Lotka-Volterra analysis of river Ganga pollution in India

Abstract

Water quality indices (WQI) are a useful tool to assess river water pollution. We defined pollution shares (indicating the relative importance of pollutants) from a WQI and studied their dynamics. Using open data from 2012 to 2020 for 105 monitoring stations along river Ganga in India, we fitted systems of generalized Lotka-Volterra (LV) differential equations to these shares. We used autonomous LV-systems (the interaction coefficients were constant) and LV-systems with variable (linear) interaction coefficients. 28 of the 105 stations had sufficient data for these models, whereby for 10 stations the autonomous system fitted well to all timeseries of the eight considered pollutants, and for 9 stations the model with linear interaction coefficients. For them we defined three candidates for “importance-growth indicators”: (a) the interaction coefficients of the autonomous LV-system, (b) the leading coefficient of the interaction coefficient of the system with linear coefficients, and (c) the roots of these linear coefficients. We explored the variability of the indicators and applied them to identify stations with a similar temporal evolution of the pollutants. Further, we suggested applications to wastewater management, as at several stations the indicators (a) and (b) forecasted an increasing relative importance of nitrates/nitrites, which currently pose no problems but finally may require an upgrading of existing wastewater treatment.

Keywords

• Differential equation model
• Ganges River
• Statistical correlation
• Water pollution
• Water quality index