Forests are a natural consumer of CO2. As CO2 has a major impact on the temperature evolution, tracking the evolution of forests and their CO2 consumption is important in order to get accurate results. Many factors can lead to a reduction of the global forests surfaces, such as consequencies of temperature change and human activities. On the other side, environmental care and policies can lead to a rise of the global forest surface.

In this forest model, the global evolution of forest are impacted by 4 activities. There are afforestation and deforestation that respectively consists on planting and cutting trees. The two other activities are managed and unmanaged wood, which consist on planting trees, then harvest wood for different purpose (industrial or energy). these two last activities expand the forest surface but also generate biomass products.

Model data

The forest model takes the following data as inputs:

• year_start, the first year of the study. Default is 2020.
• year_end, the final year of the study. Default is 2100.
• time_step, the number of year between two data computation. Default is 1.
• deforestation_investment, the money invested in the deforestation. Unit is G$.
• deforestation_cost_per_ha, the average price to deforest 1ha of land. Unit is \$/ha. Default value is 12000 \$/ha [^1].
• CO2_per_ha, the quantity of CO2 captured by 1 hectare of forest during one year. Unit is kgCO2/ha/year. Default value is 4000kgC02/ha/year [^2]. As forest captures 16 Gt of CO2 per year, reducing forest by 1% results in a deficit of CO2 captured of 160 Mt. The value of 4000kgCO2/year/ha is coherent with these data.
• Initial CO2 emissions, CO2 emissions balance of forest at the first year of the study. Unit is GtCO2. Default value is -7.9 GtCO2 at 2020, which is the value found at [^2].
• reforestation_cost_per_ha, which is the average price to plant 1ha of tree. Unit is \$/ha. The default value is 13800\$/ha splitted as 10000\$/ha for land cost and 3800\$/ha to plant trees [^3].
• reforestation_investment, the quantity of money dedicated to reforestation each year in billions of $.
• wood tehcno dict, data use to compute price and production of biomass for managed wood and unmanaged wood.
• managed wood initial prod, which is the production of biomass by managed wood at the first year of the study. Unit is TWh.
• managed wood initial surface, which is the surface dedicated to managed wood, at the first year of the study. Unit is Gha. Default is 1.15Gha, at 2020.
• managed wood invest before year start, which are the investments made into managed wood that impact the first years of the study. Unit is G$.
• managed wood investment, which are the investment made into managed wood over the years. Unit is G$.
• transport cost, which is the cost of transport of biomass. Unit is $/ton.
• margin, factor applied to the total cost of biomass to represent the commercial margin.
• protected_forest, the surface of protected forest. Unit is Gha. Protected forest represents 21% of the global 4Hha forest surface, that is to say 0.84Gha.
• unmanaged_forest_surface, the initial surface of forest that is not used for energy or industrial purpose. As 1.25Gha of forest are used, 0.84Gha are protected, and there are 4Gha of forest, the unused surface is 1.91Gha.

The outputs of the model are:

• forest_surface_df, giving the major data of forest surface evolution over the year. Unit is Gha.
• forest_surface_detail_df, giving detailed data about forest surface evolution over the year. Unit is Gha.
• CO2_emitted_df, gives evolution of CO2 captured by forest in GtCO2.
• CO2_emissions_detail_df, gives detailed data about CO2 emitted by forest activities. Unit is GtCO2.
• CO2_land_emission_df, gives information about computed land emissions. Unit is GtCO2.
• managed_wood_df, gives data about managed wood prodution.
• biomass_dry_detail_df, gives detailed data about biomass dry production.
• biomass_dry_df, gives major data about biomass dry production.
• techno_capital, which represents the total capital allocated to the reforestation technology, in G$.
• non_use_capital, which is the unused capital of reforestation du to deforestation activities. Unit is G$.

Global approach

The forest model has to track the global forest surface evolution, the wood harvested (more generally biomass) and CO2 captured. To do this, the following assumptions are made. The global forest surface is divided into 3 parts: * Managed forest. These are the forests dedicated to long term biomass production thanks to management plans. * Protected forest. These are the forests that are legally protected, and they will stay as they are. No management plan allowed. * Unmanaged forest. These are forests that are now unused but they are not protected. As a result, they can be transformed by human activities.

Then, 3 different activities will impact these surfaces taken into account. * Reforestation. This activities consists in planting trees, and thus increases the unmanaged forest surface, as the global forest surface. * Deforestation. This activities cuts trees and reduce unmanaged forest surface as the global forest surface. Deforestation can not impact protected forest. Deforestation produces biomass as a one-time activities. * Managed wood. This activities consists in managing forest to produce biomass regulary on a long term period. Investing in managed wood will increase managed forest surface and so the global forest surface.

Following paragraphs gives further details about each part of the model.

Afforestation and reforestation

Deforestation and reforestation are activities that impact the evolution of the global forest surface. They both impact unmanaged forests.

Deforestation is directly the deforestation_surface from the inputs. Reforestation is calculated by $$Reforestation\_surface = Reforestation\_investment / cost\_per\_ha$$

The cumulative value is the sum of all the forest surface evolution from the first year of the study to the given year of the data. Deforestation also produces biomass.

The surface deforested is removed from the existing forest surface. It firstly takes out unmanaged surfaces. When there is no more unmanaged trees to cut, managed one are cut. Then, when there is not more managed wood left, nothing is cut, as protected forests can not be impacted.

Managed wood

Managed wood defines all the forest under management plan in order to produce biomass on a long term period.

Surface of forest Each year, a certain amount of money is invested into managed wood. This is an input data of the model. Knowing the price per ha (in wood techno dict) the surface added each year can be deduced by $$Added\_surface = investment / price\_per\_ha$$ This price per ha take into account planting tree, preparing ground, harvesting and other activities linked to wood management. By adding the surface of forest planting each year, the cumulative surface is computed, which represent the total of managed or unmanaged wood added since the first year of the study.

Biomass production The quantity of biomass produced by 1 ha is given by $$biomasss\_per\_ha = quantity\_per\_ha * average\_density / years\_between\_harvest / (1-recycle)$$ with: quantity_per_ha : the average quantity of wood per ha in m^3/ha. This is the average between wood and residues. average_density : the average density of biomass in kg/m^3 years_between_harvest : the number of year between 2 harvesting in the same place recycle : the percentage of biomass that comes from recycling

Knowing the surface of managed wood we can deduced the quantity of biomass produced.

Biomass price Biomass is produced by managed forest and by deforestation. Each of these production way has its own price. As a result, the average price of biomass is the weighted average of managed wood and deforestation price. $$biomass\_price = managed\_wood\_price * managed\_wood\_part + deforestation\_price * deforestation\_part$$ with deforestation_part = deforestation_production / total_biomass_production managed_wood_part = managed_wood_production / total_biomass_production

CO2 emissions

The land emissions can be computed with this formula: $$CO2\_land\_emissions = Surface\_deforestation * CO2\_per\_ha - Surface\_reforestation * CO2\_per\_ha \\+ Surface\_managed\_wood * 0$$

The forest for energy emissions can be computed as following: $$CO2\_emissions = CO2(by\_use\_biomass) - CO2(captured\_from\_growing\_trees) => 0$$

As a result, deforested surfaces does not capture CO2 as they does not exist anymore. Managed surfaces are neutral in CO2 because CO2 captured in wood is likely to be released when the wood is burn.

Lost capital

In the forest model, there are 3 activities : deforestation, reforestation, managed wood, with their own investment. If reforestation and managed wood aimed at expand forest surface, deforestation diminishes it. As a result using money into opposite activities leads to a waste of money called lost capital. As an example, investing in 10Mha of reforestation and 8Mha of deforestation results in a +2Mha of forest planted. Then, investment in reforestation is not optimized. The following formula gives the detail of the lost capital computation.

First case : part of unmanaged wood is deforested In this first case, trees that were planted in the past years are cut and the land will be used for another purpose than forestry. $$reforestation\_lost\_capital = unmanaged\_deforested\_surface * reforestation\_cost\_per\_ha$$

Second case : all unmanaged wood is deforested, part of managed wood is deforested In this second case, all unmanaged wood is deforested and managed wood trees start to be cut. As in first case reforestation capital is lost. Moreover, some of managed wood capital is also lost. $$reforestation\_lost\_capital = unmanaged\_deforested\_surface * reforestation\_cost\_per\_ha$$ $$managed\_wood\_lost\_capital = managed\_deforested\_surface * managed\_cost\_per\_ha$$

Last case : all that can be cut is cut In this last case, all unmanaged wood is deforested, all managed wood is also deforested. Plus, money is over invested into deforestation. This exceed amount of money is lost because nothing can be cut. $$reforestation\_lost\_capital = unmanaged\_deforested\_surface * reforestation\_cost\_per\_ha$$ $$managed\_wood\_lost\_capital = managed\_deforested\_surface * managed\_cost\_per\_ha$$ $$deforestation\_lost\_capital = exceed\_deforestation\_investment$$

Model limitations

In this model, the quantity of CO2 captured by ha of forest is assumed to be the same all over the world. However, the CO2 captured change with the climate condition. Forest in tropical regions are more effective than forest in cold regions. As a result, cutting trees of the Amazon forest does not have the same impact than cutting trees in cold region, in term of captured CO2.

References

[^1]: LawnStarter, Pricing Guide: How much does it cost to clear land ?, found online at https://www.lawnstarter.com/blog/cost/clear-land-price/#:~:text=Expect%20to%20pay%20between%20%24733,higher%20your%20bill%20will%20be. [^2]: World Resources Institute, Forests Absorb Twice As Much Carbon As They Emit Each Year, January 21, 2021 By Nancy Harris and David Gibbs, found online at https://www.wri.org/insights/forests-absorb-twice-much-carbon-they-emit-each-year [^3]: Agriculture and Food Development Authority, Reforestation, found online at https://www.teagasc.ie/crops/forestry/advice/establishment/reforestation/