
1,24 |
1,28 |
1,30 |
1,31 |
1,32 |
1,35 |
1,28 |
|
Desember |
1,24 |
1,29 |
1,33 |
1,36 |
1,37 |
1,40 |
1,42 |
1,34 |
From the table above,
predictions for 2024-2030 show that the Leang Lonrong Cave Area has the highest
water discharge in December 2030 of 1.42 m3/s or 44.79 m3/year,
while the lowest water discharge occurs in September 2024 at 1.08 m3/s.
or 34.06 m3/year.
Graph of Water
Discharge Prediction Results in Leang Lonrong Cave Area in 2024 – 2030
Based on the graph above,
the average water discharge prediction results for 2024-2030 show that when
there is an increase or decrease in historical data, the prediction results
depend on historical data. That is why the prediction results for 2024 to 2030 tend
to have an up-and-down pattern. They follow historical data from previous
years, which also experienced ups and downs, but that way, the sustainability
of water availability can be achieved.
A steady rise in water
discharge throughout the year indicates that the volume of flowing water
continues to increase consistently throughout the period. As for the factors that
cause the forecast chart to rise
steadily:
1. Rainfall, according to Arsyad (2013), examined the discharge of underground river water in the Pangkep Karst area and how rainfall affects the availability of underground river water. High rainfall tends to increase the discharge of flowing water, but if the water discharge remains low despite high rainfall, this can be due to soil infiltration capacity being exceeded in intensive rains (Utami et al., 2024).
2. Soil Infiltration: Rain that falls in forming springs can respond quickly through the process of infiltration into groundwater and then form a rapid flow of groundwater as input from springs. Infiltration will decrease at the initial rate of a rain event (Muchtar &; Abdullah, 2007). Low rainfall throughout the year can cause the soil to become dry and less able to absorb water properly. This can result in falling rainwater not being absorbed efficiently by the soil, resulting in more water flowing into the river and increasing water discharge (Utami et al., 2024).
3.
Changes in the physical
properties of the soil, Like hard or
cracked soil due to drought, can also affect the soil's ability to absorb
water. This can cause water discharge to continue to rise despite low rainfall (Utami et al., 2024).
According to Rauf et al. (2015), soil density is influenced by the weight of
soil content, where the smaller the weight value of soil content is, the lower
the soil density will be, or the soil will have
high fertility. Conversely, the denser the soil (the higher the weight of the
content), the more conditioned the soil is to continue water or be penetrated
by roots, affecting the increase in water discharge.
Water discharge modeling based on the application of finite
difference methods
Solving Partial Differential
Equations (PDP) in numerical methods generally uses the finite difference
method. Replacing the existing derivative of the differential equation with
finite difference discretization, the finite difference equation used to
replace the second derivative in PDP, the equation will be discrete using the
difference method to an explicit scheme by evaluating in space (i,j) (Julia, 2023). The finite difference method is one of the most
popular and easy-to-use numerical methods in calculating approximations of
derivatives of a function that can be analyzed using Microsoft Excel to be
applied to water discharge.
Figure 4.
Water discharge modeling
graph based on finite difference method equation
Based on the interval graph
above on the x-axis shows that the graph drops significantly at a larger water flow interval. This graph shape
can be said to be a response to water flow that affects water discharge, where
when water flow weakens, water discharge also falls. This can be caused by
factors such as rainfall, evaporation, soil absorption, and others. As for the
relationship of height in the water flow to water discharge, based on the graph,
the height in the water flow affects the water discharge significantly. As the
height of the water flow increases, the water discharge will also increase, and
vice versa. This can be caused by factors such as soil pore capacity, soil
permeability, and water table area in the river flow system.
Valuation of Leang Lonrong River Water Utilization
The willingness of residents to provide WTP utilization of
Leang Lonrong River water
a)
Getting WTP Value
In this study,
the value of the offer used to determine the WTP value of respondents was
obtained through the open-ended question method. Through this method,
respondents are given the freedom to state a number of values that are willing
to be paid for clean water management efforts.
b)
Calculating WTP Average Value
Table 5. WTP Average Value of Population
|
No |
WTP |
Number of Respondents |
WTP × Number of Respondents |
|
(Rp) |
(person) |
(Rp) |
|
|
1 |
30.000 |
4 |
120.000 |
|
2 |
50.000 |
2 |
100.000 |
|
3 |
75.000 |
1 |
75.000 |
|
Total |
7 |
295.000 |
|
Based on the data above, the average WTP value of respondents was obtained at Rp 42,142.85 per month. The average WTP value illustrates that the community is willing to spend Rp 42,142.85 for each household per month, which can be used to cover the cost of clean water quality management efforts.
Visitors' willingness to provide WTP utilization of
Leang Lonrong River water
Figure 5.
Visitors' willingness to give WTP to contribute to
maintaining water quality management in Leang Lonrong Cave
Based on the figure above, the alleged average WTP
value of respondents is obtained based on the ratio of the number of WTP values
given by respondents to the total number of respondents who are willing to pay.
The distribution of WTP values given for contributions to maintaining water
quality management in Leang Lonrong Cave to respondents is shown.
Table 6. WTP Average Value of Visitors
|
No |
WTP |
Number of
Respondents |
Percentage |
WTP × Number of
Respondents |
|
|
(Rp) |
(Orang) |
|
(Rp) |
|
1 |
19.000 |
40 |
64,5 |
760.000 |
|
2 |
23.000 |
17 |
27,4 |
391. 000 |
|
3 |
28.000 |
3 |
4,8 |
84.000 |
|
4 |
52.000 |
2 |
3,2 |
104.000 |
|
Total |
62 |
100 |
1.339.000 |
|
|
Obtained/visited |
21.596,77 |
|||
From Table 4.8, the average WTP value of respondents
was obtained at Rp 21,596.77 per visit. The average value of WTP illustrates
that visitors are willing to spend IDR 21,596.77 each time they visit this
tourist spot, which can be used for the cost of maintaining the water quality
management of the Leang Lonrong River.
Analogy of the Physical Approach to Economics
Water Discharge Modeling of Willingness to Pay
1)
Calculate elasticity coefficient ∂Y/∂X
Percentage change =
Table 7. Percentage change
in the coefficient of elasticity
|
|
Water Debit (∂X) |
Willingness to pay |
|
|
Population |
Visitors |
||
|
Percentage change |
18,57 |
1,5 |
1,73 |
So, the coefficient of elasticity for the population:
While the coefficient of elasticity for visitors:
2)
Calculate the ratio value
Ratio value =
Table 8. The result of
calculating the ratio value
|
|
Population |
Visitors |
|
Ratio Value |
0,000065 |
0,000096 |
3)
Calculating Percentage Elasticity
E = (
E = 0.081
E = 0.0000053
For Visitors
E = (
E = 0.081
E = 0.0000078
Estimation
of River Water Availability in Leang Lonrong Cave Area
Water
discharge characteristics
Graphical
analysis of the average water discharge in the Leang Lonrong Cave Area can be
seen in Figure 4.1 shows that for 13 years (2010-2023), the lowest water
discharge occurred in September, which was 0.33 m3/ s or 10.52 m3/
year, and the highest in January which reached 6.46 m3/ s or 203.79 m3/
year. It can also be seen that the water discharge decreases starting in July,
August, September, and October. These months are marked by the dry season in
the Leang Lonrong Cave Area. Water discharge began to enlarge in November at around
0.94 m3/ s or 29.54 m3/ year. This situation lasted until
April, which was related to the rainy season in the Leang Lonrong Cave Area.
The availability of underground river water discharge is very dependent on the
rainy season in the Leang Lonrong Cave Area. However, based on the results of the
data processing obtained are not in accordance with this theory because river
water discharge can change depending on two conditions, namely first, the
presence of rainfall (precipitation), and second, the occurrence of
evapotranspiration from water bodies, soil, and plants. River discharge is
never constant but always changes according to the climate and biophysical
state of the watershed.
Prediction
of Leang Lonrong River Water Discharge Availability
The stages in making predictions with the ARIMA model include
stationary test data and determining the best ARIMA model. According to
(Rosita. et al, 2019) stationary assumptions are assumptions that must be met
in predicting data. Stationary data is a term that means that data is in
equilibrium around a constant value over a certain time (Irma. et al., 2017).
Then the determination of the best ARIMA model, according to (Nurissaidah. et
al, 2018) and (Ahmad et al, 2018) are based on AR and MA terms that have
significantly lowest (probability value smaller than 0.05). That is why the
ARIMA model used in this study is the ARIMA model (0,1,1), where the
probability value of AR and MA terms is smaller than 0.05. The results obtained
from the MAPE method are 33.7% for evaluation calculations that are calculated
using equations (3.1), and because of these results, the MAPE range ranges from
20-50%. It can be said that the results of this good cukum MAPE have decent
forecasting model capabilities, so the method used can be a reference for
determining predictions for several future time periods in 2024-2030 water
discharge.
The results of water discharge predictions with the ARIMA
model (0,1,1) for 2024-2030 tend to follow the pattern of movement of reality
that occurs. According to (Tias et al, 2017) predictions with ARIMA assume that
past patterns will continue into the future. When there is an increase or
decrease in historical data, the prediction results depend on the historical
data. That is why the prediction results for 2024 to 2030 tend to have an
up-and-down pattern; they follow historical data from previous years, which
also experienced ups and downs.
As for the application of partial differential equations
using the finite difference method based on the analysis obtained through
Microsoft Excel based on the figure, the graph for the interval on the x-axis
shows that the graph drops
significantly at a larger water flow interval. This graph shape can be said to
be a response to water flow that affects water discharge, where when water flow
weakens, water discharge also falls. This can be caused by factors such as
rainfall, evaporation, soil absorption, and others. As for the relationship of
height in the water flow to water discharge, based on the graph, the height in
the water flow affects the water discharge significantly. As the height of the
water flow increases, the water discharge will also increase, and vice versa.
This can be caused by factors such as soil pore capacity, soil permeability,
and water surface area in the river flow system.
Valuation
of Leang Lonrong Cave Underground River Water Utilization
Based on the results of the Leang Lonrong River water
utilization questionnaire, it was obtained that the dominant community utilizes
river water for various purposes, both for the fulfillment of daily needs and
for agriculture and animal husbandry. People use Leang Lonrong River water for
toilets (bathing, washing, latrines), washing eating utensils, drinking,
washing clothes, and use raw materials for drinking water, which are only used
by people living around the Leang Lonrong River area where they are quite close
to the river. Meanwhile, people who live outside the tourist area use bottled
water as raw drinking water. In addition, Leang Lonrong River water is more
widely used in agriculture and for the purposes of standard animals or
livestock.
Leang Lonrong River still has visitors even in rainy
conditions. However, when the river water flows fast, there are no visitors
around the river; this is like what happened in January when the tourist
destination Leang Lonrong was temporarily closed due to unfavorable weather
conditions. Even so, Leang Lonrong River remains one of the tourist
destinations chosen by the community as a place of recreation. This is the
utilization of Leang Lonrong River water in the field of tourism.
Willingness
to pay
The
willingness of residents to provide WTP utilization of Leang Lonrong River
water
The number of respondents was selected from residents who met
on Saturday and were willing to fill out a questionnaire. As many as 32
respondents were interested in providing WTP for the use of underground river
water. From the results of data collection regarding the willingness to provide
WTP, there were seven respondents who expressed their willingness to provide
WTP in an effort to use clean water, which was transferred to a clean water
management agency. However, there are also the remaining 25 respondents who are
not willing to provide a number of WTP values for efforts to manage the water
quality of the Leang Lonrong River.
Of the seven respondents who are willing to provide WTP, willingness
to pay is listed. The average WTP value of respondents amounted to Rp
42,142.85 per month. The average WTP value illustrates that the community is
willing to spend Rp 42,142.85 for each household per month, which can be used
for the cost of efforts to improve the water quality of the Leang Lonrong
River. Where according to the results of research conducted by Rindah (2023),
Leang Lonrong River Water for public bathing purposes does not meet water
quality according to quality standards. This is due to several parameters that
do not meet the standards, namely the clarity parameter is an average of 0.136
meters in depth, and the UV index parameter is more than three at 11.00 WITA
and 13.00 WITA. Measurement of this parameter was carried out in the field
directly, and the value showed that the water of the Leang Lonrong River
included very turbid waters to have low water productivity.
The respondents who are not willing to provide a number of
WTP values have reasons for economic limitations or economies that are less
able, so respondents are unwilling or unable to provide a number of WTP or WTP
values equal to zero, along with other reasons. This is in accordance with the
results of the analysis that income affects the willingness to pay (WTP).
Visitors'
willingness to provide WTP utilization of Leang Lonrong River water
The number of respondents was selected from visitors who came
on Sunday and were willing to fill out a questionnaire. As many as 62
respondents were interested in giving WTP to the use of underground river
water.
From the results of data collection regarding the willingness
to provide WTP, 62 respondents indicated that WTP contributed to improving the
water quality management of the Leang Lonrong River. Of the 62 respondents who are willing to
provide WTP, willingness to pay is listed in Table 4.7. obtained the average
WTP value of respondents amounting to the contribution in maintaining the
management of Leang Lonrong River water quality, visitors are willing to give
WTP of Rp. 21,596.77 each time visitors visit this tourist spot, which can be
used for contribution costs in maintaining the management of Leang Lonrong
River water quality.
Analogy of the Econophysical Approach
One possible analogy is the concept of potential. In
physics, potential is the energy stored in a system, such as gravitational
potential or electric potential. In the context of willingness to pay,
potential can be thought of as financial "energy" stored in
individuals or consumers. The level of willingness to pay a person can depend
on how much financial "potential" he has and how much benefit or
satisfaction is obtained from a product or service (Resmiyanto, 2014).
The econophysical approach used in this study refers
to Principle I, namely that society is faced with sacrifices (People face
tradeoffs). In physics, this economic
principle can be explained using the law of conservation of energy. Principle I
shows that in situations with limited natural resources, such as low river
water utilization, communities must make trade-offs or sacrifices in the
allocation of these resources to prioritize their various interests.
Water Discharge Modeling with Willingness to Pay
Elasticity analysis in modeling water discharge with
willingness to pay is a method to measure the responsiveness or sensitivity of
willingness to pay to changes in water discharge. The relationship between water
discharge has only a small impact on willingness to pay is based on the
calculation of percentage elasticity where each resident and visitor has a
percentage of elasticity smaller than one (<1). This suggests that
willingness to pay tends to be unresponsive to percentage changes in water
discharge.
In a case study of the economic valuation of groundwater
resources, it was found that the Willingness to Pay (WTP) for increased water
discharge to a willingness to pay indicates that communities are willing to pay
more to increase water availability, reflecting the economic value given to the
utilization of leading lonrong river water.
The study on
daily water discharge analysis and valuation of underground river water
utilization in the Leang Lonrong Cave Area provides valuable insights into the
dynamics of water discharge patterns and the willingness of local residents to
pay for water utilization. The analysis employed the ARIMA model to forecast
water discharge patterns and found that the ARIMA model (0,1,1) was the most
suitable for predicting water discharge, with a mean absolute percentage error
(MAPE) of 33.7%. The study also utilized a willingness-to-pay approach to
evaluate the valuation of underground river water utilization, where the
average willingness-to-pay value for maintaining the management of Leang
Lonrong river water quality was approximately IDR 21,596.77 per visit. The
findings of this study have significant implications for the management of
water resources in the Leang Lonrong Cave Area. Firstly, the ARIMA model
(0,1,1) can be used as a reliable tool for predicting water discharge patterns,
which is crucial for planning and managing water resources effectively. Secondly,
the willingness-to-pay approach highlights the importance of considering the
economic value of water utilization in environmental economic assessments. This
approach can be used to inform policy decisions and management strategies that
balance the needs of tourists and local residents with the need to protect the
environment and maintain water quality. The study suggests several
recommendations based on its findings. Firstly, integrating the ARIMA model
(0,1,1) into the water resource management system of the Leang Lonrong Cave
Area can improve the accuracy of water discharge predictions, aiding in more
effective planning and resource management. Secondly, incorporating the
willingness-to-pay approach into environmental economic assessments can offer a
more holistic understanding of the economic value of water usage, informing
policymakers' decisions regarding economic, social, and environmental factors.
Thirdly, raising public awareness through education campaigns about water
conservation and its economic importance can promote responsible water usage
and sustainable tourism practices in the area. Additionally, developing
sustainable water management strategies, such as water harvesting and efficient
irrigation systems, is vital. Regular monitoring and evaluation of water
discharge patterns are also recommended to ensure the effectiveness of
management strategies and responsiveness to environmental changes. Implementing
these recommendations can foster sustainable management of water resources in
the Leang Lonrong Cave Area, meeting the needs of both residents and tourists
while safeguarding the environment.
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Nur Azizah Jaya, Muhammad Arsyad, Pariabti Palloan (2024) |
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First publication right: Advances in Social Humanities Research |
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