The forestry module describes the constraints under which managed forest (age-class forest) exists. At the same time it calculates the corresponding carbon stocks. The module provides carbon dioxide removal (CDR) from afforestation to the GHG policy module (56_ghg_policy) as well as afforestation related costs to the costs module (11_costs).
| 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 | x |
| pm_carbon_density_ac (t, j, ac, ag_pools) |
Above ground natveg carbon density for age classes and carbon pools | \(tC/ha\) | x | x |
| pm_carbon_density_ac_forestry (t, j, ac, ag_pools) |
Above ground plantation carbon density for age classes and carbon pools | \(tC/ha\) | x | |
| sm_fix_SSP2 | year until which all parameters are fixed to SSP2 values | \(year\) | 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_land (j, land) |
Land area of the different land types | \(10^6 ha\) | x | x |
| vm_supply (i, kall) |
Regional demand | \(10^6 tDM/yr\) | x | x |
| Description | Unit | |
|---|---|---|
| vm_cdr_aff (j, ac) |
Expected CDR from afforestation depending on planning horizon | \(10^6 tC\) |
| vm_cost_fore (i) |
Afforestation costs | \(10^6 USD_{04MER}/yr\) |
| vm_landdiff_forestry | Aggregated difference in forestry land compared to previous timestep | \(10^6 ha\) |
The main feature of the this realization is afforestation for CDR. Afforestation can be modelled exogenously (prescribed by NPI/NDC policies) and/or endogenously (incentivized by a reward for CDR). National policies implemented (NPI) and nationally determined contributions to the Paris agreement (NDC) for afforestation are based on country reports. The interface vm_cdr_aff includes the expected CDR from afforestation depending on the planning horizon s32_planing_horizon. The reward for CDR from afforestation is calculated in the 56_ghg_policy module. In this realization, afforestation is modeled by default as regrowth of natural vegetation (see Humpenöder et al. (2014) for details on the implemenation). The regrowth of natural vegetation follows S-shaped growth curves, which are parametrized based on Braakhekke et al. (2019). Note that existing forestry plantations in 1995 dedicated to wood production are assumed constant throughout time.
The direct costs of afforestation vm_cost_fore include maintenance and monitoring costs for plantations (Sathaye et al. 2005). In addition, afforestation may cause costs in other parts of the model such as costs for technological change 13_tc or land expansion 39_landconversion.
\[\begin{multline*} vm\_cost\_fore(i2) = \sum_{cell(i2,j2),type32,ac,fcosts32}\left( v32\_land(j2,type32,ac) \cdot f32\_fac\_req\_ha(i2,fcosts32)\right) \end{multline*}\]
The interface vm_cdr_aff provides the projected CDR of an afforestation activity for a given planning horizon s32_planing_horizon to the 56_ghg_policy module.
\[\begin{multline*} vm\_cdr\_aff(j2,ac) = v32\_land(j2,"aff","ac0") \cdot \sum_{ct} p32\_cdr\_ac(ct,j2,ac) \end{multline*}\]
\[\begin{multline*} v32\_land(j2,"aff","ac0") \leq \sum_{ac} v32\_land(j2,"aff",ac) - \sum_{ct,ac} p32\_land(ct,j2,"aff",ac) \end{multline*}\]
The interface vm_land provides aggregated forestry land pools (type32) to other modules.
\[\begin{multline*} vm\_land(j2,"forestry") = \sum_{type32,ac} v32\_land(j2,type32,ac) \end{multline*}\]
The constraint q32_aff_pol accounts for the exogenous afforestation prescribed by NPI/NDC policies.
\[\begin{multline*} v32\_land(j2,"ndc","ac0") = \sum_{ct} p32\_aff\_pol\_timestep(ct,j2) \end{multline*}\]
The constraint q32_max_aff accounts for the allowed maximum global afforestation defined in p32_max_aff_area. Note that NPI/NDC afforestation policies are counted towards the maximum defined in p32_max_aff_area. Therefore, the right-hand side of the constraint is tightened by the value of the exogenously prescribed afforestation that has to be realized in later time steps (p32_aff_togo).
\[\begin{multline*} \sum_{\left(j2,type32,ac\right)\$\left(not sameas(type32,"plant")\right)} v32\_land(j2,type32,ac) \leq p32\_max\_aff\_area - \sum_{ct} p32\_aff\_togo(ct) \end{multline*}\]
Forestry above ground carbon stocks are calculated as the product of forestry land (v32_land) and the area weighted mean of carbon density for carbon pools (p32_carbon_density).
\[\begin{multline*} vm\_carbon\_stock(j2,"forestry",ag\_pools) = \sum_{type32,ac}\left( v32\_land(j2,type32,ac) \cdot \sum_{ct} p32\_carbon\_density\_ac(ct,j2,type32,ac,ag\_pools)\right) \end{multline*}\]
Forestry land expansion and reduction is calculated as follows:
\[\begin{multline*} vm\_landdiff\_forestry = \sum_{j2,type32,ac}\left( v32\_land\_expansion(j2,type32,ac) + v32\_land\_reduction(j2,type32,ac)\right) \end{multline*}\]
\[\begin{multline*} v32\_land\_expansion(j2,type32,ac) \geq v32\_land(j2,type32,ac) - pc32\_land(j2,type32,ac) \end{multline*}\]
\[\begin{multline*} v32\_land\_reduction(j2,type32,ac) \geq pc32\_land(j2,type32,ac) - v32\_land(j2,type32,ac) \end{multline*}\]
Wood demand is set to zero because forestry is not modeled in this realization.
vm_supply.fx(i2,kforestry) = 0;Certain areas (e.g. the boreal zone) are excluded from endogenous afforestation.
if(m_year(t) <= sm_fix_SSP2,
v32_land.fx(j,"aff","ac0") = 0;
else
v32_land.lo(j,"aff","ac0") = 0;
v32_land.up(j,"aff","ac0") = f32_aff_mask(j) * sum(land, pcm_land(j,land));
);Endogenous afforestation is limited to cells with vegetation carbon density above 20 tC/ha.
v32_land.fx(j,"aff","ac0")$(fm_carbon_density(t,j,"forestry","vegc") <= 20) = 0;
if(s32_aff_plantation = 0,
p32_carbon_density_ac(t,j,"aff",ac,ag_pools) = pm_carbon_density_ac(t,j,ac,ag_pools);
elseif s32_aff_plantation = 1,
p32_carbon_density_ac(t,j,"aff",ac,ag_pools) = pm_carbon_density_ac_forestry(t,j,ac,ag_pools);
);
p32_carbon_density_ac(t,j,"ndc",ac,ag_pools) = pm_carbon_density_ac(t,j,ac,ag_pools);
p32_carbon_density_ac(t,j,"plant",ac,ag_pools) = pm_carbon_density_ac_forestry(t,j,ac,ag_pools);CDR from afforestation for each age-class, depending on planning horizon.
p32_cdr_ac(t,j,ac)$(ord(ac) > 1 AND (ord(ac)-1) <= s32_planing_horizon/5)
= p32_carbon_density_ac(t,j,"aff",ac,"vegc") - p32_carbon_density_ac(t,j,"aff",ac-1,"vegc");Limitations Forestry activities such as establishment or harvest of plantations for wood production are not modeled.
The static realisation is very simple and does not include any equation because forestry land is assumed constant at the observed 1995 level throughout time.
Costs and CDR from afforestation are set to zero.
vm_cost_fore.fx(i) = 0;
vm_cdr_aff.fx(j,ac) = 0;All forestry land pools (aff, ndc, plant) are fixed to zero, except forestry plantations, which are fixed to the level of 1995.
v32_land.fx(j,type32,ac) = 0;
v32_land.fx(j,"plant","acx") = pcm_land(j,"forestry");Forestry above ground carbon stocks are calculated by multiplying plantations in 1995 with the forestry above ground carbon density of the current time step (pc32_carbon_density).
pc32_carbon_density(j,ag_pools) = fm_carbon_density(t,j,"forestry",ag_pools);
vm_carbon_stock.fx(j,"forestry",ag_pools) =
sum((type32,ac), v32_land.l(j,type32,ac)*pm_carbon_density_ac(t,j,ac,ag_pools));Wood demand is also set to zero because forestry is not modeled in this realization.
vm_supply.fx(i2,kforestry) = 0;Limitations Forestry activities such as establishment or harvest of plantations for wood production are not modeled. Also afforestation for CDR is not included.
| Description | Unit | A | B | |
|---|---|---|---|---|
| f32_aff_mask (j) |
Afforestation mask | \(1\) | x | |
| f32_aff_pol (t_all, j, pol32) |
Exogenous afforestation scenario | \(10^6 ha\) | x | |
| f32_fac_req_ha (i, fcosts32) |
Afforestation factor requirement costs per ha | \(USD_{04MER}/ha\) | x | |
| p32_aff_pol (t, j) |
Exogenous afforestation target as stock | \(10^6 ha\) | x | |
| p32_aff_pol_timestep (t, j) |
Exogenous afforestation target as flow per time step | \(10^6 ha/timestep\) | x | |
| p32_aff_pot (t, j) |
Potential afforestation area on cropland and pasture land | \(10^6 ha\) | x | |
| p32_aff_togo (t) |
Remaining exogenous afforestation wrt to the maximum exogenous target over time | \(10^6 ha\) | x | |
| p32_carbon_density_ac (t, j, type32, ac, ag_pools) |
Carbon density for ac and ag_pools | \(tC/ha\) | x | |
| p32_cdr_ac (t, j, ac) |
Non-cumulative CDR from afforestation for each age-class depending on planning horizon | \(tC/ha\) | x | |
| p32_land (t, j, type32, ac) |
Forestry land for each cell wood type and age class before and after optimization | \(10^6 ha\) | x | |
| p32_max_aff_area | Maximum global afforestation area that is greater or equal the exogenous policy target | \(10^6 ha\) | x | |
| pc32_carbon_density (j, ag_pools) |
Above ground carbon density in optimization | \(tC/ha\) | x | |
| pc32_land (j, type32, ac) |
Forestry land per forestry land type initialization of the optimization | \(10^6 ha\) | x | |
| q32_aff_ac0 (j) |
Afforestation constraint for ac0 | \(10^6 ha\) | x | |
| q32_aff_pol (j) |
Afforestation policy constraint | \(10^6 ha\) | x | |
| q32_carbon (j, ag_pools) |
Forestry carbon stock calculation C | \(10^6 tC\) | x | |
| q32_cdr_aff (j, ac) |
Calculation of CDR from afforestation in terms of CO2-C | \(10^6 tC\) | x | |
| q32_cost_fore_ac (i) |
Total forestry costs constraint | \(10^6 USD_{04MER}\) | x | |
| q32_land (j) |
Land constraint | \(10^6 ha\) | x | |
| q32_land_diff | Aggregated difference in forestry land compared to previous timestep | \(10^6 ha\) | x | |
| q32_land_expansion (j, type32, ac) |
Forestry land expansion | \(10^6 ha\) | x | |
| q32_land_reduction (j, type32, ac) |
Forestry land reduction | \(10^6 ha\) | x | |
| q32_max_aff | Maximum total global afforestation | \(10^6 ha\) | x | |
| s32_aff_plantation | switch for using natveg (0) or plantation (1) growth curves for afforestation | x | ||
| s32_max_aff_area | Maximum global endogenous afforestation | \(10^6 ha\) | x | |
| s32_planing_horizon | Afforestation planing horizon | \(years\) | x | |
| s32_shift | Number of 5-year age-classes corresponding to current time step length | \(1\) | x | |
| v32_land (j, type32, ac) |
Forestry land pools | \(10^6 ha\) | x | x |
| v32_land_expansion (j, type32, ac) |
Forestry land expansion compared to previous timestep | \(10^6 ha\) | x | |
| v32_land_reduction (j, type32, ac) |
Forestry land reduction compared to previous timestep | \(10^6 ha\) | x |
| description | |
|---|---|
| ac | Age classes |
| ac_sub(ac) | age classes |
| ag_pools(c_pools) | Above ground carbon pools |
| age | Population age groups |
| c_pools | Carbon pools |
| cell(i, j) | number of LPJ cells per region i |
| ct(t) | Current time period |
| fcosts32 | forestry factor cost per annum |
| i | all economic regions |
| i2(i) | World regions (dynamic set) |
| j | number of LPJ cells |
| j2(j) | Spatial Clusters (dynamic set) |
| kall | All products in the sectoral version |
| kforestry(kall) | Forestry products |
| land | Land pools |
| pol32 | afforestation policy type |
| t_all | 5-year time periods |
| t(t_all) | Simulated time periods |
| type | GAMS variable attribute used for the output |
| type32 | plantation type |
Florian Humpenöder
10_land, 11_costs, 16_demand, 52_carbon, 56_ghg_policy
Braakhekke, Maarten C., Jonathan C. Doelman, Peter Baas, Christoph Müller, Sibyll Schaphoff, Elke Stehfest, and Detlef P. van Vuuren. 2019. “Modelling Forest Plantations for Carbon Uptake with the LPJmL Dynamic Global Vegetation Model.” Earth System Dynamics Discussions, April, 1–24. https://doi.org/https://doi.org/10.5194/esd-2019-13.
Humpenöder, Florian, Alexander Popp, Jan Philip Dietrich, David Klein, Hermann Lotze-Campen, Markus Bonsch, Benjamin Leon Bodirsky, Isabelle Weindl, Miodrag Stevanovic, and Christoph Müller. 2014. “Investigating Afforestation and Bioenergy CCS as Climate Change Mitigation Strategies.” Environmental Research Letters 9 (6): 064029. https://doi.org/10.1088/1748-9326/9/6/064029.
Sathaye, Jayant, Willy Makundi, Larry Dale, Peter Chan, and Kenneth Andrasko. 2005. “GHG Mitigation Potential, Costs and Benefits in Global Forests: A Dynamic Partial Equilibrium Approach.” Lawrence Berkeley National Laboratory, March. http://escholarship.org/uc/item/92d5m16v.