Critical appraisal of water quality model parameters for an urban city in lower Ganga basin during pre- and post-COVID19 Lockdown in India

Objectives : To assess the impact of urban city Patna on water quality of the river Ganga during pre and post COVID-19 lockdown. Method: A study is done to assess the impact of point and nonpoint source pollution at diﬀerent reaches of river Ganga for the years 2017 to 2020 (at a stretch of 40 km of a urban city in lower Ganga plains). A total of 450 datasets have been collected from eight river locations and two major drains. The equations of deoxygenation and reaeration coeﬃcient used in water quality modelling have been tested for their applicability in the study area. Findings: Analysis of water quality data collected from 8 river locations and 2-drains for the year 2017-2020 shows signiﬁcant improvement in water quality variables observed in river Ganga at Patna due to reduction in inﬂux of point and non-point source pollution including ﬂoating population at Patna during COVID19 lockdown (March- June 2020). The use of BOD-DO developed by Streeter-Phelps (1925) as Oxygen-Sag curve is still valid, if input variables are limited. However, Camp (1963) and Jha et al. (2007) may be used eﬀectively for comprehensive input data sets. Moreover, the reﬁned model for predicting reaeration coeﬃcient has been tested for the developed dissolved oxygen (DO) model and biochemical oxygen demand (BOD) model for pre- and post COVID19 lockdown individually. The water quality maps developed using satellite (Landsat-8) data provides the turbidity levels during pre and post COVID19 countrywide lockdown period and resulted in a signiﬁcant improvement. Novelty: The study is unique due to water quality analysis during COVID19 and its comparison with previous year data. The deoxygenation and reaeration coeﬃcients values are established for pre-and post COVID period. Also use of Landsat-8 data is used for assessing turbidity for pre- and post-COVID19.

The River Ganga, which is the most sacred river in India, has very high self-purification capacity due to it turbulent nature, dynamic behaviour, high reaeration process, and other related factors. Due to over exploitation of freshwater and disposal of waste water in River Ganga from mega and metro cities situated along the river Ganga, the water quality of river Ganga has been deteriorating in recent past. (6,7,9,11,15,19,19,20,(20)(21)(22)22,23,23,23,24,24,25,25,25,26,26,26,27,27,27,28,28,28,29,29,30,(30)(31)(32)(33) . In most of the studies done in recent past, the variation of water quality parameters such as DO and BOD has been estimated. However, very little work has been done for water quality modelling and establishment of water quality parameters such as deoxygenation rate constant and reaeration coefficient during pre as well as post COVID period.
In general, the BOD-DO models, can be derived from Equation 1 as given below The presence of dissolved oxygen (DO) in water is the primary criterion for the water quality of streams. To model streams and to allocate waste loads, use of the reaeration coefficient, K 2 , is essential for dissolved oxygen computation. The theoretical background to the reaeration coefficient is available in many studies (2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)17) . The rate of mass transfer, dD/dt, of oxygen from the atmosphere to the body of the turbulent liquid generally is proportional to the difference between the existing concentration of dissolved oxygen, D, and the equilibrium or saturation concentration of dissolved oxygen, D 0 , in the liquid. The mathematical expressions can written as where (K 2 ) T is the reaeration coefficient at test temperature T • C. The value of (K 2 ) T is related to the value (K 2 ) 20 as follows In the present work the impact of point and non-point source pollution in the river Ganga at various locations of Patna town, Bihar, India has been assessed during pre-and post-COVID19 countrywide lockdown and predictive equations have been tested for their applicability in the River Ganga at Patna using data monitored and generated during field survey.

The Study area
The sampling locations in the study area of urban city Patna are shown in Figure 1 , which includes 8 river locations and two drains. The population of Patna urban is about 17 lakhs and the floating population, which is coming to Patna for work and business is about 2 lakhs per day. The total wastewater generation is expected to be 320 MLD. It was found that the water quality of river Ganga has improved significantly during COVID19 lockdown, so the study which was done during the years 2017-2019 was extended to the year 2020.

Water Quality Data sampling
The water samples (either collected from ground locations or obtained from different government agencies) of the river Ganga at urban areas of Patna city. All the samples collected from 10 locations were stored and preserved without delay inside acidcleaned polypropylene bottles during frozen condition using transportable ice box to reduce the biogeochemical alterations as per standard procedure (1)(2)(3)(4) . The Standard method for water samples and IS Codes for water quality testing was used to analyse pH, water temperature, dissolved oxygen (DO), and biochemical oxygen demand (BOD).
In the present work, the most commonly used models have been tested for their applicability in urban city Patna situated along river Ganga for BOD and DO simulation. (Table 1 ) (13,34) .
The performance evaluation using standard error, mean multiplicative error, and correlation coefficient of form of simplified form of refined models for BOD and DO simulations has been done. (13,34) Various model parameters are used for BOD and DO modelling. The deoxygenation rate constant, K1 (L/day), was determined from the BOD values and estimated travel time of river reaches. In this approach, the BOD values obtained for different reaches of the River Ganga were plotted on a log scale (Y axis) and the travel time is plotted on a normal scale (X axis). The slope of the line provides the values of the deoxygenation coefficient (K 1 ). The reaeration coefficient (K 2 ) was computed using the Froude number approach proposed by Jha et al. (2004). The equation is https://www.indjst.org/ Streeter and Phelps (1925)

DO Models Author Differential Equation Solution Equation used
Jha et al.

Analysis of Water Quality Data
The water quality samples collected from different locations indicate variation in their values due to influx of point source pollution (Figures 2 and 3 ). The analysed data have been utilised for water quality modelling and establishing different parameters K 1 and K 2 in BOD-DO modelling. It is observed from Figure 2  Further, to demonstrate the water quality status of River Ganga along the urban areas of Patna city, turbidity maps of the month pf April for the years 2017-2020 were analysed using Landsat-8 data. Figure 3 illustrates the water quality (turbidity) maps during the years 2017-2020. It is interesting to see that, during COVID19 countrywide lockdown period, water quality of river Ganga at Patna improved significantly, not only in terms of BOD and DO, but also I terms of turbidity due to reduction in waste water from point source pollution (municipal drains and industrial drains) as well as non-point source pollution. https://www.indjst.org/

Analysis of results using BOD-DO Modelling approach
The input parameters, required by these models for BOD and DO simulations, as given in Table 2 were estimated using methods described earlier and equation (10) above. It has been observed that the BOD and DO rate constants are too different during pre-and post-monsoon period. From Table 2(a) provides the values of deoxygenation rate constants (ranging between 0.25 to 0.45) and reaeration coefficient values (ranging between 3.6-to 5.1) during pre-COVID period, when the river was highly polluted due to influx of point and non-point source pollution. Table 2(b) provides the values of deoxygenation rate constants (ranging between 3.5 to 6.5) and reaeration coefficient values (ranging between 6.25 to 9.5) during post-COVID period, which was during lockdown period. Significant improvement observed in both the constants.
For BOD and DO modelling, Table 2 data were used. It has been observed that the results obtained using the Camp (1963) model provides better results for River Ganga in comparison to the Streeter-Phelps (1925) model (Figures 4 and 5 ). The findings show that after the entry of sewage in River Ganga, its colloidal materials were quickly coagulated and removed. As a result, the BOD was found to decrease at a faster rate at different locations in River Ganga. The model developed by Jha et al. (2007) is found to be versatile and could not be used due to insufficient data availability obtained from different sources.

Conclusions
The following Conclusions are drawn: 1. Significant improvement in water quality variables is observed in river Ganga at Patna due to reduction in influx of point and non-point source pollution including floating population. The values of deoxygenation rate constant and reaeration rate coefficients are found to be very high during lockdown period indicating quick decay process and more aeration due to high velocity and high discharge. 2. The use of BOD-DO developed by Streeter-Phelps (1925) as Oxygen-Sag curve is still valid, if input variables are limited.
However, Camp (1963) and Jha et al. (2007) may be used effectively for comprehensive input data sets. 3. The water quality maps developed using satellite (Landsat-8) data provides the turbidity levels during pre and post COVID19 countrywide lockdown period and resulted in a significant improvement.