Power-law Growth and Punctuated Equilibrium Dynamics in Water Resources Systems

Abstract:

The global rise in population-driven water scarcity and recent appreciation of strong dynamic coupling between human and natural systems has called for new approaches to predict the future sustainability of regional and global water resources systems. The dynamics of coupled human-water systems are driven by a complex set of social, environmental, and technological factors. Present projections of water resources systems range from a finite carrying capacity regulated by accessible freshwater, or `peak renewable water,’ to punctuated evolution with new supplied and improved efficiency gained from technological and social innovation. However, these projections have yet to be quantified from observations or in a comprehensive theoretical framework. Using data on global water withdrawals and storage capacity of regional water supply systems, non-trivial dynamics are identified in water resources systems development over time, including power-law growth and punctuated equilibria. Two models are introduced to explain this behavior: (1) a delay differential equation and (2) a power-law with log-periodic oscillations, both of which rely on past conditions (or system memory) to describe the present rate of growth in the system. In addition, extension of the first model demonstrates how system delays and punctuated equilibria can emerge from coupling between human population growth and associated resource demands. Lastly, anecdotal evidence is used to demonstrate the likelihood of power-law growth in global water use from the agricultural revolution 3000 BC to the present. In a practical sense, the presence of these patterns in models with delayed oscillations suggests that current decision-making related to water resources development results from the historical accumulation of resource use decisions, technological and social changes, and their consequences.