Evaluation of individual-tree growth models for <i>Picea abies</i> based on a case study of an uneven-sized stand in southern Sweden

Fagerberg, Nils; Lohmander, Peter; Eriksson, Ola; Olsson, Jan-Ola; Poudel, Bishnu Chandra; Bergh, Johan

doi:10.1080/02827581.2022.2037700

Cited by 8 publications

(7 citation statements)

References 24 publications

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“…Hatami, Lohmander et al (2018) estimate basal area growth functions for several tree species in CCF forests in Iran, via the Lohmander (2017a) differential equation with competition correction. Fagerberg, Olsson, Lohmander et al (2022b) estimate similar Lohmander (2017a) models for Norway spruce, in Sweden, with and without competition adjustment functions. Fagerberg, Lohmander et al (2022a) compare these models to other kinds of models, and discover that the Lohmander (2017a) model gives more reliable predictions than the other tested models.…”

Section: Understanding and Predicting Ccf Growthmentioning

confidence: 66%

“…Fagerberg, Olsson, Lohmander et al (2022b) estimate similar Lohmander (2017a) models for Norway spruce, in Sweden, with and without competition adjustment functions. Fagerberg, Lohmander et al (2022a) compare these models to other kinds of models, and discover that the Lohmander (2017a) model gives more reliable predictions than the other tested models.…”

Section: Understanding and Predicting Ccf Growthmentioning

confidence: 66%

“…The data represents CCF forests with the species Picea abies, in southern Sweden. The detailed background to the data, several statistical analyses and alternative modeling efforts based on these data, can be studied in Fagerberg, Olsson, Lohmander, et al (2022b), and in Fagerberg, Lohmander, et al (2022a). The data in Figure 1.…”

Section: A the Empirical Factsmentioning

confidence: 99%

“…To transform the relative size frequency results derived in the numerical model to empirically relevant absolute values, the empirically estimated average total basal area per hectare, 32.4 m 2 per hectare, is used. This parameter value is calculated from data found in Fagerberg, Olsson, Lohmander, et al (2022b). In the numerical Appendix A, this is denoted BA_TOT.…”

Section: Construction Of a Nonlinear Dynamic Optimization Modelmentioning

confidence: 99%

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Sustainable Continuous Cover Forestry Dynamics, Optimal Decisions, and Empirical Estimations

Lohmander

2024

Preprint

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Sustainable continuous cover forestry is defined and analyzed in several ways. The differential equation representing growth of the basal areas of individual trees, motivated by fundamental biological production theory by Lohmander (2017a), is analyzed and extended in different directions. From the solution of the differential equation, the basal area and the tree diameter are obtained as explicit functions of time. The diameter is a strictly increasing function of time. In the absence of competitors, the diameter increment is shown to be a strictly decreasing function of time. Hence, the diameter increment can also be interpreted as a strictly decreasing function of the diameter. Alternative forms of adjustment of the differential equation, with consideration of competition, are defined. If the competition is strong, with large trees in the vicinity of a particular tree, then the basal area increment, and the diameter increment, are reduced. The growth of a large tree is less sensitive than the growth of a small tree, to competition from other trees. Under strong competition, the basal area increment, and the diameter increment, are strictly concave functions of the size of the tree. The unique maximum of the diameter increment occurs at a higher diameter, if the competition increases. In dynamic equilibrium, the tree size frequency distribution is stationary. If natural tree mortality can be avoided via the harvest strategy, the tree size frequency distribution is a function of the size and competition dependent growth function, and the harvest strategy. Empirical tree size frequency data are used to simultaneously estimate parameters of a size and competition dependent growth function and the applied harvest strategy, via nonlinear optimization. The properties of the estimated growth function are consistent with the corresponding properties of the production theoretically motivated hypothetical function, and the properties of the estimated harvest strategy confirm the corresponding hypotheses. The R2 of the nonlinear regression exceeds 0.97. With access to an empirically estimated equilibrium tree size distribution, it is possible to: 1. Estimate size frequency relevant parameters of tree size and competition dependent growth functions for individual trees. 2. Estimate the applied harvest strategy. 3. Explain and reproduce the empirically estimated tree size equilibrium distribution.

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Section: Understanding and Predicting Ccf Growthmentioning

confidence: 66%

Section: Understanding and Predicting Ccf Growthmentioning

confidence: 66%

Section: A the Empirical Factsmentioning

confidence: 99%

Section: Construction Of a Nonlinear Dynamic Optimization Modelmentioning

confidence: 99%

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Sustainable Continuous Cover Forestry Dynamics, Optimal Decisions, and Empirical Estimations

Lohmander

2024

Preprint

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“…The largest trees are periodically harvested and the smaller trees are left in the forest to continue to grow.) Hatami, et al [12,13] are two studies where the growth functions for individual trees have been developed. With such functions, it is possible to mathematically develop economically and environmentally rational continuous cover forestry decision rules.…”

Section: Introductionmentioning

confidence: 99%

"Rational Control of Global Warming Dynamics Via the CO2 Level, Emission Reductions and Forestry Expansion"

Lohmander¹

2022

BJSTR

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First, the observed CO 2 level in the atmosphere, recorded by NOAA [1] at the Mauna Loa observatory, and the global industrial CO 2 emissions, reported by EDGAR [2], European Commission, are investigated, from 1990 until 2021. Then, a differential equation model is developed, based on two hypotheses, that explains how these time series interact. The hypotheses of the explaining model are tested with regression analysis, and it is demonstrated that no hypothesis can be rejected on statistical grounds. The parameters of the CO 2 concentration model are determined with high t-values and low p-values. The model is used to determine the time path of the CO 2 concentration of the natural system without industrial emissions, for arbitrary initial conditions. This system has a unique and stable equilibrium at 262 ppm. With constant industrial emissions, the equilibrium is found at a higher level, which is shown with an explicit equation. Comparative statics analysis shows how the equilibrium is affected by alternative parameter adjustments. An extended version of the natural differential equation, with a forcing function, representing the time paths of industrial emissions, is developed. The industrial emissions are modeled as a quadratic function of time. The general function of the time path of the CO 2 concentration of the natural system under the influence of industrial emissions, is determined for arbitrary initial conditions and parameters of the industrial emission function.The CO 2 time path function is analytically verified. Then, it is also empirically tested and found to be able to reproduce the historical CO 2 observations with high precision. Then, the time paths of the future CO 2 concentrations are calculated, for six alternative levels of change of the industrial emissions, from -1.5 Gt/year to +1.0 Gt/ year, from the year 2022 until 2100. These results are presented as a function and as graphs. The net CO 2 emissions can also be reduced over time, if forestry is gradually intensified. The rational intensity of this investment process is determined, taking the time path of the CO 2 level into consideration, during an arbitrary time interval. An explicit function for the optimal forestry intensification level, based on all CO 2 time path function parameters, the marginal cost of the CO 2 concentration, time interval parameters, rate of interest and different cost function parameters, is derived and presented.

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Forest Planning and Continuous Cover Forestry

Mehtätalo,

Kangas,

Eggers

et al. 2024

Managing Forest Ecosystems

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Forest planning requires unbiased and sufficient information on current forest resources, their anticipated dynamics under different management scenarios, and the objectives of the decision maker. Forest planning systems need to be adapted to improve their potential to deal with continuous cover forestry (CCF). The current forest planning systems and associated models can be adapted to group systems by treating each group as a separate calculation unit. In the selection system, currently available growth models may not realistically describe the growth reaction of trees, which causes additional uncertainty in forest-planning calculations. Furthermore, field-data collection based on airborne laser scanning alone is not sufficient for planning of CCF, and additional field measurements are needed. Tree-level measurements by drones open interesting opportunities for forest planning, which might be especially useful under CCF.

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Evaluation of individual-tree growth models for Picea abies based on a case study of an uneven-sized stand in southern Sweden

Cited by 8 publications

References 24 publications

Sustainable Continuous Cover Forestry Dynamics, Optimal Decisions, and Empirical Estimations

Sustainable Continuous Cover Forestry Dynamics, Optimal Decisions, and Empirical Estimations

"Rational Control of Global Warming Dynamics Via the CO2 Level, Emission Reductions and Forestry Expansion"

Forest Planning and Continuous Cover Forestry

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