Managing pollutant dynamics in a lake of varying size: a case study of Warragamba dam, Sydney, Australia

Abstract

Non-convex pollution problems characterized by non-linearities and thresholds, or tipping points, are affecting many natural systems that are of significant value for human well-being such as rivers, lakes, estuaries, marine waters and underground aquifers. This thesis is interested in studying pollutant dynamics with non-convex characteristics in a natural system that is varying in size. Significant literature has dealt with the analysis of the pollutant stock dynamics in natural systems over the last two decades or so. This includes literature on shallow lakes, resilience, regime shifts, multiple stable states and threshold effects. One shortcoming of this important literature is that it threats the size of the affected natural systems as fixed across time. However, many natural systems, particularly in the lower latitudes of the Northern Hemisphere and throughout Southern Hemisphere are often experiencing significant changes in their sizes due to variations in environmental factors, e.g. rainfall. This variation in the size of the system significantly influences the pollutant dynamics, with important implications for the economic analysis of the pollution problem and its management. These effects on the pollutant dynamics attributable to the variation in the size of a system have not been previously analyzed explicitly in the economic literature. Furthermore, the management implications from explicitly considering the variation in size are currently unknown. The aim of this study is to understand better the relationship between the variation in size and pollutant dynamics in a natural system that has regular size variation across time. The problem that this thesis is dealing with can be described by the following three vi characteristics: 1) the evolution of pollutant stock in the system across time is affected by changes in system’s size; 2) the stock of pollutant in the system is affected by variation in the inflows of pollutant over time (seasonal variation); 3) pollutant stock dynamics in the system is fundamentally driven by external inflow and internal movement of the pollutant stock within various pools in the system.