Subsidence calculation

The subsidence model calculates the gradual downward settling of the ground's surface where a peat layer is present. The 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, 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.

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:

$\Delta {T}=(T_{final}-T_{start})\cdot {\frac {y_{y}-y_{start}}{y_{final}-y_{start}}}\cdot f_{st}$

Delta micro activity is calculated as:

$\Delta {MA}=Q_{10}^{\Delta {T}/10.0}-1.0$

Delta subsidence is calculated as:

$\Delta {s_{sub}}=\Delta {MA}\cdot f_{ox}$

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

$a_{y}=a_{0}\cdot (1.0+\Delta {s_{sub}})$

where

$a_{y}$ = The a parameter for the current year.

$a_{0}$ = The a parameter value at the start of the calculation, defined by the model attribute A.

$y_{y}$ = The current year. The first year is defined by START_YEAR.

$y_{start}$ = The start year of the simulation, defined by CLIMATE_START_YEAR.

$y_{end}$ = The final year of the simulation, defined by the addition of the start year and YEARS.

$T_{start}$ = The average temperature of the start year, defined by CLIMATE_START_TEMP.

$T_{final}$ = The average temperature of the final year, defined by CLIMATE_FINAL_TEMP.

$Q_{10}$ = The Q10 factor, configured as 3. This value is currently not adjustable.

$f_{st}$ = Soil temperature factor, defined by CLIMATE_SOIL_TEMP_FACTOR.

$f_{ox}$ = Oxidation factor, defined by CLIMATE_OXIDATION.

Compaction calculation

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

$S_{C}={\begin{cases}(a_{peat}\cdot p_{c}+a_{tl}\cdot d{tl,c})\cdot log10(t_{days})+a_{h}\cdot \Delta {h}+b_{p}\cdot p_{c}+b_{tl}\cdot d_{tl,c}&{\text{if }}\Delta {h}{\text{ is larger than 0}}\\0&{\text{ otherwise}}\end{cases}}$

where

$S_{C}$ is the calculated subsidence due to compaction.

$p_{c}$ is the peat fraction of the respective grid cell c.

$d_{tl,c}$ is the top layer thickness of the respective grid cell c.

$\Delta {h}$ The terrain height increase as a result of the actions taken during a session, such as the creation of levees.

$t_{days}$ is the number of days in a year times the current year being calculated.

$a_{peat}$ is the first regression constant (0.015853041) for the effect of the peat fraction and time in days.

$a_{tl}$ is the first regression constant (0.006617643) for the top layer thickness and time in days.

$a_{h}$ is a regression constant (0.200468677) for the change in surface height, for example caused by added materials.

$b_{peat}$ is the second regression constant (0.02348519) for the effect of the peat fraction.

$b_{tl}$ 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.

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.)

See also (PDF): Wind (1986) Slootpeilverlaging en grondwaterstandsdaling in veenweidegebieden (Ditch water level reduction and groundwater level decrease in peat meadow areas - Dutch only)

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 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, creating open water, or constructing levees. These actions will result in settlement, which can be found under the Settlement result type. Creating or demolishing constructions 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.

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.	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.

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

Parameter b (Subsidence Overlay) Parameter c (Subsidence Overlay)

Icon	Attribute	Unit	Range	Description	Default value
	A			The A parameter in the Oxidation formula.	0.023537
	CLIMATE START TEMP	°C		The average temperature in the first year of the subsidence simulation.	10.1
	CLIMATE FINAL TEMP	°C		The average temperature in the final year of the subsidence simulation.	10.7
	CLIMATE_SOIL_TEMP_FACTOR			The soil temperature factor used to recalculate the climate values between 1-year calculation steps.	0.5
	CLIMATE_OXIDATION			The oxidation factor used to recalculate the climate values between 1-year calculation steps.	0.67
	DEFAULT_CLAY_THICKNESS	m		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	m		If no top layer value can be found in a particular grid cell, this value is used instead.	5.0
	HI PASSIVE DRAINAGE	m		When a drainage is active, the highest ground water level (ghg) is lowered by x meters.	-0.10
	LOW PASSIVE DRAINAGE	m		When a drainage is active, the lowest ground water level (glg) is lowered by x meters .	0.0
	YEARS	year		The amount of years to simulate during the calculation, in 1-year steps.	30