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.
| Description | Unit | A | B | C | |
|---|---|---|---|---|---|
| fm_attributes (attributes, kall) |
Conversion factors - where X is ton N P K C DM WM or PJ GE | \(X/tDM\) | x | x | |
| im_development_state (t_all, i) |
Development state according to the World Bank definition where 0=low income country 1=high income country in high income level | \(1\) | x | x | |
| vm_area (j, kcr, w) |
Agricultural production area | \(10^6 ha\) | x | x | |
| vm_prod (j, k) |
Production in each cell | \(10^6 tDM/yr\) | x | ||
| vm_prod_reg (i, kall) |
Regional aggregated production | \(10^6 tDM/yr\) | x | x |
| Description | Unit | |
|---|---|---|
| vm_cost_prod_kres (i, kres) |
Production costs of harvesting crop residues | \(10^6 USD_{05MER}/yr\) |
| vm_res_ag_burn (i, kcr, attributes) |
Regional residues burned on fields in respective attribute units DM GJ Nr P K WM C | \(10^6 tX\) |
| 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 | \(10^6 tX\) |
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.
This realization enforces cluster-level agricultural residue production, based on agricultural production at the same level. However, other uses such as burning and recycling are allowed to be balanced at the regional level, in order to reduce computational complexity.
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.
\[\begin{multline*} v18\_res\_biomass\_ag\_clust(j2,kcr) = \left(\sum_{w} vm\_area(j2,kcr,w) \cdot \sum_{ct, cell(i2,j2)} f18\_multicropping(ct,i2) \cdot f18\_cgf("intercept",kcr) + vm\_prod(j2,kcr) \cdot f18\_cgf("slope",kcr)\right) \end{multline*}\]
\[\begin{multline*} vm\_res\_biomass\_ag(i2,kcr,attributes) = \sum_{cell(i2,j2)} v18\_res\_biomass\_ag\_clust(j2,kcr) \cdot f18\_attributes\_residue\_ag(attributes,kcr) \end{multline*}\]
The BG crop residue biomass vm_res_biomass_bg is
calculated as a function of total aboveground biomass.
\[\begin{multline*} vm\_res\_biomass\_bg(i2,kcr,dm\_nr) = \left(vm\_prod\_reg(i2,kcr) + vm\_res\_biomass\_ag(i2,kcr,"dm")\right) \cdot f18\_cgf("bg\_to\_ag",kcr) \cdot f18\_attributes\_residue\_bg(dm\_nr,kcr) \end{multline*}\]
Variable of removals at regional level needs to be greater than the regionally-summed cluster-level variable. This is not an equal-to for run-time considerations, but should be noted if regional removals vm_res_biomass_ag are to be incentivised.
\[\begin{multline*} \sum_{cell(i2,j2)} v18\_res\_ag\_removal(j2,kcr,attributes) = v18\_res\_ag\_removal\_reg(i2,kcr,attributes) \end{multline*}\]
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.
\[\begin{multline*} vm\_res\_biomass\_ag(i2,kcr,attributes) = v18\_res\_ag\_removal\_reg(i2,kcr,attributes) + vm\_res\_ag\_burn(i2,kcr,attributes) + v18\_res\_ag\_recycling(i2,kcr,attributes) \end{multline*}\]
make sure removal is less than biomass produced in each cluster
\[\begin{multline*} \sum_{kres\_kcr(kres,kcr)} v18\_res\_biomass\_ag\_clust(j2,kcr) \geq v18\_prod\_res\left(j2, kres\right) \end{multline*}\]
The amount of residues burned on fields in a region
vm_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.
\[\begin{multline*} vm\_res\_ag\_burn(i2,kcr,attributes) = \sum_{ct}\left( im\_development\_state(ct,i2) \cdot i18\_res\_use\_burn(ct,"high\_income",kcr) + \left(1-im\_development\_state(ct,i2)\right) \cdot i18\_res\_use\_burn(ct,"low\_income",kcr)\right) \cdot vm\_res\_biomass\_ag(i2,kcr,attributes) \end{multline*}\]
While the residue biomass is estimated 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.
\[\begin{multline*} \sum_{kres\_kcr(kres,kcr)} v18\_res\_ag\_removal(j2,kcr,attributes) = v18\_prod\_res(j2,kres) \cdot fm\_attributes(attributes,kres) \end{multline*}\]
sum to the regional amount of residues produced for the regional interface
\[\begin{multline*} vm\_prod\_reg(i2,kres) = \sum_{cell(i2,j2)} v18\_prod\_res(j2,kres) \end{multline*}\]
Residues recycled to croplands in nutrients
vm_res_recycling(i2,"nr") are calculated 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.
\[\begin{multline*} vm\_res\_recycling(i2,"nr") = \sum_{kcr}\left( v18\_res\_ag\_recycling(i2,kcr,"nr") + vm\_res\_ag\_burn(i2,kcr,"nr") \cdot \left(1-f18\_res\_combust\_eff(kcr)\right) + vm\_res\_biomass\_bg(i2,kcr,"nr") \right) \end{multline*}\]
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.
\[\begin{multline*} vm\_res\_recycling(i2,pk18) = \sum_{kcr}\left( v18\_res\_ag\_recycling(i2,kcr,pk18) + vm\_res\_ag\_burn(i2,kcr,pk18) \right) \end{multline*}\]
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.
\[\begin{multline*} vm\_cost\_prod\_kres(i2,kres) = vm\_prod\_reg(i2,kres) \cdot fm\_attributes("wm",kres) \cdot f18\_fac\_req\_kres(kres) \end{multline*}\]
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.
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.
\[\begin{multline*} vm\_res\_biomass\_ag(i2,kcr,attributes) = v18\_res\_ag\_removal(i2,kcr,attributes) + vm\_res\_ag\_burn(i2,kcr,attributes) + v18\_res\_ag\_recycling(i2,kcr,attributes) \end{multline*}\]
The amount of residues burned on fields in a region
vm_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.
\[\begin{multline*} vm\_res\_ag\_burn(i2,kcr,attributes) = \sum_{ct}\left( im\_development\_state(ct,i2) \cdot i18\_res\_use\_burn(ct,"high\_income",kcr) + \left(1-im\_development\_state(ct,i2)\right) \cdot i18\_res\_use\_burn(ct,"low\_income",kcr)\right) \cdot vm\_res\_biomass\_ag(i2,kcr,attributes) \end{multline*}\]
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.
\[\begin{multline*} \sum_{kres\_kcr(kres,kcr)} v18\_res\_ag\_removal(i2,kcr,attributes) = vm\_prod\_reg(i2,kres) \cdot fm\_attributes(attributes,kres) \end{multline*}\]
Amount produced at cellular level is flexible, can be distributed as it wants
\[\begin{multline*} \sum_{cell(i2,j2)} vm\_prod\_reg(i2,kres) = v18\_prod\_res(j2,kres) \end{multline*}\]
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.
\[\begin{multline*} vm\_res\_recycling(i2,"nr") = \sum_{kcr}\left( v18\_res\_ag\_recycling(i2,kcr,"nr") + vm\_res\_ag\_burn(i2,kcr,"nr") \cdot \left(1-f18\_res\_combust\_eff(kcr)\right) + vm\_res\_biomass\_bg(i2,kcr,"nr") \right) \end{multline*}\]
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.
\[\begin{multline*} vm\_res\_recycling(i2,pk18) = \sum_{kcr}\left( v18\_res\_ag\_recycling(i2,kcr,pk18) + vm\_res\_ag\_burn(i2,kcr,pk18) \right) \end{multline*}\]
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.
\[\begin{multline*} vm\_cost\_prod\_kres(i2,kres) = vm\_prod\_reg(i2,kres) \cdot fm\_attributes("wm",kres) \cdot f18\_fac\_req\_kres(kres) \end{multline*}\]
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.
No representation of crop residues in the model. Residual biomass
aboveground (vm_res_biomass_ag) and belowground
(vm_res_biomass_bg) are set to 0, as well as biomass to be
recycled (vm_res_recycling) or burned as agricultural
residues (vm_res_ag_burn). Therefore, these types of crop
residues are left unaccounted for within any modules using these
interface variable.
Limitations Should not be used if emission estimates are required or climate policies are activated.
| Description | Unit | A | B | C | |
|---|---|---|---|---|---|
| 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 | 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 | x | |
| f18_cgf (cgf, kve) |
Crop growth functions for all vegetation types containing slope intercept and belowground to aboveground ratio | \(1\) | x | x | |
| f18_fac_req_kres (kres) |
Factor requirements | \(USD_{05MER}/tDM\) | x | x | |
| f18_multicropping (t_all, i) |
Multicropping indicator as ratio of area harvested by physical area | \(1\) | x | x | x |
| f18_res_combust_eff (kve) |
Combustion efficiency of residue burning | \(1\) | x | x | |
| f18_res_use_burn (t_all, burn_scen18, dev18, kcr) |
Minimum and maximum burn share use for residues developing over time | \(1\) | x | x | |
| i18_res_use_burn (t_all, dev18, kcr) |
Share of residues burned on field | \(1\) | x | x | |
| q18_clust_field_constraint (j, kres) |
Make sure the amount removed in any cluster does not exceed the amount available | \(10^6 tDM\) | x | ||
| q18_cost_prod_res (i, kres) |
Production costs of harvesting crop residues | \(10^6 USD_{05MER}\) | x | x | |
| q18_prod_res_ag_clust (j, kcr) |
Cluster-level production constraint of aboveground residues | \(10^6 tDM\) | x | ||
| q18_prod_res_ag_reg (i, kcr, attributes) |
Regional production constraint of aboveground residues | \(10^6 tDM\) | x | x | |
| q18_prod_res_bg_clust (i, kcr, dm_nr) |
Cluster-level production constraint of belowground residues | \(10^6 tDM\) | x | ||
| q18_prod_res_bg_reg (i, kcr, dm_nr) |
Production constraint of belowground residues | \(10^6 tDM\) | x | ||
| q18_prod_res_cell (j, kres) |
Allows for distribution of residues to cellular level | \(10^6 tDM\) | x | ||
| q18_prod_res_reg (i, kall) |
Regional production of residues | \(10^6 tDM\) | x | ||
| q18_regional_removals (i, kcr, attributes) |
Calculation of regional level removals | \(10^6 tX\) | x | ||
| q18_res_field_balance (i, kcr, attributes) |
Calculation of the residues amount recycled to soils | \(10^6 tDM\) | x | 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 | x | |
| q18_res_recycling_nr (i) |
Nutrient recycling of reaactive nitrogen | \(10^6 tNr\) | x | x | |
| q18_res_recycling_pk (i, pk18) |
Nutrient recycling of phosphorus and potash | \(10^6 tX\) | x | x | |
| q18_translate (j, kres, attributes) |
Transformation of the multiple crop residues into supply balance crop residues in respective attribute units DM GJ Nr P K WM C | \(10^6 tX\) | x | x | |
| v18_prod_res (j, kres) |
Cluster-level production of residues | \(10^6 tDM\) | x | x | |
| v18_res_ag_recycling (i, kcr, attributes) |
Recycling of crop residues to soils in respective attribute units DM GJ Nr P K WM C | \(10^6 tX\) | x | x | |
| v18_res_ag_removal (j, kcr, attributes) |
Removal of crop residues in respective attribute units DM GJ Nr P K WM C | \(10^6 tX\) | x | x | |
| v18_res_ag_removal_reg (i, kcr, attributes) |
Regional removal of crop residues in respective attribute units DM GJ Nr P K WM C | \(10^6 tX\) | x | ||
| v18_res_biomass_ag_clust (j, kcr) |
Production of aboveground residues in each cluster | \(10^6 tDM\) | x |
| description | |
|---|---|
| attributes | Product attributes characterizing a product (such as weight or energy content) |
| burn_scen18 | scenario for burning residues on field |
| cell(i, j) | number of LPJ cells per region i |
| cgf | Residue production functions |
| ct(t) | Current time period |
| dev18 | country development indicator |
| dm_nr(attributes) | dry matter and nr |
| i | all economic regions |
| i2(i) | World regions (dynamic set) |
| j | number of LPJ cells |
| j2(j) | Spatial Clusters (dynamic set) |
| k(kall) | Primary products |
| kall | All products in the sectoral version |
| kcr(kve) | Cropping activities |
| kres_kcr(kres, kcr) | mapping of crops to different residue types |
| kres(kall) | Residues |
| kve(k) | Land-use activities |
| nonused18(kcr) | crops that are not used as residues |
| npk(nutrients) | Plant nutrients |
| nutrients(attributes) | Nutrient related product attributes |
| pk18(npk) | subset of npk containing P and K nutrients |
| t_all(t_ext) | 5-year time periods |
| t(t_all) | Simulated time periods |
| type | GAMS variable attribute used for the output |
| w | Water supply type |
Benjamin Leon Bodirsky
09_drivers, 11_costs, 16_demand, 17_production, 30_croparea, 50_nr_soil_budget, 51_nitrogen, 53_methane