Oxidation
Process
Oxidation occurs in organic rich layers (e.g. peat) above the groundwater table.
Calculation methods
For oxidation two approaches are supported (Bootsma et al., 2020): a more comprehensive organic mass based approach where the organic matter content determines the potential amount of surface lowering and a more simple oxidation at a constant rate.
Organic based approach (CarbonStore)
All voxels are initially assigned an organic mass fraction: \[ F_{org} = \frac{M_{org}}{M_{org} + M_{min}} \tag{1}\]
where org and min denote organic and mineral respectively. \(F_{org}\) is identical to the LOI (loss on ignition) quantity that is used for the characterization of organic matter content of subsurface materials. The organic and the mineral mass content of a voxel (per \(m^2\) in map view) is calculated from:
\[ M_{org} = F_{org}\rho_{bulk}H \tag{2}\] \[ M_{min} = (1-F_{org})\rho_{bulk}H \tag{3}\]
where \(\rho_{bulk}\) is the dry bulk density and \(H\) is the momentary voxel height. The initial bulk density (\(kg/m^3\)) is modelled with an empirical relationship obtained from a large set of observational data of Dutch peat samples (Erkens, Van der Meulen, and Middelkoop 2016):
\[ \rho_{bulk} = \frac{100}{F_{org}}(1-e^{-F_{org}/0.12}) \tag{4}\]
In each time step \(\Delta t\), organic mass loss is modelling using a constant rate law for the (part of) the voxels that are shallower than a specified height above the MLGT and not deeper than 1.2 m below the surface level:
\[ \Delta M_{org} = -\alpha_{m}H\Delta t \tag{5}\]
\(\alpha_{m}\) is an empirical constant estimated from a dataset with observations over several of land subsidence in peat-meadow areas in the Netherlands (Van den Akker et al. 2007). Organic mass loss of each voxel is then converted to a height loss with:
\[ \Delta H^{ox} = \Delta M_{org}\hat{V} \tag{6}\]
where \(\hat{V}\) is called the “specific volume of oxidation”. Direct measurements of this quantity do not exist. For high \(F_{org}\) (i.e. regular peat) \(\hat{V}\) can likely be approximated by the reciprocal of the dry bulk organic matter density. Below \(F_{org} \approx 0.3\) (i.e. transition to organic rich clay), \(\hat{V}\) is expected to decrease as the bulk volume is more strongly determined by the mineral framework rather than by the organic matter. These concepts are captured by the following equation:
\[ \hat{V} = \frac{0.5}{F_{org}\rho_{bulk}} \left( 1+erf \left( \frac{F_{org}-0.2}{0.1} \right) \right)\; \; [m^3/kg/m^2] \tag{7}\]
Each time step, \(M_{org}\) and \(F_{org}\) (Equation 1) are updated for organic mass loss. The thickness of the voxel (\(H\)) is updated with the combined result of the consolidation, oxidation and shrinkage. Subsequently, \(\rho_{bulk}\) is updated using:
\[ \rho_{bulk} = \frac{M_{org} + M_{min}}{H} \tag{8}\]
This organic-mass based approach of oxidation provides a consistent framework to account for the mineral content of organic soils. While the organic mass fraction decreases by oxidation, the mineral mass fraction increases and ultimately, the non-oxidizable residue remains. The approach also allows modelling of oxidation-caused subsidence contributions of organic-rich clays and is not limited to oxidation of peat.
Constant rate (ConstantRate)
Add explanation of constant rate calculations…