Melt Damage Update Steps

For each drainage basin $k$ do

1. Calculate the central damage zone damage probability $p_{damage}^{central}$using equation eq:central-damage-probability with characteristic magmatic crust height $H_{mc,k}$ calculated during melt extraction.
2. Calculate the x-coordinate limits of the melt damage zone $x_{damage}^{min}$ and $x_{damage}^{max}$ and the y-coordinate limit $y_{damage}^{max}$ using equations eq:melt-damage-zone-limits with the average x-coordinate of the shallowest partially molten mantle marker $x'_{shallow,pm,k}$ and average y-coordinate of the shallowest partially molten mantle marker $y'_{shallow,pm,k}$ calculated during melt extraction.
3. Calculate the melt damage factor for each marker (Melt Damage Marker Update).

Melt Damage Marker Update

For each marker $m$ do:

1. Calculate the damage probability of the marker $p_{damage,m}$ using equation eq:melt-damage-probability with the x-coordinate of the marker $x_m$, $x'_{shallow,pm,k}$, $p_{damage}^{central}$, $x_{damage}^{min}$ and $x_{damage}^{max}$.
2. Calculate a random number $r$ between 0 and 1.
3. Assign the marker damage factor $f_{damage,m}$ using equation eq:melt-damage-factor with $p_{damage,m}$ and $r$.