Power Law Growth and Delayed Feedbacks in Socio‐Hydrological Systems

Abstract

Water infrastructure dynamics result from coupled social and physical hydrological processes embedded in “socio‐hydrological systems” (SHSs). Freshwater fuels socioeconomic activity, which in turn exerts pressure on water resources through increased water demand and water quality degradation. Many factors emphasize the need for quantitative tools to predict the future of these systems, including SHS failures due to growing water scarcity from population growth and climate change. However, unfolding the interactions between social and hydrological factors continues to resist theoretical treatment, impeding progress toward a predictive framework. To resolve this issue, we propose and evaluate time delays as surrogates for the social dynamics in SHS models. This approach permits the development of models that describe SHS dynamics in terms of observable, physical, hydrological state variables. We apply this approach to two case studies: (a) reservoir storage capacity growth in the world and the U.S. Water Resources Regions and (b) global water withdrawals. Substantial variability was identified in empirical estimates of growth rates and time delays. Reservoir construction typically follows a saturating, logistic curve with periodic, punctuated equilibria, separated by delays ranging from 5 to 20 years both globally and regionally. In contrast, global water withdrawal data display faster‐than‐exponential growth, characteristic of a positive feedback through which water use drives further water development. Historical analysis suggests that growth trends in water resources systems are superimposed by recurring periods of innovation and inactivity which are indicative of slow memory dissipation and delayed effects of past water use on current water infrastructure decisions.