The module 71_disagg_lvst calculates the livestock distribution within a region onto cellular level. Without constrains in this module cellular livestock production is determined by the modules 40_transport accounting for transport costs and module 42_water_demand connecting livestock production to water demand and thus to water availability.
| Description | Unit | A | B | C | |
|---|---|---|---|---|---|
| fm_feed_balanceflow (t_all, i, kap, kall) |
Balanceflow balance difference between estimated feed baskets and FAO | \(10^6 tDM\) | x | x | |
| im_feed_baskets (t_all, i, kap, kall) |
Feed baskets in tDM per tDM livestock product | \(1\) | x | x | |
| pcm_land (j, land) |
Land area in previous time step including possible changes after optimization | \(10^6 ha\) | x | ||
| pm_land_start (j, land) |
Land initialization area | \(10^6 ha\) | x | x | |
| vm_prod (j, k) |
Production in each cell | \(10^6 tDM/yr\) | x | x | |
| vm_prod_reg (i, kall) |
Regional aggregated production | \(10^6 tDM/yr\) | x | x |
| Description | Unit | |
|---|---|---|
| vm_costs_additional_mon (i) |
Punishment cost for additionally transported monogastric livst_egg | \(10^6 USD_{05MER}/yr\) |
The foragebased_aug18 realization constrains the cellular ruminant livestock production by the feed availability for grazed pasture and fodder crops. This accounts for the fact that pasture and fodder (summarized with forage) feed stuff is usually not transported over long distances and at the same time is very essential in livestock diets. Internally it distinguishs between extensively and intensively fed ruminants. The monogastric livestock is distributed following the idea that these animals are held close to densely populated areas. For more detailed information on cellular livestock distribution see Robinson et al. (2014), which inspired this realization. This realization includes a minimal lower bound for ruminant production to avoid avoid GAMS corner solutions at higher spatial resolutions.
Ruminant livestock production within a cell is determined by the production of the non-transportable feed items grazed pasture and fodder. These must be larger than the ruminant feed requirements that are given by the product of ruminant production and the respective feed baskets:
\[\begin{multline*} vm\_prod\left(j2, kforage\right) \geq \sum_{kli\_rum}\left( v71\_prod\_rum\left(j2, kli\_rum, kforage\right) \cdot \sum_{ct, cell(i2,j2), kforage2}\left( im\_feed\_baskets\left(ct, i2, kli\_rum,kforage2\right)\right) \cdot v71\_feed\_balanceflow\_share\left(j2, kli\_rum, kforage\right)\right) \end{multline*}\]
The above equation contains a split of pasture and fodder fed ruminants, since we assume that depending on the intensity level of the livestock production, ruminants will graze on pastures (extensive systems) or will be fed via harvested fodder crops (intensive systems). A regional balance flow accounts in 70_livestock q70_feed(i2,kap,kall) for inconsistencies with the FAO inventory of national feed use. On cellular level we distribute the regional balance flow as a multiplicative correction term (introduced in q71_feed_rum_liv) that is given by
\[\begin{multline*} v71\_feed\_balanceflow\_share\left(j2, kli\_rum, kforage\right) = 1 + \sum_{ct, cell(i2,j2)}\left(\frac{ fm\_feed\_balanceflow\left(ct, i2, kli\_rum, kforage\right) }{ \left(im\_feed\_baskets\left(ct, i2, kli\_rum, kforage\right) \cdot vm\_prod\_reg\left(i2, kli\_rum\right) + 10^{\left(-10\right)}\right)}\right) \end{multline*}\]
The total cellular ruminant production is then given by
\[\begin{multline*} vm\_prod(j2,kli\_rum) = \sum_{kforage}v71\_prod\_rum(j2,kli\_rum,kforage) \end{multline*}\]
To account for the above mentioned fact that monogastric livestock are held close to the population, it is distributed based on urban area by the formula
\[\begin{multline*} vm\_prod(j2,kli\_mon) \leq i71\_urban\_area\_share(j2) \cdot s71\_scale\_mon \cdot \sum_{cell(i2,j2)}vm\_prod\_reg(i2,kli\_mon) + v71\_additional\_mon(j2,kli\_mon) \end{multline*}\]
Note that s71_scale_mon relaxes the constraint (per default by 10%) and v71_additional_mon ensures feasability by punishing additonal monogastric production within a cluster. The punishmment of additional monogastric livestock production are calculated via
\[\begin{multline*} vm\_costs\_additional\_mon(i2) = \sum_{cell(i2,j2),kli\_mon} v71\_additional\_mon(j2,kli\_mon) \cdot s71\_punish\_additional\_mon \end{multline*}\]
Note that the punishment costs are based on transport costs and scaled up by one order of magnitude of the average transport costs to account for additional transport between clusters.
Limitations Distribution of monogastrics do not account for feed availability within a cell. Crop residue feed stuff for ruminant production is also not considered to restrict livestock production. Forage feed stuff is consider not to be transported, but is in reality.
The foragebased_jul23 realization constrains the cellular ruminant livestock production by the feed availability for grazed pasture and fodder crops. This accounts for the fact that pasture and fodder (summarized with forage) feed stuff is usually not transported over long distances and at the same time is very essential in livestock diets. The monogastric livestock is distributed following the idea that these animals are held close to densely populated areas. For more detailed information on cellular livestock distribution see Robinson et al. (2014), which inspired this realization. This realization includes a minimal lower bound for ruminant production to avoid avoid GAMS corner solutions at higher spatial resolutions. It also has a linearized version, which can be switch on via s71_lp_fix.
Ruminant livestock production within a cell is determined by the production of the non-transportable feed items grazed pasture and fodder (kforage). Forage production must be larger than the ruminant feed requirements (v71_feed_forage) adjusted by a balance flow (v71_feed_forage).
\[\begin{multline*} vm\_prod(j2,kforage) \geq v71\_feed\_forage(j2,kforage) + v71\_feed\_balanceflow(j2,kforage) \end{multline*}\]
Ruminant feed requirements are given by the product of ruminant production and the respective feed baskets.
\[\begin{multline*} \sum_{kforage} v71\_feed\_forage(j2,kforage) = \sum_{kli\_rum,kforage}\left( vm\_prod(j2,kli\_rum) \cdot \sum_{ct,cell(i2,j2)}im\_feed\_baskets(ct,i2,kli\_rum,kforage)\right) \end{multline*}\]
The above equation contains a split of pasture and fodder fed ruminant feed requirements, since we assume that depending on the intensity level of the livestock production, ruminants will graze on pastures (extensive systems) or will be fed via harvested fodder crops (intensive systems). The balance flow for pasture and fodder production (kforage) accounts as in 70_livestock q70_feed(i2,kap,kall) for inconsistencies with the FAO inventory of national feed use. In each cluster the balance flow is constrained by its share of livestock production regarding the regional level by
\[\begin{multline*} \sum_{kforage} v71\_feed\_balanceflow(j2,kforage) = \sum_{ct,cell(i2,j2),kli\_rum,kforage}\left( fm\_feed\_balanceflow(ct,i2,kli\_rum,kforage) \cdot \left(\frac{vm\_prod(j2,kli\_rum) }{ vm\_prod\_reg(i2,kli\_rum)}\right)\right) \end{multline*}\]
To account for the above mentioned fact that monogastric livestock are held close to the population, it is distributed based on urban area by the formula
\[\begin{multline*} vm\_prod(j2,kli\_mon) \leq i71\_urban\_area\_share(j2) \cdot s71\_scale\_mon \cdot \sum_{cell(i2,j2)}vm\_prod\_reg(i2,kli\_mon) + v71\_additional\_mon(j2,kli\_mon) \end{multline*}\]
Note that s71_scale_mon relaxes the constraint (per default by 10%) and v71_additional_mon ensures feasability by punishing additonal monogastric production within a cluster. The punishmment of additional monogastric livestock production are calculated via
\[\begin{multline*} vm\_costs\_additional\_mon(i2) = \sum_{cell(i2,j2),kli\_mon} v71\_additional\_mon(j2,kli\_mon) \cdot s71\_punish\_additional\_mon \end{multline*}\]
Note that the punishment costs are based on transport costs and scaled up by one order of magnitude of the average transport costs to account for additional transport between clusters.
Limitations Distribution of monogastrics do not account for feed availability within a cell. Crop residue feed stuff for ruminant production is also not considered to restrict livestock production. Forage feed stuff is consider not to be transported, but is in reality.
The off realization does not account for any further restriction of the livestock distribution.
Limitations This realization underestimates real world drivers for livestock distribution.
| Description | Unit | A | B | C | |
|---|---|---|---|---|---|
| i71_urban_area_share (j) |
Share of urban area within a region | \(1\) | x | x | |
| q71_balanceflow_constraint (j, kli_rum, kforage) |
Nonlinear balanceflow constraint for cellular forage feed products | \(10^6 tDM/yr\) | x | ||
| q71_feed_balanceflow_lp (i) |
Linear balanceflow constraint for forage feed products | \(10^6 tDM/yr\) | x | ||
| q71_feed_balanceflow_nlp (j) |
Non-linear balanceflow constraint for forage feed products | \(10^6 tDM/yr\) | x | ||
| q71_feed_forage (j) |
Forage feed constraint | \(10^6 tDM/yr\) | x | ||
| q71_feed_rum_liv (j, kforage) |
Production constraint for ruminant livestock products | \(10^6 tDM/yr\) | x | x | |
| q71_prod_mon_liv (j, kli_mon) |
Production constraint for monogastric livestock products | \(10^6 tDM/yr\) | x | x | |
| q71_punishment_mon (i) |
Punishment for additional monogastrics | \(10^6 USD_{05MER}/yr\) | x | x | |
| q71_sum_rum_liv (j, kli_rum) |
Total production of forage fed ruminants | \(10^6 tDM/yr\) | x | ||
| s71_lp_fix | Switch to fix equations to linear relation | \(Logical\) | x | ||
| s71_punish_additional_mon | Scaling factor for transport punishment | \(USD_{05MER}/tDM\) | x | x | |
| s71_scale_mon | Scalar for flexible distribution of monogastrics | \(1\) | x | x | |
| v71_additional_mon (j, kli_mon) |
Additional punished production of monogastric livestock | \(10^6 tDM/yr\) | x | x | |
| v71_feed_balanceflow (j, kforage) |
Cellular feed balanceflow for forage feed for ruminant livestock | \(10^6 tDM/yr\) | x | ||
| v71_feed_balanceflow_share (j, kli_rum, kforage) |
Cellular feed balanceflow multiplier for forage feed for ruminant livestock | \(1\) | x | ||
| v71_feed_forage (j, kforage) |
Production of forage within a cell | \(10^6 tDM/yr\) | x | ||
| v71_prod_rum (j, kli_rum, kforage) |
Production of forage fed ruminants within a cell | \(10^6 tDM/yr\) | x |
| description | |
|---|---|
| cell(i, j) | number of LPJ cells per region i |
| ct(t) | Current time period |
| 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 |
| kap(k) | Animal products |
| kforage(k) | Forage feed categories |
| kli_mon(kli) | Monogastric livestock |
| kli_rum(kli) | Ruminant livestock |
| kli(kap) | Livestock products |
| land | Land pools |
| t_all(t_ext) | 5-year time periods |
| t(t_all) | Simulated time periods |
| type | GAMS variable attribute used for the output |
Kristine Karstens, Benjamin Bodirsky
10_land, 11_costs, 17_production, 70_livestock, 71_disagg_lvst