Catastrophic Regime Shift in Water Reservoirs and S\~ao Paulo Water Supply Crisis

TL;DR

This paper demonstrates that water reservoirs can exhibit bistability with high and low water levels due to nonlinear feedbacks, and that the São Paulo water crisis was likely a regime shift, emphasizing the need for reservoir management to consider these dynamics.

Contribution

It introduces a mathematical and stochastic modeling framework revealing the existence of alternative stable states in reservoirs, supported by empirical data analysis from São Paulo.

Findings

Detected strong signals of a regime shift in São Paulo's reservoir data.

Developed a mechanistic model explaining bistability in reservoir water levels.

Built a stochastic model that fits observed reservoir data well.

Abstract

The relation between rainfall and water accumulated in reservoirs comprises nonlinear feedbacks. Here we show that they may generate alternative equilibrium regimes, one of high water-volume, the other of low water-volume. Reservoirs can be seen as socio-environmental systems at risk of regime shifts, characteristic of tipping point transitions. We analyze data from stored water, rainfall, and water inflow and outflow in the main reservoir serving the metropolitan area of S\~ao Paulo, Brazil, by means of indicators of critical regime shifts, and find a strong signal of a transition. We furthermore build a mathematical model that gives a mechanistic view of the dynamics and demonstrates that alternative stable states are an expected property of water reservoirs. We also build a stochastic version of this model that fits well to the data. These results highlight the broader aspect that reservoir management must account for their intrinsic bistability, and should benefit from dynamical systems theory. Our case study illustrates the catastrophic consequences of failing to do so.