# With such a water constraint

Taking into account groundwater sustainability policies

The TF–EP framework envisions the optimal pathway to balance the trade-offs between hydroelectric generation and groundwater abstraction, which in reality is over-optimistic and may not be achievable owing to a set of physical, political and economic constraints. One possible constraint comes from regulation policies, which could act as a barrier to achieving the social optimum, such as the recently passed Sustainable Groundwater Management Act (SGMA) in California. Such quantity-oriented regulations set the limit for groundwater abstraction ($${g}_{{{{w}}}}$$) (see the schematic illustration in Fig. 2a), under which the optimal point can only fall into the hatched area. For years with relatively low surface water availability, this groundwater cap ($${g}_{{{{w}}}}^{{\rm{Cap}}}$$) reduces efficiency even with high penetration of SWE, as the optimal condition is not attainable (that is, the optimal point $${O}_{{{{C}}}}/{O}_{{{{F}}}}$$ moves to $$A$$). As water availability further increases, imposing limitations via regulations may not influence the optimal point under future penetration of SWE (as $${O}_{{{{F}}}}^{^{\prime} }$$ is still in the hatched area), whereas under current penetration the optimal point is shifted from $${O}_{{{{C}}}}^{^{\prime} }$$ to $$A^{\prime}$$. Limiting groundwater use in turn increases the risk of crop failure and therefore reduces the crop revenue. To quantify this, we define the relative revenue loss ($$\delta$$) as: $$\delta =1-\frac{R({g}_{{{{w}}}}\le {g}_{{{{w}}}}^{{\rm{Cap}}})}{R({g}_{{{{w}}}}\le \infty )}$$, which has a range from 0 to 1, with 0 indicating zero revenue loss and the optimal point still achievable. Intuitively according to Fig. 2a, this implies that control on groundwater abstraction is not stringent enough to move the optimal point out of the hatched area, which means regulation policies do not exert any impacts on the optimal water allocation and therefore the total revenue is not influenced. As $$\delta$$ increases, we face higher revenue loss either because we have a stricter groundwater cap, or there is lower surface water availability. With fixed surface water availability (Fig. 2b), $$\delta$$ monotonically decreases as $${g}_{{{{w}}}}^{{\rm{Cap}}}$$ increases for both current penetration ($${P}_{{{{C}}}}^{1}\to {P}_{{{{C}}}}^{2}$$) and future penetration ($${P}_{{{{F}}}}^{1}\to {P}_{{{{F}}}}^{2}$$). In other words, as we loosen the limit on groundwater use, the relative loss will be reduced. This further implies that groundwater sustainability is put at risk for economic revenue.

Fig. 2

Impact of regulation policy on groundwater–hydropower trade-offs. a Schematic illustration of how groundwater abstraction cap ($${g}_{{{{w}}}}^{{\rm{Cap}}}$$) shifts the trade-offs optimal point. $${O}_{{{{C}}}}/{O}_{{{{C}}}}^{^{\prime} }$$ and $${O}_{{{{F}}}}/{O}_{{{{F}}}}^{^{\prime} }$$ represent the optimal point given current (17%) and future (40%) penetration of SWE in the normal/wet year without $${g}_{{{{w}}}}^{{\rm{Cap}}}$$. The vertical dashed line sets the limit of groundwater abstraction to meet certain regulations. With such a water constraint, the optimal point can only fall into the hatched area. When surface water is not abundant (e.g., during a normal year), the optimal point $${O}_{{{{C}}}}/{O}_{{{{F}}}}$$ will not be attainable, and therefore $$A$$ becomes the new optimal under the regulation.

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