# Subsidence calculation

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The subsidence calculations are a number of semi-independant calculations which have effects on one another. Subsidence is, among other things, based on a ground water level, which is based on the surface water level, which in turn is influenced by the progression of subsidence. For this reason, for insight into why a certain result is given after the calculations are completed, insight into each formula and their interactivity is required.

The total subsidence is currently calculated as the result of oxidation and compaction over the years. The ground water level is calculated from water level defined by data, and adjusted based on the adjustment of the surface water level in related to the surface of the land over the years.

The calculation model is implemented in the subsidence overlay. The model for each overlay will be identical, but their parameters vary. Each can be configured differently, so multiple scenario's can be simulated in parallel.

## Calculations

During a calculation step, the following aspects are calculated in order:

• The temperature at the start of the year is calculated
• Based on that, the "a" parameter of the oxidation formula is calculated
• The oxidation subsidence is calculated
• The compaction subsidence is calculated
• The water level is lowered by the amount of subsidence times the indexation
• The ground water level is lowered based on the change in water level compared to the surface of the terrain
• The new ground water level serves as input for the next calculation step

### Oxidation calculation

The amount of subsidence due to oxidation is calculated by the following formula:

`Subsidence = ground water level * a - clay thickness * b - c`
• The ground water level (expressed in meters below surface), most commonly the lowest ground water level. This value is recalculated as part of the calculations over multiple years. (This value is capped as 1.2m. If the ground water level is further from the surface than 1.2m, 1.2m is used.)
• The clay thickness is an attribute in the project. The exact attribute which provide this value can be configured as keys in the overlay.
• The a, b and c parameters are climate values which can be configured as attributes in the overlay. the a value is also recalculated as part of the calculations over multiple years.

This formula was provided by experts, who have established this formula empirically.

### Compaction calculation

The amount of subsidence due to compaction is calculated by the following formula:

```Subsidence = (Peat fraction * PEAT_A + Top layer * TOP_LAYER_A) * log10(days)
+ Peat fraction * PEAT_B
+ Top Layer * TOP_LAYER_B
+ Height Increase * HEIGHT```
• The peat fraction and thickness of the top layer are attributes in the project. The exact attributes which provide these can be configured as keys in the overlay.
• The height increase is a result of the actions taken during a session, such as the creation of levees.
• The days are equal to the number of days in a year, times the current year being calculated.
• PEAT_A (0.015853041) is a constant, for the effect of the peat fraction over time.
• PEAT_B (0.02348519) is a constant, for the base effect of the peat fraction.
• TOP_LAYER_A (0.006617643) is a constant, for the effect of the top layer thickness over time.
• TOP_LAYER_B (-0.010061616) is a constant, for the base effect of the top layer thickness.
• HEIGHT (0.200468677) is a constant, for the base effect of the height of added materials.

This formula is based on provided expert data in the form of a reference table, indicating the amount of subsidence based on the parameters used in the formula above. The formula's results conform to the reference table to within an average of a tenth of the margin of error of the original table.

### Ground Water change calculation The effect of changes on surface water level on the ground water level. The x-axis indicates the distance between the land surface and the surface water level. The y-axis indicates the meters of change to the ground water level, per meter change in surface water level.

During a session, the surface water level can change. This affects the ground water level. The change in surface water level affecting the ground water level is the difference between the CURRENT and MAQUETTE values of the WATER_LEVEL attribute of areas.

When the distance between the surface water level and the surface of the land changes, the ground water level changes proportionally. However, as the surface water comes closer to the surface, the ground water level changes less than the surface water level. Specifically: if the distance between the surface of the land and the surface water level is greater than 1 meter, the ground water level is moved exactly as much as the surface water level. If the distance between the surface of the land and the surface water level is less than 0.6 meters, the ground water level changes by only 60% of the change in surface water level. Between 0.6 and 1 meter, the change in ground water level is interpolated accordingly.

For example:

Surface land height Water level height (start) Water level height (changed) Change in distance between ground water level and surface
2.4 1.1 1.3 -0.2
2.4 2.1 2.3 -0.12
2.4 1.4 1.6 -0.18

This method of ground water level adjustment is applied when, during a session, the surface water level changes. This can be due to user input (i.e.: the user changes the water level attribute of an area), or because indexation (or lack thereof) moves the surface water level (and thus the ground water level) relative to the surface.

#### Notes about ground water level

Different ground water levels can be relevant for different use-cases. For subsidence, the lowest ground water level (Mean Lowest Watertable, or MLW, in English. GLG in Dutch.) is most commonly used. An overlay is also included for the highest water level. (Mean Highest Watertable, or MHW, in English. GHG in Dutch.)

### Indexation

Indexation is the policy of keeping the surface water level at the same distance from the surface of the land. A water level area which is fully indexed (100%) will have its surface water level lowered by the same amount as the surface of the land has lowered due to subsidence. Because it lowers just as much as the land 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 distance between the surface of the land and the surface water level. This will also cause a change in the ground water level relative to the surface of the land. The exact amount is dictated by the ground water level calculation. An area indexed by 50% will have the surface water level lower by half of the amount of subsidence.

Note that 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 level area on land (not on water), variations in the subsidence and ground water levels, and variations in terrain height.

### Drainage calculation

Drainage can be added to the 3D World as a construction, which affects the ground water levels. Two types of drainage exist: passive and active drainage.

#### Passive Drainage

When passive drainage is applied, the lowest and highest ground water levels are adjusted to match the surface water level, plus their respective PASSIVE_DRAINAGE attributes. This effect is applied once, at the start of the subsidence calculations. Afterwards, the values of the ground water level can vary due to indexation.

#### Active Drainage

When active drainage is applied, the ground water levels are set to a specific level relative to the surface. The exact distance between the ground water level and the surface is defined by the "drainage" Function Value of the construction placed. This effect is continuous; at the end of the calculation and for all intermediate steps the ground water level will still be at that same level.

### Land surface

The height of the land can be manipulated during a session by stakeholders taking a land sculpting action, building open water, or levees. Creating or demolishing constructions does not change the height of the land, and does not affect the subsidence calculations. (At most indirectly due to drainage.)

## Configuring overlays

The subsidence overlay has a number of ways to configure it. Both values which serve as input for the overlays directly, as references to attributes of areas which provide input for the calculations.

### Keys

The subsidence overlay has a "Keys" tab in the right panel in the editor. Most keys are attributes of areas. When the overlay calculates, it will look per grid cell for the existence of these attributes.

Attribute Default Description Example Remark
Water level WATER_LEVEL The surface water level, measured in meters from Amsterdam Ordnance Datum (NAP). -2.90 When absent, "0" is assumed.
Output Level WATER_LEVEL_OUTPUT The attribute to write the final water level value to. -3.20 If the water level is indexed, subsidence will cause the water level to lower. By writing it into an attribute, the end value can be used. This option can be disabled by unchecking the related checkbox. This value is measured in meters from Amsterdam Ordnance Datum (NAP).
Ground Water Level (GLG) GROUND_WATER_LEVEL The Ground Water Level, measured in meters from the surface of the terrain. 0.5 This value is overruled when a GeoTiff is loaded in. Regardless of whether a geojson or GeoTiff is used, this should be a non-negative value. Negative values would represent water on the surface of the land, and may lead to unpredictable behavior.
Indexation INDEXATION The amount of indexation the water is subject to, from 0 (0%) to 1 (100%) 1 The surface water level is lowered each year by an amount equal to the subsidence times the indexation. From the perspective of the surface of the terrain, the water level in a location with 0% indexation will appear to increase as subsidence takes place.
Clay Thickness CLAY_THICKNESS The thickness of the clay layer on the peat, for the calculation of the oxidation component of subsidence. 0.2 When absent, the attribute DEFAULT_CLAY_THICKNESS of the overlay is used. Both are measured in meters.
Toplayer Thickness TOPLAYER_THICKNESS The thickness of the layer covering the peat, for the calculation of the compaction component of subsidence. 5 When absent, the attribute DEFAULT_TOP_LAYER_THICKNESS of the overlay is used. Both are measured in meters.
Peat Fraction PEAT_FRACTION The fraction of the soil composed of peat, for the calculation of the compaction component of subsidence. 0.4 When absent, the attribute DEFAULT_PEAT_FRACTION of the overlay is used. Valid fraction range is 0.0 to 1.0.
Subsidence SUBSIDENCE Whether or not subsidence should be calculated in a given area. Subsidence is calculated when the value is greater than 0. 1 When absent, "1" is assumed (and thus subsidence is calculated). This attribute is only useful when you want to limit the amount of areas for which subsidence will be calculated.

Besides these attributes, 2 more model parameters can be configured.

Years
The amount of years to simulate during the calculation, in 1-year steps. It is possible to set this value anywhere between 1 to 1000. This parameter is linked to the YEARS attribute of the Subsidence overlay. Changing the value of this parameter changes the attribute as well.

Ground Water Tiff
If the option to use a Ground Water Tiff is checked, a GeoTiff can be selected to use for the ground water levels. You can either use any of the provided default GeoTiffs, or upload and use your own.

Three ground water GeoTiffs covering the Netherlands are available by default. These GeoTiffs are a combination between a high resolution GeoTiff containing ground water levels for rural areas and a low resultion GeoTiff containing ground water levels for city areas, where data from the low resolution GeoTiff was only used to fill the gaps in the high resolution GeoTiff. One of the available ground water GeoTiffs, relevant for the Subsidence, is the Mean Lowest Watertable (MLW, or GLG in Dutch).

### Attributes

The subsidence overlay also has attributes. All attributes have a default value, but can be changed to configure the subsidence calculation.

Attribute Description Default value Remark
A The A parameter in the Oxidation formula. 0,023537 This value is recalculated between 1-year time steps of the calculation.
B The B parameter in the Oxidation formula. 0,01263
C The C parameter in the Oxidation formula. 0,00668
CLIMATE_FINAL_TEMP The final temperature in the final year of the total simulation time. 10,7 This is the temperature at the end of the year. The last 1-year calculation step uses the temperature from the beginning of that year.
CLIMATE_OXIDATION The oxidation factor used to recalculate the climate values between 1-year calculation steps. 0,67
CLIMATE_SOIL_TEMP_FACTOR The soil temperature factor used to recalculate the climate values between 1-year calculation steps. 0,5
DEFAULT_CLAY_THICKNESS If no clay thickness value can be found in a particular grid cell, this value is used instead. 0,2
DEFAULT_PEAT_FRACTION If no peat fraction value can be found in a particular grid cell, this value is used instead. 0,4
DEFAULT_TOP_LAYER_THICKNESS If no top layer value can be found in a particular grid cell, this value is used instead. 5,0
HI_PASSIVE_DRAINAGE When passive drainage is applied, the GHG (highest ground water level) is increased by this amount. -0,10 Due to definitions "Increase" means that the distance between the surface and this ground water level increases. The default value causes the ground water level to come closer to the surface.
LOW_PASSIVE_DRAINAGE When passive drainage is applied, the GLG (lowest ground water level) is increased by this amount. 0 Due to definitions "Increase" means that the distance between the surface and this ground water level increases. The default value does not affect the ground water level.
YEARS The amount of years to simulate during the calculation, in 1-year steps. It's possible to set this value anywhere between 1 to 1000. 30 This attribute is linked to one of the keys of the overlay. When this attribute is changed the key is changed as well.