Abstract: Plantations with fast-growing species play a crucial role in reducing global warming and have great carbon capture potential. The...
Abstract: Plantations with fast-growing species play a crucial role in reducing global warming and have great carbon capture potential. Therefore, determining optimal management strategies is a challenge in the management of forest plantations to achieve the maximum carbon capture rate. The objective of this work is to determine optimal rotation strategies that maximize carbon capture in forest plantations. By evaluating an ecological optimal control problem, this work presents a method that manages forest plantations by planning activities such as reforestation, felling, thinning, and fire prevention. The mathematical model is governed by three ordinary differential equations: live biomass, intrinsic growth, and burned area.
The characterization of the optimal control problem using Pontryagin’s maximum principle is analyzed. The model solutions are approximated numerically by the fourth-order Runge–Kutta method. To verify the efficiency of the model, parameters for three scenarios were considered: a realistic one that represents current forestry activities based on previous studies for the exotic species Pinus radiata D. Don, another pessimistic, which considers significant losses in forest productivity; and a more optimistic scenario which assumes the creation of new forest areas that contribute with carbon capture to prevent the increase in global temperature.
The model predicts a higher volume of biomass for the optimistic scenario, with the consequent higher carbon capture than in the other two scenarios. The optimal solution for the felling strategy suggests that, to increase carbon capture, the rotation age should be prolonged and the felling rate decreased. The model also confirms that reforestation should be carried out immediately after felling, applying maximum reforestation effort in the optimistic and pessimistic scenarios. On the other hand, the model indicates that the maximum prevention effort should be applied during the life cycle of the plantation, which should be proportional to the biomass volume. Finally, the optimal solution for the thinning strategy indicates that in all three scenarios, the maximum thinning effort should be applied until the time when the fire prevention strategy begins. Keywords: ecological model; biomass volume; carbon dioxide; optimal control; numerical simulation 1. Introduction Carbon dioxide (CO2) is one of the main greenhouse gases (GHG) in the atmosphere. Multiple human activities in most industrialized countries have contributed to the increase in this gas and have exacerbated the negative effects of climate change. According to the latest report of the Intergovernmental Panel on Climate Change (IPCC), climate change is devastating today, in particular, because of the changes in the patterns of humidity, temperature, winds, snow, and ice, especially in coastal zones. These changes in climate conditions could have negative impacts on human health, agriculture, and the economy [1–3]. Under this worldwide situation, governments are making cooperative efforts agreements (e.g., the Paris Agreement and the Kyoto Protocol) to create new forest areas to help prevent the global average temperature rising more than 2 ◦C during the 21st century [4–6]. Forest ecosystems cover approximately 4100 billion hectares of the Earth’s surface and have a huge potential for Forests 2023, 14, 82. https://doi.org/10.3390/f14010082 https://www.mdpi.com/journal/forests Forests 2023, 14, 82 2 of 17 carbon capture [7]. Of this total area, approximately 45% are exotic plantations whereas the other 55% corresponds to native forests [8]. Because forest ecosystems can store the largest amounts of carbon [9], it has been suggested that expanding forest areas and prolonging the rotation age (i.e., the growth period required to derive maximum value from a stand of timber), especially in exotic forest plantations [10], are key strategies to maximize carbon capture and mitigate the negative effects of global climate change [11]. There is a large body of literature where carbon capture is estimated [12,13]. In a temperate forest in Southern Europe, the aboveground carbon capture in the species Eucalyptus nitens (Deane and Maiden), Eucalyptus globulus Labill, and P. radiata, with rotation ages ranging from 10 to 35 years, was estimated to be from 443 to 634 Tn C ha−1 [14]. The carbon sequestration with the same species established in Chile was 212 Tn C ha−1 for P. radiata, 180 Tn C ha−1 for E. nitens, and 117 Tn C ha−1 for E. globulus (age of 20–24 years for P. radiata and 10–14 years for Eucalyptus) [15]. On the other hand, in Panama the carbon stored in Tectona grandis E.L (Teca) plantations during 1 and 10 years was estimated to be 2.9 Tn C ha−1 and 40.7 Tn C ha−1 , respectively [16]. On the other hand, there are studies on the oil palm (Elaeis guineensis Jacq) which, due to its high biomass production and expansion dynamics, plays an important role in carbon capture [17]. By means of mathematical modelling the dynamics of both oil production and carbon capture have been studied [18]. In [19], they formulated an optimal control problem based on a system of ordinary differential equations that relate the dynamics of young and mature trees and considers felling as a control variable. The authors concluded that palm oil production and carbon capture increases with a controlled felling rate. Notwithstanding, to increase CO2 capture the trees must remain for longer periods in the field, which delays the rotation age [20,21]. However, in some situations, it is risky to prolong the rotation age in order to increase carbon capture, since it increases the probability of forest fires when there is more fuel in the field. More frequent forest fires will increase CO2 levels in the atmosphere, causing extreme climate events and decreasing relative humidity in many regions of the world [22]
. To model the probability of forest fire occurrence some authors have used the Faustmann model generalized to the stochastic Poisson process [23], whereas others have studied this phenomenon by using the Bellman equation to determine the optimal rotation age in a forest stand that produces timber and carbon benefits under fire risk [24]. The authors showed that higher fire risk will reduce the optimal rotation age due to a lack of fire prevention and low carbon prices, while a higher carbon price will increase the rotation age, thus obtaining a higher ecological benefit. It is known that fires contribute to the increase of CO2 in the atmosphere.
In [25] they developed a meteorological fire index to predict the risk of fire occurrence and help forest managers take appropriate preventive measures. The authors determined that relative humidity is a simple and feasible parameter to describe the occurrence of fires. Several mathematical models have been developed to describe the dynamics of CO2 capture in reforestation projects [26–28]. The atmospheric CO2 concentration decreases as the rate of reforestation increases. Also in [29], they presented a study to model the greenhouse effect caused by CO2 emissions through the optimal control theory. In the model, the authors addressed the optimization of investments in reforestation and clean technologies associated with state variables such as CO2 emissions, planted area, and Gross Domestic Product (GDP). They concluded that it is more efficient to invest in reforestation than in clean technologies. Because forested areas can contribute to climate change mitigation, it is necessary to find optimal management strategies that maximize carbon capture. Strategies such as large-scale reforestations are efficient in capturing huge amounts of carbon [30], whereas the optimization of thinning, fire prevention, and harvesting strategies can also reduce CO2 emissions in forest plantation management [31]. In [32] they applied a thinning strategy in Korean pine (Pinus koraiensis Sieb. et Zucc.) forest plantations and determined that the optimal rotation age that maximizes wood production and carbon capture was at the age of 86 years. In another study on oil palm [18], they applied the optimal control theory to model the dynamics of biomass growth and intrinsic biomass growth as state variables and considered felling as a control variable. The authors showed that the maximum oil Forests 2023, 14, 82 3 of 17 production and carbon capture was reached at the age of 20 years. However, to our knowledge, no mathematical models have simultaneously modeled the relationship between the living biomass, the intrinsic biomass growth, the burned area, the reforestation, the felling and thinning, the fire prevention, and the relative humidity. Recently,
[33] modeled the effects of the dynamics of living biomass, intrinsic growth, and burned area on carbon capture in forest plantations. The authors showed that biomass decreases in each cycle of regeneration because of forest fires, and suggested a strategy based on fire prevention in order to obtain maximum carbon capture. In this context, the objective of the present work is to determine optimal rotation strategies that maximize carbon sequestration in forest plantations. Based on the optimal control theory, a mathematical model is proposed to describe the dynamic relationship of carbon capture in forest plantations with control strategies such as reforestation, felling, fire prevention, and thinning, which are associated with state variables such as living biomass, intrinsic growth, and burned area. To verify the efficiency of the model, three scenarios are considered: realistic, pessimistic, and optimistic, using numerical methods to approximate its solution. In the case of the realistic scenario we tested with data of the species P. radiata.
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