Although it seems impossible to measure how much water is stored in the deep soil, it is often possible to notice if it runs out. We had that last summer in the Netherlands. I suppose knowing we reached zero, and knowing the influx (mm rain, and the flow of the Rhine), and then also knowing the outflow means you can make a some sound estimate.
However, that requires a high density of weather stations and tooling at the influx and outputs.
It's not something you can just do through some regulation targeted at the water company. You'll need a specific branch of the government, since messing with water affects everyone, from erosion to trade, to agriculture to climate (the presence of water makes the climate a more mild climate)
In the Netherlands, this is all done by an independent water government, a democracy older than our democracy itself. It even predates notions of citizenship.