جداسازی کربن و تصمیم گیری برداشت از جنگل بهینه: روش برنامه ریزی پویا با توجه به زیست توده و ماده آلی مرده

Carbon sequestration in forests is being considered as a mechanism to slow or reverse the trend of increasing concentrations of carbon dioxide in the atmosphere. We present results from a dynamic programming model used to determine the optimal harvest decision for a forest stand in the boreal forest of western Canada that provides both timber harvest volume and carbon sequestration services. The state of the system at any point in time is described by stand age and the amount of carbon in the dead organic matter pool. Merchantable timber volume and biomass are predicted as a function of stand age. Carbon stocks in the dead organic matter pool changes as a result of decomposition and litterfall. The results of the study indicate that while optimal harvest age is relatively insensitive to carbon stocks in dead organic matter, initial carbon stock levels significantly affect economic returns to carbon management.

In response to global concern about climate change, policy makers and scientists are searching for ways to slow or reverse the trend of increasing concentrations of greenhouse gases, especially carbon dioxide (CO2), in the atmosphere. Forests are viewed as potential carbon sinks. As trees grow, photosynthesis converts CO2 into cellulose and other plant material, temporarily removing it from the atmosphere. In addition, a substantial amount of carbon is stored in forests as dead organic matter (DOM) in standing snags, on the forest floor, and in the soil until the process of decomposition releases it back to the atmosphere. The Intergovernmental Panel on Climate Change (IPCC) provides guidelines for the calculation and reporting of changes in stocks of forest carbon (IPCC, 2006) as it relates to national greenhouse gas inventories. The IPCC identifies three tiers for reporting changes in stocks of forest carbon. These tiers reflect the relative importance of forest carbon stocks to greenhouse gas inventories and the sophistication of the data collection and monitoring infrastructure of countries. Canada has elected to use tier 3 methodologies (with the most detailed reporting requirements) for reporting changes to carbon stocks on managed forest lands. The IPCC specifies five carbon pools that must be accounted for: above-ground biomass, below-ground biomass, dead wood, litter, and soil carbon. The Canadian Forest Service developed the Carbon Budget Model of the Canadian Forest Sector (CBM-CFS3) to track and report changes in forest carbon stocks (Kull et al., 2007). CBM-CFS3 is a detailed model that recognizes more than 20 different carbon pools within a forest stand and tracks the transfer of carbon between these pools and the atmosphere (Fig. 1). Full-size image (46 K) Fig. 1. The carbon pool structure of the CBM-CFS3. Very fast, fast, medium, and slow refer to relative decomposition rates for pools. Curved arrows represent transfers of carbon to the atmosphere, and straight arrows represent transfers from one pools to another. SW is softwood, HW is hardwood, AG is above ground, and BG is below ground. Illustration courtesy of the Canadian Forest Service, reproduced with permission from Kull et al. (2007, Fig. 1-1). Figure options The classic problem in forest economics is the determination of the harvest age for an even-aged forest stand which maximizes the net present value of an infinite series of timber regeneration, growth, and harvest cycles. Faustmann (1849) is usually attributed with the first correct solution to this problem when only timber values are considered. Samuelson (1976) provides a more formal mathematical specification of the problem. Hartman (1976) extends the model to include values associated with standing trees (e.g. wildlife habitat) as well as the extractive value of timber harvest. In the forest economics literature, most of the analysis of carbon sequestration has focused on the carbon pools in living biomass. However, the DOM carbon pool can represent a substantial proportion of the total carbon stored in forest stands and management decisions such as harvest age can have a substantial effect on soil carbon stocks (Aber et al., 1978 and Kaipainen et al., 2004). Covington (1981) found that forest floor mass declines sharply following harvest, with about half of forest floor organic matter lost in the first 20 years. DOM may increase immediately following harvest as a result of slash and other debris left on site (Black and Harden, 1995). Despite the importance of the DOM pool in the carbon cycle of a forest stand, it has received limited attention in the literature on the economics of forest carbon sequestration, perhaps because of the difficulty of tracking a large number of carbon pools in an optimization model. The Hartman model is used by van Kooten et al. (1995) in an early exploration of the effect of carbon prices on optimal forest harvest age in western Canada. In their analysis, the amount of carbon stored in the forest stand is proportional to volume of merchantable timber on the site at a particular stand age. The forest owner is paid for the accumulation of carbon in biomass associated with growth, and pays for carbon released to the atmosphere at harvest. Some of the harvested timber is assumed to be permanently stored in structures and landfills. There is no recognition of DOM or soil carbon in the van Kooten analysis. Dynamic programming has been used in a some recent papers as an approach to stand level optimization with respect to timber values and carbon sequestration. Spring et al. (2005b) formulated and solved a stochastic dynamic program to maximize the expected net present value of returns from timber production and carbon storage in a forest stand subject to stochastic fire. They modeled the decision problem using stand age as the state variable: timber production and carbon storage were both treated as functions of stand age. In Spring et al. (2005a), the same authors used stochastic dynamic programming to determine the rotation age considering timber production, water yield, and carbon sequestration under stochastic fire occurrence, again using stand age as the only state variable. Chladná (2007) used dynamic programming to examine the optimal forest stand harvest decision when timber and carbon prices are stochastic. Chladná used stand volume per hectare, timber price, and carbon price as state variables. Yoshimoto and Marusak (2007) optimized timber and carbon values in a forest stand using dynamic programming in a framework where both thinnings and final harvest were considered. In this case, the state variables for the problem were stand age and stand density (number of trees per ha). Gutrich and Howarth (2007) developed a simulation model of the economics of timber and carbon management for five different forest types in New Hampshire, USA. Their model includes representation of carbon stored in live biomass, dead and downed wood, soil carbon, and wood products. Annual transfers of carbon between pools are modeled. For each timber type, an initial stock of carbon in the dead and downed wood pool is assumed. A grid search is performed to find the harvest age that maximizes net present value given the initial stock of carbon in the non-biomass pools. To the best of our knowledge, Gutrich and Howarth (2007), were the first to publish a study where the amount of carbon stored in the DOM pool was considered in determining the economically optimal timber harvest age. They do not, however, consider the effect of different initial stocks in the DOM pool. At the forest level, McCarney (2007) uses a linear programming model which includes carbon stocks in both DOM and biomass pools in a model optimizing the net present value of timber harvest and carbon sequestration. Initial DOM stocks are fixed in McCarney’s analysis. In this paper, we develop a dynamic programming model to find the optimal stand management policy when both timber harvest and carbon sequestration values are considered. We describe the forest stand being modeled in terms of its age and the mass of carbon stored in the DOM pool. The management decisions available to the decision maker are to clearcut a stand of a given age and with a DOM pool of a given size, or to defer the harvest decision. Because the amount of carbon stored in the DOM pool is a substantial fraction of the carbon stored by the stand, consideration of the DOM pool could be of considerable economic interest. To the best of our knowledge, this is the first paper to examine the role of variable DOM stocks in the optimal forest harvest decision at the stand level. As we demonstrate later in this paper, the size of the DOM pool controlled by a forest owner may affect the incentives associated with carbon management and the attractiveness of participating in carbon markets to forest landowners. We use the dynamic programming model presented here to: 1. examine the sensitivity of optimal harvest age to stocks of carbon in DOM and carbon prices, 2. examine the sensitivity of the net present value of forested land to stand age, stocks of carbon DOM, and carbon prices, 3. examine projected trajectories of carbon stocks in DOM given optimal harvest rules for a given carbon price, and 4. examine the impact of ignoring carbon stocks in DOM on the optimal harvest decision.

In this study we presented the formulation of, and results from, a dynamic programming model used to determine the optimal harvest decision for a forest stand used to provide both timber harvest volume and carbon sequestration services. The forest stand is described using two state variables: stand age and the stocks of carbon stored in the DOM pool. To the best of our knowledge, this is the first article to examine the impact of varying DOM on the optimal harvest age. This study provides a basic framework for assessing the economic implications of alternative methods of accounting for C stocks in DOM. We use the model to examine optimal harvest decisions for a lodgepole pine stand in the boreal forest of western Canada. We draw the following main conclusions from our study: 1. The optimal decision is sensitive to current stocks of carbon in the DOM pool, especially when carbon prices are high and initial DOM stocks are low. 2. For many realistic combinations of the initial stand age and DOM carbon stocks, a non-zero carbon price reduced the value of land, timber, and carbon sequestration services relative to the zero case. To some readers, this may be counter-intuitive as the storage of carbon in forests is often considered to be a benefit. However, because of the decomposition of DOM, forest stands can be a net carbon source for several years after stand initiation (Fig. 2). Coupled with a positive discount rate, DOM carbon stocks can represent a significant liability to the landowner, especially if she is required to pay for net carbon emissions in the year that they occur. Because of this, it is quite possible (perhaps even probable) that the economically optimal DOM stocks are smaller than in the initial state (Fig. 4). 3. Compared to the case where changes in carbon stock in only the biomass pool is considered, optimal harvest ages are younger and equilibrium carbon stocks are lower when changes in carbon stocks in the DOM pool are rewarded or penalized. This article presented the results of an optimal harvesting model for a forest stand where the landowner is paid for net increases in total ecosystem carbon in the stand, and pays for net decreases, on an annual basis. By approximating a detailed carbon budget simulation model using two carbon pools, we were able to develop a dynamic programming model of the system which captures the important elements of the system for an economic analysis. We plan to use variants of this model to explore alternative forms of carbon markets, including one which accounts for carbon pools in forest products. We demonstrated that the optimal management policy can be substantially different between cases where the market considers and ignores carbon in the DOM pool. This raises an interesting issue because the size of the DOM pool is important from a carbon flux standpoint, but is more difficult to measure than biomass. We conducted our analysis considering an isolated timber stand, where prices of timber and carbon storage services were determined exogenously. If a large forest area was participating in this market it would change the timber supply and could affect the prices of timber, which would feed back into the optimal harvest decision. The direction of this effect is not clear, as equilibrium timber production (measured by mean annual increment), increased in our example until carbon prices reached about 10 CAD/tCO2. When carbon prices are high enough, rotation ages lengthen considerably and mean annual increment declines. In these cases, there would be pressure for both higher timber prices and the possibility of increased substitution of building materials such as concrete and steel for wood. We did not examine any effects of this substitution on national or global carbon accounts. This paper presents a model used for the determination of the optimal harvest age of a single forest stand in the tradition of Faustmann (1849) and Hartman (1976), with the inclusion of a price and a cost associated with the annual sequestration and emission of CO2. The general results reported here can be expected to differ from forest-level analyses such as those reported by McCarney (2007) and McCarney et al. (2008) because of the effect of inter-period flow constraints imposed on forest-level models. The results can also be expected to differ from those reported in other stand-level models (e.g. van Kooten et al., 1995, Spring et al., 2005a, Spring et al., 2005b and Chladná, 2007) because we recognize that a forest stand has both carbon sink (the living biomass) and carbon source (the DOM pool) components. Our results can also be expected to differ from other analyses because of the particular form of the carbon market we assume. In this analysis, the landowner pays for emissions and gets paid for sequestration in the year of occurrence. Other market structures such as those based on the difference from a business-as-usual baseline or on a contracted amount of carbon storage at a particular point in time could lead to qualitatively different results.