Forestry Land Module (32_forestry)


The forest land module describes the constraints under which managed forest (age-class forest) exists. At the same time it calculates the corresponding carbon stocks.



Name Description Unit A B
$fm\_carbon\_density(t,j,land,c\_pools)$ carbon density in vegetation, soil and litter of current time step tC per ha x x
$sm\_invest\_horizon$ investment time horizon years x
$vm\_land(j,land,si)$ areas of the different land types mio. ha x x
$pcm\_land(j,land,si)$ current area of different land types mio. ha x x
$vm\_carbon\_stock(j,land,c\_pools)$ The cell and carbon pool specific carbon stock of the forest land pool Mio tC x x
$sm\_years$ length of current time step years x

The last columns of the table indicate the usage in the different realizations (numbered with capital letters)


Name Description Unit
$vm\_cost\_fore(i)$ Afforestation costs mio. US$
$vm\_exp\_emis\_affore(j,emis_co2_forestry)$ total additional co2_c emissions beyond current time step according to sm_invest_horizon Tg CO2-C

Interface plot

Figure 0: Information exchange among modules


(A) static (default)

In the static realisation forestry land is hold fixed on the observed 1995 level. This represents a static forestry sector, assuming that the roundwood demand can be fulfilled with current areas.

static forestry sector
vm_cost_fore and vm_exp_emis_affore are fixed to 0;

(B) affore_apr15

In the affore realisation, the forestry sector is static as described in the static realisation. But on top of the existing forestry land in 1995, forestry land can increase in size due to afforestation.
The incentive for afforestation is cost reduction (objective function of MAgPIE) through generation of negative carbon emissions. If a carbon price is applied on carbon emissions, negative emissions return a negative cash flow, reducing global production costs. Negative emissions on forestry land can be generated by increasing carbon stocks through afforestation.

In general an afforestation activity takes places if the benefits outweigh the costs (NPV > 0) based on a investment horizon of 30 years ($sm\_invest\_horizon$).

Calculation of the benefit of an afforestation activity, represented by the annual cost reduction through afforestation, is splitted in the GAMS code. The forestry module calculates expected cumulative negative carbon emissions through afforestation beyond the current time step until the end of the 30 year time horizon (equation 1) and stores the information in the interface $vm\_exp\_emis\_affore$. The set $ac$ starts with $ac0$ and not $ac5$. This is accounted for in equation 1 by subsetting $ord(ac)$ accordingly ($ord(ac0)$ = 1, $ord(ac5)$ = 2). Based on $vm\_exp\_emis\_affore$ the maccs module (57_maccs) calculates the average annual cost reduction by application of carbon price, discount factor and annuity factor.

Equation 1:
vm\_exp\_emis\_affore(j,emis\_co2\_forestry) =\\
\sum_{ord(ac) > 1}^{ord(ac)-1 \leq \frac{sm\_invest\_horizon}{5}} \sum_{si} \sum_{emis\_co2\_to\_forestry}
v32\_land\_fore(j,\text{"new"},si) * \\
(pc32\_carbon\_density\_ac(j,ac-1,c\_pools) - pc32\_carbon\_density\_ac(j,ac,c\_pools))\\
The costs of an afforestation activity are represented by the sum of annual costs for land conversion into foresty land, calculated by the land conversion costs module (39_landconversion), and annual factor requirement costs (equation 2):

Equation 2:
vm\_cost\_fore(i,\text{"ac"}) = \sum_{i(j)} \sum_{si} \sum_{land32!=\text{"old"}} \sum_{fcosts} v32\_land\_fore(j,land32,si)*f32\_fac\_req\_ha(i,fcosts)

Vegetation, litter and soil carbon densities are organized in age-classes
The cellular long-term equilibrium carbon densities for vegetation, litter and soil are derived from LPJmL5 ($fm\_carbon\_density$).
Age-class dependent vegetation carbon density $pc32\_carbon\_density\_ac(j,ac,\text{"vegc"})$ is calculated using the Chapman-Richards volume growth model based on Murray/Gadow1 (1993) and Gadow/von Hui2 (2001).

Equation 3:
pc32\_carbon\_density\_ac(j,ac,\text{"vegc"}) =\\
fm\_carbon\_density(t,j,\text{"forestry"},\text{"vegc"})\cdot(1-e^{-f32\_growth\_par(i(j),\text{"k"}))\cdot 5(ord(ac)-1)})^{f32\_growth\_par(i(j),\text{"m"})}

Figure 1: Vegetation carbon density growth curves for different climate regions calculated with the Chapman-Richards volume growth model7

Litter carbon density is assumed to increase linear starting from 0 in ac0 towards a long-term equilibrium in ac20.
Soil carbon density is assumed to increase linear starting from the mean of cropland and pasture soil carbon density in ac0 (this is a trade-off since we can't track the history of land pools within a cell) towards a long-term equilibrium in ac20.
The speed of convergence (20 years) is based on assumptions in the IPCC Guidelines for National Greenhouse Gas Inventories8.

Age-class growth is simulated by shifting age-classes between the time steps according to time step length $sm\_years$ (e.g. from ac10 to ac20 if the time step length is 10 years).

Forestry land is calculated according to equation 4:

vm\_land(j,\text{"forestry"},si) = \sum_{land32} v32\_land\_fore(j,land32,si)

Forestry carbon stocks are calculated according to equation 5:

vm\_carbon\_stock(j,\text{"forestry"},c\_pools) = \sum_{land32} \sum_{si} v32\_land\_fore(j,land32,si)*pc32\_carbon\_density(j,land32,c\_pools)

$pc32\_carbon\_density(j,land32,c\_pools)$ is an area weighted mean of $pc32\_carbon\_density\_ac(j,ac,c\_pools)$

The decision for afforestation is binding according the time horizon ($sm\_invest\_horizon$), i.e. afforested land is not availalbe for land conversion for 30 years after planting. After 30 years, afforested land can be converted to other land types, but the associated carbon emissions have to compensated by payments according to the current carbon price.

static forestry sector

(C) affore_aug15

affore_aug15 is based on the affore_apr15 realization. In addition, affore_aug15 includes the option to prescribe afforestation rates at the regional level.


Name Description Unit A B
$pc32\_carbon\_density\_ac(j,ac,c\_pools)$ age-class and carbon pool dependent carbon density tC/ha x
$f32\_fac\_req\_ha(i,fcosts)$ Factor requirement costs US$/ha x
$f32\_growth\_par(i,chap_par)$ parameters for chapman-richards equation - x
$v32\_land\_fore(j,land32,si)$ Forestry land mio. ha x
$land32$ Forestry land pools (new, prot, grow, old) - x
$pc32\_carbon\_density(j,land32,c\_pools)$ Area-weighted mean of pc32_carbon_density_ac(j,ac,c_pools) tC/ha x

The last columns of the table indicate the usage in the different realizations (numbered with capital letters)


Florian Humpenöder

See Also

core, 39_landconversion, 57_maccs, 52_carbon, Overview


1 Murray, D.M., von Gadow, K., 1993. A Flexible Yield Model for Regional Timber Forecasting. Southern Journal of Applied Forestry 17, 112–115.

2 Gadow, K. von, Hui, G., 2001. Modelling Forest Development. Springer.

3 IPCC, 2000. Land Use, Land-Use Change and Forestry. Cambridge University Press, UK.

4 IPCC, 2006. 2006 IPCC Guidelines for National Greenhouse Gas Inventories, Prepared by the National Greenhouse Gas Inventories Programme. IGES, Japan.

5 Bondeau, A., Smith, P.C., Zaehle, S., Schaphoff, S., Lucht, W., Cramer, W., Gerten, D., Lotze-Campen, H., Müller, C., Reichstein, M., Smith, B., 2007. Modelling the role of agriculture for the 20th century global terrestrial carbon balance. Glob Change Biol 13, 679–706.

6 Sathaye, J., Makundi, W., Dale, L., Chan, P., Andrasko, K., 2005. GHG Mitigation Potential, Costs and Benefits in Global Forests: A Dynamic Partial Equilibrium Approach. Lawrence Berkeley National Laboratory.

7 Humpenöder F, Popp A, Dietrich J P, Klein D, Lotze-Campen H, Bonsch M, Bodirsky B L, Weindl I, Stevanovic M and Müller C 2014 Investigating afforestation and bioenergy CCS as climate change mitigation strategies Environ. Res. Lett. 9 064029

8 IPCC. 2006. 2006 IPCC Guidelines for National Greenhouse Gas Inventories, Prepared by the National Greenhouse Gas Inventories Programme. Chapter 2 Generic Methodologies applicable to multiple land-use categories.