Open Access proceedings Journal of Physics: Conference series Civil and Environmental Science Journal Vol. 5, No. 1, pp. 064-077, 2022 64 Mathematical model distribution of some water quality parameters in the reservoir R W Sayekti1,*, Moh. Sholichin1, M. Bisri1, Heri Suprijanto1, Nadya A. Nathania1 1Water Resources Engineering Department, Universitas Brawijaya, Malang, 65145, Indonesia *rini_ws@ub.ac.id Received 13-04-2022; accepted 29-04-2022 Abstract. Sutami Reservoir is one of the largest reservoirs in East Java Province and is very useful in the life of people in Malang. However, the water quality of Sutami reservoir currently degrades due to waste. This study aims to determine water quality using the pollution index method and mathematical modeling. Polynomial regression is the most suitable mathematical model. It was obtained by statistical testing and adjusted based on population index data. Sutami Reservoir is classified as a reservoir with a eutrophic trophic status. The load capacity in eutrophic conditions at the monitoring station revealed that the levels exceeded the maximum pollution load limit. The relevant authorities need to take action to overcome the waste problems which contribute to the degradation of water quality in Sutami reservoir. Keywords: water quality, pollution index, mathematical model, regression 1. Introduction The water quality (WQ) of watershed systems is affected by high anthropogenic pressures, including domestic wastewater discharges and industrial and agricultural activities [1]. The deterioration of the water environment has led to the reduction of available water resources and damaged a healthy aquatic ecosystem. The water environment system is very complicated and depends on weather, water body hydraulic characteristics, pollutant discharge, and the aquatic biological impact. Therefore, it is necessary to predict the water quality evolution process [2]. The main purpose of the water quality monitoring system is to generate sufficient and timely information to establish water quality management plans and make environmental policies [3]. Sutami Reservoir or also known as Karangkates Reservoir, is one of the largest reservoirs in East Java, built-in 1964-1973. This reservoir is located in Karangkates Village, Sumberpucung, Malang Regency. It has three main benefits: the first as a flood control reservoir for the 50-year return period, the second as a provider of irrigation water sources in the downstream area with a discharge of 24 m3/second in the dry season to serve 34,000 Ha. The last one is a hydropower plant with 488 million kWh/year [4]. In addition, this reservoir is used as a tourist attraction and freshwater fisheries. The Sutami Reservoir gets its water source from the Brantas River. The current condition of the Brantas River has decreased the quantity and quality of its water. In the upstream area of the Brantas River, there is environmental damage and the conversion of protected forest functions into agricultural, Civil and Environmental Science Journal Vol. 5, No. 1, pp. 064-077, 2022 65 industrial, and other building areas. It causes the river water quality to decrease due to pesticides and chemical fertilizers. In addition to the consequences of agriculture, the increase in water pollution is also caused by domestic waste and industrial waste disposal. According to the President Director of Perum Jasa Tirta I, around 60% of the waste that pollutes the Brantas River comes from household waste. The rest comes from industrial waste and toxic and hazardous materials. Under these conditions, the reservoir water will be polluted by these wastes, namely organic agricultural waste, domestic and industrial waste, and other toxic or hazardous materials. It can worsen the condition of the reservoir water in the Sutami Reservoir because this reservoir gets its water supply from the Brantas River [5]. Due to the increasing pollution of the Sutami Reservoir, it is necessary to determine the water quality status and the pollution load capacity. A water quality model is the mathematical representation of pollutant fate and transport within a water body that may be coupled with a mathematical expression of the movement of pollutants from land movement from land-based sources to a water body [6]. Process-based hydrodynamic and water quality models have been widely applied for simulating and predicting temperature dynamics and constituent transport in surface water bodies such as lakes, rivers, and estuaries [7], [8], [9], [10], [11], [12], [13]. The linear regression analyses are used for the water quality parameters. They measure higher and better levels of significance in their correlation coefficient. The systematic calculation of regression analysis provides indirect means for the fast monitoring of water quality [14]. This study aimed to determine water quality, water quality status, and mathematical modelling (regression analysis) of water quality status in Sutami Reservoir. 2. Material and Methods 2.1. Study location Sutami Reservoir is located in Karangkates Village, Sumber Pucung District, Malang Regency (Figure 1). The water quality monitoring is carried out by Perum Jasa Tirta I. The water quality monitoring stations in the Sutami Reservoir are divided into 3, namely the Upstream Sutami Reservoir Monitoring Station, the Middle Sutami Reservoir Monitoring Station, and the Downstream Sutami Reservoir Monitoring Station. The Upstream Sutami Reservoir Monitoring Station is divided into two depths, namely Depth I (0.3 m) and Depth II (4 m). The Middle Sutami Reservoir Monitoring Station is divided into three depths, namely Depth I (0.3 m), Depth II (5 m), and Depth III (10 m). At the Downstream Sutami Reservoir Monitoring Station, it is divided into three depths, namely Depth I (0.3 m), Depth II (5 m), and Depth III (10 m) (Figure 2). Figure 1. Research site map Civil and Environmental Science Journal Vol. 5, No. 1, pp. 064-077, 2022 66 Figure 2. Details of the depth of the Sutami Reservoir Monitoring Station 2.2. Data Collection Field data are essential for models to predict assumed scenarios or future events [15]. This study uses secondary data. The data collection used in this study to obtain a mathematical model of the water quality status of the Sutami Reservoir is as follows: 1. Rainfall data around the Sutami Reservoir consisting of St. Kalipare, St. Geophysics, St. Sumberpucung, St. Kepanjen, St. Ngajum, St. Karangsuko, and St. Gondanglegi in 2010-2019. 2. Data on water quality BOD, COD, DO, NH3-N, TSS, and pH in the Upper Sutami Reservoir at Depth I (0.3 m) and Depth II (4 m) in 2015-2019. 3. Data on water quality BOD, COD, DO, NH3-N, TSS, and pH in the Middle Sutami Reservoir at Depth I (0.3 m), Depth II (5 m), and Depth III (10 m) in 2015-2019. 4. Data on water quality BOD, COD, DO, NH3-N, TSS, and pH in the Sutami Downstream Reservoir at Depth I (0.3 m), Depth II (5 m), and Depth III (10 m) in 2015-2019. 2.3. Work steps In general and concise, the steps in this research are as follows: a. Collecting rainfall data at rainfall stations around the Sutami Reservoir consisting of St. Kalipare, St. Geophysics, St. Sumberpucung, St. Kepanjen, St. Ngajum, St. Karangsuko, and St. Gondanglegi to determine the average rainfall area using the arithmetic mean method. The average or arithmetic method is very simple in determining the average rainfall in a certain area [16]. b. Determine the dry season in the area around the Sutami Reservoir. In determining the dry season, using the BMKG rules, the dry year is the amount of rainfall less than 85% of the average rainfall observed [17]. c. Collecting water quality data in the Sutami Reservoir at each water quality monitoring station. d. Grouping the water quality data in the Sutami Reservoir at each water quality monitoring station for the dry season. Civil and Environmental Science Journal Vol. 5, No. 1, pp. 064-077, 2022 67 e. Conduct a data homogeneity test at each water quality monitoring station using the F test. The amount of F is in the form of a ratio (ratio). Fcr values can be obtained from table F for various values of Level of Significance (α) [18]. f. Analyzing water quality at each water quality monitoring station using the Pollution Index Method [19]. g. Determine the water quality status at each monitoring station according to water quality standards [20]. h. Determining water quality modeling at each monitoring station according to linear regression models, exponential regression models, logarithmic regression models, polynomial regression models, and multiple regression models [21]. 2.4. The formulas used in this article a. Trend test with Mann-Whitney test The following is the correlation coefficient formula using the Mann and Whitney method: Statistical parameter value calculation formula: U1 = N1 × N2 + ( N1 N2 ) × (N1 + 1) − Rm (1) U2 = N1 × N2 − U1 (2) Z = U−(N1N2) 2 ( 1 12 {N1N2(N1+N2+1)}) 1 12 (3) b. Variant stability test The following is the formula for the variance stability test (F-Test): F = 𝑁1.𝑆1 2(𝑁2−1) 𝑁2.𝑆2 2(𝑁1−1) (4) c. Stationer test The following is the formula for the stability test of the average value (T-Test): σ = ( 𝑵𝟏.𝑺𝟏 𝟐 +𝑵𝟐.𝑺𝟐 𝟐 𝑵𝟏+𝑵𝟐−𝟐 ) 𝟏 𝟐 (5) t = 𝑿𝟏̅̅̅̅ −𝑿𝟐̅̅̅̅ 𝝈( 𝟏 𝑵𝟏 + 𝟏 𝑵𝟐 ) 𝟏 𝟐 (6) d. Fisher's test In this study, the analysis of variance used the F test (Fisher's test) F = (𝑛−𝑘).∑ 𝑛1(𝑋𝑖̅̅ ̅−�̅�) 2𝑘 𝑖=1 (𝑛−𝑘).∑ ∑ (𝑋𝑗𝑖̅̅̅̅̅−�̅�)2 𝑗=𝑛𝑗 𝑗=1 𝑘 𝑖=1 (7) Where; U1, U2 = Statistical parameter for each group Rm = Maximum rating total value N1, N2 = Total data for each group Z = Test coefficient S1, S2 = standard deviation of group 1 data, the standard deviation of group data 2 F = F test count value t = t test count value 𝑋1,̅̅̅̅ 𝑋2,̅̅̅̅ = the average value of group 1 data, the average value of group 2 data Civil and Environmental Science Journal Vol. 5, No. 1, pp. 064-077, 2022 68 3. Result and Discussion 3.1. Hydrological Test and Determination of Seasonal Division 3.1.1. Double Mass Curve Consistency Test To test the consistency of the data, one of them can use multiple mass curve analysis. This multiple mass curve analysis is for annual rainfall data from an area. Multiple mass curves are one of the graphical methods for testing the consistency and similarity of hydrological data types from a rainfall station [21]. In the consistency test, it is illustrated on line 45 on the scatter diagram. Determine if there is a change in the slope of the scatter diagram. Suppose the graph shows a point with a change in slope. In that case, it is necessary to correct the recording of rain data using a correction factor. The double mass curve test results show that the maximum annual daily rainfall for the seven stations is 1354 mm – 3785 mm, with an average of 2198. The following are the analysis results using the Multiple Mass Curve Test (Table 1). Table 1. Hydrological analysis with double mass curve test Year Annual rainfall Data (mm) St. Kalipare St. Geofisika St. Sumberpucung St. Kepanjen St. Ngajum St. Karangsuko St. Gondanglegi 2010 3017 3238 3049 3228 3265 3214 3225 2011 1621 1680 1551 1673 1716 1602 1572 2012 2117 2139 1983 2084 2145 2009 2052 2013 2599 2470 2677 2749 2742 2645 2550 2014 1543 1973 1681 1549 1625 1560 1354 2015 1879 1731 1972 1972 2041 1991 2031 2016 3092 3785 3231 3319 3272 3239 3323 2017 2627 2066 2356 2290 2345 2244 2240 2018 1514 1397 1613 1720 1598 1544 1671 2019 1677 1685 1809 1719 1697 1640 1646 3.1.2. Absence of Trend Test with Mann-Whitney Test The Mann-Whitney correlation test tests two data groups to determine whether the data come from the same population. By using equation (1-3), it was found that the value of Z count. Based on the table of tc values for normal distribution [21], for a 5% confidence degree, the value of Zc = -1.96 is obtained because Z count < Z table. Therefore, the results obtained that the hypothesis was accepted. The measurement station data was data that came from the same population. Thus the rain station data comes from the same population (Table 2). 3.1.3. Stationer Test with Variant Stability Test A stationary test is used to test the stability of the variance and the average of hydrological data. From the test results, it will be known whether the value of the data variance is homogeneous or not. At the degrees of freedom dk1 = n1 – 1 = 4 and dk2 = n2 – 1 = 4 and the degree of confidence is 5%, the f table is 6.39. Using equation (4), the calculated F value is smaller than the F table value = 6.39. Then the hypothesis is accepted (Table 3). Civil and Environmental Science Journal Vol. 5, No. 1, pp. 064-077, 2022 69 Table 2. Hydrological analysis with the Mann-Whitney Test Mann Whitney Test Rainfall Station Kalipare Geofisika Sumber pucung Kepanjen Ngajum Karangsuko Gondanglegi Rm 29 34 31 28 32 28 29 U1 11 6 9 12 8 12 11 U2 14 19 16 13 17 13 14 Z count -0.31 -1.36 -0.73 -0.10 -0.94 -0.10 -0.31 Z table 1.96 1.96 1.96 1.96 1.96 1.96 1.96 Result Accepted Accepted Accepted Accepted Accepted Accepted Accepted Table 3 shows that the rain data at seven rain stations around the Sutami Reservoir are accepted, meaning the variance value is stable or homogeneous. Table 3. Hydrological analysis with Variant Stability Test (F Test) F Test Rainfall Station Kalipare Geofisika Sumberpucung Kepanjen Ngajum Karangsuko Gondanglegi n1.S1(n2-1) 4306664 9144898 8183346 13743466 10860026 12459010 15008674 n2.S2(n1-1) 15548514 9878444 7332564 11037090 8480386 9272980 11732524 F count 0.28 0.93 1.12 1.25 1.28 1.34 1.28 F table 6.39 6.39 6.39 6.39 6.39 6.39 6.39 Result Accepted Accepted Accepted Accepted Accepted Accepted Accepted 3.1.4. Stationer Test with Stability Test Average Value By using equation (5-6), the results obtained for the degrees of freedom dk = N1 + N2 -2 = 5 + 5 – 2 = 8, and the degree of confidence 0.025 in the two-way test, the t-table value = 2.31. The value of t count is smaller than the t table value = 2.31. Then the hypothesis is accepted. It is found that the rainfall data at seven rain stations around the Sutami Reservoir are all accepted, which means the variance value is stable or homogeneous. (Table 4). Table 4. Hydrological analysis with Average Value Stability Test (T-Test) T-test Rainfall Station Kalipare Geofisika Sumberpucung Kepanjen Ngajum Karangsuko Gondanglegi α 787.70 771.02 696.33 880.00 777.42 824.09 914.15 t -0.16 0.86 -0.45 0.12 0.56 0.15 -0.40 t Table 5% 2.31 2.31 2.31 2.31 2.31 2.31 2.31 Result Accepted Accepted Accepted Accepted Accepted Accepted Accepted 3.1.5. Determination of Season Determination of the dry and wet seasons is based on the regional average rainfall, which is calculated using the arithmetic mean method. According to BMKG, the wet (W) year is the rainfall greater than 115% of the observed average. The dry year (D) is less than 85% of the observed average rainfall [17]. The following is the result of determining the distribution of seasons in the Sutami Reservoir area (Table 5). Civil and Environmental Science Journal Vol. 5, No. 1, pp. 064-077, 2022 70 Table 5. The analysis of the Seasons Determination Year Month/Rainfall (%) Annual Rainfall Jan Feb March Apr May Jun Jul Aug Sep Oct Nov Dec 2010 86 105 101 122 75 65 48 34 107 87 147 66 87 2011 71 65 46 89 40 7 0 0 0 25 87 106 45 2012 114 99 111 70 50 3 3 0 0 20 59 150 57 2013 117 145 88 64 92 90 2 0 0 24 90 179 75 2014 98 58 67 52 41 44 1 0 0 0 73 156 50 2015 102 127 102 167 52 5 0 0 0 0 57 108 60 2016 114 164 101 117 92 75 36 26 95 114 154 105 99 2017 173 119 137 155 44 29 50 1 14 51 153 112 87 2018 137 150 127 75 27 58 9 0 18 2 126 126 71 2019 151 123 159 93 58 1 0 0 0 0 29 115 61 Average 116 116 104 100 57 37 17 6 24 32 97 122 Result W W W W D D D D D D W W The calculation above shows that November – April is the wet month, and June–October is a dry month. This dry month determines water quality status because the research only focuses on the dry. 3.2. Water Quality Analysis The quality of the reservoir water flow regime or the level of water pollution is defined by several physical, chemical, and biological-microbiological materials and various other unique indicators [22]. 3.2.1. Water Quality Test Testing of water quality data is carried out by testing the homogeneity of the data or commonly called analysis of variance. The homogeneity test of this data is necessary before determining the water quality status. The homogeneity test of this data is used to determine the uniformity of the data because it was taken from several points for six years, from 2015 to 2020. In this study, the analysis of variance used the F test (Fisher's test). Table 6 is an example of an F test that has been carried out at several depths. Because F count < F table, the data is homogeneous. The same is found in all ranges of years of observation and depth. Table 6. Analysis of water quality Homogeneity Test Variance (F Test) Monitoring Station Parameter Fcount Ftable Summary Sutami Reservoir Depth I (0,3 m) BOD 0.438 19.43 Homogenous COD 0.474 19.43 Homogenous DO 0.058 19.43 Homogenous NH3-N 0.078 19.43 Homogenous TSS 2.932 19.43 Homogenous pH 0.574 19.43 Homogenous Civil and Environmental Science Journal Vol. 5, No. 1, pp. 064-077, 2022 71 3.2.2. Determination of Water Quality Status by Pollution Index Method The analysis of determining the water quality status is carried out monthly with a class II water quality class. According to the Pollution Index method, the water quality index value of the Sutami Reservoir for the Upstream-Middle-Downstream Sutami Reservoir Monitoring Station from 2015 to 2019 are as follows (Figure 3-5). Figure 3. Pollution index values at the Upstream Sutami Reservoir Monitoring Station Figure 3 shows the Pollution index values at the Upstream Sutami Reservoir Monitoring Station. The analysis was carried out at a depth of 0.3 m and 4. Sampling was taken from May-October, assuming it was in the dry season. Because the majority index value is 1.0 < Pij < 5.0, it can be categorized as lightly polluted. Figure 4. Pollution index values at Middle Sutami Reservoir Monitoring Station Figure 4 shows the Pollution index values at Middle Sutami Reservoir Monitoring Station. The analysis was carried out at three depths, namely 0.3 m, 5 m, and 10. It is because the depth of the reservoir in the middle is deeper than in the upstream. Sampling is still the same, taken in May-October, assuming it is in the dry season. Due to the majority index value being 1.0 < Pij < 5.0 can be categorized as lightly polluted. Civil and Environmental Science Journal Vol. 5, No. 1, pp. 064-077, 2022 72 Figure 5. Pollution index values at the Sutami Downstream Reservoir Monitoring Station Figure 5 shows the same results as Figures 3 and 4. The Sutami Downstream Reservoir Monitoring Station water is included in the lightly polluted category. Although currently, all observations are still in the lightly polluted category, it should be noted that the level of pollution is increasing from year to year. The pollution index in 2015 was around 0.9, but by the end of 2019, it rose to around 2.4. It needs attention from the authorities to prevent the pollution index from increasing. From the results of determining the water quality status using the Pollution Index Method, the percentage of water pollution in the Sutami Reservoir is as follows (Table 7). Tabel 7. Percentage of water quality status in 2015 to 2019 monitoring station Class Monitoring Station Upper Sutami Reservoir Middle Sutami Reservoir Downstream Sutami Reservoir 0,3 m 4 m 0,3 m 5 m 10 m 0,3 m 5 m 10 m Meets Quality Standards 13% 10% 10% 7% 7% 10% 13% 3% Lightly Polluted 87% 90% 90% 93% 93% 90% 87% 97% Conclusion Lightly Polluted Lightly Polluted Lightly Polluted Lightly Polluted Lightly Polluted Lightly Polluted Lightly Polluted Lightly Polluted The table above shows that the percentage of water that meets the quality standard is very small, ranging from 3%-13%, while lightly polluted is 87%-93%. 3.2.3. Mathematical Modelling of Water Quality Status with Regression Model Determination of the water quality characteristics of the Sutami Reservoir consists of; determining the status of water quality using the Pollution Index Method, which is then carried out by mathematical modeling using a regression model; as well as determining the trophic status (Total-P parameter), which is used to determine the carrying capacity of the Total-P pollutant load in the Sutami Reservoir. Determination of water quality characteristics of the Sutami Reservoir for three monitoring point locations with each depth. Modeling the water quality status is determined after determining the water quality status using the Pollution Index method. The modeling used is the linear regression model, polynomial regression Civil and Environmental Science Journal Vol. 5, No. 1, pp. 064-077, 2022 73 model, logarithmic regression model, exponential regression model, and multiple regression model (power). The following is the result of analyzing the mathematical model of water quality status (Table 8-10 and Figure 6-7). Table 8. Mathematical modeling of water quality status for Upstream Sutami Reservoir Monitoring Station Mathematical Model Upstream Monitoring Station 0.3 m 4 m Linear Regression y = 0.0497x + 0.9638 y = 0.0479x + 1.1074 R2 = 0.6822 R2 = 0.6693 Polynomial Regression y = -0.0001x2 + 0.0529x + 0.9464 y = -0,002x2 + 0,1089x + 0,7818 R2 = 0.6824 R2 = 0.7368 Exponential Regression y = 0.9976e0.032x y = 1,0809e0,0313x R2 = 0.6133 R2 = 0.5711 Logarithmic Regression y = 0.4587ln(x) + 0.592 y = 0,507ln(x) + 0,5881 R2 = 0.5432 R2 = 0.6996 Multiple Regression (power) y = 0.7687x0.3043 y = 0,7443x0,3446 R2 = 0.5162 R2 = 0.6479 From Table 8 above, it is found that the R2 value that is the largest or close to 1 for the upstream Monitoring Station 1st depth (0.3 m) is a polynomial regression model with an R2 value of 0.6423 and for the upstream Monitoring Station, 2nd depth (4 m) is a polynomial regression model with an R2 value of 0.7368 so that the most suitable regression model with the variation of the PIj value of the Upper Sutami Reservoir is the polynomial regression model. Table 9. Mathematical modeling of water quality status for Middle Sutami Reservoir Monitoring Station Mathematical Model Middle Monitoring Station 0.3 m 5 m 10 m Linear Regression y = 0,0535x + 0,9124 y = 0,0454x + 1,1249 y = 0,0443x + 1,2099 R2 = 0.7204 R2 = 0.6570 R2 = 0.6382 Polynomial Regression y = -0,0009x2 + 0,0813x + 0,764 y = -0,0005x2 + 0,0595x + 1,0494 y = -0,0009x2 + 0,0736x + 1,0535 R2 = 0.7326 R2 = 0.6610 R2 = 0.6556 Exponential Regression y = 0,95e0,0351x y = 1,1378e0,0277x y = 1,1958e0,027x R2 = 0.6625 R2 = 0.5616 R2 = 0.5501 Logarithmic Regression y = 0,5278ln(x) + 0,428 y = 0,4358ln(x) + 0,7436 y = 0,4632ln(x) + 0,7439 R2 = 0.6546 R2 = 0.5656 R2 = 0.651 Multiple Regression (power) y = 0,6524x0,3699 y = 0,8909x0,2709 y = 0,8608x0,3004 R2 = 0.6850 R2 = 0.5007 R2 = 0.6346 Civil and Environmental Science Journal Vol. 5, No. 1, pp. 064-077, 2022 74 Table 9 shows that the R2 value is the largest or close to 1 for the middle monitoring station in the 1st depth (0.3 m), which is a polynomial regression model with an R2 value of 0.7326, for the 2nd depth (5 m) it is a polynomial regression model with an R2 value of 0.6570, and for 3rd depth (10 m) it is a polynomial regression model with an R2 value of 0.6556 so that the most suitable regression model with variations in the PIj value of the Central Sutami Reservoir is the polynomial regression model. Table 10. Mathematical modeling of water quality status for Downstream Sutami Reservoir Monitoring Station Mathematical Model Downstream Monitoring Station 0.3 m 5 m 10 m Linear Regression y = 0,0463x + 1,0683 y = 0,0509x + 1,0633 y = 0,0364x + 1,3856 R2 = 0.6902 R2 = 0.7585 R2 = 0.6577 Polynomial Regression y = -0,0001x2 + 0,0499x + 1,0489 y = -0,0021x2 + 0,1165x + 0,7132 y = -0,0008x2 + 0,0623x + 1,2473 R2 = 0.6905 R2 = 0.8371 R2 = 0.6785 Exponential Regression y = 1,0917e0,0288x y = 1,0732e0,0321x y = 1,3903e0,0203x R2 = 0.6060 R2 = 0.6933 R2 = 0.6050 Logarithmic Regression y = 0,4445ln(x) + 0,6789 y = 0,5421ln(x) + 0,5027 y = 0,3868ln(x) + 0,9868 R2 = 0.5950 R2 = 0.8039 R2 = 0.6940 Multiple Regression (power) y = 0,82x0,2944 y = 0,7299x0,3546 y = 1,0803x0,2278 R2 = 0.5909 R2 = 0.7913 R2 = 0.7109 Figure 6. Depiction of the mathematical model in the Sutami Reservoir (side view) Civil and Environmental Science Journal Vol. 5, No. 1, pp. 064-077, 2022 75 Table 10 revealed that the R2 value, which is the largest or close to 1 for the downstream Monitoring Station 1st depth (0.3 m), is a polynomial regression model with an R2 value of 0.6905, for the 2nd depth (5 m) is a polynomial regression model with an R2 value of 0.8371, and for 3rd depth (10 m) is a polynomial regression model with an R2 value of 0.7109. So that the most suitable regression model for the variation of the PIj value of the Sutami Hilir Reservoir. Obtained a regression model with the highest R2 value at the upstream, middle, and downstream Sutami Reservoir Monitoring Stations for each depth (8 points of depth), namely the polynomial regression model. It means that the most suitable regression model for the variation of PIj data is the polynomial regression model. It shows that this polynomial regression model is in the form of a curved line that tends to increase over time and then flatten to decrease at the end of the period. It means that the trend of the level of pollution tends to continue to rise and starts to stabilize until it decreases at the end of the period studied. Figure 7. Depiction of the mathematical model in the Sutami Reservoir (top view) Figure 7 summarizes the results of research that has been carried out, namely that at all sampling locations, the best mathematical model is polynomial regression, and the reservoir water quality condition is lightly polluted. 4. Conclusions This research has succeeded in determining water quality status using the pollution index method and mathematical modeling. The levels of parameters BOD, COD, DO, and pH has exceeded the existing quality standard values. Meanwhile, the levels of TSS and NH3-N parameters have not exceeded the existing quality standard values. The status of water quality using the Pollution Index method is in the lightly polluted category. The value of the Total-P capacity that enters the Sutami Reservoir exceeds the maximum quality standard. The polynomial regression model is the most suitable mathematical model for the pollution index method data (PIj). This research can be used as a reference for the management to determine the steps in managing industrial and residential areas and limiting the use of pollutant materials. Civil and Environmental Science Journal Vol. 5, No. 1, pp. 064-077, 2022 76 Acknowledgments The authors share their appreciation of the sponsorship of this study to the Faculty of Engineering, the University of Brawijaya, Research and Community Service (BPPM-FT UB); Public Works and Water Resources of Malang Regency, Jasa Tirta 1 Public Corporation, and BPDAS Brantas for providing secondary data for this research. References [1] F. Khorashadi Zadeh, J. Nossent, B. T. Woldegiorgis, W. Bauwens, and A. 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