# Compaction formula (Subsidence Overlay)

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.