A drop of rainwater against a drop of groundwater: does rainwater harvesting really allow us to spare Groundwater?

This paper is concerned with groundwater management issues in the presence of rainwater harvesting (RWH). Namely, we propose a two-state model in order to take into account the standard dynamics of the aquifer and the dynamics of the storage capacity since the collected rainwater reduces the natural recharge. We analyze the trade-off between these two water harvesting techniques in an optimal control model. We notably show that, when these techniques are pure substitutes, the development of RWH conducts in the long run to a depletion of the water table even if pumping is reduced.