# Indexation formula (Subsidence Overlay)

Indexation is the policy of managing the surface water level such that it keeps the nearby ground water levels (more or less) at the same depth.

A water area which is fully indexed (1.0 = 100%) will have its surface water level lowered by the same amount as the terrain height has lowered due to subsidence. Since it lowers just as much as the terrain itself, the ground water level(s) relative to the surface of the land will remain the same.

In a water area which is not indexed (0%) the surface water level remains at the same level. Any subsidence taking place will lower the land, and thus reduce the relative water depth. An area indexed by 50% will have the surface water level lower by half of the amount of subsidence.

To make matters a bit more complex, the change in surface water level rarely changes the ground water level with the same amount. Instead, the amount the ground water level changes is estimated using the ground water depth formula for water areas.

The indexation formula is as followed:

$S_{a}={\frac {\sum (S_{c,y})}{n_{a}}}$ $\Delta {d_{a,y}}=-S_{a}\cdot i_{a}$ where:

$S_{a}$ is the average subsidence for water area a.
$S_{c,y}$ is the subsidence in grid cell c for year y.
$n_{a}$ is the number of non-water grid cells within water area a.
$\Delta {d_{a,y}}$ is the amount the water area is changed in meters.
$i_{a}$ is the indexation fraction for area a.