Optimal groundwater extraction under uncertainty: Resilience versus economic payoffs Pamela Katic a , R. Quentin Grafton b,⇑ a International Water Management Institute (IWMI), PMB CT 112, Cantonments, Accra, Ghana b Crawford School of Economics & Government, Crawford Building (132), Lennox Crossing, The Australian National University, Acton, ACT 0200, Australia article info Article history: Received 22 January 2011 Received in revised form 12 May 2011 Accepted 25 June 2011 Available online 7 July 2011 This manuscript was handled by Geoff Syme, Editor-in-Chief, with the assistance of Ratna Reddy, Associate Editor Keywords: Groundwater Resilience Uncertainty Irreversible thresholds summary This paper evaluates the trade-off between resilience and economic payoffs in terms of groundwater extraction where there is a risk of an irreversible and catastrophic event. A dynamic and spatial model is developed that incorporates a stochastic recharge process and the risk of an irreversible catastrophic event (such as saltwater intrusion) that arises when hydraulic heads fall below a given threshold. The results show that if the threshold is uncertain then controlling both the rate and depth of extraction can generate a higher economic return and a lower probability of crossing the threshold than only con- trolling the rate of extraction. This occurs even if the extraction rate is set optimally and is less than the extraction rate than when two forms of control are used. The model and findings provide an applied framework to understand and to quantify where there might be ‘win–win’ outcomes, and trade-offs between economic payoffs and resilience in terms of groundwater extraction. Ó 2011 Elsevier B.V. All rights reserved. 1. Introduction Groundwater extraction is typically undertaken with multiple uncertainties including the size, shape and recharge rate of the aquifer. In addition, there may be uncertain and irreversible thresholds that, once crossed, change the net benefits of extraction, such as saltwater intrusion in freshwater aquifers. If such a thresh- old is breached the economic-hydrological system and the net ben- efits of extraction irreversibly shift to a different state of the world. This can be represented as a problem of resilience, which we define as the time the hydrological system persists until it crosses an undesirable and irreversible threshold, as represented by saltwater intrusion. We examine this challenge by developing a modeling framework to quantify resilience and to determine how alternative groundwater management instruments affect economic payoffs and resilience. There is a large literature on reversible, uncertain events or thresholds (Brock and Starrett, 2003; Carpenter et al., 1999; Lud- wig et al., 2003; Maler et al., 2003; Peterson et al., 2003; Tsur and Zemel, 1998, 2004), but there is only a very limited literature that accounts for irreversible and uncertain events (Clarke and Reed, 1994; Keller et al., 2004; Naevdal, 2001, 2006; Tsur and Ze- mel, 1996, 2004). As far as we are aware, and until now, there has been no study that models optimal groundwater extraction in the presence of uncertain, irreversible events from the perspec- tive of instrument or policy choice while also comparing the resil- ience-economic benefits trade-off of different management approaches. The economic theory of instrument choice for optimal environ- mental management has typically focused on the use of one instru- ment or compared two or more instruments. This literature is based on the assumption that a policymaker with more instru- ments than targets is free to discard the excess instruments, and it makes no difference which ones are discarded (Tinbergen, 1952). The validity of this result is questioned in practice by the frequent use of multiple policy instruments over a broad range of environmental and resource issues. For instance, multiple instru- ments are often used to manage many aquifers under the threat of saltwater intrusion–extraction controls, well depth limits, well locations, freshwater reinjection, electricity quotas (Custodio, 2005; Ferreira da Silva and Haie, 2007; Spechler, 1994; Zekri, 2008). Our study enriches the current body of work on instrument choice (Pigou, 1920; Tinbergen, 1952) under uncertainty (Jacoby and Ellerman, 2004; Pizer, 2002; Weitzman, 1974, 1978) by explic- itly considering irreversibility (Pindyck, 1991) within a context of multiple instruments (Bennear and Stavins, 2007). First, we show that under uncertainty, with one target (eco- nomic benefits) and two possible instruments (rate and also depth of extraction); a combination of both instruments can be preferred to the use of a single, optimally determined instrument. This is be- cause additional instruments can increase both system resilience 0022-1694/$ - see front matter Ó 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.jhydrol.2011.06.016 ⇑ Corresponding author. Tel.: +61 2 6125 6558. E-mail address: quentin.grafton@anu.edu.au (R. Quentin Grafton). Journal of Hydrology 406 (2011) 215–224 Contents lists available at ScienceDirect Journal of Hydrology journal homepage: www.elsevier.com/locate/jhydrol