Pearson‘s correlation and trend analysis for physico-chemical parameters of Mansagar Lake, Jaipur

The article reviews the constituent‘s physico-chemical parameters in the water of the Mansagar Lake of the Jaipur City. The water quality is also investigated using evaluated physico-chemical parameters with in-depth study of their distribution as per sample location-wise and season-wise. A detailed discussion on the associationship among parameters (pH, Conductivity, turbidity, dissolved Oxygen, chemical and Biochemical Oxygen demand, etc.) using the Pearson‘s analytical method is also presented. The strength of the article is the graphical presentation of evaluated physico-chemical parameters and the water quality indices for sample station-wise and the season-wise. To our best of understanding, first time such details have been clubbed together and discussion in brief for studied lake.

depth. The water quality index (WQI) is one of the most effective tools to develop management strategies to control surface water pollution [8][9][10]. Some of the dominant parameters evaluated were then used to determine the WQI for the studied Jalmahal (Mansagar) lake and the results are plotted to check their distribution profile as per the pre vailing and other external environmental situations. The correlation analysis among the physico-chemical parameters for a water body is a bivariate analysis, which defines the strength and direction of association between two parameters. The Pearson's correlation is a method of covariance, it is considered as the best method to measure the association between two continuous variables [11]. In the later part of the article, we have also outlined the calculated associationship among evaluated physico-chemical parameters with use of Pearson's correlation method concepts.

Study Area: The Mansagar (Jalmahal) Lake, Jaipur
The Mansagar Lake is located in the northwest part of the city with a palace in the middle; the Jalmahal built by Mansingh (I), in the year 1610. The Lake is located in the middle surrounding three hills and was constructed by building a dam over a river; the Dravawati, to address the drought in the surrounding lands [12]. During post-independence era, especially in the year 1962, the city administration diverted the sewage disposal of two large drainstowards the lake and from that stage the situation started getting worst for the fresh water source of the Pink city [12][13][14]. The dimension of the lake can be classified as the water surface area about 139 hectares and the catchment area of 23.5 sq. km with an average depth ranging 1.5m to 4.5m. Nearly half of its catchment area located near to dense urban area and the remaining area is covered by denuded hills. Due to discharge of organic waste the aquatic weeds started growing over the lake, which suppresses the aquatic life in the lake.
In view of maintaining its heritage value, year 1999 onwards, the responsible Government agencies started taking strict action for the revival of the Jalmahal region. The present status of the lake is much better as it has been developed into a tourist attraction as shown in the figure 1(a). However with increasing tourist activities, the lake front has been fuelled with solid waste and bread crum feeding since long. Also mixing of waste food, paper and plastic in the lake have been a challenging issue for management of the lake since long. The ground water sources near to the lake have been found affected with severe contaminations caused by mixing of untreated sewage water with the lake since long. Therefore, most of nearby water sources are unfit for their use as drinking source and posing serious health hazard to living beings.
Moreover, situation becomes worse during rainy seasons, when the excess rain water flow into the lake with mingled with the pollution contents from adjoining rough areas and the roads.
For our study, we have selected the samples collection station on the basis of anthropologicalactivities around the lake, and the surroundings. After a detailed study on previous water quality report and the restoration works done in past, eleven important sites were chosen to collect and monitor the water quality for two applicable seasons (Pre-and Postmonsoon). As shown in the figure 1(b), the stations from L 1 to L 5 were chosen at the edge of the lake, while the stations from L 6 to L 11 were across its width in almost in the centre. To analysis the water quality assessment of the studied lake, rigorous efforts have been placed to evaluate important physico-chemical parameters for its water. Standard procedures for sample collection and evaluation of physico-chemical parameters have been applied as discussed in our previous work [14]. As part of exercises, many roundsphysical and chemical tests were performed to calculate factors like pH, turbidity, DO, COD, BOD and many others.

Evaluation and distribution plots of Physico-chemical parameters and metal constituents:
In this section, we shall be discussing corresponding distribution plots as per sample locations and their maximum,  [15][16][17]. The conductivity for the Mansagar lake water found to be in higher ranges, which indicate excess clay and limestone mixing with the lake from the surrounding hills. With our study, the conductivity of the lake water remains in the range 1019 µS/cm-1477 µS/cm with a mean value; 1291.64 µS/cm for samples collected post-monsoon days. Also reason for conductivity may remains at higher levels during the pre-monsoon days due to extreme temperature and huge evaporation process in peak summers. The observed conductivity range was 1650 µS/cm-1890 µS/cm with a mean value; 1763.64 µS/cm for samples collected pre-monsoon days, which actually correlate its values with impact of varied environmental conditions.  The relative clarity of a water body can be measured in terms of turbidity. Highly turbid water scatters more sun light, and may contain particles, which are not good for human consumption.The particle can be added from any source like limit in most cases. Perhaps, the illegal garbage dumping, leaked sewage, rain runoff and waste discharges from the tourist and locals results in high valued COD in post-monsoon days as well, while rainy days causes inflow of organic streams in to the lake. found to be fluctuated with values of 20.6 mg/L and 9.8 mg/L at the edges and 14.0 mg/L and 11.2 mg/L at stations taken across width (middle) of the lake during post-and pre-monsoon days respectively. Figure 3 represent levels for COD, DO and BOD parameters graphically for pre-and post-monsoon sampling. The high BOD concentrations at the most of the stations located at the edges of the lake has been due to the ongoing fencing restoration works and logging activities, which causes loading of the organic matters from the anthropogenic activities. Chloride contents indicate additional presence of organic pollutants caused by increased domestic pollution activities.
The non point streams of sewage, fertilizers and road ran off are major threat. It was noticed that elevation in the Chloride concentrations in the lake water may take place due to road ran off and remain with increasing trends during pre-monsoon days. Such imbalance creates risk for nearby infrastructures as well as aquatic to ecosystems in future. The plots depicted by figure 4, can be used to understand variation in the TOC and Chloride contents with respect environmental conditions and the sample locations.

Water quality index determination:
The water quality index indicates the value of water quality at a specific location and time based on the single value of selected variable [19]. In our study, the objective to estimate the water quality index at sample locations was to represent the complex data into the water quality information, which is easy to understand and usable by the public and reader of this work. Although water quality represented by a single number cannot tell about complete story of the water quality; there were many other water quality parameters, which were not included in calculating the index. In general, use of important parameters such as temperature, DO, pH, COD, TDS, BOD, turbidity, etc. have been in practice to estimate the water quality index [20][21][22][23][24][25][26][27]. The water quality index is based on the level of the water quality (Q) and weigh factor (w) that gives the relative importance of a parameter with overall quality. The WQI based on certain important quality parameters can indicate quality of the water as per range shown in the table 3. Water quality index was calculated by using the weighted arithmetic index method as described by Curtis G. Cude, 2001 [25].  [21][22] have modified this method in which various water quality factors are multiplies with a weighting factor and then calculated by taking arithmetic means in the process of calculating the water quality first the quality rating using following equation [21][22][23][24][25]; (1) In this Q i is the quality rating of i th parameter for n water quality parameters, V o is the actual value of the water quality parameter obtained from analysis and V s is the recommended standard value. While the V id is the ideal value of that water quality parameter, which has been referenced from the standard tables; for example, the V id for pH is 7 and for other parameters it equals to zero, and for the dissolved oxygen, the V id is 14.6 mg/L. Thereafter, the relative value of weight was determined by the relation W i = I/S i , where W i is the n th , S i is the value of permissible standard for n th parameter and the I is the proportionality constant and taken as; 1.8615. The overall water quality index can be determined by aggregating rating of quality with weight using below mentioned equation [21][22][23][24][25]: (2) Where, Q i is the quality rating and W i is the relative (unit) weight. The relative unit weightW i values for each parameter are considered as pet table 4. In our study, the WQI levels were categorized based on permissibility for human consumption or uses and the standard value of maximum permissible WQI value for domestic uses. We also aimed for assessing the surface water WQI for all chosen sample locations by monitoring and evaluating collected samples for varied environmental conditions. The mean valued data have been used subsequently for calculation of WQI using mean arithmetic methods. We preferred to calculate the WQI values using dominant parameters only such as pH, turbidity, TDS, BOD, DO, TOC, and chlorides contents. Table 5 depicts calculated WQI values for samples collected duringpre-and post-monsoon days for chosen locations; L 1 -L 11 . As reported earlier, these strategic locations were chosen on the basis of availability of water for testing, which constitutes possible contamination and mixing of water contents from treatment plant and the major effluents inlets. From table 5, it is clear that the WQI values remain high sample collected from most locations during post-monsoon days. The WQI values for stations; L 1 to L 11 were found in the ranges; 104.59 -135.82 and 135.08 -219.75 for pre-and postmonsoon days of investigations. Further, it is apparent from obtained WQI values, that the studied lake water quality belongs to poor to very poor water quality classification during post-monsoon days, while the quality belongs to moderate to poor water classifications during pre-monsoon days.Also, high WQI values for test sample collected from evaluated WQI values can be set as a benchmark for easy understanding of overall water quality and the water management techniques to be adopted for taken care of its water quality. The water quality ratings at most of the sampling sites indicate clearly that the quality of the lake water has been degrading. Since the evaluated WQI values are not in acceptable range as described by the WHO standards and guidelines, the lake water cannot be recommended for its uses for domestic and drinking purposes. It was also observed that the pollution load was relatively high post-monsoon days/months as compared to the pre-monsoon season. We also conclude that, discharges from of nearby domestic and industry applicants and ever-increasing anthropogenic activities are primary concerns, thereby regular monitoring for Mansagar Lake is recommended.

Pearson's correlation analysis:
The Pearson's correlation coefficient; ‗r' is the mathematical correlation coefficientthat measures the strength of statistical relationship, or association between two continuous variables on the same interval or ratio scale and can be calculated by [34]; Where ‗x i ' and 'y i ' is values of x-and y-variables in a sample, whereas x' and y' are mean values of x-and y-variables.
Range of Pearson coefficient is from +1 to -1. Using the coefficient value, we calculate predict the linearity among the parameters. The strength of association should be higher as the resemblance to a straight line comes closer. If the value of Pearson coefficient takes values equal to +1, -1 or zero, the relationship between two variables can be defined as perfectly positive, negative or no correlation respectively [35]. Apart from these levels of correlation factor, there are many intermediate stages/levels, which have been used to define relationship among the parameters with more details.
The table 6 depicts the interpretations for different values of the Pearson's correlation coefficient (r), as described by Haldun Akoglu, 2018 [36]. Other important characteristic of the Pearson' coefficient, that it represents a pure number means, it has different measurements unit as it is independent of the unit of measurement. Also, it possesses similarity properties means, the correlation of the coefficient between two variables are similar in nature i.e., the coefficient value will remain same between x and y or y and x [11], [37]. These concepts have been used to determine the Pearson's correlation coefficient  indicates very strong negative relation between pH and BOD (-0.70), a strong negative relation between pH with turbidity, TOC and Chloride as -0.66, -0.40 and -0.40 respectively. On similar ways we can define the association between other parameters and for the table 6.3, which co-relates the parameters for evaluated samples of pre-monsoon days.  ' from table 7

Conclusion:
We have discussed trends of evaluated physico-chemical parameters with respect to the locations and season for the surface water of the Mansagar Lake. It has been noticed that the contaminations have been added in the lake by point sources and non point sources pollutant agents. The experimental outcomes for collected samples indicated that this lake have been vulnerable for sewage intake, waste dumping due to the pressure from the unplanned urban developmental works and increasing human population. The WQI values and the associationship among the physicochemical parameters are explained to establish its water quality, whichmay useful for its ecological applications. The calculated parameters such as WQI, Pearson's correlation coefficients can be use to prepare scientific measures for better management of the lakes. Also these parameters may be utilized to formulate optimal network design for quality assured monitoring of water bodies.