# Optimal and Sustainable Groundwater Extraction

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Groundwater as a Renewable Resource

_{min}characterizes the minimum stock level, below which saltwater intrusion occurs. The constraint is analogous to a stock/concentration/pollution threshold in other resource management problems.

## 3. Sustainable Yield as a Management Strategy Is at Best Incomplete

_{min}and MSY is a suitable target, we still have the open question of how to get there, i.e., how to transition from an initial stock level to X

_{min}. Figure 2 illustrates a few of the infinitely possible extraction paths that can ultimately lead to the MSY steady state. Starting from an initial stock level X

_{0}, extraction (x) can approach from above or below MSY, or be maintained at MSY indefinitely.

## 4. Optimal Extraction Is Sustainable, but “MSY Always” Is Not Optimal

_{min}[15]. If so, optimal extraction is sustainable in the long run, and moreover, the optimal steady state rate of extraction coincides with MSY. The optimal path of extraction is characterized by MSY in no more than a single period prior to arrival at the steady state, however. For rapidly increasing extraction cost, or more formally if the extraction cost function is very convex, the steady state stock is likely to be above the MSY stock level [8]. Intuitively, the potential gains from extracting MSY at the steady state are more than offset by higher extraction costs sustained into the future.

_{0}before declining to the steady state equilibrium level X

^{eq}at year T. Extracting MSY from the outset would result in the stock declining monotonically. Even when the optimal steady state rate of extraction q

^{eq}coincides with MSY, MSY is on the optimal extraction path (q*) for only a single instant of time prior to the steady state. Before that period, MSY is too high, and afterward MSY is too low (Figure 3b).

**Figure 3.**(a) Optimal stock can approach the steady state non-monotonically. (b) Optimal extraction is not constant over time.

## 5. Managing Multiple Aquifers

^{s}denotes the period after which extraction optimally becomes positive for both aquifers.

**Figure 4.**(a) Inefficiency increases if optimality calls for zero extraction for a period of time. (b) Extracting MSY from the second aquifer is still inefficient.

## 6. Sustaining the Watershed

## 7. Optimal Wastewater Recycling

## 8. Conclusions

## Acknowledgements

## References and Notes

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Roumasset, J.A.; Wada, C.A.
Optimal and Sustainable Groundwater Extraction. *Sustainability* **2010**, *2*, 2676-2685.
https://doi.org/10.3390/su2082676

**AMA Style**

Roumasset JA, Wada CA.
Optimal and Sustainable Groundwater Extraction. *Sustainability*. 2010; 2(8):2676-2685.
https://doi.org/10.3390/su2082676

**Chicago/Turabian Style**

Roumasset, James A., and Christopher A. Wada.
2010. "Optimal and Sustainable Groundwater Extraction" *Sustainability* 2, no. 8: 2676-2685.
https://doi.org/10.3390/su2082676