Subsidence calculation

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This article is a stub.

Overlays

The following overlays are part of the Subsidence Collection:

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 = GLG * a - clay thickness * b - c
  • The GLG is 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 dikes.
  • 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

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 by only about 60% of the surface water level. 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 1.2 -0.1
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.

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.

Configuring overlays

The overlays part of the Subsidence collection of overlays all have a number of ways to configure them. Both values which serve as input for the overlays directly, as references to attributes of areas which provide input for the calculations.

Keys

Each overlay part of the Subsidence collection 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 The Ground Water Level, measured in meters from the surface of the terrain. 0.5
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. Both are measured in meters. 0.2 When absent, the attribute DEFAULT_CLAY_THICKNESS of the overlay is used.
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 keys can be configured.

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. This key is linked to one of the attributes of the overlay. Changing this value 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. By default, a few GeoTiffs are available with open data concerning ground water levels.

Attributes

Each overlay part of the Subsidence collection 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. 0,67 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
HI_PASSIVE_DRAINAGE When passive drainage is applied, the GHG (highest ground water level) is increased by this amount. -0.1 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. 0 This attribute is linked to one of the keys of the overlay. When this attribute is changed the key is changed as well.
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