Does Wood Bioenergy Increase Carbon Stocks in Forests?

J. For. 110(6):304 –311 http://dx.doi.org/10.5849/jof.11-073 Copyright © 2012 Society of American Foresters

RESEARCH ARTICLE

policy

Does Wood Bioenergy Increase Carbon Stocks in Forests? Roger Sedjo and Xiaohui Tian Wood bioenergy is touted as carbon neutral because biological regrowth recaptures the carbon released in energy production. However, some argue that using wood as an energy feedstock will result in decreased forest stocks and thereby a net reduction of carbon sequestered by forests. Such arguments fail to recognize that increased demand for wood bioenergy could increase stocks of wood, a renewable resource. We address the carbon neutrality question using a dynamic optimization forest management model to examine the effect of increasing or decreasing wood bioenergy demand on an existing forest, both in the amount of carbon lost by harvests and in that captured by forest management adjustments that change forest stocks under various wood demand and land supply scenarios. The results suggest for a managed regulated forest using foresight, an anticipated substantial increase in future wood biomass demand will not reduce forest and forest carbon stocks, but rather will increase the forest and forest carbon, thus being somewhat self-regulating. Keywords: carbon, carbon neutrality, wood bioenergy, forest, harvests, rational expectations

T

his study suggests that increased demand for wood biomass for energy purposes not only results in increased harvests, the effect of which is to reduce the forest stock, but the anticipation of increased future demand generates economic incentives to increase the stock of wood, thereby offsetting part or all of the forest reductions from the harvesting. Furthermore, the increases in forest stocks anticipating harvests may predate the subsequent harvests, negating the creating of a forest carbon debt. The driver of this phenomenon is the anticipation of raising wood commodity prices, which serve to provide incentives to expand forest carbon stocks. This behavior can negate much of the concern over a negative effects of biomass energy on forest carbon stocks. Renewable resources, including wood

and biomass, are an alternative to fossil fuels. In 2010, biomass provided about 4% of all the energy consumed in the United States, more than half of that from wood (US Energy Information Administration 2011). Fossil fuels are a problem because their use generates nonreversible emissions of greenhouse gases, especially carbon dioxide. Fossil fuel emissions, unlike biomass emissions, can not return to their earlier form. Malmsheimer et al. (2011) have identified several definitional stances and accounting issues related to emissions from burning wood as an energy feedstock. Until recently, the conventional wisdom was that the use of wood energy as a substitute for fossil fuels would result in an overall decrease in net carbon emissions. This would be the case because the wood bioenergy would reduce the use of and emis-

sions associated with fossil fuels while forest regrowth would then recapture the carbon back into the forest (Pingoud et al. 2006). Stated differently, wood bioenergy would generally be viewed as carbon neutral, because the emissions would be offset by regrowth. This widely accepted viewpoint on carbon neutrality is that “plants take up carbon dioxide from the air while they are growing and then return it to the air when they are burned, thereby causing no net increase” (US Environmental Protection Agency 2012). In addition, “considering the entire [wood bioenergy production] process cycle, there are no net carbon dioxide emissions from burning the biomass” (Matthews and Robertson 2005). However, this viewpoint is being challenged on the grounds that the use of wood as an energy feedstock will result in a decrease of the forest stock creating a “carbon debt” and thereby a net reduction of the total carbon sequestered in the forest, at least for a period of time, thereby offsetting some or all of the gains due to the decreased use of fossil fuels, at least for long periods (Marland and Marland 1992). Depending on how forests are managed, this carbon debt from comparing wood bioenergy emissions to fossil fuel emissions may persist for 50 years in Massachusetts (Manomet Center for Conservation Sciences 2010). Most of the assessments of the relation-

Received September 23, 2011; accepted May 3, 2012; published online July 5, 2012. Affiliations: Roger Sedjo ([email protected]) is director, Forest Economics and Policy Program, Resources for the Future, 1616 P Street, Washington, DC 20036. Xiaohui Tian ([email protected]) is graduate student, Ohio State University, Columbus, OH 43210. Acknowledgments: The authors acknowledge the useful suggestions of Jay O’Laughlin. However, any errors that may remain are solely those of the authors. 304

Journal of Forestry • September 2012

ship between the carbon sequestered in the forest and the net carbon emissions associated with wood bioenergy use an accounting stance based on static relationships in a single forest stand. In essence, the analysis is a life cycle analysis of a single forest stand— not of a dynamic forest system. For example, the Manomet Center for Conservation Sciences (2010) report’s conclusions on carbon neutrality were from the perspective of an individual mature forest stand analysis on which external harvest decisions are applied. Even when making an assessment over time each stand and each period is treated more or less independently of other stands and periods. This narrowly defined problem makes it difficult to address two key questions: (1) how to maintain forests as carbon sinks over the long term and (2) how to optimize the production of biomaterials and bioenergy that help reduce demand for fossil energy (Birdsey et al. 2006). Forest management decision models that include market factors for wood products and bioenergy can help address these key questions. Forest management does not involve simply harvesting individual mature stands and replanting them in isolation. Rather, forest management responding to the markets for wood products involves the simultaneous management of multiple stands and an anticipation of future market conditions. Indeed, the market coordinates wood use and forest management across many stands and ownerships as multiple managers and forests are directed by market signals. In effect, the market’s invisible hand creates an owner-regulated forest across many ownerships. This intertemporal management process for the forest system can be simulated by using a dynamic optimization approach whereby the entire intertemporal system is modeled and solved simultaneously, with the specified future conditions directly affecting current decisions. Changes in demand in one forest will be transmitted throughout the multiforest system. A decision to harvest in one forest in a particular time period involves related forest management decisions on other acres, other forests, and in other time periods. If future demand is expected to increase, forest managers behave differently than they would if future demand were expected to be constant or decrease. Higher expected future prices will elicit forest expansion, with more active forestland management, treeplanting, and silviculture. Indeed, if future prices are expected to be significantly higher than cur-

rent prices, current harvest can actually decline as managers “save” the wood for future sale at higher prices. This phenomenon is not limited to the behavior of one forest manager on one forest but rather will be transmitted via market signals (prices) throughout the system to all forest managers. For example, when the demand for corn for ethanol production increased, not only did the price of corn rise, so did the amount of land planted in corn, reflecting the actions of many farmers. A similar response by forest managers, including perhaps dedicated wood biomass forests, could be expected. In a world of scarce energy with rising prices, where biomass is beginning to play a substantive role, future wood prices can be expected to rise. Indeed, some of the industrial wood mills have expressed concerns over having to compete with the biomass feedstock market and these concerns about rising future wood prices may well be valid (Sedjo and Sohngen 2012). Conceptually, a rising wood price should elicit forest management changes in the direction of increasing levels production by planting additional areas of forest as well as other management to increase forest density and traditional waste, which now have economic value. Enhancing forest growth rates also provides an element of unintended carbon self-regulation. This article uses a dynamic optimization forest management model (Sohngen et al. 1999) to examine in detail the likely effect of the introduction of a changing wood biomass demand on the existing forest and the amount of carbon captured by the forest system.

Analytical Methods Our basic methodology uses a dynamic programming model to examine the relationship between carbon in a forest and the use of woody biomass for energy production. The approach begins with a simple dynamic forest model of a multiaged regulated forest, i.e., a sustainable forest capable of continuously producing a consistent amount of harvested product. The basic approach is to use this stylized forest model to examine the implications of hypothetical changes in demand on forest stocks and stored carbon under different conditions. Within the model framework a stylized representative forest is developed to examine the carbon neutrality question. Specifically, we examine how changes in demand for wood for biomass energy affect the forest

area, forest stock, and volume of forest carbon. We show under what conditions these variables would decline, remain constant, or increase. The analysis begins by presenting an optimal control model, developed by Sedjo and Lyon (1990) and Sohngen et al. (1999). We address the forest as a system and incorporate the assumption of rational expectations. By using a dynamic optimization approach, the entire multiple-stand intertemporal system is solved simultaneously, with the future conditions and prices directly affecting current decisions. The biomass price is determined within the system in a way that maximizes the present value of the wood biomass market and thereby reflects the scarcity of timber stocks.

Rational Expectations Models in Forest Management Although the expectations of individuals may turn out to be incorrect, the “rational expectations” approach assumes that individual decisions are correct on average. This approach contrasts with earlier modeling techniques in forestry, in which the current-period decision was based entirely on current and past conditions, thus not allowing any future expectations to directly inform current decisions. Muth (1961) noted that earlier intertemporal analysis ignored expectations of future in the management decisions, instead basing its behavioral assumptions on past experience while noting that future expectations are often far different from past experience. This is certainly the case if biomass energy should become a major substitute for fossil fuels. Takayama and Judge (1971) developed forward-looking spatial and temporal price and allocation models that built future expectations explicitly into prior management decisions. These forward-looking or rational expectations models are now commonly used in forestry projections, e.g., the global scale timber supply model (e.g., Sedjo and Lyon 1990, Sohngen et al. 1999) and the Food and Agricultural Sector Optimization model (Alig et al. 1997). The anticipation of future conditions is not an unusual feature of management decision processes. For example, benefit– cost analysis is by nature intertemporal, comparing current investment costs with the value of future benefits. Obviously, future benefits are not known with certainty. Instead, judgments are made as to likely future economic Journal of Forestry • September 2012

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Table 1. Model parameters and values.

Figure 1. Forest planting in the United States by region, 1952–2006. (Source: US Forest Resource Facts and Historical Trends, 2009, www.fia.fs.fed.us/library/brochures/ default.asp; US Forest Service 2009.)

conditions and market prices. Then, the cost of the investment is compared with those future conditions to determine the investment’s economic viability over time. In a dynamic optimization approach, the entire intertemporal system is solved simultaneously, with the specified anticipated future conditions directly affecting current decisions. Such a perspective changes forest management decisions. If trees are planted in anticipation of their future use as bioenergy feedstocks, the carbon released on the burning of the wood was previously sequestered in the earlier (anticipating) biological growth process. From a broad forest system perspective, burning of the biomass does not release new carbon but simply releases carbon that was previously sequestered in an earlier period in anticipation of future biomass burning. Forestry, by its nature, involves many intertemporal decisions that take place over many decades. Treeplanting is an investment that generally takes at least 25 years to reach fruition. For example, forest planting in the United States rose after 1950 (Figure 1) in anticipation of future wood shortages as the nation was expected to gradually draw down its old-growth stocks of timber in the face of rising demand. However, beginning in the late 1980s treeplanting started to decline as its forest sector analysts began to recognize that future timber stocks likely would be adequate, in part because of the intense planting both domestically and internationally (United Nations Food and Agriculture Organization 2005) and the recognition that future demand growth in the United States would be modest. In this analysis the area of forest, the level of demand change, and the land supply elasticity, which will change the area of forest, are allowed to change according to the specifications in Table 1. In addition, the 306


Parameters

Value

Demand function Discount rate Carbon conversation rate Demand increase and decrease scenarios Yield functions

Q(t)(tc) ⫽ 95.334 ⫺ 0.4768 ⴱ p(t)($/tc) 0.95 0.20 tC/m3 See Table 2 Base yield function: ln(V(a)) ⫽ 7.82 ⫺ (52.9/a) Short-rotation yield function: ln(V(a)) ⫽ 7.3 ⫺ (27/a) Constant land rent of $200/ha Land supply elasticity of 0.5: R ⫽ (L/1.265)2 Land supply elasticity of 1.0: R ⫽ L/1.60

Land supply function

wood production function can be changed. However, experiments with such modifications did not substantively change the basic findings presented here and thus were omitted. The initial conditions of the modeled forest provide for a regulated forest with a given amount of forestland. The forest is homogeneous with a stand growth and yield function applied to each hectare. The amount of carbon captured is a fixed percentage of the forest volumes as indicated previously. Because this analysis is focused on the forest as a bioenergy feedstock, it is assumed that all carbon in the wood harvest is immediately released into the atmosphere. To avoid dealing with a separate type of problem, it is assumed that the amount of waste wood is zero. Furthermore, a summary of the technical aspects of the model are provided in a short Appendix.

Numerical Results The approach now examines a base case and three scenarios, described in Table 2. In all scenarios but the base case, the forests are initially in equilibrium under the baseline demand condition in which price equates current demand for wood biomass for energy with the anticipated wood volume. The base case is included to provide a flavor for the model. Scenario 1 examines the effects of different levels of demand increase. Scenario 2 examines the effects on the forest system of different degrees of land availability for forests as captured in land supply elasticities. Scenario 3 complements scenario 1 and examines the effects of anticipated demand decrease. The Base Case The base case scenario (Figure 2) imposes a new intertemportal demand on the initial conditions of the forest system. A level of demand is specified and the forest system is allowed to adapt to facilitate meeting the intertemporal demand in an economically

efficient manner. This is the stylized model from which the subsequent scenarios are developed. It also gives the reader a flavor of how demand will impact the forest. The base case results in Figure 2a present the carbon capture path for an initial 16 million– ha forest. If the baseline demand is assumed to be fixed at a low “baseline” level and not changing over time, Figure 2b shows the regulated forest area declining from 16 million to about 6 million ha over a period of about 30 years. The initial 16 million ha are harvested over time; however, only 6 million ha are need to meet the low level of anticipated demand and only that amount of area is reforested. The remaining 10 million ha now fall out of the regulated forest and are assumed to be available for nonforest uses after they have been harvested. Note that with this much forest, the initial harvests are relatively high (Figure 2b) while the price is low (Figure 2c). However, as the long-run equilibrium is approached circa year 40, the price rise chokes off some of the harvest. The decline in forest area is associated with a decline in forest carbon and hence we get a carbon forest decline. By contrast, the slow demand growth in Figure 2d projects the harvest path for a demand growth of 2%/year. for 40 years after which demand stabilizes at the long-term equilibrium that higher level with a forest area having expanded from 16 million to about 35 million ha. The harvest level and wood price also increase throughout that period as they approach the long-term equilibrium. The main lesson here is that if demand is less than the sustainable harvest potential of the forest, the wood price will decline and with it the forest area and forest carbon. If, however, demand is greater than the sustainable harvest of the forest, prices will rise, the forest area will expand to meet the increasing demand, and, in the process, will capture and store more forest carbon.

Table 2. Description of wood bioenergy demand scenarios. Land supply conditions

Initial area million ha

Initial age classes

Demand comparison scenarios

Base case

Constant land rent

16

32 Equal age classes

Scenario 1

Constant land rent

6


Scenario 2

Land supply elasticity of 0.5

9.69


Scenario 3

Constant land rent

6


Constant demand compared with increase 2%/yr for 40 yr followed by constant demand Constant demand compared with increases of 2 and 4%/yr for 40 yr followed by constant demand Constant demand compared with increases of 2 and 4%/yr for 40 yr followed by constant demand Constant demand compared with decrease of 1%/yr for 40 yr followed by constant demand

Figure 2. Forest carbon base case illustration. Wood bioenergy constant demand compared with increase of 2%/year followed by constant demand; constant land rent. (a) Carbon capture path. (b) Forest area path. (c) Wood biomass price path. (d) Harvest path. Note: Start with 16 million ha in 32 equal age classes, base yield function, and constant land rent.

The Scenarios Three scenarios are examined (Figures 3–5) that depart from the base case presented previously. In each of these the level of initial demand is set just adequate to fully using the existing forest. When the rate of growth of demand is increased by some amount, as, e.g., reflecting the onset of an increased demand for biomass energy as renewables increasingly replace fossil fuels, the system adapts. As demand changes, the system converges to a new equilibrium path consistent with that demand and generates new intertemporal price, harvest, and forest area paths. Scenario 1: Alternative Demands. This scenario examines three levels of de-

mand for a regulated forest of about 6 million ha and 28 age classes. This size forest is chosen because it is consistent with the size required for the long-run equilibrium for the level of constant demand chosen for this illustrative case. Demand is set at a given constant level indefinitely, representing a situation where only a modest amount of wood is used for bioenergy and this condition has been in effect for some time. We can view this demand as consistent with the era before emergence of wood bioenergy demand. The forestland supply curve is infinitely elastic at a $200 rental price. Figure 3 presents the 90-year time path for the constant demand level. For the baseline scenario where demand is relatively low and constant, the ini-

tial condition is one of equilibrium for a forest area of 6 million ha and a carbon content of about 225 million tn. As Figure 3a shows, these levels remain constant over the approximately 90-year time period examined. Figure 3a also examines situations where demand is posited as increasing at a rate of 2% and 4%/year for 40 years and then remains at this level indefinitely. This can be viewed as the onset of the widespread introduction of wood biomass energy into a system. As Figure 3 makes clear, the volumes of carbon captured, forest area, biomass wood price, and harvest levels all increase over the 40-year period of rising demand and then stabilize in year 40 at the higher levels. Of particular interest is the effect of Journal of Forestry • September 2012

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Figure 3. Forest carbon scenario 1: Wood bioenergy constant demand compared with increases of 2 and 4%/year followed by constant demand and constant land rent. (a) Carbon capture path. (b) Forest area path. (c) Wood biomass price path. (d) Harvest path. Note: Start from 6 million ha in 28 equal age classes, constant land rent, and base yield function.

Figure 4. Forest carbon scenario 2: Wood bioenergy constant demand compared with increases of 2 and 4%/year followed by constant demand and land supply elasticity of 0.5. (a) Carbon capture path. (b) Forest area path. (c) Wood biomass price path. (d) Harvest path. Note: Start with 9.69 million ha in 28 equal age classes, land supply elasticity of 0.5, and base yield function.

increased demand on forest carbon capture in Figure 3a. Note that the carbon stock 308


does not decline even for the increased wood demand scenarios. This is the case because as

prices rise as shown in Figure 3c, the area of forest is increased (Figure 3b). Indeed, Fig-

Figure 5. Forest carbon scenario 3: Wood bioenergy constant demand compared with decrease of 1%/year followed by constant demand and constant land rent. (a) Carbon capture path. (b) Forest area path. Note: Start from 6 million ha in 28 equal age classes, constant land rent, and base yield function.

ure 3d shows harvest actually declining slightly in the face of the higher demand (4%/year) relative to the constant demand case in the earliest periods. This reflects producers withholding product from the market in anticipation of higher future prices. Scenario 2: Land Supply Constraints. Scenario 1 (Figure 3) assumed availability of unlimited supplies of forestland at a constant price. What happens if we add an upward rising supply curve? This should diminish the harvest and carbon levels as well as forestland use, for any given demand increase. Scenario 2 (Figure 4) changes the assumption regarding the forestland supply curve so that it is now less price responsive, with an elasticity of 0.5 throughout. This elasticity indicates that the land supply curve will rise sharply as new land is added to the regulated forest to provide for increased production. The rising land prices are expected to choke off forest expansion to a degree. For this case, the initial conditions are modified to provide an initial equilibrium state of 9.69 million ha of forest divided into 28 equal age classes, with 370,000 ha in each class. As in scenario 1, this amount of forestland is consistent with the constant demand condition. It includes more land than scenario 1 because the supply conditions are different. The long-term price peaks and stabilizes at an indexed price of 850 with the 2% annual increase and 4,200 with the 4% increase (Figure 4d). Also, note that in the earlier years the harvest path is lower for the two cases where the level of demand is increasing over time. This reflects optimizing behavior resulting from rational expectations that delay harvests until prices have risen. Note that while the rate of demand

growth is increasing, the area of forest continues to increase despite rising land costs. What happens to forest carbon in this scenario? The forest carbon path increases in the early years, reaches a peak, and declines until it stabilizes after about 45 years. Thus, for those two intervening decades there are net carbon releases to the atmosphere. However, the forest carbon capture for increased wood biomass demand is always greater than that for the constant demand. Thus, the increased demand does not reduce total forest carbon in either the short or long term compared with the constant demand case in scenario 1. Scenario 3: Demand Decline. Figure 5 examines the effects of an anticipated decline in demand. Not surprisingly, the results indicate that under decreased demand pressures the forest area will decline, with the land converting to nonforest uses and with it a declining stock of forest carbon. Finally, note that not all the carbon released from bioenergy production is necessarily captured, but rather some positive portion is recaptured in the expanded forest that would otherwise be in the atmosphere. This contrasts with a situation where wood is not used as a fossil fuel substitute, and fossil fuel use continues. In this case, forest area is reduced and subsequently more carbon persists in the atmosphere. With no new forest, there will be no new sink to capture carbon released by fossil fuel use into the atmosphere. Additional Scenarios. A number of additional scenarios were constructed and run through the model but are not reported here. For these additional scenarios we found that for all forests in initial wood biomass harvest equilibrium, an increase in de-

mand would not initially reduce forest carbon. This was found to be true even for the case of a completely inelastic supply of new forestland, which is similar to the case study analyzed in the Manomet Center for Conservation Sciences (2010) report.

Discussion Using woody biomass as a substitute for fossil fuels has carbon management implications. The Manoment Center for Conservation Sciences (2010) report suggested that a full offset of carbon releases would require that the harvest of live wood used to produce biomass energy and substitute for fossil fuels would need to be totally regrown before the carbon releases would be offset. For an individual mature forest stand this would take decades and perhaps centuries. However, forest management involves more than simply harvesting mature stands and replanting them without consideration of adjacent stands. Rather, forest management responding to markets involves the simultaneous management of many multiaged stands and an anticipation of future market conditions. Indeed, the market coordinates wood use and forest management across many stands and ownerships. Thus, at the scale of a timbershed for a forest products conversion facility, the regulated forest need not be managed by a single individual but rather multiple managers whose forest management decisions are directed by market signals. The intertemporal management decision process for the forest system can be simulated by using a dynamic optimization approach whereby the entire intertemporal system is modeled and solved simultaneously, with the specified future market conJournal of Forestry • September 2012

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ditions directly affecting current forest management decisions. A forward-looking rational expectations approach as described previously is now commonly used in forestry decision models. In such a system future anticipated prices are incorporated into current management decisions. Applying this approach to wood bioenergy production, our results show that managers would, on the average, be expected to anticipate increases in the future demand and adjust their management and harvesting practices so that forest size and harvests will accommodate the future demand. Indeed, although the model only allows adjustments of forest size and harvest levels, in the real world, forest managers would also include additional silvicultural practices such as fertilization and genetic improvement. For simplicity this analysis ignores ancillary fossil fuel emissions such that are associated with harvest, transport, and the like. Research in Montana has indicated that for every unit of fossil energy used to collect and transport biomass, the wood-fired boiler heating systems studied return approximately 20 times the energy from fossil fuel use (Jones et al. 2010). Is wood bioenergy carbon neutral? That is, should emissions be viewed as offset in the short term? The question is whether the increased demand for wood bioenergy is expected to continue long enough to justify the appropriate adjustments in forest management practices. A surge in demand for a single decade is unlikely to result in a decision to expand forest area. A critique of our approach of this article is the argument that many individual forests do not comprise a regulated forest. However, although this may be true of individual forests in a given timbershed, collectively, at larger scales, the forest system fits the regulated forest model paradigm because planted and naturally managed forests would be expected to increase at the large scale, reflecting investment opportunities in anticipation of future economic returns. One additional concern is with regard to a potential long-term trend of forestland converted to other nonforestland uses. This would not arise from timber harvesting for industrial roundwood or wood bioenergy use but rather be attributed to alternative land uses, including agricultural production. This situation, however, does not provide any direct information as to the question at 310


hand, which is the carbon footprint effect of forest harvests for bioenergy production.

Conclusions Our analysis shows the effect on the forest and forest carbon stocks of using wood for bioenergy has two strong driving components: (1) harvests, which reduce the forest stock, and (2) forest management, which increases the forest stock in response to increased demand. Our results suggest that, contrary to some recent analyses, including the Manomet Center for Conservation Sciences (2010) report, for a regulated forest system the forest stock will generally expand in the face of increasing demand. This analysis recognizes that commercial forests are not static and without foresight. For a managed regulated forest using foresight, an anticipated substantial increase in future demand will not reduce forest carbon, as some have argued, but rather will increase the forest and forest carbon stocks because of expansive forest management activities. This carbon self-regulating result occurs when forest managers are driven by anticipation of economic returns on their forest investments. Our approach maintains that when economic market conditions for wood bioenergy will lead managers to regenerate forests after a wood bioenergy harvest, returning the forest to preharvest conditions. These results occur not only for an individual forest stand or ownership but also for an interconnected forest system where various managers respond to market forces. Decisions in one forest affect decisions in the others. Similarly, for such a forest system, a substantial decline in wood bioenergy demand will result in management that reduces forest area and carbon stocks. Our reply to the question of wood bioenergy carbon neutrality is that using wood to produce energy results in no new net carbon emissions as long as the harvested area is replanted to forest. Furthermore, our results suggest that in response to market forces there should be an increased use of woody biomass, as the pressures to reduce the forest stock are offset by economic forces to increase the forest stock and with it the forest carbon stock.

Literature Cited ALIG, R.J., D.M. ADAMS, J.M. CALLAWAY, S.M. WINNETT, AND B.A. MCCARL. 1997. Assessing effects of mitigation strategies for global climate change with an intertemporal model of the US forest and agriculture sectors. Environ. Resour. Econ. 9:259 –274.

BIRDSEY, R., K. PREGITZER, AND A. LUCIER. 2006. Forest carbon management in the United States: 1600 –2100. J. Environ. Qual. 35: 1461–1469. JONES, G., D. LOEFFLER, D. CALKIN, AND W. CHUNG. 2010. Forest treatment residues for thermal energy compared with disposal by onsite burning: Emissions and energy return. Biomass Bioenergy 34:737–746. MALMSHEIMER, R.W., J.S. BOWYER, J.S. FRIED, E. GEE, R.L. IZLAR, R.A. MINER, I.A. MUNN, E. ONEIL, AND W.C. STEWART. 2011. Forest carbon stocks and flows. SAF Task Force Report: Managing forests because carbon matters: Integrating energy, products, and land management policy, Sec. 2. J. For. 109(7S): S14 –S20. MANOMET CENTER FOR CONSERVATION SCIENCES. 2010. Massachusetts biomass sustainability and carbon policy study: Report to the Commonwealth of Massachusetts Department of Energy Resources. Natural Capital Initiative Report NCI-2010-03. Brunswick, ME. Available online at www.manomet.org/sites/manomet. org/files/Manomet_Biomass_Report_Full_ LoRez.pdf; last accessed Feb. 29, 2012. MARLAND, G., AND S. MARLAND. 1992. Should we store carbon in trees? Water Air Soil Pollut. 64(1–2):181–195. MATTHEWS, R., AND K. ROBERTSON. 2005. Answers to ten frequently asked questions about bioenergy, carbon sinks and their role in global climate change, 2nd Ed. IEA Bioenergy Task 38, Greenhouse Gas Balances of Biomass and Bioenergy Systems, International Energy Agency, Rotorua, NZ. 7 p. Available online at www.iea bioenergy-task38.org/publications/faq/; last accessed Feb. 29, 2012. MUTH, J.F. 1961. Rational expectations and the theory of price movements. Reprint, P. 3–23 in The new classical macroeconomics, Vol. 1 (1992), Hoover, K.D. (ed.). International Library of Critical Writings in Economics, Vol. 19. Elgar, Aldershot, U.K. PINGOUD K., K. SKOG, D.L. MARTINO, M. TONOSAKI, Z. XIAOQUAN, AND J. FORDROBERTSON. 2006. Harvested wood products, Chap. 12. P. 12.1–12.33 in 2006 IPCC Guidelines for National Greenhouse Gas Inventories, Vol. 4: Agriculture, forestry and other land use. Intergovernmental Panel on Climate Change, Geneva, Switzerland. SEDJO, R.A., AND K.S. LYON. 1990. The long-term adequacy of world timber supply. RFF Press, Washington, DC. 230 p. SEDJO, R.A., AND B. SOHNGEN. 2012. Wood as a major feedstock for biofuel production in the U.S.: Impacts on forests and international trade. J. Sustain. For. In press. SOHNGEN, B., AND R. SEDJO. 1998. A comparison of timber market models: Static simulation and optimal control approaches. For. Sci. 44: 24 –36. SOHNGEN, B., R. MENDELSOHN, AND R. SEDJO. 1999. Forest management, conservation, and global timber markets. Am. J. Agric. Econ. 81(1):1–13.

TAKAYAMA, T., AND G.G. JUDGE. 1971. Spatial and temporal price and allocation models. North Holland Press, Amsterdam, The Netherlands. 528 p. UNITED NATIONS FOOD, AND AGRICULTURE ORGANIZATION (UNFAO). 2005. The state of the world’s forests. UNFAO, Rome, Italy. 128 p. US ENERGY INFORMATION ADMINISTRATION (EIA). 2011. Annual energy review 2010. Office of Energy Statistics, US Dept. of Energy, Washington, DC. 363 p. US ENVIRONMENTAL PROTECTION AGENCY (EPA). 2012. Air emissions: Non-hydroelectric renewable energy—Biomass. Available online at www.epa.gov/cleanenergy/energy-and-you/ affect/air-emissions.html; last accessed Feb. 29, 2012. US FOREST SERVICE. 2009. Forest resource facts and historical trends. Available online at www. fia.fs.fed.us/library/brochures/default.asp; last accessed May 2012.

Appendix The Model A continuous time optimal control model is presented. The basic model is a simple variant of a model developed by Sedjo and Lyon (1990), Sohngen and Sedjo (1998), and Sohngen et al. (1999, 2003). The objective of this model posits that a social planner attempts to maximize the net present value of net surplus in wood biomass markets. Net surplus is defined as the area between the biomass demand curve and the land rent cost, often simply characterized as profit. Modifying Sohngen and Sedjo (1998), the social planner’s problem is,

max 兵H共t兲,G共t兲其

再冕

冕

⬁

e

⫺rt

0

冎

Q共t兲

D共Q共H共t兲,V共a兲兲兲dQ ⫺ R共t兲 X共t兲 dt

0

Xˆ ⫽ ⫺ H共t兲 ⫹ G共t兲 H共t兲 ⱖ 0;

G共t兲 ⱖ 0;

(1) (2)

X共0兲

is given

where D(䡠) is a downward sloping demand function given the wood biomass quantity per period; Q(䡠) is the total quantity harvested generated by the demand function; H(䡠) is the hectares harvested; G(䡠) the hectare planted and V(a) is the wood biomass yield function, where a is the age of plants harvested; R(䡠) represents land rent or the opportunity cost of maintaining land as forest rather than allowing it for alternatives uses; X(䡠) is the forestland hectares; and r is the interest rate that should reflect the risk with carbon uptake service (e.g., fire risk, slower than expected tree growth, to name a few). The state variable here is X(t). The choice variables are H(t) and G(t). The state variable will vary over time according to Equation 2, where Xˆ is the increased hectares of forests between current period and the next period. We further modify the earlier model in Sohngen and Sedjo (1998), where forestland is fixed, to allow land of wood biomass to expend or decrease by plantation and harvest

(Equation 2). So there is the possibility that some harvested land may not be replanted, thereby falling out of forest, and also the possibility that additional land will be converted to forest. These adjustments need not release significant amounts of carbon above that captured by demand. Although silvicultural practices can increase the wood (and carbon) volume over short periods, e.g., through tree improvement or fertilization, the only management practices allowed in this analysis are those of adjusting the amount of land in forest and the length of the timber rotation in the context of a regulated forest. The approach is to use a general stylized forest sector model to examine the effects of an increase in the use of wood biomass energy on the amount of carbon captured in the forest over time under a number of hypothetical conditions. These effects will be examined for different rates of demand growth, different elasticities of forestland supply, and different yield and growth functions. Also, the relation of the initial increase in demand to equilibrium conditions is examined. The model parameters and values for the representative forest are given in Table 1. As noted, the model assumes a regulated forest, i.e., an even-aged forest where harvest acres are replanted in the next time period and management driven by profit maximizing economic considerations. A series of scenarios are examined in which the underlying conditions are varied to assess how the amount of forest carbon might change.


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