# 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:

${\displaystyle S_{a}={\frac {\sum (S_{c,y})}{n_{a}}}}$

${\displaystyle \Delta {d_{a,y}}=-S_{a}\cdot i_{a}}$

where:

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

#### Notes

• Manage water areas can overlap terrain with and without occurring subsidence. The average subsidence is thereby calculated for non-water terrains with and without occurring subsidence. The resulting average subsidence can therefore be (much) less than the section of the manage water area that actually suffered from subsidence.
• In real-life situations with more complex datasets, it may be difficult to manually calculate the proper amounts of indexation in a way that matches the Tygron Platform. This can be due to subtleties such as the fact that the subsidence used for this calculation is the average subsidence for the water area on land (not on water), variations in the subsidence and ground water levels, and variations in terrain height.