Costs of forest carbon sequestration in the presence of climate change impacts

The data on CCI on forests are obtained from the MC2 DGVM (Kim et al 2017) developed by the US Forest Service and its collaborators. Representing land surface as a grid, MC2 reads as input elevation, soil, and climate projections on a monthly time step, and calculates plant productivity, and carbon and water fluxes through above- and below-ground pools. MC2 simulates CO₂ effects on NPP and potential evapotranspiration, simulates fire occurrence as a function of the current vegetation type and fuel conditions, and calculates fire consumption of vegetation and the associated ecosystem carbon pools (Conklin et al 2016).

Two key results from MC2 are passed to the dynamic forward-looking economic optimization model of global land use. First, NPP is used to perturb forest yields. NPP is the gross carbon allocated to plant growth annually after respiration and is calculated by the MC2 DGVM without accounting for disturbance. The forest growth functions used in the economic model are also gross yield functions, measured in cubic meters of biomass per hectare (m³ha⁻¹) before disturbance. Second, in MC2 changes in disturbance by biome are measured as changes in consumption of aboveground biomass by fires. In the economic model, disturbance is applied equally to all age classes of hectares as a direct reduction in the stock of forests.

MC2 estimates the impacts of climate change on forests at the 0.5° resolution at a monthly time step, while the economic land-use model solves for forest harvest, agricultural output, timber investment, and land-use allocation at the biome level at decadal step. To pass information from MC2 to the economic model, the MC2 results are aggregated across space and time to represent changes over a decade at the biome level. Because NPP generated by MC2 at the biome level of aggregation is correlated with atmospheric CO₂ concentration, a unique function is calibrated for each biome, linking changes in NPP to CO₂ concentration. A similar approach is used to model forest dieback, in which biome-specific functions are calibrated to link MC2-generated dieback rates to global surface temperature. These functions are then incorporated into the economic optimization to determine forest growth and dieback in each future time period in the model.

Information on CCI on crops is obtained from a meta-analysis by Challinor et al (2014) that finds an average yield loss of 4.9% per 1 °C increase in temperature. In the economic model, crop output depends not only on inputs used and improvements in technology but also on changes in global surface temperature.

We develop a dynamic forward-looking economic optimization model (Judd 1998, Cai 2019) of global land use with a detailed representation of the timber sector (model equations are listed in the SI). In the model, a representative household derives utility from the consumption of land-based goods and other goods and services. Global welfare, represented by the sum of discounted global utilities, is maximized subject to endowments and production function constraints, and equations of motion:

$$\begin{equation}\mathop {\max }\limits_D \sum\limits_t {{\delta _t}} {\Pi _t}u({y_{t{} }})\end{equation} \tag{ 1 }$$

$$\begin{equation*}s.t.{\mkern 1mu} {y_t} = F\left( {{D_t},{\mkern 1mu} {A_t},{\mkern 1mu} {\Pi _t},{\mkern 1mu} {O_t},{\mkern 1mu} {C_t}} \right)\end{equation*}$$

$$\begin{equation*}{O_t} = {E_t}\end{equation*}$$

where D is a set of control variables (investment in timber management, harvested and planted hectares in managed forests, accessed natural forest area, and allocation of land and other resources), $\delta$ is the compound utility discount factor, $\Pi$ is global population, u is per capita utility derived from final consumption goods y, and t is time period in the model. F represents a vector of production functions, with A denoting a vector of exogenous sectoral technology variables, C denoting exogenous climate variables, and O representing other goods and services, set equal to exogenous path E determined by global income growth. For a consistent representation of the future global economy, including population, income, and climate, we use the 'business as usual' (SSP2) scenario available in Shared Socioeconomic Pathways database (Riahi et al 2017).

Preferences of a global representative consumer are modeled with An Implicit Directly Additive Demand System (Rimmer and Powell 1996). This demand system is very flexible in its description of the evolution of consumer demands, with marginal budget shares for staple foods falling toward zero as per capita income rises. This flexibility plays an important role in governing the competition for land over a long time horizon with significant increases in per capita income.

We highlight the United States—a region where we have better data, and disaggregate the production side of the global economy into the USA and the Rest of the World (RoW). Within each of the two regions, the global land endowment is split into biomes, and competition for land between agriculture and forests occurs within each biome (figure 2(a)). Crop, livestock, and timber production functions are biome-specific. Crop and livestock production activities are represented with nested constant elasticity of substitution functions. The timber sector output in each biome and each forest age class is a product of harvested area and timber yield. Timber yield functions for accessible and inaccessible forests are based on Tian et al (2016). The important difference between the two is that the specification of accessible forest yield considers the impacts of timber management on biophysical yield.

Zoom In Zoom Out Reset image size

Production of the land-based consumption goods, as well as intermediate inputs required to produce these goods, are explicitly modeled within this framework. A composite of all other goods and services is used as intermediate input as well as representing competing final consumption. The production of these other goods and services is not explicitly modeled but is set equal to exogenous path E in (1), and for this reason, the model is termed partial equilibrium.

By solving the global welfare maximization problem (1) we find the optimal age class and area of timber harvest, optimal paths of the intensity of investments in forest management at replanting time (which are fixed for the life of the tree), the area of forests to manage for timber production, the area of forests to leave in a natural state, cropland and pasture areas, and other resource allocation. The solution also finds optimal forest stocks which are a function of the timber investments and the land area in forests (both managed and natural). Details of the model and implementation of the forest carbon sequestration policies are provided in the SI.

To gauge the ecological effects of climate change on forest carbon stock, in isolation from market interventions, we examine the output from MC2 DGVM runs under the Reference emissions scenario (Kim et al 2017), a scenario analogous to Representative Concentration Pathway 8.5 (RCP 8.5) used by the IPCC (Riahi et al 2011). The model predicts that while most of the biomes are geographically stable (Kim et al 2017), the carbon stocks of most forests around the world will increase over the course of this century. Large gains are projected in tropical forests in South America, Sub-Saharan Africa, and South-East Asia. In contrast, temperate forest regions are projected to see productivity increases offset by carbon loss to fire, and boreal forests in Alaska, Canada and Russia are projected to lose carbon (figures 2(b) and (c)).

Impacts of climate change on forests simulated by MC2 are passed to the economic model in the form of calibrated functions (figure 3). When the effects of climate change on managed and natural forests are integrated with the economic drivers under SSP2 assumptions, but no carbon policies are considered, the integrated model projects that global forest carbon stocks increase by 121 gigatons of carbon (Gt C) by 2100, a significant increase relative to the 263 Gt C at the beginning of the century. Most of this increase in carbon, 104 Gt C, or 86%, results from changes that are predicted to occur without climate change (table 1). A large increase (520 Mha) in managed forest area globally leads to a 44.2 Gt C increase in carbon storage by 2100. This increase in managed forests is derived from existing natural forests (33%) and pastureland (67%). Cropland increases modestly, by about 14 Mha by the end of the century, but most increases in food production occur through intensification of existing crop and livestock production. There is a small increase in the carbon stock of 2.3 Gt C (0.02 t C ha⁻¹ yr⁻¹) in managed forests, resulting from the combined effects of increases in management intensity and changes in timber rotation ages. A large increase in carbon, 69.4 Gt C (0.22 t C ha⁻¹ yr⁻¹), occurs in natural forests, resulting from shifts in the age class distribution toward older trees.

Zoom In Zoom Out Reset image size

In our integrated model, climate change is projected to add 17 Gt C (0.04 t C ha⁻¹ yr⁻¹) in aboveground carbon storage globally by 2100 (table 1). This net change is composed of a 10 Gt C emission due to additional dieback in forests, a 30 Gt C increase due to additional carbon fertilization, and a 3 Gt C loss due to deforestation caused by the encroachment of cropland into forests in the wake of reduced farm productivity. The effects of climate change on forests, both through dieback and forest growth, accelerate through the century.

Considering the effects of climate change on forest growth in isolation from the effects on dieback and crop yields, nearly all forested regions in the world are predicted to experience an increase in biomass by 2100 compared to the no-climate-impact baseline (green bars in figure 4). Even though climate change causes forest growth to increase in the temperate warm biome of the rest of the world (figure 3(a)), the increase is the smallest across biomes. This gives agricultural activities in this biome a comparative advantage relative to biomes with larger increases in timber growth. As a result, pasture and cropland expand, and forests contract in the Temperate Warm biome in the RoW, relative to the baseline.

Zoom In Zoom Out Reset image size

If dieback is the only effect of climate change, the integrated model predicts that all forested biomes, except the Temperate Warm biome in the RoW, will contain less carbon in 2100 compared to the baseline without climate impacts (orange bars in figure 4). The forest carbon losses are the largest in forest types that have the largest increases in dieback with global warming, such as Southern Mixed forests in the United States and Temperate Cool forests in the RoW. While these changes are largely driven by the direct effect of climate change on forest stocks (figure 3(b)), the indirect price effects also play an important role. More dieback makes forestry less productive, thereby raising timber prices, and inducing natural forests with high carbon stocks to be harvested and converted to managed forests and agriculture. Increasing dieback also alters the comparative advantage of forestry and agriculture across biomes. Dieback rates in the Temperate Warm biome of the RoW are small initially and not very sensitive to global warming (figure 3(b)), making this biome relatively more attractive for forestry production. As a result, managed forests expand mostly at the expense of agricultural lands, and forest carbon stock increases relative to the baseline in the Temperate Warm biome of the RoW.

Global warming results in reduced average crop yield (Challinor et al 2014), which in turn leads to larger cropland area to meet global food demand. This is achieved by the conversion of forests to agricultural lands and results in a 0.8% reduction in global forest carbon stocks by the end of the century. Of course, this abstracts from other potential climate impacts. Globally, this indirect impact is small compared to the direct impacts of climate change on forests. The largest impact is observed in the Temperate Warm biome in the RoW where a global reduction in crop yields results in the expansion of agricultural lands at the expense of forests, and 4.7% reduction in carbon stock relative to the baseline (yellow bars in figure 4).

When all three climate effects are modeled together (brown bars in figure 4), all U.S. biomes experience an increase in carbon stock, with Northern Mixed gaining the most in relative terms. In the RoW, temperate biomes accumulate less carbon when all of the effects of climate change are considered. The Temperate Cool biome of the RoW experiences a reduction in carbon over the century because the increase in forest carbon stock in this biome due to the global effects of climate change on forest growth is not large enough to overcome the global effects of dieback and increased demand for land caused by the climate-driven reduction in crop yields. In the Temperate Warm biome of the RoW, the comparative advantage in timber production due to small and insensitive to climate change dieback rates does not offset the comparative disadvantage due to low increase in timber growth rates and effects of the global reduction in crop yields.

To consider the effects of CCI on the cost of carbon policy, we explore the costs implications of reaching three higher levels of the global forest carbon stock by 2100—low (5% higher), medium (10% higher) and high (20% higher). Each of these policies is implemented as a lower bound constraint on forest carbon stock in the model. The target forest carbon stock in 2100 is calculated relative to the projected stock of 368 Gt C in 2100 in the no-climate-impact baseline, resulting in 386, 405, and 442 Gt C targets in 2100. The first set of bars in figure 5 (All CCI) reports the consequences for the cost of achieving these three levels of carbon sequestration when all three climate impacts are factored into the analysis. In every case, the central outcome involves a cost reduction, ranging from 86% reduction for the low to 64% reduction in the case of the high increase in the global forest carbon stock. However, our bounding analysis shows that we cannot rule out the possibility that climate impacts might raise mitigation costs. The potential increase in costs is driven explicitly by scenarios that assume dieback rates take on their most extreme values (upper bounds in figure 3(b)). However, as the overall carbon sequestration target becomes more ambitious, the uncertainty range of relative change in costs is diminished.

Zoom In Zoom Out Reset image size

We find that accumulation of carbon due to the aging of global natural forests in the no-climate-impact baseline results in increase in forest carbon stock by 0.22 t C ha⁻¹ yr⁻¹ over the course of the 21st century. The accumulation starts from a rate of 0.44 t C ha⁻¹ yr⁻¹ during the first decade (2000–10) that declines toward the end of the century (table 4 in the SI). The predicted global annual increases in our model are smaller than 1.04 t C ha⁻¹ yr⁻¹ for the period 1990–2007 calculated using inventory data in Pan et al (2011), but our no-climate-impact baseline does not include changes in carbon fertilization and we do not measure carbon in soil. In tropical natural forests, the model predicts increase in carbon storage by 0.39 t C ha⁻¹ yr⁻¹, starting from a rate of 0.72 t C ha⁻¹ yr⁻¹ in the first decade that gradually declines to 0.08 t C ha⁻¹ yr⁻¹ by the end of the century (table 4 in the SI). For purposes of comparison, using African inventory plots and published inventory data for Amazonian forests, Hubau et al (2020) report a stable carbon sink in aboveground biomass at 0.66 t C ha⁻¹ yr⁻¹ in African but a decline from 0.35 to 0.24 t C ha⁻¹ yr⁻¹ in Amazonia tropical forests over 1985–2015.

The 17 Gt C increase in aboveground forest carbon stock due to impacts of climate change in this study is smaller than the 26 Gt C potential by 2115 suggested in Tian et al (2016), as Tian et al (2016) do not account for the effects of climate change in the agricultural sector and their impacts on forests. Favero et al (2021) use the LPX-Bern DGVM model (Stocker et al 2013) and a dynamic economic model (Sohngen et al 2001, Sohngen and Mendelsohn 2003, Favero et al 2018), and report an increase of 88 Gt C under RCP 8.5 in all forest carbon pools in 2100, 10% more than under their no-climate-change scenario. To compare in relative terms, we calculate 16% increase (17 Gt C) relative to our no-climate-change baseline in 2100 (104 Gt C). There are other differences between Favero et al (2021) and this study. SSP5 economic growth and RCP 8.5 temperature increases behind Favero et al (2021) results are stronger than SSP2 economic growth and the ensuing changes in climate used in this analysis. The predicted change in land use also plays an important role in the difference between the results. Our integrated model finds a more limited expansion in forest area under climate change because of competition with agriculture. A large and important uncertainty that influences carbon, however, relates to the potential expansion of forests in regions that currently are classified as tundra. Favero et al (2021) allow substantial increases in temporal and boreal forests, but those increases occur largely after 2100 in that analysis.

We find that when all three impacts of climate change on forests are taken into account, the central outcome is the reduction in costs of forest carbon sequestration. For each policy considered—low, medium and high ambition, the reduction is decomposed by the underlying drivers of CCI on the forest carbon sequestration costs. The second set of bars in figure 5 shows that the changes in forest growth rates caused by climate change are projected to lower the costs of climate mitigation in the range from 99% for the low to 81% for the highest increase in the global forest carbon stock. In fact, the changes in forest growth are almost sufficient to achieve 386 Gt C of forest carbon stock in 2100, our low target, without any additional policy measures. As a result, the incremental cost of attaining a modest forest carbon policy goal would be negligible. However, as the ambition of the sequestration target rises, the proportional reduction in cost contributed by increasing forest growth rates declines.

In contrast to the impact of the climate-driven increase in forest growth rates, the climate-driven increase in dieback rates raises the cost of forest carbon sequestration policy by more than 70%, although the proportional effect on costs declines as policy ambition increases (third set of bars). The uncertainty range stemming from the parametric bounding analysis also shrinks as the policy ambition increases from low to high suggesting that when growth and dieback effects are combined (fourth set of bars), the error bars no longer extend into the positive region. That is, even with the largest climate-driven increases in dieback and lowest increases in forest growth we examine, climate change is expected to reduce the costs of climate change mitigation in forestry. This allows us to conclude that, for an ambitious forest carbon sequestration policy, climate impacts on forests are expected to reduce the global economic costs of achieving this target.

The last set of bars in figure 5 adds the final piece of climate impacts to our analysis—namely the consequences of reduced crop yields. As expected, when rising temperatures lead to lower global average crop yields, there is an incentive to expand cropland area, relative to the no-climate-impact baseline. This creates additional competition for land, thereby raising the cost of forest carbon sequestration by 11%–38%. The increase, relative to the baseline, is diminished as the carbon sequestration policy becomes more ambitious. However, in every case, the uncertainty bars show that the cost of forest carbon sequestration increases. And it is the inclusion of the impacts on agriculture, in addition to the direct impacts of climate change on forests carbon stocks, that widens the uncertainty range, making the increase in mitigation costs a potential outcome (contrast the error bars associated with the first set of columns with those associated with the fourth set). This highlights the importance of including agricultural impacts in any analysis of climate change and forest carbon sequestration policies.

Limitations exist in our current model, which provide directions for future work. First, the model is highly spatially aggregated, with only two regions (the United States and the Rest of the World), six biomes, and a single agricultural output in each biome. The aggregation does not allow the representation of detailed climate impacts and the economic responses in the Rest of the World region. An increase in the number of regions and biomes will allow accounting for the differential effects of climate change across space. Second, while forests will be shaped by multiple disturbance agents in the future, including drought, fire, and insect and pathogen outbreaks, here we focus primarily on changes in fire regimes. Third, MC2 simulations indicate that while climate change leads to a reduction in forest carbon stock in some biomes and an increase in others, globally forest carbon stock may increase under a warmer climate, driven by longer growing seasons and the positive effect of CO₂ enrichment that outweigh the negative effect of higher dieback rates. However, recent studies call into question whether higher CO₂ concentrations will enhance the capacity of mature forests to act as carbon sinks (Jiang et al 2020). On the other hand, forest wildfires may lead to shifts in tree species that effectuate a net increase in carbon storage (Mack et al 2021). Indeed, the role of wildfire is a key source of uncertainty in global vegetation simulations. More research is needed to quantify uncertainty in the impacts of climate change on forests.