Performance of Water Extraction in an Endangered Aquifer when Management Is Not All-Powerful: A Theoretical Framework Based on a Viability Theory

We address the performance of an aquifer system where water is extracted at a given baseline pumping rate under the following conditions: 1) catastrophic events such as saltwater intrusion or pollution can interrupt water extraction, 2) recharge is a stochastic process, and 3) the possibility of management to reduce the pumping rate if necessary is limited. We argue that the mathematical framework of stochastic viability theory is relevant for addressing this problem and for complementing the usual performance indicators of reliability, resiliency, and vulnerability (R-R-V), which alone are not adapted to describe situations where the baseline pumping rate cannot be restored. Indeed, viability theory allows for the derivation of the stochastic viability kernel, defined as the set of all the values of the aquifer storage for which the baseline pumping rate can be applied while ensuring continued water extraction with a high probability in a large time horizon. For lower values of aquifer storage, pumping has to be reduced to avoid adverse events, so that the baseline pumping rate cannot be met. Viability theory allows for finding the management actions that minimize the risk of event occurrence. For a given baseline pumping rate and for given limits to management, one can then derive R-R-V indicators to describe the performance of the system. This viability framework provides insights into the connection between the choice of higher baseline extraction rates and a lower system performance. Besides, the values of these indicators increase when management can reduce pumping rates more quickly, thus showing the importance of empowering management instances, both to avoid catastrophes and to have an effective extraction policy. The applicability of the framework to conditions of extreme droughts is also discussed.