We study the economics of carbon storage using a model that includes forest size structure and determines the choice between rotation forestry and continuous cover forestry. Optimal harvests may rely solely on thinning, implying infinite rotation and continuous cover forestry, or both thinning and clearcuts, implying finite rotation periods. Given several carbon prices and interest rates, we optimize the timing and intensity of thinnings along with the choice of management regime. In addition to the carbon storage in living trees, we include the carbon dynamics of dead trees and timber products. Forest growth is specified by an empirically validated transition matrix model for Norway spruce (Picea abies (L.) Karst.). The optimization problem is solved in its general dynamic form by applying bilevel optimization with gradient-based interior point methods and a genetic algorithm. Carbon pricing postpones thinnings, increases stand density by directing harvests to larger trees, and typically yields a regime shift from rotation forestry to continuous cover forestry. In continuous cover solutions, the steady-state harvesting interval and the diameter distribution of standing and harvested trees are sensitive to carbon price, implying that carbon pricing increases the sawlog ratio of timber yields. Additionally, we obtain relatively inexpensive stand-level marginal costs of carbon storage.
We extend the study of economically optimal carbon storage to a previously unexplored forest type, mixed-species size-structured stands. The ecological model applied in the study is a transition matrix model with growth functions for boreal Norway spruce (Picea abies (L.) Karst.), birch (Betula pendula Roth and B. pubescens Ehrh.), and other broadleaves. The other broadleaved trees are assumed to have no commercial value. We maximize the sum of timber revenues and the value of carbon storage by optimizing the timing and intensity of thinnings and the potentially infinite rotation age. The optimization problem is solved in its general dynamic form using gradient-based interior point methods and a genetic algorithm. We present results for a mixed stand of Norway spruce and birch, and a mixed stand of Norway spruce, birch, and other broadleaves, and compare these to a pure Norway spruce stand. We show that carbon pricing increases stand volume by postponing harvests and limiting them to larger trees, and changes the optimal species composition by increasing the share of Norway spruce relative to birch. Further, carbon pricing incentivizes maintaining other broadleaves in the stand despite their lack of commercial value, thus increasing tree species diversity. We find that sawlog and total yields increase with carbon price. We show that the higher the number of tree species in a stand, the lower the marginal cost of carbon storage.
We study the effects of forest carbon storage on optimal stand management by applying a model where optimal harvests are partial cuttings, implying uneven-aged forestry, or both partial cuttings and clearcuts, implying even-aged forestry. Optimal carbon storage postpones partial cuttings and increases stand volume along the rotation. Carbon pricing may shorten or lengthen the rotation period depending on interest rate and speed of carbon release from wood products. If the carbon price is high, the shadow value of forest biomass is negative, implying that a higher interest rate leads to higher stand density. In empirically realistic examples, carbon pricing causes a switch from clearcuts to continuous cover management rather than vice versa.
Forests play a vital role in mitigating climate change, as they sequester and store large quantities of carbon. This dissertation examines how carbon storage may be increased by changing forest management at the stand level. To extend the economics of forest carbon storage beyond single-species even-aged stands, this dissertation develops a bioeconomic model framework that incorporates the size and species structure of the stand, and the optimal choice between continuous cover forestry and forestry based on clearcuts. The studies apply empirically estimated growth models for boreal conifer and broadleaf tree species. The dissertation consists of a summary section and three articles. The first article presents an analytically solvable economic model for timber production and carbon storage with optimized management regime choice between continuous cover and rotation forestry. Continuous-time optimal control theory is utilized to solve the thinning path and the potentially infinite rotation age: if no optimal finite rotation age exists, thinnings are performed indefinitely while maintaining continuous forest cover. The second article extends this model by applying a size-structured growth model for Norway spruce (Picea abies (L.) Karst.), roadside pricing of sawlog and pulpwood, variable and fixed harvesting costs, and several carbon pools. The timing and intensity of thinnings, the rotation age, and the management regime are optimized numerically. In the third article, the optimization approach of the second article is extended to mixed-species size-structured stands. Species mixtures include the commercially valuable Norway spruce and birch (Betula pendula Roth and B. pubescens Ehrh.), and other broadleaves (e.g. Eurasian aspen, Populus tremula L., and maple, Acer sp.) that have no market value. Optimal rotation age is shown to either increase or decrease with carbon price depending on interest rate and the speed of carbon release from harvested wood products. Given empirically realistic assumptions, carbon pricing increases the rotation period and eventually causes a regime shift from rotation management to continuous cover management. Hence, carbon pricing heightens the importance of determining the management regime-continuous cover or rotation forestry-through optimization. Optimal thinnings are invariably targeted to the largest size classes of each tree species. Carbon pricing postpones thinnings and increases the average size of harvested and standing trees, hence increasing mean stand volume. Without carbon pricing, commercially nonvaluable other broadleaves are felled during each harvesting operation. When carbon storage is valued, some of the other broadleaves are retained standing until they are large, thus increasing tree species diversity and deadwood quantity. The results suggest that moderate carbon price levels increase timber yields, especially of sawlog that may be used for long-lived products. Increasing carbon storage through changes in forest management is shown to be relatively inexpensive, ...
We analyze economically optimal continuous cover forestry with dead wood as a biodiversity indicator. We study mixed-species stands consisting of Norway spruce (Picea abies [L.] Karst.), birch (Betula pendula Roth.), and other broadleaves (e.g., oak [Quercus sp.], maple [Acer sp.]). The analysis is based on an economic description of continuous cover forest management using an empirically estimated size-structured transition matrix model. We use size-specific decomposition rates for dead wood, with the lower limit on total dead wood volume varying between 0 and 40 m3 ha–1. The optimization problem is solved in its general dynamic form using gradient-based interior point methods. Increasing the dead wood volume requirement affects total stand density only slightly, but increases stand heterogeneity as other broadleaves are grown in higher numbers. In addition, increasing the dead wood requirement has only a minor effect on the total felled volume, but harvests shift from timber harvests to biodiversity fellings to maintain the required dead wood volume. In the optimal steady state with a high dead wood requirement, two harvesting cohorts emerge: one for timber harvests and the other for biodiversity fellings. Increasing the dead wood requirement decreases steady-state net timber income by up to 30 percent compared to the unconstrained solution.
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