in future research to provide a more complete analysis of these issues in a dynamic framework: first, estimating the effects of climate change on forest growth, merchantable yields, dieback, and biome shifts on regional biomass supply; and second, analyzing how emerging technological and/or social transformation processes may affect the projected demand for woody biomass, especially over a long time horizon. Taking this more complex and integrated approach might not change our overall findings but rather provide more insight into additional risks that could be considered when designing bioenergy and forest carbon sequestration policies.
max sum from 0 to ∞ of ρt\ integral from 0 to Qttot of \ D(Qtind,Zt, RCP)+D(Qt, RCPwbio)-C(Qttot)\ d Qttot-; sum over i of CGi(mti,Gti)- sum over i of CNi(mti,Nti)- sum over i of Rti(sum over a of Xa,ti)+CCt, RCP, policy \
(1)
In Eq. 1, ρt is a discount factor, D(Qtind, Zt, RCP) is a global demand function for industrial wood products Qtind and average global consumption per capita Zt, RCP from the International Institute of Applied Systems Analysis (IIASA) SSP database (33). In particular, we use the SSP2 IAM marker scenario from MESSAGE GLOBIOM under each of the five IPCC RCPs [according to the IIASA SSP database (33), the global consumption per capita under the SSP2 IAM marker scenario does not change across RCPs].
Industrial timber demand follows the general functional form Qtind = At(Zt, RCP)θPtω, where At is a constant, θ is the income elasticity, Pt is the timber price, and ω is the price elasticity. The global demand function is for industrial round wood, which is itself an input into products like lumber, paper, plywood, and other manufactured wood products.
Wood demand for bioenergy production Qt,RCPwbio is estimated by adjusting the total bioenergy consumption in the IIASA SSP database Qt,RCPbio with the proportion of global biomass energy produced from wood by following similar assumption as in Lauri et al. (34). Figure S2 (A and B) shows total bioenergy consumption and total woody biomass supply under each RCP for the SSP2.
We assume there is an international market for timber that leads to a global market clearing price. As the price of wood for bioenergy rises to compete with industrial timber, both timber and bioenergy will be traded internationally (49). Competition for supply will equilibrate their prices.
Equation 2 shows that the total quantity of wood depends on the area of land harvested in the timber types in i for each age a and time t(Ha,ti) and the yield function (Va,ti), which is itself a function of ecological forest productivity θti and management intensity ma,ti.
Qttot = sum over i of (sum over a of Ha,tiVa,ti(θ ti, m a,ti))
(2)
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The forestry model used in this analysis is the GTM, which was initially developed to study dynamic forest markets and policies (4, 30). GTM combines the spatially detailed data on forests with an economic model that weighs optimal forest management alternatives. This version of the model does not include climate change impacts, but the land classes in the model can be linked to vegetation types represented in ecosystem models such as BIOME/LPX-Bern (43, 44) or MC2 (45, 46). The baseline scenario used in this study is consistent with current climatic conditions. Moreover, GTM incorporates overall constraints on land areas derived from the ecological models, such that only land that is capable of naturally supporting forests can be converted to forestland (44). For this specific study, we included more restricted limitations on regional land that can be converted to forest following the estimates presented in Bastin et al. (36) of 1.6 billion ha and 0.9 billion ha.
GTM was recently used in a validation exercise to provide a historical assessment of global and regional timber harvesting, timber management, and carbon stocks from 1900 to 2010 in Mendelsohn and Sohngen (47). Thus, our first simulation period (a decade) overlaps with the historical decade. Furthermore, Sohngen et al. (48) conducted a Monte Carlo analysis with the model to assess how uncertainty in the land supply elasticity and forest biomass (yield) parameters would affect timber supply and carbon outcomes. The historical validation illustrates that the model can reproduce forestry management, land areas, timber prices, and timber stocks. The Monte Carlo illustrates that the model is most sensitive to the yield function parameters in terms of the carbon outcomes and timber supply outcomes. Land supply elasticity is uncertain, but given that the elasticity parameter is likely not to vary systematically, uncertainty in the land supply elasticity does not have strong effects on carbon or timber supply.
GTM contains 200 forest types i in 16 regions. Figure S1 shows the regional disaggregation. Forest resources are differentiated by ecological productivity and by management and cost characteristics. To account for differences in ecological productivity, different land classes in different regions have different yield functions for timber, derived from the underlying inventory data. Moreover, forests are broken into different types of management classes. The first type is moderately valued forests; these are forests managed in rotations and located primarily in temperate regions. The second type is natural inaccessible forests, located in regions that are costly to access. To be conservative, inaccessible forests are assumed to be in equilibrium, such that they are neither accumulating nor releasing carbon. Inaccessible forests are unmanaged and located in places that are costly to access for timber market reasons. Over time, some of them in our model become accessible due to economic reasons, e.g., timber prices rise, making additional hectares economically efficient to harvest. If they become accessible, they are harvested, and when regrown, they are subject to applicable forest growth functions. The third type is low-value forests located in temperate and boreal areas that are lightly managed, if they are managed at all. The fourth category includes low-value timberland in inaccessible and semi-accessible regions of the tropical zones. The fifth type includes the high-valued timber plantation that is managed intensively; these forests can principally be found in subtropical regions of the United States, South America, southern Africa, the Iberian Peninsula, Indonesia, and Oceania.
they become accessible, they are harvested, and when regrown, they are subject to applicable forest growth functions. The third type is low-value forests located in temperate and boreal areas that are lightly managed, if they are managed at all. The fourth category includes low-value timberland in inaccessible and semi-accessible regions of the tropical zones. The fifth type includes the high-valued timber plantation that is managed intensively; these forests can principally be found in subtropical regions of the United States, South America, southern Africa, the Iberian Peninsula, Indonesia, and Oceania.
GTM is an economic model of forests that maximizes the net present value of consumers' and producers' surplus in the forestry sector. By maximizing the net present value, the model optimizes the age of harvesting timber a and the intensity of regenerating and managing forests mti. It is an optimal control problem, given the aggregate demand function, starting stock, costs, and growth functions of forest stocks.
GTM relies on forward-looking behavior and solves all time periods at the same time; this means that when land owners make decisions today about forest management, they do so by considering the implications of their actions today on forests in the future with complete information. The result is a forecast of what a competitive market would also do with forestland.
Mathematically, this optimization problem is written as