# Model Documentation

### | Version 4.0

created with goxygen 0.21.1

# 59_som

# Soil organic matter (59_som)

## Description

The soil organic matter module calculates the soil organic carbon loss due to landuse activities. It also estimates the nitrogen release due to the soil organic carbon turnover.

## Interfaces

Interfaces to other modules

### Input

module inputs (A: cellpool_aug16 | B: off)
| Description | Unit | A | B
--- | --- | --- | --- | ---
pcm_land (j, land) | Land area in previous time step | \(10^6 ha\) | x |
pm_climate_class (j, clcl) | Koeppen-Geiger climate classification on the simulation cluster level | \(1\) | x |
vm_area (j, kcr, w) | Agricultural production area | \(10^6 ha\) | x |
vm_land (j, land) | Land area of the different land types | \(10^6 ha\) | x |

### Output

module outputs
| Description | Unit
--- | --- | ---
vm_costs_overrate_cropdiff (i) | Punishment costs for overrated cropland difference | \(10^6 USD_{05MER}/yr\)
vm_nr_som (j) | Release of soil organic matter | \(Tg N/yr\)

## Realizations

### (A) cellpool_aug16

The cellpool_aug16 realization is built on the IPCC 2006 Guidelines for National Greenhouse Gas Inventories (IPCC (2006).). It calculates based on the idea of stock change factors regarding the potential natural vegetation the loss of soil carbon due to cropping activities and management. This approach also accounts for the temporal dimension of soil organic carbon change, since it assumes a gradual step of 15% in the direction of the new equilibrium soil organic carbon pool each year.

For every cell a new equilibrium value for the soil organic carbon pool on cropland as the sum over all crop types is calculated

\[\begin{multline*} v59\_som\_target(j2,"cropland") = \sum_{kcr,w}\left( vm\_area(j2,kcr,w) \cdot i59\_cratio(j2,kcr)\right) \cdot \sum_{ct}f59\_topsoilc\_density(ct,j2) \end{multline*}\]

as well as for all non cropland given by

\[\begin{multline*} v59\_som\_target(j2,"noncropland") = \sum_{noncropland59} vm\_land(j2,noncropland59) \cdot \sum_{ct}f59\_topsoilc\_density(ct,j2) \end{multline*}\]

Depending on the setting of `c59_som_scenario`climate impacts (`cc`) are taken into account or not (`nocc`). For a static climate `f59_topsoilc_density` is set to the value of 1995 within the input of the module realization. To account for the transfer of carbon rich soils from natural vegetation to cropland as well as the transfer of depleted soils from cropland to regrowing natural land, the cropland expansion and reduction of each cell is calculated via

\[\begin{multline*} v59\_crop\_reduction(j2) - v59\_crop\_expansion(j2) = pcm\_land(j2,"crop") - vm\_land(j2,"crop") \end{multline*}\]

The following nonlinear constraint

\[\begin{multline*} vm\_costs\_overrate\_cropdiff(i2) = s59\_punish\_cropdiff \cdot \sum_{cell(i2,j2)}\left(v59\_crop\_reduction(j2) \cdot v59\_crop\_expansion(j2)\right) \end{multline*}\]

ensures that no extra cropland reduction and expansion at the same time is happening. Note that this nonlinear realization needs two to three times longer runtime and is thus by default not switch on. The actually carbon transfer from cropland as well as to cropland soils is then given by

\[\begin{multline*} v59\_som\_transfer\_to\_cropland(j2) = \sum_{ct}\left( v59\_crop\_expansion(j2) \cdot p59\_carbon\_density(ct,j2,"noncropland") - v59\_crop\_reduction(j2) \cdot p59\_carbon\_density(ct,j2,"cropland")\right) \end{multline*}\]

To get the current size of the soil organic carbon pool, the pool of the previous timestep corrected by the carbon transfer is developing into the direction of the above calculated target values taken the timestep depending lossrate into account by

\[\begin{multline*} v59\_som\_pool(j2,"cropland") = \sum_{ct} i59\_lossrate(ct) \cdot \left(v59\_som\_target(j2,"cropland") - \left(p59\_som\_pool(j2,"cropland") + v59\_som\_transfer\_to\_cropland(j2)\right)\right) + \left(p59\_som\_pool(j2,"cropland") + v59\_som\_transfer\_to\_cropland(j2)\right) \end{multline*}\]

and

\[\begin{multline*} v59\_som\_pool(j2,"noncropland") = \sum_{ct}i59\_lossrate(ct) \cdot \left(v59\_som\_target(j2,"noncropland") - \left(p59\_som\_pool(j2,"noncropland") - v59\_som\_transfer\_to\_cropland(j2)\right)\right) + \left(p59\_som\_pool(j2,"noncropland") - v59\_som\_transfer\_to\_cropland(j2)\right) \end{multline*}\]

The annual nitrogen release (or sink) for cropland soils is than calculated by the loss of soil organic carbon given by

\[\begin{multline*} vm\_nr\_som(j2) = \frac{ \sum_{ct}i59\_lossrate(ct)}{m\_timestep\_length} \cdot \frac{1}{15 } \cdot \left(p59\_som\_pool(j2,"cropland") + v59\_som\_transfer\_to\_cropland(j2) - v59\_som\_target(j2,"cropland")\right) \end{multline*}\]

with the carbon to nitrogen ratio of soils assumed to be 15:1.

The cellpool_aug16 calculates the carbon loss with the assumption of a lossrate of 15% per year resulting in 44% in 5 years, 80% in 10 years and 96% in 20 years. The lossrate for a given timestep is than calculate by

    i59_lossrate(t)=1-0.85**m_yeardiff(t);

The stock change factors are implemented for cropland subsystems divided by MAgPIE crop types as well as potentially for tillage and input management. So far it just tracks the subsystem component due to missing data for the other categories. They are set to the following default values:

    i59_tillage_share(i,tillage59)=0;
    i59_tillage_share(i,"full_tillage")=1;
    i59_input_share(i,inputs59)=0;
    i59_input_share(i,"medium_input")=1;

The stock change factor in each cell for every crop type also takes into account the climate variability of these factors and is therefor given by:

    i59_cratio(j,kcr) = sum((cell(i,j),tillage59,inputs59,climate59),
                     sum(clcl_climate59(clcl,climate59),pm_climate_class(j,clcl))
                     * f59_cratio_landuse(climate59,kcr)
                     * i59_tillage_share(i,tillage59)
                     * f59_cratio_tillage(climate59,tillage59)
                     * i59_input_share(i,inputs59)
                     * f59_cratio_inputs(climate59,inputs59));

> Limitations There are no known limitations.

### (B) off

This realization does not track soil organic matter turnover.

> Limitations The release of nitrogen due to soil organic matter loss is not calculated.

## Definitions

### Objects

module-internal objects (A: cellpool_aug16 | B: off)
| Description | Unit | A | B
--- | --- | --- | --- | ---
f59_cratio_inputs (climate59, inputs59) | Ratio of soil carbon relative to potential natural vegetation soil carbon for different input intensity | \(1\) | x |
f59_cratio_landuse (climate59, kcr) | Ratio of soil carbon relative to potential natural vegetation soil carbon for different landuse | \(1\) | x |
f59_cratio_tillage (climate59, tillage59) | Ratio of soil carbon relative to potential natural vegetation soil carbon for different soil management | \(1\) | x |
f59_som_initialisation_pools (t_all, j, pools59) | Initialisation pools for soil organic carbon | \(10^6 tC\) | x |
f59_topsoilc_density (t_all, j) | LPJ topsoil carbon density for natural vegetation | \(tC/ha\) | x |
i59_cratio (j, kcr) | Ratio of carbon density of land relative to natural vegetaion | \(1\) | x |
i59_input_share (i, inputs59) | Share of land under input class | \(1\) | x |
i59_lossrate (t) | Rate of loss or recovery of SOM pool per timestep | \(1\) | x |
i59_tillage_share (i, tillage59) | Share of land under tillage class | \(1\) | x |
p59_carbon_density (t_all, j, pools59) | Carbon density of a hectare of land | \(tC/ha\) | x |
p59_som_pool (j, pools59) | Actual C pool | \(10^6 tC\) | x |
q59_crop_diff_constraint (i) | Cropland difference constraint | \(10^6 USD_{05MER}/yr\) | x |
q59_crop_diff (j) | Cropland difference | \(10^6 ha\) | x |
q59_nr_som (j) | Soil organic matter loss | \(Tg N/yr\) | x |
q59_som_pool_cropland (j) | Actual C pool in croplands | \(10^6 tC\) | x |
q59_som_pool_noncropland (j) | Actual C pool in non-croplands | \(10^6 tC\) | x |
q59_som_target_cropland (j) | Estimates the long-term target state of cropland | \(10^6 tC\) | x |
q59_som_target_noncropland (j) | Estimates the long-term target state of noncropland | \(10^6 tC\) | x |
q59_som_transfer_to_cropland (j) | Estimates the transfer of carbon pools due to land conversion | \(10^6 tC\) | x |
s59_punish_cropdiff | Punishment costs per croparea squared | \(USD_{05MER}/10^6/ha^2\) | x |
v59_crop_expansion (j) | Crop land expansion | \(10^6 ha\) | x |
v59_crop_reduction (j) | Land reduction | \(10^6 ha\) | x |
v59_som_pool (j, pools59) | Soil organic matter pool | \(10^6 tC\) | x |
v59_som_target (j, pools59) | Long-term target state of C pool | \(10^6 tC\) | x |
v59_som_transfer_to_cropland (j) | Transfer of SOM from other land to cropland | \(10^6 tC\) | x |

### Sets

sets in use
| description
--- | ---
clcl | climate classification types
climate59 | Climate classes of IPCC 2006
i | World regions
inputs59 | Input management categories of IPCC
kcr(kve) | Cropping activities
land | Land pools
pools59 | Carbon differentiating landuse types
t_all | 5-year time periods
tillage59 | Tillage categories of IPCC
t(t_all) | Simulated time periods
w | Water supply type

## Authors

Benjamin Leon Bodirsky, Kristine Karstens

## See Also

10_land, 11_costs, 30_crop, 45_climate, 50_nr_soil_budget, 51_nitrogen

## References

IPCC. 2006. “2006 IPCC Guidelines for National Greenhouse Gas Inventories, Prepared by the National Greenhouse Gas Inventories Programme.”