# Model Documentation

### | Version 4.0

created with goxygen 0.21.1

# 31_past

# Pasture (31_past)

## Description

The pasture module determines land used as pasture for livestock rearing. At the same time, it calculates geographically explicit production of pasture biomass and the carbon content of pasture land. Therefore, the module requires cellular information about the carbon density related to the different pasture carbon pools. Furthermore, it delivers regional production costs associated with pastures.

## Interfaces

Interfaces to other modules

### Input

module inputs (A: endo_jun13 | B: static)
| Description | Unit | A | B
--- | --- | --- | --- | ---
fm_carbon_density (t_all, j, land, c_pools) | LPJmL carbon density for land and carbon pools | \(tC/ha\) | x | x
pcm_land (j, land) | Land area in previous time step | \(10^6 ha\) |  | x
vm_carbon_stock (j, land, c_pools) | Carbon stock in vegetation soil and litter for different land types | \(10^6 tC\) | x | x
vm_cost_prod (i, kall) | Factor costs | \(10^6 USD_{05MER}/yr\) | x | x
vm_land (j, land) | Land area of the different land types | \(10^6 ha\) | 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 |
vm_yld (j, kve, w) | Yields (variable because of technical change) | \(tDM/ha/yr\) | x |

### Output

## Realizations

### (A) endo_jun13

In the endo_jun13 realization, pasture area and related carbon stocks are modelled endogenously. The initial spatially explicit patterns of pasture are defined in the module 10_land by the land use input data set. For future time steps, pasture area depends on the demand for biomass from pastures to feed livestock as calculated in the module 70_livestock and from the intensity of pasture utilization ("pasture yield") as determined in the module 14_yields.

Production of pasture biomass is restricted to pasture area which is delivered as module output together with the resulting geographically explicit production of pasture biomass. Cellular production is calculated by multiplying pasture area `vm_land` with cellular rainfed pasture yields `vm_yld` which are delivered by the module 14_yields:

\[\begin{multline*} vm\_prod(j2,"pasture") = vm\_land(j2,"past") \cdot vm\_yld(j2,"pasture","rainfed") \end{multline*}\]

On the basis of the required pasture area, cellular carbon stocks are calculated:

\[\begin{multline*} vm\_carbon\_stock(j2,"past",c\_pools) = \sum_{ct}\left( vm\_land(j2,"past") \cdot fm\_carbon\_density(ct,j2,"past",c\_pools)\right) \end{multline*}\]

In the initial calibration time step, where the pasture calibration factor is calculated that brings pasture biomass demand and pasture area in balance, small costs are attributed to the production of pasture biomass in order to avoid overproduction of pasture in the model:

\[\begin{multline*} vm\_cost\_prod(i2,"pasture") = vm\_prod\_reg(i2,"pasture") \cdot s31\_fac\_req\_past \end{multline*}\]

For all following time steps, factor requriements `s31_fac_req_past` are set to zero.

> Limitations No consideration of generic differences between extensive and intensive grazing systems, of explicit pasture management options and of related degradation of pastures.

### (B) static

In the static realization, pasture areas are constant over time, independent from developments in the livestock sector and land competition.

Pasture areas are fixed to the initial spatially explicit patterns defined in the module 10_land by the land use input data set.

    vm_land.fx(j,"past") = pcm_land(j,"past");

Correspondingly, also the carbon stocks related to pasture areas are fixed.

    vm_carbon_stock.fx(j,"past",c_pools) =
              pcm_land(j,"past")*fm_carbon_density(t,j,"past",c_pools);

Regional costs associated with pasture management are set to zero.

    vm_cost_prod.fx(i,"pasture") = 0;

> Limitations There are no computational limitations to this realization. Since pasture areas are static, they do not respond to demand trajectories and trends in the land use and agricultural sectors like intensification pathways, increasing production of animal products, bioenergy production or afforestation policies. This may lead to an inconsistent overall picture of future land use dynamics.

## Definitions

### Objects

module-internal objects (A: endo_jun13 | B: static)
| Description | Unit | A | B
--- | --- | --- | --- | ---
q31_carbon (j, c_pools) | Carbon content calculation for pasture | \(10^6 tC\) | x |
q31_cost_prod_past (i) | Costs for putting animals on pastures | \(10^6 USD_{05MER}/yr\) | x |
q31_prod (j) | Cellular pasture production constraint | \(10^6 tDM/yr\) | x |
s31_fac_req_past | Factor requirements | \(USD_{05MER}/tDM\) | x |

### Sets

sets in use
| description
--- | ---
c_pools | Carbon pools
i | World regions
kall | All products in the sectoral version
k(kall) | Primary products
kve(k) | Land-use activities
land | Land pools
t_all | 5-year time periods
w | Water supply type

## Authors

Isabelle Weindl, Jan Philipp Dietrich

## See Also

10_land, 14_yields, 17_production, 38_factor_costs, 52_carbon

## References