ORIGINAL CONTRIBUTION Modelling Dissolved Pollutants in Krishna River Using Adaptive Neuro Fuzzy Inference Systems C. S. Matli • N. V. Umamahesh Received: 13 June 2012 / Accepted: 26 March 2014 / Published online: 16 May 2014 Ó The Institution of Engineers (India) 2014 Abstract Water quality models are used to describe the discharge concentration relationships in the river. Number of models exists to simulate the pollutant loads in a river, of which some of them are based on simple cause effect relationships and others on highly sophisticated physical and mathematical approaches that require extensive data inputs. Fuzzy rule based modeling extensively used in other disciplines, is attempted in the present study for modeling water quality with respect of dissolved pollutants in Krishna river flowing in Southern part of India. Adaptive Neuro Fuzzy Inference Systems (ANFIS), a recent devel- opment in the area of neuro-computing, based on the concept of fuzzy sets is used to model highly non-linear relationships and are capable of adaptive learning. This paper presents the results of the application of ANFIS for modeling dissolved pollutants in the Krishna River. The application and validation of the models is carried out using water quality and flow data obtained from the mon- itoring stations on the river. The results indicate that the models are quite successful in simulating the physical processes of the relationships between discharge and concentrations. Keywords Non-point pollution  Indirect approaches  Water quality modeling  Pollutant loads  Fuzzy inference systems Introduction Discharge—concentration relationships generally are used for water quality studies in the river basins. Traditionally, this task has been accomplished using methods ranging from those that are based on empirical relationships to those that are based on cause-effect relationships. In using models that are based on cause-effect relationships, rigor- ous mathematical equations are often used to describe the physical, chemical and biological processes. Solutions of such models often require vast data and it is often neces- sary to estimate input parameters specific to the basin being modeled. In many instances (especially in large river basins), a large number of hydrological parameters are involved and there is no unique way of estimating them. However, they are to be determined subjectively, based on the judgment and the effect is normally manifested in the model output. Hence, these deterministic models, which require large quantity of data in terms of model parameters, have limited applicability in basins where there are data constraints. Therefore, models which are easy to handle and have minimum data requirement are often sought to solve problems where data availability is limited and is difficult to obtain data by experimental investigations and monitoring, which would be very expensive and cumbersome [14]. Recently mathematical models using fuzzy variables rather than numerical variables are encroaching into water quality related studies. In water quality modeling, there are many domains which can be best characterized by lin- guistic terms rather than directly, by numbers. For instance, a modeler in a particular domain will employ terms such as large flows and low flows to describe the discharge con- ditions in a river. The problem faced, then, is how to deal with what has been described—imprecision, uncertainty C. S. Matli (&)  N. V. Umamahesh Water & Environment Division, Department of Civil Engineering, National Institute of Technology, Warangal 506 004, India e-mail: 380mcs@gmail.com 123 J. Inst. Eng. India Ser. A (January–March 2014) 95(1):29–38 DOI 10.1007/s40030-014-0064-0