Subsidence calculation: Difference between revisions

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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 subsidence model calculates the gradual downward settling of the ground's surface where a peat layer is present. The considered subsidence takes place due to oxidation and compaction of the peat layer.  
The total subsidence is currently calculated as the result of oxidation and compaction over the years. Oxidation is dependent on the ground water level and the clay thickness. Compaction is dependent on the toplayer thickness, the peat fraction and raised surface terrain.  


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 ground water level is initialized by either raster or surface area data and optionally adjusted each year (indexation). When indexation is active, the surface water level is adjusted for the settling each year and the ground water levels will change accordingly.


The calculation model is implemented in the [[Subsidence (Overlay)|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.
The calculation model is configured by the subsidence overlay wizard and it's result are visualized with the [[Subsidence (Overlay)|subsidence overlay]].


==Calculations==
==Calculations==
During a calculation step, the following aspects are calculated in order:
During a calculation step, the following aspects are calculated in order:
* The temperature at the start of the year is calculated
* The temperature at the start of the year is calculated
* Based on that, the "a" parameter of the oxidation formula is calculated
* Based on that, [[#Yearly recalculation of Parameter A|parameter a]] of the oxidation formula is calculated
* The [[Subsidence (Overlay)#Oxidation|oxidation subsidence]] is calculated
* The [[#Oxidation calculation|oxidation subsidence]] is calculated
* The [[Subsidence (Overlay)#Compaction|compaction subsidence]] is calculated
* The [[#Compaction calculation|compaction subsidence]] is calculated
* The water level is lowered by the amount of subsidence times the indexation
* The surface water levels are lowered by the amount of subsidence times the [[#Indexation|indexation]]
* The ground water level is lowered based on the change in water level compared to the surface of the terrain
* The [[#Ground water depth|ground water level]] is lowered based on subsidence and surface water level indexation
* The new ground water level serves as input for the next calculation step
* The new ground water level serves as input for the next calculation step


===Oxidation calculation===
===Yearly recalculation of Parameter A===
The amount of subsidence due to oxidation is calculated by the following formula:
{{:Parameter a recalculation formula (Subsidence Overlay)}}
{{code|1= 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.)
===Ground water depth===
* The clay thickness is an attribute in the project. The exact attribute which provide this value can be configured as {{inlink|Keys}} in the overlay.
{{:Ground water depth formula (Subsidence Overlay)}}
* The a, b and c parameters are climate values which can be configured as {{inlink|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.
===Oxidation calculation===
 
{{:Oxidation formula (Subsidence Overlay)}}
====Yearly recalculation of parameter a====
The a parameter is recalculated yearly, to account for the progression of changes in climate. it is recalculated based on a temperature factor for that year, which is defined by a fixed starting temperature and a parameter for an end temperature.
 
Calculations start in the year 1990. From 1990 onwards, rises in temperature and changes in the a parameter will occur. Subsidence will only be tracked beginning in the indicated starting year, and complete in the indicated amount of years after that starting year.
 
The temperature for any given year is calculated as follows:
 
<math>t_{y} = (t_{end}-t_{1990})*\frac{y_{y}-1990}{y_{end}-1990}+t_{1990} </math>
 
* <math>t_{y}</math> = The temperature for the calculation in the current year.
* <math>t_{end}</math> = The defined temperature of the final year.
* <math>t_{1990}</math> = The temperature in 1990, defined as 10.1{{celsius}}.
* <math>y_{y}</math> = The current year.
* <math>y_{end}</math> = The defined final year.
 
The value of the a parameter for any given year is then calculated as follows:
 
<math>a_{y} = (((Q_{10}^{(t_{y}-t_{1990})*\frac{f_{st}}{10}}-1)*f_{ox})+1)*a_{0}</math>
 
* <math>a_{y}</math> = The a parameter for the current year.
* <math>Q_{10}</math> = The Q10 factor.
* <math>t_{y}</math> = The temperature for the calculation in the current year.
* <math>t_{1990}</math> = The temperature in 1990, defined as 10.1{{celsius}}.
* <math>f_{st}</math> = Soil temperature factor, defined by {{inlink|CLIMATE_SOIL_TEMP_FACTOR}}.
* <math>f_{ox}</math> = Fraction of oxidation, defined by {{inlink|CLIMATE_OXIDATION}}.
* <math>a_{0}</math> = The defined a parameter to start the calculation with.


===Compaction calculation===
===Compaction calculation===
The amount of subsidence due to compaction is calculated by the following formula:
{{:Compaction formula (Subsidence Overlay)}}
{{code|1= 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|keys]] in the overlay.
* The height increase is a result of the actions taken during a [[session]], such as the creation of [[levee]]s.
* 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===
[[File:ground-water-graph.jpg|300px|thumb|right|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 [[Map_Type|CURRENT and MAQUETTE]] values of the [[#Keys|WATER_LEVEL]] attribute of [[area]]s.
 
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:


{| class="wikitable"
===Subsidence calculation===
! Surface land height
{{:Subsidence formula (Subsidence Overlay)}}
! 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.)
 
See also (PDF): [[Media:Wind (1986) Slootpeilverlaging en grondwaterstandsdaling in veenweidegebieden.pdf|Wind (1986) Slootpeilverlaging en grondwaterstandsdaling in veenweidegebieden (Ditch water level reduction and groundwater level decrease in peat meadow areas - Dutch only)]]


===Indexation===
===Indexation===
Indexation is the policy of managing the surface water level such that it remains 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_change_calculation|ground water level calculation]]. An area indexed by 50% will have the surface water level lower by half of the amount of subsidence.
{{:Indexation formula (Subsidence Overlay)}}


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 {{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.
===Terrain height===
 
The height of the terrain can be manipulated during a session by stakeholders taking a land sculpting [[action]], creating [[open water]], or building [[levee]]s. These actions will result in settlement, which can be found under the Settlement result type. Creating or demolishing [[building]]s generally do not change the height of the land, and do not result in changes in the settlement results.
===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|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 Values|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]], creating [[open water]], or constructing [[levee]]s. These actions will result in settlement, which can be found under the Settlement result type. Creating or demolishing [[construction]]s generally do not change the height of the land, and do not result in changes in the settlement results.


==Configuring overlays==
==Configuring overlays==
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The subsidence overlay has a "Keys" tab in the [[right panel]] in the editor. Most keys are [[attribute]]s of [[area]]s. When the overlay calculates, it will look per [[Grid overlay|grid cell]] for the existence of these attributes.
The subsidence overlay has a "Keys" tab in the [[right panel]] in the editor. Most keys are [[attribute]]s of [[area]]s. When the overlay calculates, it will look per [[Grid overlay|grid cell]] for the existence of these attributes.


{| class="wikitable"
{{Overlay keys|suppresscategory=true|
! Attribute
{{:Water level (Subsidence Overlay)}}
! Default
{{:Water level output (Subsidence Overlay)}}
! Description
{{:Indexation (Subsidence Overlay)}}
! Example
{{:Subsidence (Subsidence Overlay)}}
! Remark
{{:Clay thickness (Subsidence Overlay)}}
|-
{{:Peat fraction (Subsidence Overlay)}}
| Water level
{{:Toplayer thickness (Subsidence Overlay)}}
| WATER_LEVEL
{{:Drainage (Subsidence Overlay)}}
| 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.
| 1.2 m
| 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
| By default the terrain's subsidence value is used. However, this subsidence value can be overridden by an overlapping Area which also contains this attribute.
|-
|}
Besides these attributes, 2 more model parameters can be configured.
Besides these attributes, 2 more model parameters can be configured.


{{anchor|Years}}
{{anchor|Years}}
'''Years'''<br>
'''Years'''<br>
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.
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 can be configured with the [[Years (Subsidence Overlay)|YEARS]] model attribute of the Subsidence overlay.


'''Ground Water Tiff'''<br>
'''Ground Water Tiff'''<br>
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. <br>
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. <br>


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.
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).
One of the available ground water GeoTIFFs, relevant for the Subsidence, is the Mean Lowest Watertable (MLW, or GLG in Dutch).


===Attributes===
===Attributes===
The subsidence overlay also has [[attribute]]s. All attributes have a default value, but can be changed to configure the subsidence calculation.
The subsidence overlay also has [[Model attributes (Subsidence Overlay)|model attribute]]s. All attributes have a default value, but can be changed to configure the subsidence calculation.
{| class="wikitable"
 
! Attribute
{{overlay attributes|suppresscategory=true|allowselflinks=true|
! Description
{{:A (Subsidence Overlay)}}
! Default value
{{:B (Subsidence Overlay)}}
! Remark
{{:C (Subsidence Overlay)}}
|-
{{:Climate start temp (Subsidence Overlay)}}
| A
{{:Climate final temp (Subsidence Overlay)}}
| The A parameter in the [[#Oxidation Calculation|Oxidation formula]].
{{:Climate soil temp factor (Subsidence Overlay)}}
| 0,023537
{{:Climate oxidation (Subsidence Overlay)}}
| This value is recalculated between 1-year time steps of the calculation.
{{:Default clay thickness (Subsidence Overlay)}}
|-
{{:Default peat fraction (Subsidence Overlay)}}
| B
{{:Default top layer thickness (Subsidence Overlay)}}
| The B parameter in the [[#Oxidation Calculation|Oxidation formula]].
{{:Hi passive drainage (Subsidence Overlay)}}
| 0,01263
{{:Low passive drainage (Subsidence Overlay)}}
|
{{:Years (Subsidence Overlay)}}
|-
}}
| C
 
| The C parameter in the [[#Oxidation Calculation|Oxidation formula]].
{{SubsidenceOverlay_nav}}
| 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 calculation. 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.
|-
|}

Latest revision as of 14:10, 28 February 2024

The subsidence model calculates the gradual downward settling of the ground's surface where a peat layer is present. The considered subsidence takes place due to oxidation and compaction of the peat layer. The total subsidence is currently calculated as the result of oxidation and compaction over the years. Oxidation is dependent on the ground water level and the clay thickness. Compaction is dependent on the toplayer thickness, the peat fraction and raised surface terrain.

The ground water level is initialized by either raster or surface area data and optionally adjusted each year (indexation). When indexation is active, the surface water level is adjusted for the settling each year and the ground water levels will change accordingly.

The calculation model is configured by the subsidence overlay wizard and it's result are visualized with the subsidence overlay.

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, parameter a of the oxidation formula is calculated
  • The oxidation subsidence is calculated
  • The compaction subsidence is calculated
  • The surface water levels are lowered by the amount of subsidence times the indexation
  • The ground water level is lowered based on subsidence and surface water level indexation
  • The new ground water level serves as input for the next calculation step

Yearly recalculation of Parameter A

The a parameter is recalculated yearly, to account for a changing climate. The new value for the a parameter is obtained by multiplying the original Parameter a is with a factor. This factor is calculated based on an interpolated average temperature for that year, a soil temperature factor, micro activity and an oxidation factor.

The value of the a parameter is updated each year as follows:

Delta temperature is calculated as:

Delta micro activity is calculated as:

Delta subsidence is calculated as:

The new parameter a value for year y is calculated as:

where

= The a parameter for the current year.
= The a parameter value at the start of the calculation, defined by the model attribute A.
= The current year. The first year is defined by START_YEAR.
= The start year of the simulation, defined by CLIMATE_START_YEAR.
= The final year of the simulation, defined by the addition of the start year and YEARS.
= The average temperature of the start year, defined by CLIMATE_START_TEMP.
= The average temperature of the final year, defined by CLIMATE_FINAL_TEMP.
= The Q10 factor, configured as 3. This value is currently not adjustable.
= Soil temperature factor, defined by CLIMATE_SOIL_TEMP_FACTOR.
= Oxidation factor, defined by CLIMATE_OXIDATION.

Ground water depth

At the start of a simulation, the ground water depth is initialized with the ground water depth GeoTIFF (if provided) and is optionally overwritten by (managed) water areas' water level.

Furthermore, the ground water level can be managed with drainages (provided as underground buildings), either actively or passively.

Additionally the terrain height can change due to subsidence that occurred in previous years and due to actions taken that raised the terrain. Managed water areas can react to these changes when indexation is configured. For indexation, see indexation formula.

The following formulas describe how the yearly adjusted ground water depths are obtained.

Ground water level managed by drainages

where

is the calculated ground water depth of a grid cell at year y.
is the ground water depth actively maintained by a drainage
is the ground water depth of the managed water area.
is the area water level adjustment for year y.
is the ground water level passively maintained by drainages.
is the ground water level increase calculated based on the are water level adjustment due to indexation and the subsidence in the previous year.

Ground water level managed by water areas

The effect of changes of managed surface water levels (by water areas) on the ground water level. The x-axis indicates the relative depth of the managed surface water level. The y-axis indicates the meters of change to the ground water level, per meter change in surface water level. The smaller the relative depth is, the less the ground water level equalizes with changes in the managed surface water level.

The ground water level can also be managed by water areas, which control the surface water levels. To make sure ground water levels do not rise (too much), surface water levels in the water areas can be lowered automatically with respect to the subsidence. This process is called indexation. The new ground water level can then be estimated based on the indexation on the managed water level of surface water and the calculated subsidence of the previous year. The increment in ground water level is rarely exactly the adjustment of the managed surface water level and is often less, depending on the relative depth of the surface water level. The following formulas have been developed to estimate the increase of the ground water level.

The new relative surface water level depth is calculated as:

Next, based on the old and new depths, the ground water depth change is divided into three sections, each which its own rate of contribution.

Finally, the ground water depth change is calculated and the new ground water depth is obtained:

where

is the current relative water depth of water area a.
is the adjusted relative water depth of water area a.
is the water level adjustment for indexation of current year y.
is the subsidence that occurred up to year y.
is the calculated adjusted ground water depth for year y, based on the occurred subsidence and indexation of previous years.
is the initial ground water depth at the start of the simulation.
is the estimated change of the ground water level based on occurred subsidence and indexation.

Oxidation calculation

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

where

is the subsidence due to oxidation.
is the calculated ground water depth for year y in cell c.
is the calculated a parameter value for the current year .
is the clay thickness of the terrain in cell c, defined by CLAY_THICKNESS
is the b parameter value, defined by the model attribute B
is the c parameter value, defined by the model attribute C

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

Compaction calculation

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

where

is the calculated subsidence due to compaction.
is the peat fraction of the respective grid cell c.
is the top layer thickness of the respective grid cell c.
The terrain height increase as a result of the actions taken during a session, such as the creation of levees.
is the number of days in a year times the current year being calculated.
is the first regression constant (0.015853041) for the effect of the peat fraction and time in days.
is the first regression constant (0.006617643) for the top layer thickness and time in days.
is a regression constant (0.200468677) for the change in surface height, for example caused by added materials.
is the second regression constant (0.02348519) for the effect of the peat fraction.
is the second regression constant (-0.010061616) for the top layer thickness.

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.

Subsidence calculation

The total subsidence for year y is calculated as:

where

is the peat fraction of the respective grid cell c.
is the top layer thickness of the respective grid cell c.
is the maximum possible subsidence in year y.
is the total subsidence in year y
is the subsidence due to oxidation in year y.
is the subsidence due to compactions in year y.

Indexation

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.

Terrain height

The height of the terrain can be manipulated during a session by stakeholders taking a land sculpting action, creating open water, or building levees. These actions will result in settlement, which can be found under the Settlement result type. Creating or demolishing buildings generally do not change the height of the land, and do not result in changes in the settlement results.

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.

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 can be configured with the YEARS model attribute of the Subsidence overlay.

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 model attributes. All attributes have a default value, but can be changed to configure the subsidence calculation.