MAgPIE - An Open Source land-use modeling framework

4.8.2

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Cropland (29_cropland)

Description

Cropland is defined as the sum of croparea, fallow land and tree cover on cropland. Croparea and corresponding carbon stocks are provided from [30_crop]. Area and carbon stocks for fallow land and tree cover are defined in this module.

Interfaces

Input

Output

Realizations

(A) detail_apr24

In this realization, total cropland equals the sum of croparea,
fallow land and tree cover on cropland. Correspondingly, cropland carbon stocks consist of carbons stocks for croparea, fallow land and tree cover on cropland. The development of fallow land and tree cover on cropland depends on targets defined as a certain fraction of total cropland. These targets can be either exogenously enforced (rule-based) or endogenously incentivized by a penalty term, which enters the objective function. This realisation also includes the option to reserve a minimum semi-natural vegetation share within the total available cropland for other land cover classes, including grassland, forest, and other land (by a given target year), in order to provide species habitats and to benefit from ecosystem ervices in agricultural landscapes.

Total cropland is calculated as the sum of croparea, fallow land and tree cover area.

$$\begin{multline*} vm\_land(j2,"crop") = \sum_{kcr,w} vm\_area(j2,kcr,w) + vm\_fallow(j2) + \sum_{ac} v29\_treecover(j2,ac) \end{multline*}$$

We assume that crop production can only take place on suitable cropland area. We use a suitability index (SI) map from Zabel, Putzenlechner, and Mauser (2014) to exclude areas from cropland production that have a low suitability, e.g. due to steep slopes, to estimate the available cropland area. The cultivated area therefore has to be smaller than the available cropland area. Moreover, the available cropland can be reduced by constraining the cropland area in favour of other land types, in order to increase compositional heterogeneity of land types at the cell level.

$$\begin{multline*} vm\_land(j2,"crop") \leq \sum_{ct} p29\_avl\_cropland(ct,j2) \end{multline*}$$

Total cost for the cropland module.

$$\begin{multline*} vm\_cost\_cropland(j2) = v29\_cost\_treecover\_est(j2) + v29\_cost\_treecover\_recur(j2) + v29\_fallow\_missing(j2) \cdot \sum_{ct} i29\_fallow\_penalty(ct) + v29\_treecover\_missing(j2) \cdot \sum_{ct} i29\_treecover\_penalty(ct) \end{multline*}$$

The carbon stocks of total cropland are calculated as the sum of carbon stocks in cropland, fallow land and tree cover area.

$$\begin{multline*} vm\_carbon\_stock(j2,"crop",ag\_pools,stockType) = vm\_carbon\_stock\_croparea(j2,ag\_pools) + vm\_fallow(j2) \cdot \sum_{ct} fm\_carbon\_density(ct,j2,"crop",ag\_pools) + m\_carbon\_stock\_ac(v29\_treecover,p29\_carbon\_density\_ac,"ac","ac\_sub") \end{multline*}$$

The semi-natural land constraint in cropland areas for sustaining critical regulating NCP for agricultural production is added on top of land conserved for other reasons (e.g. conservation of intact ecosystems or protection of biodiversity hotspots).

$$\begin{multline*} \sum_{land\_snv} vm\_land(j2,land\_snv) \geq \sum_{ct} p29\_snv\_shr(ct,j2) \cdot vm\_land(j2,"crop") + \sum_{ct,land\_snv,consv\_type} pm\_land\_conservation(ct,j2,land\_snv,consv\_type) \end{multline*}$$

The semi-natural vegetation constraint for cropland areas has been suggested at the per square kilometer scale. The amount of cropland requiring relocation has therefore been derived from exogeneous high-resolution land cover information from the Copernicus Global Land Service (Buchhorn et al. (2020)).

$$\begin{multline*} \sum_{land\_snv} vm\_lu\_transitions(j2,"crop",land\_snv) \geq \sum_{ct} p29\_snv\_relocation(ct,j2) \end{multline*}$$

A penalty is applied for the violation of fallow land rules. The penalty applies to the missing fallow land, i.e. where fallow land is lower than a certain fraction of total cropland.

$$\begin{multline*} v29\_fallow\_missing(j2) \geq vm\_land(j2,"crop") \cdot \sum_{ct} i29\_fallow\_target(ct) - vm\_fallow(j2) \end{multline*}$$

$$\begin{multline*} vm\_fallow(j2) \leq vm\_land(j2,"crop") \cdot s29\_fallow\_max \end{multline*}$$

Fallow land biodiversity value is based on perennial crops.

$$\begin{multline*} vm\_bv(j2,"crop\_fallow",potnatveg) = vm\_fallow(j2) \cdot fm\_bii\_coeff("crop\_per",potnatveg) \cdot fm\_luh2\_side\_layers(j2,potnatveg) \end{multline*}$$

Interface vm_treecover for other modules.

$$\begin{multline*} vm\_treecover(j2) = \sum_{ac} v29\_treecover(j2,ac) \end{multline*}$$

A penalty is applied for the violation of treecover rules. The penalty applies to the missing treecover area, i.e. where treecover area is lower than a certain fraction of total cropland.

$$\begin{multline*} v29\_treecover\_missing(j2) \geq vm\_land(j2,"crop") \cdot \sum_{ct} i29\_treecover\_target(ct,j2) - \sum_{ac} v29\_treecover(j2,ac) \end{multline*}$$

$$\begin{multline*} \sum_{ac} v29\_treecover(j2,ac) \leq vm\_land(j2,"crop") \cdot s29\_treecover\_max \end{multline*}$$

Depending on s29_treecover_bii_coeff, tree cover biodiversity value is based on natural vegetation or plantation BII coefficients.

$$\begin{multline*} vm\_bv(j2,"crop\_tree",potnatveg) = \sum_{bii\_class\_secd}\left( \sum\left(ac\_to\_bii\_class\_secd(ac,bii\_class\_secd), v29\_treecover(j2,ac)\right) \cdot p29\_treecover\_bii\_coeff(bii\_class\_secd,potnatveg)\right) \cdot fm\_luh2\_side\_layers(j2,potnatveg) \end{multline*}$$

Cropland tree cover annuity cost.

$$\begin{multline*} v29\_cost\_treecover\_est(j2) = \sum_{ac\_est} v29\_treecover(j2,ac\_est) \cdot s29\_cost\_treecover\_est \cdot \sum_{cell(i2,j2),ct}\left(\frac{pm\_interest(ct,i2)}{\left(1+pm\_interest(ct,i2)\right)}\right) \end{multline*}$$

Cropland tree cover recurring cost.

$$\begin{multline*} v29\_cost\_treecover\_recur(j2) = \sum_{ac\_sub} v29\_treecover(j2,ac\_sub) \cdot s29\_cost\_treecover\_recur \end{multline*}$$

Cropland tree cover establishment rules for distributing areas equally to age-classes. For a 5-year time step ac_est includes only ac0. But for a 10-year time step ac_est includes ac0 and ac5.

$$\begin{multline*} v29\_treecover(j2,ac\_est) = \frac{ \sum_{ac\_est2} v29\_treecover(j2,ac\_est2)}{card(ac\_est2)} \end{multline*}$$

Switch for tree cover on cropland: 0 = Use natveg growth curve towards LPJmL natural vegetation 1 = Use plantation growth curve (faster than natveg) towards LPJmL natural vegetation

Minimum semi-natural vegetation (SNV) share is fading in after 2020

p29_snv_shr(t,j) = i29_snv_scenario_fader(t) *
  (s29_snv_shr * sum(cell(i,j), p29_country_weight(i))
  + s29_snv_shr_noselect * sum(cell(i,j), 1-p29_country_weight(i)));

Cropland relocation in response to SNV policy is based on exogeneous land cover information from the Copernicus Global Land Service (Buchhorn et al. (2020)). The rate of the policy implementation is derived based on the difference of scenario fader values in consecutive time steps

p29_snv_relocation(t,j) = (i29_snv_scenario_fader(t) - i29_snv_scenario_fader(t-1)) *
  (i29_snv_relocation_target(j) * sum(cell(i,j), p29_country_weight(i))
  + s29_snv_shr_noselect * sum(cell(i,j), 1-p29_country_weight(i)));

The following lines take care of mismatches in the input data (derived from satellite imagery from the Copernicus Global Land Service (Buchhorn et al. (2020))) and in cases of cropland reduction

p29_max_snv_relocation(t,j) = p29_snv_shr(t,j) * (i29_snv_scenario_fader(t) - i29_snv_scenario_fader(t-1)) * pcm_land(j,"crop")
                              - sum(ac, pc29_treecover(j,ac));
p29_max_snv_relocation(t,j)$(p29_max_snv_relocation(t,j) < 1e-6) = 0;  
p29_snv_relocation(t,j)$(p29_snv_relocation(t, j) > p29_max_snv_relocation(t,j)) = p29_max_snv_relocation(t,j);

Area potentially available for cropping

p29_avl_cropland(t,j) = f29_avl_cropland(j,"%c29_marginal_land%") * (1 - p29_snv_shr(t,j));

Limitations There are currently no known limitations of this realization.

(B) simple_apr24

In this realization, total cropland equals croparea because fallow land and tree cover on cropland are fixed to zero. Therefore, also cropland carbon stocks consist only of croparea carbon stocks. Biodiversity BII values are fixed to zero. Costs are fixed to zero. This realisation also includes the option to reserve a minimum semi-natural vegetation share within the total available cropland for other land cover classes, including grassland, forest, and other land (by a given target year), in order to provide species habitats and to benefit from ecosystem ervices in agricultural landscapes.

Total cropland equals croparea, because fallow land is fixed to zero and tree cover on cropland does not exist in this realization.

$$\begin{multline*} vm\_land(j2,"crop") = \sum_{kcr,w} vm\_area(j2,kcr,w) \end{multline*}$$

We assume that crop production can only take place on suitable cropland area. We use a suitability index (SI) map from Zabel, Putzenlechner, and Mauser (2014) to exclude areas from cropland production that have a low suitability, e.g. due to steep slopes, to estimate the available cropland area. The cultivated area therefore has to be smaller than the available cropland area.

$$\begin{multline*} vm\_land(j2,"crop") \leq \sum_{ct} p29\_avl\_cropland(ct,j2) \end{multline*}$$

The carbon stocks of total cropland are calculated as the sum of carbon stocks in cropland, fallow land and tree cover area.

$$\begin{multline*} vm\_carbon\_stock(j2,"crop",ag\_pools,stockType) = vm\_carbon\_stock\_croparea(j2,ag\_pools) \end{multline*}$$

The semi-natural land constraint in cropland areas for sustaining critical regulating NCP for agricultural production is added on top of land conserved for other reasons (e.g. conservation of intact ecosystems or protection of biodiversity hotspots).

$$\begin{multline*} \sum_{land\_snv} vm\_land(j2,land\_snv) \geq \sum_{ct} p29\_snv\_shr(ct,j2) \cdot vm\_land(j2,"crop") + \sum_{ct,land\_snv,consv\_type} pm\_land\_conservation(ct,j2,land\_snv,consv\_type) \end{multline*}$$

The semi-natural vegetation constraint for cropland areas has been suggested at the per square kilometer scale. The amount of cropland requiring relocation has therefore been derived from exogeneous high-resolution land cover information from the Copernicus Global Land Service (Buchhorn et al. (2020)).

$$\begin{multline*} \sum_{land\_snv} vm\_lu\_transitions(j2,"crop",land\_snv) \geq \sum_{ct} p29\_snv\_relocation(ct,j2) \end{multline*}$$

Minimum semi-natural vegetation (SNV) share is fading in after 2020

p29_snv_shr(t,j) = i29_snv_scenario_fader(t) *
  (s29_snv_shr * sum(cell(i,j), p29_country_weight(i))
  + s29_snv_shr_noselect * sum(cell(i,j), 1-p29_country_weight(i)));

Cropland relocation in response to SNV policy is based on exogeneous land cover information from the Copernicus Global Land Service (Buchhorn et al. (2020)). The rate of the policy implementation is derived based on the difference of scenario fader values in consecutive time steps

p29_snv_relocation(t,j) = (i29_snv_scenario_fader(t) - i29_snv_scenario_fader(t-1)) *
  (i29_snv_relocation_target(j) * sum(cell(i,j), p29_country_weight(i))
  + s29_snv_shr_noselect * sum(cell(i,j), 1-p29_country_weight(i)));

The following lines take care of mismatches in the input data (derived from satellite imagery from the Copernicus Global Land Service (Buchhorn et al. (2020))) and in cases of cropland reduction

p29_max_snv_relocation(t,j) = p29_snv_shr(t,j) * (i29_snv_scenario_fader(t) - i29_snv_scenario_fader(t-1)) * pcm_land(j,"crop")
                              - vm_treecover.l(j);
p29_max_snv_relocation(t,j)$(p29_max_snv_relocation(t,j) < 1e-6) = 0;  
p29_snv_relocation(t,j)$(p29_snv_relocation(t, j) > p29_max_snv_relocation(t,j)) = p29_max_snv_relocation(t,j);

Area potentially available for cropping

p29_avl_cropland(t,j) = f29_avl_cropland(j,"%c29_marginal_land%") * (1 - p29_snv_shr(t,j));

Limitations Fallow land and tree cover on cropland are fixed to zero

Definitions

Objects

Sets

Authors

Florian Humpenöder, Benjamin Bodirsky, Patrick v. Jeetze

See Also

10_land, 11_costs, 12_interest_rate, 22_land_conservation, 30_croparea, 32_forestry, 44_biodiversity, 50_nr_soil_budget, 52_carbon, 56_ghg_policy, 59_som

References