Saltwater Intrusion at Kapuas Besar Estuary Using 1-Dimensional Analytical Method

The Kapuas Besar Estuary in West Kalimantan is vital for both the local community’s ecological and economic well-being. One major issue faced in this estuary is saltwater intrusion. This study aims to investigate saltwater intrusion variation using a one-dimensional (1D) analytical model. The model input data includes estuary geometry, tides, salinity, and river discharge. Simulation results demonstrate the effectiveness of the 1D analytical model in predicting saltwater distance based on the Root Mean Square Error (RMSE), Percent Bias (PBIAS), and Nash-Sutcliffe Efficiency (NSE) values between the analytical model results and observed data ranging from 0.82-1.70 psu, 1.64-2.85%, and 0.96-0.99 respectively. The model proves applicable during the May-October period, subject to the condition that the river discharge remains below 3,200 m3/s. However, during November-April the model tends to underestimate compared to actual distance. Model results show saltwater intrusion increasing from December to June by 49 km, then decreasing from July to November by 38 km. The minimum distance of saltwater intrusion occurred in May (1 km from the estuary mouth) when river discharge of 8,853.82 m3/s. Conversely, the maximum saltwater intrusion distance was observed in June (71 km from the estuary mouth) with a river discharge of 1,034.55 m3/s.


Introduction
Estuaries, which are complex coastal ecosystems, are known as highly productive coastal ecosystems and sensitive to both human-induced and natural environmental pressures [3].Estuaries are widely used to support human life activities such as water supply systems, agricultural irrigation channels to industrial matters.One common occurrence in estuaries is the mixing of water masses with different salinities, resulting in brackish conditions.This process is known as saltwater intrusion (SWI) [12].saltwater intrusion has several factors that affect the amount of distance generated, including tides, river discharge, and the geometry of the estuary itself.These conditions ultimately affect the distance of saltwater intrusion and can reach deep into the upstream river resulting in salinity contamination of freshwater irrigation channels.
The saltwater intrusion phenomenon in the Kapuas Besar Estuary and watershed has several possibilities to occur with different distance variations at certain periods.The saltwater intrusion distance can be predicted by knowing several physical factors that occur when the phenomenon takes place with the support of adequate salinity field observation data both temporally and spatially [10].To address the issue of seawater intrusion, Savenije (2012) developed a one-dimensional analytical modeling system that considers estuary geometry, river discharge, and curve fitting of field observation data.This modeling approach has been applied in numerous studies on seawater intrusion in 33 estuaries

Study Area
This research study area is located on the Kapuas Besar estuary in West Kalimantan, Indonesia.The domain model is focused on the estuary geometry, including width, depth, and cross-sectional area.The continuous discharge of the Kapuas Besar River begins from the river source in Kapuas Hulu Regency and flows downstream into different regions, including Sungai Raya District, Kubu Raya District, and Rasau Jaya District, before reaching the Kapuas Besar estuary (Figure 1).The Kapuas River has a catchment area of 99,00 km2.The river discharge is influenced by the west and east monsoon cycle, ranging from 1,000 m3/s in the dry season to 10,000 m3/s in the wet season [6] and an average discharge of 5,500 m3/s [2].The estuary mouth (x0) point will be placed at the Padu Empat trifurcation point, 11 km from the sea.

Data
The data used in this research are estuary geometry, tides, salinity, and river discharge data from December 2011 to April 2015 (Tables 1 & 2).The estuary geometry data were obtained using estimated measurements from Google Earth with the average width and depth at the estuary mouth and every segment (1 km interval).The tides data were obtained from Tide Model Driver with the point of interest at the estuary mouth at the Padu Empat trifurcation point (0 km).The river discharge data were taken 3 from the Regional Office of Kalimantan I River Basin, West Kalimantan Province, every day during the period 1998-2013.The salinity data were obtained from the field observation data logger [6] with a depth of 4,6 m at 24 km (Rasau Jaya Station) and 36 km (Kubu Raya Station) from the estuary mouth every 30 minutes from August 2014 until April 2015.The field data has to be synchronized based on the tides (spring tide) to gain a slack water condition (high-water slack and low-water slack) when the current is near 0 m/s.Therefore, the salinity data doesn't need a tide correction in this model (Figure 2).

Geometry analysis method
The geometry analysis method for the Kapuas Besar Estuary was based on the Savenije approach theory [11] for alluvial estuaries.The width, depth, and cross-sectional area are exponentially changing in this prismatic scheme.The value for A0, B0, and h0 (Equations ( 1) to ( 3)) was obtained by fitting the simulated geometry characteristics to the observed data and will be used as boundary input data for the onedimensional analytical model.
Where A, B, and h represent the cross-sectional area, width, and depth at the distance of x.A0, B0, and h0 represent the cross-sectional area, width, and depth at the estuary mouth and a, b, and d are the cross-sectional area, width convergence length, and d can be found with d=ab/(b-a).The Padu Empat trifurcation point is chosen to be the area of interest for this study referring to the geometry terms and condition approach on the alluvial estuary and the ideal estuary as can be seen in Figure 3 below.

One-dimensional analytical model
The model solves the saltwater intrusion distance prediction using Savenije's one-dimensional analytical approach for alluvial estuary [11].The model is used to predict the saltwater intrusion distance with multiple scenarios during high, low, and average river discharge.In this model, the salinity distribution will be simulated under Tidal Average (TA) conditions and then converted into high-water slack (HWS) and low-water slack (LWS) conditions to determine the maximum and minimum saltwater intrusion conditions and determine the limits of saltwater intrusion in the study area.This analytical model assumes that the saltwater intrusion that occurs has no salinity stratification and uses the upstream prediction method towards the upstream of the river and the estuary is considered prismatic and shrinks upstream with a minimum width of the river width upstream.The calculation of salinity values in the Kapuas Besar Estuary will be done by segment with an average cross-sectional area of each segment.The distance between segments has a value of 1,000 m and the visualization of the geometry of measuring salinity values until it reaches a value of 0 psu (x0, x1, x2, x3, x4, x5, x6, etc.) as it can be seen with Figure 4 below.The equations applied in the 1-dimensional model by Savenije [x] are derived from the salt equilibrium equations for HWS, LWS, and TA as follows in Equation ( 4): Where Si is the salinity value sought at the x distance and Sf is the salinity limit for water flowing upstream which under the conditions in this study is 0 psu, Di is the dispersion coefficient at the x distance, and Ai is the cross-sectional area at the x-point.Furthermore, the Van der Burgh coefficient (K) can help the calculation of the salt equilibrium equation as a shape factor coefficient for longitudinal salinity distribution in the estuary with an empirical method approach based on the average tidal dispersion under effective tidal dispersion conditions [13].The coefficient is obtained from the results of consistent reduction of upstream tidal flow and the plot of effective dispersion against river discharge velocity with a narrowing cross-sectional area.The results of the Van der Burgh Coefficient can be written as in Equation ( 5) assuming 1 dimension on the x-axis.
Di is obtained as a dispersion coefficient that will change exponentially upstream.Combining Equations (4, 5, & 6), the salinity and dispersion equations are expressed as Equation ( 7) below.
S0 and D0 are the boundary conditions for salinity and longitudinal dispersion in the 1-dimensional analytical model, the longitudinal dispersion equation can be solved by substituting changes in the value of the dispersion coefficient D into Equation (8) as follows: With β, the dispersion reduction for each x-distance is as follows, Then by substituting Equations ( 7)-( 9), the saltwater intrusion distance equation can be simplified and written as in Equation (10).The value of the saltwater intrusion distance can be found with the condition where the salinity value sought has the same value as the freshwater salinity (0 psu) (Si = Sf).Therefore when the seawater has a maximum distance upstream, it can be stated with x = L.
The resulting saltwater intrusion distance (L) is in TA conditions, so it must be converted into HWS and LWS distance conditions with Equations ( 11) and ( 12), where E0 is the horizontal tidal excursion distance obtained based on the results of curve-fitting calibration between the results of the model salinity curve and field salinity observation data on HWS and LWS conditions.
The calibrated parameters in this saltwater intrusion model are the Van der Burgh coefficient (K), dispersion coefficient at the mouth of the estuary (D0), tidal excursion at the mouth of the estuary (E0), and seawater salinity (S0) [5].The input parameters that can be changed in the saltwater intrusion model are river discharge (Q), tidal excursion (H), and saltwater salinity at the mouth of the estuary (S0) which are adjusted based on the scenario conditions of the saltwater intrusion model in the seasonal period.Freshwater salinity (Sf) will be equated to a value of 0 in order to get the saltwater intrusion distance limit with a salinity of 0 psu.

Error analysis
Root Mean Squared Error (RMSE) error analysis method is used for the validation and performance of the 1D saltwater intrusion analytical model.Percentage Bias (PBIAS) and Nash-Sutcliffe Efficiency (NSE) coefficients are also used to determine the predictive power of the salt intrusion model.The equations of RMSE, PBIAS, and NSE are as follows: Where:

Geometry result of the estuary
The start point (0 km) for the utilization of Equation ( 1)-( 3) is at the Padu Empat trifurcation point before entering the Kapuas Delta (Figure 4.1).The geometry of the estuary in this area is similar to the ideal estuary proposed by Savenije [11].Based on the observation data [6] the Kapuas Besar River has varying depths with a maximum depth of up to 17 m (from 0-76 km) and an average width of 600 m with the maximum width in the river reaching ±1,705 m at the bifurcation point branch [6].
The bathymetry of the Kapuas Besar watershed has silted up towards the downstream (estuary mouth) to an average depth of 8.8 m at the Padu Empat trifurcation point.Kastner's research [6] explained that there is a slope upstream so that the siltation that occurs in the Kapuas Besar Estuary has minimal effect on the river flow that flows towards the estuary mouth.Therefore, the resulting graph has been adjusted based on the ground elevation from the Padu Empat trifurcation point (1 m above sea level) to a distance of 76 km (9 m above sea level).The geometry characteristics of the Kapuas Besar Estuary that will be used as input data for the saltwater intrusion analytical model are shown in Table 3 as it follows.

Model calibration
The calibration carried out in this model is a curve-fitting process based on salinity data at 2 observation stations at a distance of 24 km and 36 km.The seasonal calibration results of the model in the Kapuas Besar Estuary have a bell-shaped saline intrusion curve.
Based on the calibration results, it is found that the difference in the resulting curve is largely influenced by the condition of the input parameters from each season, namely the dispersion coefficient at the mouth of the estuary (D0) as the magnitude of salinity dispersion at each x-distance, then seawater salinity (S0) as the initial value of salinity which affects the initial value of salinity at the mouth of the estuary and how much salinity will be dispersed at the x-distance, and the Van der Burgh coefficient (K) affected the slope of the curve in the salinity dispersion process until the salinity reaches a value of 0 psu at the x-distance point.Each seasonal calibration result of the saltwater intrusion model (Figure 5) will be the main reference model for various river discharge scenarios (minimum, maximum, and average discharge) in the monthly scenario.The west monsoon season (DJF) calibration curve is used as the main reference for the model in December, January, and February, then the first transitional season (MAM) is used as the main reference for the model in March, April and May, then the east monsoon season (JJA) is used as the reference for the model in June, July, and August, and the second transitional season (SON) is used as the reference for the model in September, October and November.

Saltwater intrusion results
Based on the estuary number, the Kapuas Besar Estuary has a highly-stratified salinity stratification type from the Padu Empat trifurcation point (0 km) to a distance of 3.1 km upstream.While from a distance of 3.1 km to 73 km upstream has a well-mixed type of salinity stratification [4].This is caused by the mixing process at a distance of 0-3.1 km then turned into a well-mixed after a distance of 3.1 km.With the result of well-mixed salinity stratification, the 1D saltwater intrusion model can be used in this study to predict the salinity value until the distance of 80 km.

Monthly saltwater intrusion distance prediction.
In general, the saltwater intrusion distance in December-February lengthens and shortens again in March, then lengthens again until June and shortens further until November.The range of saltwater intrusion distance differences in HWS and LWS conditions is 6,000 m (December-May) and 8,000 m (June-November), which is influenced by the calibration process for the four seasons.The largest margin value of the saltwater intrusion distance was obtained in July with a value of 45,000 m, while the smallest margin was obtained in April with a value of 7,000 m (see: Table 4).In the maximum monthly discharge scenario (Figure 6B & 8), most of the saltwater intrusion distances are quite low with values not exceeding 33,000 m with conditions of increasing and decreasing distance similar to the conditions of the minimum discharge scenario.However, it can be seen that there is an outlier in the June salinity curve with a distance of 48,000 m (HWS) and 40,000 m (LWS).It was influenced by maximum river discharge flow in June of only 2,109.94m 3 /s which is very different from other months with maximum discharges above 3,282.92m 3 /s.In the monthly average river discharge scenario (Figure 6C & 9) has a more detailed visualisation of the increased and decreased amount of river discharge between months.The graph generated in the average river discharge scenario looks smoother than other scenarios, this is due to the lack of inequality in the average river discharge between months.The distribution of the saltwater intrusion distance has similarities with the distribution at the minimum and maximum discharge with the saltwater intrusion distance being the median between the minimum and minimum distance each month.There is a fairly drastic increase in river discharge in March and November which results in outliers in the minimum and maximum saltwater intrusion distances in the monthly period.One of the factors that affect the saltwater intrusion distance in each model scenario is the rainfall that affects the amount of river discharge from the month before and after.In addition, the influence at the time of calibration of the saltwater intrusion graph also contributed to the resulting output, as for example in May and June which have a minimum river discharge that is not much different (1,520.08m 3 /s and 1,034.55m 3 /s) have much different results.One of the main reasons is that in May, the calibration curve will follow the first transitional season (MAM), whereas in June, it will follow the calibration curve for the east monsoon season (JJA) with distinct calibration input parameters.In the minimum river discharge scenario (Figure 10A), most of the saltwater intrusion has passed into Rasau Jaya Sub-district and is spread into 2 parts, namely in Rasau Jaya Sub-district and the next part has passed the observation station point of Kubu Raya Station to Sungai Raya Sub-district with the furthest point in June almost approaching the bifurcation point of the Kapuas Kecil River.The maximum river discharge scenario (Figure 10B) produced saltwater intrusion distances that were mostly spread from the Padu Empat bifurcation point to the Rasau Jaya sub-district boundary, but in this scenario, two saltwater intrusion points were obtained in June that had passed Rasau Jaya sub-district as outliers.In the scenario of average river discharge (shown in Figure 10C), the points of saltwater intrusion distance are evenly spread every month, with a reasonable distance between each point.The fairly even distribution of saltwater intrusion points starts from a distance of 9,000 m from the mouth of the estuary (0 km) to 59,000 m which has entered Sungai Raya Sub-district.
Reverse flow can be a factor in the long saltwater intrusion distances that occur in the Kapuas Besar River if the river discharge is <5000 m 3 /s [6], where there will be changes in the direction of river discharge propagation from going downstream to the opposite direction.This condition happens because of the inability of the river discharge to withstand the mass of seawater entering upstream, resulting in water with high salt concentration entering far upstream of the Kapuas Besar watershed.
The results obtained in this study are in line with several previous studies, as stated by Kastner [6] that salinity is only detected at the Kubu Raya bifurcation point (data collection station) which is 36 km away with a very low river discharge and salinity never touches the Kapuas Kecil bifurcation point (85 km from the outer limit of the sea in the Kapuas Besar delta).
The results of this study can be used to determine the optimal location for installing water intake stations as a source of livelihood for communities around the Kapuas Besar watershed.The recommended location of the intake station installation point is to pass through the Kapuas Kecil bifurcation point as the furthest saltwater intrusion point, which is more than 71 km from the estuary mouth to avoid salinity contamination thus the irrigation water sources and raw water sources will be protected from seawater intrusion.

Maximum and minimum saltwater intrusion distance comparison.
The minimum saltwater intrusion distance was obtained in March with the maximum discharge scenario (8,853.82m 3 /s) and LWS conditions, resulting in a distance of 1,000 m located not far from the Padu Empat trifurcation point.Meanwhile, the maximum saltwater intrusion distance was obtained in June with the maximum discharge scenario (1,034.55m 3 /s) and HWS conditions, resulting in a distance of 71,000 m with a point in Sungai Raya District, as shown in Figure 11   The range of saltwater intrusion distance between the maximum and minimum values is 70,000 m, which is mostly caused by differences in the initial value and river discharge in each month.The minimum saltwater intrusion is given a salinity input of 15 psu, a tidal excursion of 6,000 m, a Van der Burgh coefficient of 0.5, and a dispersion coefficient at the mouth of the estuary of 5,000 m 2 /s, whilst the maximum saltwater intrusion is given a salinity input of 24 psu, a tidal excursion of 2,500 m, a Van der Burgh coefficient of 0.4, and a dispersion coefficient at the mouth of the estuary of 8,250 m 2 /s.

Error analysis
The model has good performance with the minimum river discharge scenario based on the RMSE values of 0.82 psu (HWS) and 1.70 psu (LWS), which particularly still quite good due to the complexity of the 1298 (2024) 012003 IOP Publishing doi:10.1088/1755-1315/1298/1/01200314 calibration process for the 1D analytical saltwater intrusion model compared to the RMSE value of the average discharge scenario (3.58 psu for HWS and 5.11 psu for LWS) and the maximum discharge scenario (6.71 psu for HWS and 7.99 psu for LWS).The PBIAS and NSE values for HWS and LWS tidal conditions in 3 river discharge scenarios has the same effect as the RMSE values (Table 6).The minimum discharge scenario will result in smaller PBIAS value (1.64% for HWS and 2.85% for LWS) and NSE (0.99 for HWS and 0.96 for LWS) values than the average discharge scenario with PBIAS (4.67% for HWS and 9.27% for LWS) and NSE (0.82 for HWS and 0.63 for LWS) as well as the maximum discharge scenario with the highest PBIAS values (8.61% for HWS and 14.73% for LWS) and NSE (0.37 for HWS and 0.09 for LWS).The RMSE value (Table 5) shows that in the minimum river discharge scenario each season has a fairly good accuracy with a low error value compared to the average and maximum river discharge scenarios.The average RMSE value obtained in HWS (0.82 psu) and LWS (1.70 psu) conditions shows that the 1D analytical saltwater intrusion model is more accurate and suitable for use in discharge conditions <3,200 m 3 /s in each month.The model worked quite well with an accuracy of 50% of the 1year period, namely in May-October (6 months) with the average river discharge successively being 2,194.43m 3 /s, 1,467.58m 3 /s, 2,361.36m 3 /s, 2,246.63m 3 /s, 2,654.62 m 3 /s, and 3,139.35m 3 /s.Therefore, the greater the river discharge will produced the greater the RMSE value and likely underestimated the saltwater intrusion calculation with shorter distances due to the high error values of salinity in the Estuary and Kapuas Besar watershed.

Conclusions
In summary, the investigation of saltwater intrusion in the Kapuas Besar Estuary has been a successful endeavor and confirmed as appropriate for this case study.Moreover, successful salinity intrusion investigations have been carried out for the Kapuas Besar Estuary during both high-water slack (HWS) and low-water slack (LWS) conditions based on the resulting RMSE error values ranging from 0.82 psu to 1.70 psu, PBIAS values ranging from 1.64% to 2.85%, and NSE values ranging from 0.99 to 0.96.
The 1D saltwater intrusion analytical model is applicable during the May-October period with an average river discharge of less than 3,200 m 3 /s, while in November-April it produces an underestimated model where model results are shorter than the actual distance.The saltwater intrusion distance increased in December-June by 49 km (due to a decrease in river discharge of 3,434.77m 3 /s) and decreased in the July-November period by 38 km (due to an increase in river discharge of 4,292.04m 3 /s).The minimum distance occurred in March (1 km from the estuary mouth) when the river discharge was 8,853.82m 3 /s, while the maximum distance occurred in June (71 km from the estuary mouth) when the river discharge was 1.034,55 m 3 /s with an estimated point in the Teluk Bayur area, Kubu Raya District (10 km from the Kapuas Kecil bifurcation point).
In summary, the salt intrusion model proves to be highly dependable for investigating salt intrusion in the Kapuas Besar Estuary.Consequently, it is believed that the 1-D saltwater intrusion analytical model could serve as a valuable tool for determining the optimal location for installing water intake stations based on the salinity distribution of the Kapuas Besar Estuary.

Figure 1 .
Figure 1.The study area and observation point of the model with the observation points (estuary mouth, point A, and point B) represent the distance of 0 km, 24 km, and 36 km.

Figure 3 .
Figure 3. Point of interest for geometry analysis at Kapuas Besar Estuary.

Figure 4 .
Figure 4. Geometry analysis application for the 1D model.

Figure 7 .
Figure 7. Saltwater intrusion model prediction results on minimum discharge scenario.

Figure 8 .
Figure 8. Saltwater intrusion model prediction results on maximum discharge scenario.

Figure 9 .
Figure 9. Saltwater intrusion model prediction results on average discharge scenario.

Figure 10 .
Figure 10.Spatial map for monthly saltwater intrusion distance prediction with several discharge scenarios (minimum (A), maximum (B), and average (C) from January (I) to December (XII) with HWS (red label) and LWS (blue label) conditions. below.

Table 2 .
Salinity input at point A (24 km) and point B (36 km).

Table 3 .
Geometry input value for the 1D model.