# Model Documentation

### | Version 4.0

created with goxygen 0.21.1

# 18_residues

# Residues (18_residues)

## Description

The residues module calculates the production of crop residues (straw etc.) and its subsequent use. Residues can be burned, used for feed, recycled to soils or used for other purposes (construction, fuel etc).

The module also calculates the costs of crop residue harvest when it is used for feed or material purposes.

## Interfaces

Interfaces to other modules

### Input

module inputs (A: flexreg_apr16 | B: off)
| Description | Unit | A | B
--- | --- | --- | --- | ---
fm_attributes (attributes, kall) | Conversion factors - where X is ton N P K C DM WM or PJ GE | \(X/tDM\) | x |
im_development_state (t, i) | Development state according to the World Bank definition where 0=low income country 1=high income country in high income level | \(1\) | x |
vm_area (j, kcr, w) | Agricultural production area | \(10^6 ha\) | x |
vm_cost_prod (i, kall) | Factor costs | \(10^6 USD_{05MER}/yr\) | x |
vm_prod_reg (i, kall) | Regional aggregated production | \(10^6 tDM/yr\) | x |

### Output

module outputs
| Description | Unit
--- | --- | ---
vm_res_biomass_ag (i, kcr, attributes) | Production of aboveground residues in each region | \(10^6 tDM\)
vm_res_biomass_bg (i, kcr, dm_nr) | Production of belowground residues in each region | \(10^6 tDM\)
vm_res_recycling (i, npk) | Residues recycled to croplands in respective nutrients Nr P K units | \(10^6 tX\)

## Realizations

### (A) flexreg_apr16

As official global statistics exist only for crop production and not for crop residue production, the biomass of residues is obtained in MAgPIE by using crop-type specific plant growth functions based on crop production and area harvested. Plant biomass is divided into three components: the harvested organ as listed in FAO, the aboveground (AG) and the belowground (BG) residues.

IPCC (2006) offers one of the few consistent datasets to estimate both AG and BG residues. Also, by providing crop-growth functions (CGF, `f18_cgf`) instead of fixed harvest indices, it can be used to depict current international differences of harvest indices and their development in the future. The methodology is thus well eligible for global long-term modelling. IPCC (2006) provides linear CGFs with positive slope and intercept for cereals, leguminous crops, potatoes and grasses. As no values are available for the oilcrops rapeseed, sunflower, oilpalms as well as sugar crops, tropical roots, cotton and others, we use fixed harvest-indices (positive slope without intercept) for these crops based on Wirsenius (2000), Lal (2005) and Feller et al. (2007). If different CGFs are available for crops within a crop group, we build a weighted average based on the production in 1995.

The AG crop residue biomass `vm_res_biomass_ag` is calculated as a function of harvested area `vm_area` and production `vm_prod_reg`. `f18_cgf` contains slope and intercept parameters of the CGFs.

\[\begin{multline*} vm\_res\_biomass\_ag(i2,kcr,attributes) = \left(\sum_{cell(i2,j2),w} vm\_area(j2,kcr,w) \cdot \sum_{ct}f18\_multicropping(ct,i2) \cdot f18\_cgf("intercept",kcr) + vm\_prod\_reg(i2,kcr) \cdot f18\_cgf("slope",kcr)\right) \cdot f18\_attributes\_residue\_ag(attributes,kcr) \end{multline*}\]

The BG crop residue biomass `vm_res_biomass_bg` is calculated as a function of total aboveground biomass.

\[\begin{multline*} vm\_res\_biomass\_bg(i2,kcr,dm\_nr) = \left(vm\_prod\_reg(i2,kcr) + vm\_res\_biomass\_ag(i2,kcr,"dm")\right) \cdot f18\_cgf("bg\_to\_ag",kcr) \cdot f18\_attributes\_residue\_bg(dm\_nr,kcr) \end{multline*}\]

In contrast to AG biomass, AG production `vm_res_biomass_ag(i,kcr,attributes)` is defined as the part of residues which is removed from the field. The difference between biomass and production is either burned on field or remains on the fields (either incorporated in soils or not) and decays. The field balance equations ensures that the production of AG residues `vm_res_biomass_ag(i,kcr,attributes)` is properly assigned to different uses: removal, on-field burning and recycling of AG residues.

\[\begin{multline*} vm\_res\_biomass\_ag(i2,kcr,attributes) = v18\_res\_ag\_removal(i2,kcr,attributes) + v18\_res\_ag\_burn(i2,kcr,attributes) + v18\_res\_ag\_recycling(i2,kcr,attributes) \end{multline*}\]

The amount of residues burned on fields in a region `v18_res_ag_burn` is determined by the share (ic18_res_use_min_shr) of AG residue biomass. Based on Smil (1999), residue burning is fixed to 15% of total AG crop residue dry matter in developed and 25% in developing regions for each crop. For future time steps, these rates are scenario dependent, and either kept constant or reduced to 10% and 0% in 2050.

\[\begin{multline*} v18\_res\_ag\_burn(i2,kcr,attributes) = \sum_{ct}\left( im\_development\_state(ct,i2) \cdot i18\_res\_use\_burn(ct,"high\_income",kcr) + \left(1-im\_development\_state(ct,i2)\right) \cdot i18\_res\_use\_burn(ct,"low\_income",kcr)\right) \cdot vm\_res\_biomass\_ag(i2,kcr,attributes) \end{multline*}\]

While the residue biomass is estiamted with a crop-specific nutrient composition (which is required for consistent nutrient budgets), the removed residues are assumed to have homogeneous properties (to reduce the number of commodities in MAgPIE) within three crop residue groups (cereal straw, fibrous residues that cannot be digested by monogastrics, and non-fibrous residues that can be digested). The following constraint, in combination with the field balance equation, guarantees that mass balances are not violated while a homogeneous good is extracted from heterogeneous goods.

\[\begin{multline*} \sum_{kres\_kcr(kres,kcr)} v18\_res\_ag\_removal(i2,kcr,attributes) = vm\_prod\_reg(i2,kres) \cdot fm\_attributes(attributes,kres) \end{multline*}\]

Residues recycled to croplands in nutrients `vm_res_recycling(i2,"nr")` are calcualted based on the amount of AG residues left on field for recycling, the nutrients coming from burned residues, and on biomass that is left in BG residues. They are calculated to be transmitted to the nitrogen budget module 50_nr_soil_budget.

\[\begin{multline*} vm\_res\_recycling(i2,"nr") = \sum_{kcr}\left( v18\_res\_ag\_recycling(i2,kcr,"nr") + v18\_res\_ag\_burn(i2,kcr,"nr") \cdot \left(1-f18\_res\_combust\_eff(kcr)\right) + vm\_res\_biomass\_bg(i2,kcr,"nr") \right) \end{multline*}\]

Similar to the recycled nutrients, the potash recycling is determined by the amount of AG residues with the potash content and the amounts of potash from burning residues. As P and K are not volatile and hardly water soluble, only removed aboveground crop residues have to be considered, while nutrients from burned AG as well as BG stay on the field.

\[\begin{multline*} vm\_res\_recycling(i2,pk18) = \sum_{kcr}\left( v18\_res\_ag\_recycling(i2,kcr,pk18) + v18\_res\_ag\_burn(i2,kcr,pk18) \right) \end{multline*}\]

Costs of residues production are determined as factor costs per ton assuming 15 USD per ton, using the lower range from this source, 10USD baling costs per large round bale plus 2USD pro bale stocking and hauling, 1 large round bale is approximately 500 kg, resulting in 24USD per ton, for developing prices see here. Tha calcuated factor costs per ton are therefore 24 for `res_cereals`, `res_fibrous` and `res_nonfibrous`.

\[\begin{multline*} vm\_cost\_prod(i2,kres) = vm\_prod\_reg(i2,kres) \cdot f18\_fac\_req\_kres(kres) \end{multline*}\]

Trade of AG residues is not considered, so that all produced AG residues have to be assigned to uses within the respective world region.

> Limitations There are no known limitations.

### (B) off

No representation of crop residues in the model.

> Limitations Should not be used if emission estimates are required or climate policies are activated.

## Definitions

### Objects

module-internal objects (A: flexreg_apr16 | B: off)
| Description | Unit | A | B
--- | --- | --- | --- | ---
f18_attributes_residue_ag (attributes, kve) | Nutrient content of aboveground crop residues in respective attribute units DM GJ Nr P K WM C | \(X/DM\) | x |
f18_attributes_residue_bg (dm_nr, kve) | Nutrient content of belowground crop residues in reactive nitorgen and carbon units Nr C | \(X/DM\) | x |
f18_cgf (cgf, kve) | Crop growth functions for all vegetation types containing slope intercept and belowground to aboveground ratio | \(1\) | x |
f18_fac_req_kres (kres) | Factor requirements | \(USD_{05MER}/tDM\) | x |
f18_multicropping (t_all, i) | Multicropping indicator as ratio of area harvested by physical area | \(1\) | x |
f18_res_combust_eff (kve) | Combustion efficiency of residue burning | \(1\) | x |
f18_res_use_burn (t_all, burn_scen18, dev18, kcr) | Minimum and maximum burn share use for residues developing over time | \(1\) | x |
i18_res_use_burn (t_all, dev18, kcr) | Share of residues burned on field | \(1\) | x |
q18_cost_prod_res (i, kres) | Production costs of harvesting crop residues | \(10^6 USD_{05MER}\) | x |
q18_prod_res_ag_reg (i, kcr, attributes) | Production constraint of aboveground residues | \(10^6 tDM\) | x |
q18_prod_res_bg_reg (i, kcr, dm_nr) | Production constraint of belowground residues | \(10^6 tDM\) | x |
q18_res_field_balance (i, kcr, attributes) | Calculation of the residues amount recycled to soils | \(10^6 tDM\) | x |
q18_res_field_burn (i, kcr, attributes) | Fixing of the residues amount burned in a region in respective attribute units DM GJ Nr P K WM C | \(10^6 tX\) | x |
q18_res_recycling_nr (i) | Nutrient recycling of reaactive nitrogen | \(10^6 tNr\) | x |
q18_res_recycling_pk (i, pk18) | Nutrient recycling of phosphorus and potash | \(10^6 tX\) | x |
q18_translate (i, kres, attributes) | Transformation of the multiple crop residues into supply balance crop redisues in respective attribute units DM GJ Nr P K WM C | \(10^6 tX\) | x |
v18_res_ag_burn (i, kcr, attributes) | Residues burned on fields in respective attribute units DM GJ Nr P K WM C | \(10^6 tX\) | x |
v18_res_ag_recycling (i, kcr, attributes) | Recylcing of crop residues to soils in respective attribute units DM GJ Nr P K WM C | \(10^6 tX\) | x |
v18_res_ag_removal (i, kcr, attributes) | Removal of crop residues in respective attribute units DM GJ Nr P K WM C | \(10^6 tX\) | x |

### Sets

sets in use
| description
--- | ---
attributes | Product attributes characterizing a product (such as weight or energy content)
burn_scen18 | scenario for burning residues on field
cgf | Residue production functions
dev18 | country develoment indicator
dm_nr(attributes) | dry matter and nr
i | World regions
kall | All products in the sectoral version
kcr(kve) | Cropping activities
kres(kall) | Residues
kve(k) | Land-use activities
npk(nutrients) | Plant nutrients
pk18(npk) | subset of npk containing P and K nutrients
t_all | 5-year time periods
t(t_all) | Simulated time periods
w | Water supply type

## Authors

Benjamin Leon Bodirsky

## See Also

09_drivers, 16_demand, 17_production, 30_crop, 38_factor_costs, 50_nr_soil_budget, 51_nitrogen

## References

Feller, C., M. Fink, H. Laber, A. Maync, P. Paschold, H. Scharpf, J. Sclaghecken, K. Strohmeyer, U. Weier, and J. Ziegler. 2007. “Düngung Im Freilandgemüsebau.” Schriftenreihe Des Leibniz- Instituts Für Gemüse- Und Zierpflanzenbau (IGZ), 265.

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

Lal, R. 2005. “World Crop Residues Production and Implications of Its Use as a Biofuel.” Environment International 31 (4): 575–84. doi:10.1016/j.envint.2004.09.005.

Smil, Vaclav. 1999. “Nitrogen in Crop Production: An Account of Global Flows.” Global Biogeochemical Cycles 13 (2): 647–62. doi:10.1029/1999GB900015.

Wirsenius, Stefan. 2000. “Human Use of Land and Organic Materials: Modeling the Turnover of Biomass in the Global Food System.” Doctoral thesis, Chalmers University of Technology. http://publications.lib.chalmers.se/publication/827-human-use-of-land-and-organic-materials-modeling-the-turnover-of-biomass-in-the-global-food-system.