Like most other forest sector models that account for carbon, the Global Timber Model (GTM) keeps track of carbon in the forest ecosystem and wood products and models the exchange of that carbon with the atmosphere. The actual calculation of carbon in the model was first described in Sohngen and Sedjo (2000), however, the description of the interaction with the atmosphere was described later in Sohngen and Mendelsohn (2003). That study described an integrated assessment model approach, where flux in the forest directly influences carbon in the atmosphere.
The basic routines for handling carbon in the Global Timber Model remain largely the same as those described in Sohngen and Sedjo (2000) to this day, although the parameters and some of the functions have been updated to account for new studies over time. Also, estimates in the United States rely on calculations from the most recent US Forest Service Forest Inventory and Analysis data (FIA).
For the United States, aboveground carbon is calculated in two steps. The first step involves developing a biomass expansion factor (BEF):
BEFa = A + B(ln(GSVa))
Where GSVa is the growing stock volume at age “a”. The biomass expansion factor provides the tons C per m3 of growing stock. In the second step, aboveground carbon is calculated by multiplying the biomass expansion factor by the growing stock volume:
Aboveground C = BEFa * GSVa.
For the purposes of GTM, the biomass expansion factor has been calculated in terms of tons C, so no additional adjustments for the proportion of aboveground biomass that is carbon are needed. The proportion of deadwood, litter and belowground carbon associated with this aboveground biomass are also determined from the FIA data and those proportions are applied to the aboveground C stock to determine total live and dead carbon above- and below-ground.
For forests in other regions, GTM relies on the IPCC Good Practice Guidance (GPG):
Above and belowground C = GSV*D*BEF*(1+R)*CF
Where D is wood density, usually expressed as grams per cm3. Wood density varies greatly across species, but for the aggregated species in GTM, we have generally used wood densities in the range of 0.3 to 0.6. The biomass expansion factor adjusts the growing stock (GSV) for branches and other non-growing stock components of trees. In GTM for most species around the world it ranges from 1.3 to 1.6. R is the root to shoot ratio to account for roots, ranging from 0.2 to 0.4 in GTM. CF is the proportion of biomass that is carbon, usually around 50%. For non-US regions, we add in a litter component of 15-40 tons C per hectare and we include a deadwood component of 5-12% of total aboveground C.
When wood is harvested, only the growing stock, or GSV, is removed from the forest and taken to the mill. Branches, leaves, understory and litter are all left in the forest to decompose. Some live trees may also be left, and some of this material is burned. Starting with the United States, GTM predicts that 433 million m3 per year are harvested in the first decade in the current baseline (Table 1). This harvest required 241.8 Tg C per year in aboveground carbon to be cut. Of that carbon, 99.3 Tg C are exported to the mill as logs, and 20% of this is emitted immediately so that 79.4 Tg C entered into wood product pools of some storage duration > 1 year. This means 241.8 Tg C – 99.3 Tg C, or 142.5 Tg C, are left in the forest. In GTM, 33.2 Tg C entered into deadwood pools maintained onsite as a result of the harvest operation, the rest is assumed to go into the atmosphere immediately. So, for the United States, 53% of the aboveground carbon affected by a harvesting operation becomes an immediate emission to the atmosphere. The rest is stored in a carbon pool of some duration.
Table 1: Wood harvest and allocation of carbon to wood product and slash pools at harvesting site in the United States in the first decade of the 2022/23 baseline of GTM.
| Category |
Amount (m3 or Tg C) |
| (1) Wood harvest in United States in million m3/yr |
433 |
| (2) Aboveground C of wood harvested (Tg C) |
241.8 |
| (3) Amount exported to mill (Tg C) |
99.3 |
| (4) Amount stored in wood products for > 1 year (Tg C) |
79.4 |
| (5) Deadwood left in forest (Tg C) |
142.5 |
| (6) Deadwood stored in slash pool (Tg C) |
33.2 |
| (7) Immediate emissions (2- 4 – 6) |
128.4 (53%) |
Tables 2 and 3 presents similar estimates from GTM for the world for the same baseline projection. Over the 40-year period from 2025 to 2075, roundwood harvests are projected to increase 17%. Average annual harvest is 2.3 billion m3. Prices rise as well. Aboveground C stock increases, so forests in 2075 store 6.2% more carbon than they did in 2025. GTM does not track woodfuel consumption in developing countries, although we do track it and capture it when it is used industrially, such as for biomass electricity. It is part of the model’s pulpwood demand since biomass energy (often pellets) competes directly with the pulpwood sector. GTM does track losses of forests to deforestation as well. Global net deforestation and tropical net deforestation in hectares for the baseline projection are shown in Table 2. Globally, GTM projects more net deforestation in the first decade than FAO suggests happened in the 2010 to 2020 period. However, the projection and historical data align reasonably well for just the tropics.
The GTM estimated global aboveground carbon stock excluding roots is shown in Table 3. This stock is estimated based on growing stock volume estimates from individual countries, where available, or FAO (i.e., FAO 2020). From 2025 to 2075, the aboveground stock increases by 7,701 Tg C, or 4%. The average annual net increase in carbon stock is 230 Tg C yr-1, or 844 Tg CO2 yr-1. Following conventions in the atmospheric sciences, this increase is measured as a negative in Table 3 under “net flux” because the carbon is being withdrawn from the atmosphere. The future predicted average annual increase in the world’s aboveground carbon stock is smaller than that estimated by the IPCC and the Global Carbon Project (Friedlingstein et al., 2022) for the last decade or so. These estimates are shown also in Table 3. A number of factors could explain the difference between the GTM projections and those of the Global Carbon Project, including differences in how the models treat carbon fertilization and other processes, or differences in the land base.
Table 2: Annual baseline sawtimber and pulpwood production in GTM, global average prices, aboveground C stocks, excluding roots, flux in aboveground C and Flux in market C.
| Industrial roundwood | Prices | Global | Tropical | ||||
| million m3/yr | $/m3 | Net deforestation | |||||
| Sawtimber | Pulpwood | Total | Sawtimber | Pulpwood | Million ha/yr | ||
| 2025 | 1,362 | 737 | 2,099 | $113.86 | $58.94 | 6.0 | 7.3 |
| 2035 | 1,391 | 769 | 2,161 | $137.15 | $65.23 | 6.0 | 6.0 |
| 2045 | 1,450 | 830 | 2,279 | $151.43 | $71.08 | 4.4 | 4.8 |
| 2055 | 1,502 | 858 | 2,359 | $158.54 | $74.24 | 3.3 | 4.4 |
| 2065 | 1,552 | 904 | 2,456 | $164.69 | $78.70 | 2.9 | 3.4 |
| Avg. 2020-70 | 1,451 | 820 | 2,271 | 4.5 | 5.2 | ||
| FAO (2010-20) | 1,909 | 4.7 | 7.8 | ||||
Table 3: Annual baseline sawtimber and pulpwood production in GTM, global average prices, aboveground C stocks, excluding roots, flux in aboveground C and Flux in market C.
|
Aboveground Carbon Stock |
Net
Flux in |
Net
Flux in |
|
|
no roots |
AG C | Mkt C | |
| Tg C | TgC/yr |
TgC/yr |
|
|
2025 |
184,910 | (94.7) | (101.2) |
|
2035 |
185,856 | (159.4) | (121.3) |
|
2045 |
187,450 | (211.2) |
(131.3) |
| 2055 | 189,562 | (304.9) |
(142.7) |
| 2065 | 192,611 | (379.5) |
(139.1) |
|
Avg. 2020-70 |
(230) | (127) | |
| IPCC (2022) | (1,798) |
|
|
| Global C Project1 | (1,500) –
(2,100) |
|
1 The Global Carbon Project data can be found in (Friedlingstein et al. 2022)
The net flux in forests can be broken into component parts. Harvesting for wood products removes wood from the forest, as does deforestation. The average aboveground carbon removed from the forest due to industrial wood harvesting and deforestation over the next 50 years is shown in the first column in Table 4 as 1,703 Tg C/yr. This carbon moves into products, deadwood, or directly to the atmosphere as an emission. The emission may happen right when the forest is cut, such as happens with deforestation, it may happen at a lumber mill or pulp mill, or it may happen somewhere else in the value chain. At the global level, GTM calculates that 26% of all removals move directly into wood products of some storage duration, 57% is emitted directly, and the rest is stored in deadwood. Both the deadwood and the product storage will oxidize over time, leading to future emissions. These emissions are not shown in table 4, however they are tracked by GTM and included in our typical outputs. Forests grow every year, some after being planted. The average gross growth in GTM is shown in Table 4 as 1,933 Tg C/yr. On net, forests are estimated to remove 230 Tg C/yr, shown in the last column of Table 4.
The net flux/growth columns in Tables 3 and 4 are the same, as expected. The net effect of carbon changes in forest can be determined by calculating the change in stocks over time, as done in Table 3, or by monitoring fluxes, as done in Table 4. The IPCC has always recognized either of these approaches to determining the annual forest carbon flux for a country. Wood removals for industrial wood markets and deforestation are a significant potential emission source – as much as 1,703 Tg C/yr, or 6.3 Pg CO2/yr . However, 439 Tg C/yr makes it way into wood products, and 298 Tg C is left as deadwood in the forest, leaving a maximum of 966 Tg C/yr emitted immediately under these demand projections. Most of this is emission arises from deforestation, not wood harvesting.
Table 4: wood removals, emissions, and growth in global forests. Positive numbers are emissions from forests to atmosphere, negative numbers are removals from the atmosphere and sequestration into forests.
| Gross | Net | |||||
|
Removal |
Emission | Products | Deadwood | Growth | Growth | |
|
Tg C/yr |
||||||
|
2025 |
1,518 | 838 | (395) | (285) | (1,613) | (95) |
|
2035 |
1,659 | 945 | (421) | (292) | (1,818) | (159) |
|
2045 |
1,747 | 1,002 | (444) | (301) | (1,958) |
(211) |
| 2055 | 1,790 | 1,019 | (465) | (306) | (2,095) |
(305) |
| 2065 | 1,801 | 1,022 | (472) | (308) | (2,181) |
(380) |
| Avg 2020-70 | 1,703 | 965 | (439) | (298) | (1,933) |
(230) |
Net Growth = Gross growth + removal.
There is lots of interest in attributing carbon fluxes on the landscape to particular activities, such as timber harvesting or deforestation. It’s possible to mine the GTM data outputs to provide information that helps us better understand where fluxes are arising, either positive or negative.
In table 5, I show estimates from the baseline in GTM again, but the carbon fluxes are broken out by managed forests and secondary forests. Managed forests are those forests that have been, are, or will be managed for timber somewhere in the world. There are nearly a billion hectares of these types of forests at the start of the simulation, although land use conversion leads to a smaller set of them over time. In GTM, about 10% of these managed forests, or 90 million hectares, is fast-growing plantation types. These plantations produce about 30% of the total timber produced. Other plantations, such as longer-lived species in Nordic countries, Canada, and Russia, East Asia, and Japan bring the total of plantation production to about 40% as of today.
The rest of the managed forestland is managed lightly in the sense that forests are cut periodically in 30 to more than 100-year cycles. The shorter cycles will happen in tropical forests and the longer cycles in Europe, Russia, and Canada. The average age of these managed forests globally is 40 years old, meaning they are maintained at a relatively young age overall.
Table 5: Managed and primary (un-managed and old growth) forest aboveground carbon storage and annual C flux in aboveground carbon. Fluxes in this table do not include wood product storage pools.
|
Managed forest types |
Primary forest |
All forests |
||||
|
Aboveground Tg C |
Flux
Tg C/yr |
Area
(ha) |
Aboveground
Tg C |
Flux
Tg C/yr |
Aboveground TgC/yr |
|
|
2025 |
42,734 | -368.3 | 982.9 | 142,176 | 273.6 |
-94.7 |
|
2035 |
46,417 | -290.8 | 973.9 | 139,440 | 131.5 | -159.4 |
|
2045 |
49,325 | -293.2 | 958.0 | 138,125 | 82.0 |
-211.2 |
|
2055 |
52,257 | -358.2 | 952.5 | 137,306 | 53.3 |
-304.9 |
| 2065 | 55,839 | -439.2 | 955.5 | 136,773 | 59.6 |
-379.5 |
|
Avg 2020-2070 |
-327.6 | 135.1 |
-192.5 |
|||
These younger, managed forest types are projected to sequester on net 328 Tg C/yr (Table 5).This net calculation accounts for all losses form harvesting and all gains from growth. From a carbon cycling perspective, these younger forests sequester considerable carbon on an annual basis because they are young, and growing fairly rapidly. Younger trees are susceptible to smaller lifetime probabilities of loss due to disturbance, and younger trees, especially replanted ones, gain the most benefits from carbon fertilization (Davis et al., 2022). There are an additional 100 Tg C/yr sequestered in wood products on net (after accounting for emissions from historical wood product storage that is oxidizing), although this storage in wood products is not shown in Table 5.
The average age of unmanaged forests is more than 100 years old. These older forests are projected to emit 135 Tg C/yr over the next 50 years, despite the effects of carbon fertilization that are built into GTM. Some of this loss is due to deforestation as many tropical unmanaged forests are converted to agricultural uses. Other losses happen because there is some harvesting of unmanaged and inaccessible forests for wood products in temperate and boreal regions due to modestly rising prices. Regrowth rates on these forests are relatively slow, leading to a modest, but temporary carbon loss. And finally, GTM does include routines to account for fire losses in unmanaged parts of boreal regions in Canada and Russia. In carbon accounting, we have only built natural fire cycles into natural forests in Canada and Russia, but with growing evidence that forests in other regions may be locked away from human use either administratively or economically, we will work to include natural fire cycles in other regions as well in future versions of the model.
The tables above present key outputs in carbon accounting from GTM, but I have excluded some of the key processes from those calculations in order to focus on the direct, first order effects of forest removal and growth calculations in the model. For instance, the aboveground measures above do not include roots because we do not assume roots create emissions at harvest time. Trees and their roots do regrow however, when forests come back, and the old roots become part of the soil carbon pool. Similarly, in wood product pools, some wood in those pools may burn or may decompose in a landfill each year, releasing carbon.
The full accounting of carbon pools and fluxes for the baseline in GTM is presented in Tables 6 and 7. Table 6 shows the total stocks, and table 7 shows the annual fluxes. Total flux in forests is increasing, meaning forests are storing more carbon over time. About 72% of this new storage happens in aboveground C pools (including roots), while the rest happens in products. Soils emit carbon, due to deforestation, but this process slows over time.
Table 6: Global carbon stocks in various pools based on GTM baseline projection 2022/23
|
|
Aboveground | Products | Slash | Soil | Total |
|
|
Pg C | ||||
|
2025 |
252.7 | 39.8 | 5.5 | 676.3 | 974.3 |
|
2035 |
253.7 | 40.8 | 5.3 | 676.0 |
975.8 |
| 2045 | 255.6 | 42.0 | 5.3 | 675.8 |
978.8 |
| 2055 | 258.4 | 43.3 | 5.3 | 675.8 |
982.8 |
| 2065 | 262.3 | 44.7 | 5.4 | 675.8 |
988.2 |
Table 7: Global carbon fluxes in various pools based on GTM baseline projection 2022/23
|
|
Aboveground | Products | Slash | Soil | Total |
|
|
Tg C/yr | ||||
|
2025 |
-97.7 | -101.2 | 17.6 | 29.1 | -152.2 |
|
2035 |
-193.3 | -121.3 | 1.3 | 15.3 | -298.0 |
| 2045 | -274.5 | -131.3 | -2.5 | 6.5 |
-401.8 |
| 2055 | -393.4 | -142.7 | -3.8 | 2.4 |
-537.6 |
| 2065 | -493.4 | -139.1 | -0.9 | -3.8 |
-637.2 |
| Avg 2020-60 | -290.5 | -127.1 | 2.3 | 9.9 |
-405.4 |
References
FAO. 2020. “Global Forest Resources Assessment 2020 Main Report.” Rome: United Nations Food and Agricultural Organization. https://doi.org/10.4060/ca9825en.
Friedlingstein, Pierre, Michael O’sullivan, Matthew W. Jones, Robbie M. Andrew, Luke Gregor, Judith Hauck, Corinne Le Quéré, Ingrid T. Luijkx, Are Olsen, and Glen P. Peters. 2022. “Global Carbon Budget 2022.” Earth System Science Data Discussions 2022: 1–159.
Peng, Liqing, Timothy D. Searchinger, Jessica Zionts, and Richard Waite. 2023. “The Carbon Costs of Global Wood Harvests.” Nature, 1–6.
Sohngen, Brent, and Robert Mendelsohn. 2003. “An Optimal Control Model of Forest Carbon Sequestration.” American Journal of Agricultural Economics 85 (2): 448–57. https://doi.org/10.1111/1467-8276.00133.
Sohngen, Brent, and Roger Sedjo. 2000. “Potential Carbon Flux from Timber Harvests and Management in the Context of a Global Timber Market.” Climatic Change 44 (1–2): 151–72.