Indexation formula (Subsidence Overlay): Difference between revisions

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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.  
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 level 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.  
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 level 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.
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 (Subsidence Overlay)#Ground water level managed by water level areas|ground water depth formula]] for water level areas.
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 (Subsidence Overlay)#Ground water level managed by water areas|ground water depth formula]] for water areas.


The indexation formula is as followed:
The indexation formula is as followed:


<math>S_{wa} = \frac{\sum(S_{c,y})}{n_{a}}</math>
<math>S_{a} = \frac{\sum(S_{c,y})}{n_{a}}</math>


<math>\Delta{d_{a,y}} = -S_{wa} \cdot i_a</math>
<math>\Delta{d_{a,y}} = -S_{a} \cdot i_a</math>


where:
where:
: <math>S_{a}</math> is the average subsidence for water level area a.
: <math>S_{a}</math> is the average subsidence for water area a.
: <math>S_{c,y}</math> is the subsidence in grid cell c for year y.
: <math>S_{c,y}</math> is the subsidence in grid cell c for year y.
: <math>n_a</math> is the number of non-water grid cells within water level area a.
: <math>n_a</math> is the number of non-water grid cells within water area a.
: <math>\Delta{d_{a,y}}</math> is the amount the water level area is changed in meters.
: <math>\Delta{d_{a,y}}</math> is the amount the water area is changed in meters.
: <math>i_a</math> is the indexation fraction for area a.
: <math>i_a</math> is the [[Indexation (Subsidence Overlay)|indexation fraction]] for area a.<noinclude>


====Notes====
====Notes====
* Manage water level 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 level area that actually suffered from subsidence.
* 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 {{software}}. This can be due to subtleties such as the fact that the subsidence used for this calculation is the average subsidence for the water level area on land (not on water), variations in the subsidence and ground water levels, and variations in terrain height.
* 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 {{software}}. 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.


{{Template:SubsidenceOverlay_nav}}
{{Template:SubsidenceOverlay_nav}}
</noinclude>

Latest revision as of 07:13, 28 May 2021

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:

where:

is the average subsidence for water area a.
is the subsidence in grid cell c for year y.
is the number of non-water grid cells within water area a.
is the amount the water area is changed in meters.
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.
Subsidence Module
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Group
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Overview • Calculation • Theory
Formulas
Parameter a recalculation • Ground water depth • Oxidation • Compaction • Subsidence • Indexation
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