Estimation of re-aeration coefficient using MLR for modelling water quality of rivers in urban environment

Highlights

• Re-aeration coefficient simulated using MLR for Yamuna River.

• MLR models were developed using combinations of hydraulic and water quality parameters.

• Velocity is most important hydraulic parameter and BOD is important among water quality parameter for re-aeration coefficient.

• MLR produces the better results than empirical equation available for the prediction of re-aeration coefficient.

Abstract

Re-aeration is the natural phenomenon responsible for the generation of oxygen through the air water interface, advection, dispersion and transient storage reactions. The rate of re-aeration changes significantly when these reactions get coupled with the wastewater pollutants from domestic, industrial and agricultural discharges. Re-aeration coefficient (K₂) is the function of water quality and hydraulic parameters need to be evaluated to predict the water quality. Predictive equations available for the assessment of re-aeration coefficient are based on only hydraulic parameters and are empirically evaluated using local conditions. Therefore, a model is required that is capable of evaluating coefficient based on both the hydraulic and water quality parameters. In this study, multivariate linear regression (MLR) is used for the prediction of re-aeration coefficient in the stretch of river Yamuna. The selected stretch of river extended from North to South in Delhi, India. Five models are designed using different combinations of parameters. The developed models are trained, tested and validated using experimental data of five years. Performance of models were evaluated using coefficient of determination (R²), correlation coefficient (R) and root mean square error (RMSE). Results indicate that the MLR model developed using water quality and hydraulic parameters produces the most accurate correlation between the observed and predicted re-aeration coefficient. Correlation coefficient obtained for the best fit model was 0.896.

Introduction

Urban hydrology becomes the complex process with the significant variation in flow and deterioration in water quality due to increasing anthropogenic activities (Schirmer et al., 2013). Abrupt variation occurs in flow with the release of domestic, agricultural and industrial wastewater through drains/tributaries during the low flow period (Parmar and Keshari, 2012) and abstraction of freshwater for the water supply to the adjoining areas. Low flow in rivers and discharge of untreated wastewater have been the major reasons behind the vanishing of the river's ecosystem (Parmar, 2008, Kisi et al., 2013). With the discharge of untreated or partially treated wastewater from different sources that contains higher concentration of chemical and biological impurities also hampers the water quality at spatial and temporal scales (CPCB, 2006). Majorly biological waste is from urban distributed sources which joins the river and undergoes biological and chemical changes using dissolved oxygen. Concentration of dissolved oxygen indicates the health of the ecosystem (Hanbay et al., 2008) and biochemical oxygen demand (BOD) indicates the concentration of organic matter present in water (Dogan et al., 2009). However, due to spatial and temporal variations in hydrochemical and biological properties, continuous and regular monitoring programmes are required to have reliable information about the water quality (Singh et al., 2004).

To maintain the ecology of river, re-aeration is the most important process. Re-aeration is defined as the rate of transfer of oxygen from the atmosphere to water at the air-water interface (Grace and Imberger, 2006). Re-aeration process aids to minimize the oxygen deficit and leads to several changes in the metabolism of stream (Izagirre et al., 2008; Aristegi et al., 2009). The process is described by the rate of constants K₂ as first order processes that is proportional to DO deficit. Re-aeration process mainly depends upon the degree of turbulence that can be measured directly, however, it is highly variable in both the space and time. This makes it difficult to measure re-aeration from stream turbulence (Tsivoglou et al., 1969, Thackston and Krenkel, 1969, Thackston and Dawson, 2001). Another method of re-aeration measurement is through the identification of oxygen balance of river, which is an indirect method and poorly understood (St. John et al., 1984, Moog and Jirka, 1995; Haider et al., 2003). Using the chemical, biological and hydraulic properties of water, several methods have been developed to measure the re-aeration coefficient (K₂) of river such as tracer gases (Tsivoglou, 1967, Rathbun et al., 1978), empirical equations using hydraulic parameters (Melching and Flores, 1999), oxygen balance and diurnal variation in oxygen concentration (Hornberger and Kelly, 1975, Mcbride, 2002). Benson et al., 2014 used gas tracer technique to measure the re-aeration rate and conducted experiments at different creeks in the Sierra Nevada of California. Results obtained from the experiments were also compared with the established empirical formulas which show poor correlation between the data for the prediction of re-aeration coefficient. Numerous studies have been performed using predictive equations to measure the re-aeration coefficient (Moog and Jirka, 1995, Jha et al., 2001, Jha et al., 2004, Jain and Jha, 2005, Ugbebor et al., 2012). Applicability of predictive equations has been evaluated by Moog and Jirka, 1995 using mean multiplicative error and observed high errors for equation for low slopes. Most of these equations are based on the stream hydraulic parameters, such as depth, velocity, discharge and slope (Cox, 2003b, Raymond et al., 2012). However, none of the previously developed equations able to predict the accurate re-aeration coefficient and indicates that some more additional parameters should be considered in order to improve the accuracy (Wilson and MacLeod, 1974, Moog and Jirka, 1995, Melching and Flores, 1999, Haider et al., 2013, Benson et al., 2014).

Deterministic models are more realistic for accurate prediction, but require large amount of input data to simulate the water quality (Vieira et al., 2013). However, tradition method of data analysis are rarely being used now a days due to the involvement of large number of parameters causing variation in the water quality (Xiang et al., 2006). With the use of artificial computing techniques, challenges of hydrodynamic and water quality models can be minimized, which has wide application in water resource related problems. Multivariate Linear Regression (MLR) is the most commonly used and accepted machine learning method. It has a wide application in water-related research to identify the direct relation between the predictor and response variable as it generates minimum data set of indicators (Doran and Parkin, 1996). Using MLR, all the variables can be incorporated in to single model for the estimation of degree of interaction between the variables. Mustapha and Aris (2012) used MLR model to predict the pollution load in the Jakara-Getsi river system. Chenini and Khemiri (2009) also used the MLR model to investigate the relation between parameters using the hydro-chemical data to quantify the composition of groundwater samples in Maknassy Basin, central Tunisia. Chen and Liu (2015) developed a model using MLR to simulate the water quality of reservoir. Arora and Keshari (2016) developed a re-aeration model using MLR and established predictive equation. Water quality index was designed by Nasir et al. (2011) to predict the water quality of Klang River, Malaysia using MLR model. Kumar and Padhy (2014), have compared the various multivariate tools and their application on classification, monitoring and assessment of surface water quality parameters. All these studies indicate that, MLR model can be used as a suitable tool for water quality modelling, yet the design of adequate formulation for assessment of the re-aeration coefficient remains a problem.

Therefore, present study was carried out with the objective to develop set of models using MLR to estimate the re-aeration coefficient (K₂) that could be applicable to a wide range of study areas and identification of best fit model on the basis of their applicability and performance analysis using RMSE, R² and R. The model obtained can be coupled with the water quality model to design the pollution control strategies for the urban water management.