Compaction formula (Subsidence Overlay): Difference between revisions

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


<math>S_{C} = ( a_{peat} \cdot p_{x,y} + a_{tl} \cdot tl_{x,y} ) \cdot log10(t_{days}) + a_h \cdot \Delta{h} + b_p \cdot p_{x,y} + b_{tl} \cdot tl_{x,y}</math>
<math>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}
</math>


where
where
 
: <math>S_{C}</math> is the calculated subsidence due to compaction.
* <math>S_{C}</math> is the calculated subsidence due to compaction.
: <math>p_{c}</math> is the [[Peat fraction (Subsidence Overlay)|peat fraction]] of the respective grid cell c.
* <math>p_{x ,y}</math> is the [[Peat fraction (Subsidence Overlay)|peat fraction]] of the cell at coordinate (x,y)
: <math>d_{tl,c}</math> is the [[Toplayer thickness (Subsidence Overlay)|top layer thickness]] of the respective grid cell c.
* <math>tl_{x,y}</math> is the [[top layer thickness]] of the cell at coordinate (x,y)
: <math>\Delta{h}</math> The terrain height increase as a result of the actions taken during a [[session]], such as the creation of [[levee]]s.
* <math>\Delta_h</math> The height increase as a result of the actions taken during a [[session]], such as the creation of [[levee]]s.
: <math>t_{days}</math> is the number of days in a year times the current year being calculated.
* <math>t_{days}</math> is the number of days in a year times the current year being calculated.
: <math>a_{peat}</math> is the first regression constant (0.015853041) for the effect of the peat fraction and time in days.
* <math>a_{peat}</math> is the first regression constant (0.015853041) for the effect of the peat fraction and time in days.
: <math>a_{tl}</math> is the first regression constant (0.006617643) for the top layer thickness and time in days.
* <math>a_{tl}</math> is the first regression constant (0.006617643) for the top layer thickness and time in days.
: <math>a_h</math> is a regression constant (0.200468677) for the change in surface height, for example caused by added materials.
* <math>a_h</math> is a regression constant (0.200468677) for the change in surface height, for example caused by added materials.
: <math>b_{peat}</math> is the second regression constant (0.02348519) for the effect of the peat fraction.
* <math>b_{peat}</math> is the second regression constant (0.02348519) for the effect of the peat fraction.
: <math>b_{tl}</math> is the second regression constant (-0.010061616) for the top layer thickness.
* <math>b_{tl}</math> 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.<noinclude>
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.<noinclude>
{{Template:SubsidenceOverlay_nav}}
{{Template:SubsidenceOverlay_nav}}
</noinclude>
</noinclude>

Latest revision as of 10:55, 16 February 2021

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.