Stand growth projection: simultaneous estimation of growth and mortality using a single probabilistic function

Logistic regression analysis can be used to estimate the probability of a binary event. In forestry, its use largely has been limited to predicting the probability of mortality of individual trees. However, the potential for broader application in forest growth and yield modelling has largely been overlooked. A logistic model to predict the probability that a tree will attain a specified future diameter can be produced by establishing a series of growth "success" criteria. Given the initial diameter distribution of a forest stand, a future diameter distribution and stand characteristics can be estimated probabilistically by estimating the proportion of stems in each diameter class of the distribution which attains a specified future diameter (the "success" criterion) and the proportion which fails to achieve at least zero growth (i.e., mortality). Using permanent plot data, such a logistic model was calibrated and validated for an oak–hickory forest in southeastern Missouri. Validation indicated that the model performs satisfactorily (estimates are unbiased) for individual trees over a 5-year prediction period, and for stand characteristics over 5-, 10-, 15-, and 20-year prediction periods though precision suffers as prediction period lengthens.

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A Blind Spot in the Use of the Weibull Function for Modeling Diameter Distributions

Forest Science ◽

10.1093/forsci/fxaa042 ◽

2020 ◽

Author(s):

Adrian Norman Goodwin

Keyword(s):

Lower Bound ◽

Blind Spot ◽

Forest Growth ◽

Growth And Yield ◽

Diameter Distribution ◽

Absolute Difference ◽

Weibull Function ◽

Distribution Models ◽

Difference Statistic ◽

Diameter Distributions

Abstract Diameter distribution models based on probability density functions are integral to many forest growth and yield systems, where they are used to estimate product volumes within diameter classes. The three-parameter Weibull function with a constrained nonnegative lower bound is commonly used because of its flexibility and ease of fitting. This study compared Weibull and reverse Weibull functions with and without a lower bound constraint and left-hand truncation, across three large unthinned plantation cohorts in which 81% of plots had negatively skewed diameter distributions. Near-optimal lower bounds for the unconstrained Weibull function were negative for negatively skewed data, and the left-truncated Weibull using these bounds was 14.2% more accurate than the constrained Weibull, based on the Kolmogorov-Smirnov statistic. The truncated reverse Weibull fit dominant tree distributions 23.7% more accurately than the constrained Weibull, based on a mean absolute difference statistic. This work indicates that a blind spot may have developed in plantation growth modeling systems deploying constrained Weibull functions, and that left-truncation of unconstrained functions could substantially improve model accuracy for negatively skewed distributions.

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Development and Use of Bounding Functions in a Forest Growth Model

Western Journal of Applied Forestry ◽

10.1093/wjaf/8.1.24 ◽

1993 ◽

Vol 8 (1) ◽

pp. 24-27

Author(s):

K. Leroy Dolph ◽

Gary E. Dixon

Keyword(s):

Computer Simulation ◽

Simulation Models ◽

Height Growth ◽

Forest Growth ◽

Growth And Yield ◽

Forest Growth Model ◽

Individual Trees ◽

Computer Simulation Models ◽

Forest Growth And Yield

Abstract Erroneous predictions of forest growth and yield may result when computer simulation models use extrapolated data in repeated or long-term projections or if the models are used outside the range of data on which they were built. Bounding functions that limit the predicted diameter and height growth of individual trees to maximum observed values were developed to constrain these erroneous predictions in a forest growth and yield simulator. Similar techniques could be useful for dealing with extrapolated data in other types of simulation models. West. J. Appl. For. 8(1):24-27.

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Variance propagation in growth and yield projections

Canadian Journal of Forest Research ◽

10.1139/x86-213 ◽

1986 ◽

Vol 16 (6) ◽

pp. 1196-1200 ◽

Cited By ~ 25

Author(s):

H. T. Mowrer ◽

W. E. Frayer

Keyword(s):

Forest Growth ◽

Growth And Yield ◽

Yield Model ◽

Estimation Errors ◽

Bias Assessment ◽

Substantial Error ◽

Growth And Yield Model ◽

Growth Projection ◽

Variance Estimates ◽

Assessment Procedures

This paper reports the results of a study on the propagated variance associated with stand estimates in a forest growth and yield model. A cumulative variance as a result of input measurement and regression estimation errors is propagated in a growth and yield model using the method of statistical differentials. To provide an assessment of relative performance, these variance estimates are compared with a Monte Carlo simulation estimate of propagated error for increasing levels of sampling intensity. The method of statistical differentials is used to estimate the propagated variance through five 10-year growth projections. The results indicate growth projection estimates may have substantial error components that are not readily apparent from model calibration statistics or bias assessment procedures.

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Deriving Tree Diameter Growth and Probability of Survival Equations from Successive Diameter Distributions

Forest Science ◽

10.1093/forestscience/54.1.31 ◽

2008 ◽

Vol 54 (1) ◽

pp. 31-35

Author(s):

Thomas G. Matney ◽

Emily B. Schultz

Keyword(s):

General Procedure ◽

Growth And Yield ◽

Diameter Distribution ◽

Diameter Growth ◽

Individual Tree ◽

Statistical Probability ◽

Growth And Survival ◽

Tree Diameter ◽

Growth And Yield Models ◽

Diameter Distributions

Abstract Many growth and yield models have used statistical probability distributions to estimate the diameter distribution of a stand at any age. Equations for approximating individual tree diameter growth and survival probabilities from dbh can be derived from these models. A general procedure for determining the functions is discussed and illustrated using a loblolly pine spacing study. The results from the spacing study show that it is possible to define tree diameter growth and survival probability functions from diameter distributions with an accuracy sufficient to obtain a link between the individual tree and diameter growth and yield models.

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Mixed Regional Shifts in Conifer Productivity under 21st-Century Climate Projections in Canada’s Northeastern Boreal Forest

Forests ◽

10.3390/f12020248 ◽

2021 ◽

Vol 12 (2) ◽

pp. 248

Author(s):

Tyler Searls ◽

James Steenberg ◽

Xinbiao Zhu ◽

Charles P.-A. Bourque ◽

Fan-Rui Meng

Keyword(s):

Climate Change ◽

Model Validation ◽

21St Century ◽

Black Spruce ◽

Abies Balsamea ◽

Acer Rubrum ◽

Forest Growth ◽

Balsam Fir ◽

Growth And Yield ◽

Climate Projections

Models of forest growth and yield (G&Y) are a key component in long-term strategic forest management plans. Models leveraging the industry-standard “empirical” approach to G&Y are frequently underpinned by an assumption of historical consistency in climatic growing conditions. This assumption is problematic as forest managers look to obtain reliable growth predictions under the changing climate of the 21st century. Consequently, there is a pressing need for G&Y modelling approaches that can be more robustly applied under the influence of climate change. In this study we utilized an established forest gap model (JABOWA-3) to simulate G&Y between 2020 and 2100 under Representative Concentration Pathways (RCP) 2.6, 4.5, and 8.5 in the Canadian province of Newfoundland and Labrador (NL). Simulations were completed using the province’s permanent sample plot data and surface-fitted climatic datasets. Through model validation, we found simulated basal area (BA) aligned with observed BA for the major conifer species components of NL’s forests, including black spruce [Picea mariana (Mill.) Britton et al.] and balsam fir [Abies balsamea (L.) Mill]. Model validation was not as robust for the less abundant species components of NL (e.g., Acer rubrum L. 1753, Populus tremuloides Michx., and Picea glauca (Moench) Voss). Our simulations generally indicate that projected climatic changes may modestly increase black spruce and balsam fir productivity in the more northerly growing environments within NL. In contrast, we found productivity of these same species to only be maintained, and in some instances even decline, toward NL’s southerly extents. These generalizations are moderated by species, RCP, and geographic parameters. Growth modifiers were also prepared to render empirical G&Y projections more robust for use under periods of climate change.

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Ontario's forest growth and yield modelling program: Advances resulting from the Forestry Research Partnership

The Forestry Chronicle ◽

10.5558/tfc84694-5 ◽

2008 ◽

Vol 84 (5) ◽

pp. 694-703 ◽

Cited By ~ 14

Author(s):

Mahadev Sharma ◽

John Parton ◽

Murray Woods ◽

Peter Newton ◽

Margaret Penner ◽

...

Keyword(s):

Tree Species ◽

Stand Density ◽

Forest Growth ◽

Growth And Yield ◽

Research Partnership ◽

Wood Supply ◽

Permanent Sample Plots ◽

Forestry Research ◽

Research Activities ◽

Forest Growth And Yield

The province of Ontario holds approximately 70.2 million hectares of forests: about 17% of Canada’s and 2% of the world’s forests. Approximately 21 million hectares are managed as commercial forests, with an annual harvest in the early part of the decade approaching 200 000 ha. Yield tables developed by Walter Plonski in the 1950s provide the basis for most wood supply calculations and growth projections in Ontario. However, due to changes in legislation, policy, and the planning process, they no longer fully meet the needs of resource managers. Furthermore, Plonski`s tables are not appropriate for the range of silvicultural options now practised in Ontario. In October 1999, the Canadian Ecology Centre- Forestry Research Partnership (CEC-FRP) was formed and initiated a series of projects that collectively aimed at characterizing, quantifying and ultimately increasing the economically available wood supply. Comprehensive, defensible, and reliable forecasts of forest growth and yield were identified as key knowledge gaps. The CEC-FRP, with support from the broader science community and forest industry, initiated several new research activities to address these needs, the results of which are outlined briefly in this paper. We describe new stand level models (e.g., benchmark yield curves, FVS Ontario, stand density management diagrams) that were developed using data collected from permanent sample plots and permanent growth plots established and remeasured during the past 5 decades. Similarly, we discuss new height–diameter equations developed for 8 major commercial tree species that specifically account for stand density. As well, we introduce a CEC-FRP-supported project aimed at developing new taper equations for plantation grown jack pine and black spruce trees established at varying densities. Furthermore, we provide an overview of various projects undertaken to explore measures of site productivity. Available growth intercept and site index equations are being evaluated and new equations are being developed for major commercial tree species as needed. We illustrate how these efforts are advancing Ontario’s growth and yield program and supporting the CEC-FRP in achieving its objective of increasing the supply of fibre by 10% in 10 years while maintaining forest sustainability. Key words: permanent sample plots (PSPs), permanent growth plots (PGPs), normal yield tables, sustainable forest management, NEBIE plot network, forest inventory, Forest Vegetation Simulator

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How random are predictions of forest growth? The importance of weather variability

Canadian Journal of Forest Research ◽

10.1139/cjfr-2019-0366 ◽

2020 ◽

Author(s):

Joanna Horemans ◽

Olga Vindušková ◽

Gaby Deckmyn

Keyword(s):

Climate Change ◽

Uncertainty Analysis ◽

Climate Models ◽

Global Climate ◽

Basal Area ◽

Random Order ◽

Forest Growth ◽

Global Climate Models ◽

Growth And Yield ◽

Weather Variability

Quantifying the output uncertainty and tracking down its origins is key to interpreting the results of model studies. We perform such an uncertainty analysis on the predictions of forest growth and yield under climate change. We specifically focus on the effect of the inter-annual climate variability. For that, the climate years in the model input (daily resolution) were randomly shuffled within each 5-year period. In total, 540 simulations (10 parameter sets, 9 climate shuffles, 3 global climate models and 2 mitigation scenarios), were made for one growing cycle (80 years) of a Scots pine forest growing in Peitz (Germany). Our results show that, besides the important effect of the parameter set, the random order of climate years can significantly change results such as basal area and produced volume, and the response of these to climate change. We stress that the effect of weather variability should be included in the design of impact model ensembles, and the accompanying uncertainty analysis. We further suggest presenting model results as likelihoods to allow risk assessment. For example, in our study the likelihood of a decrease in basal area of >10% with no mitigation was 20.4%, while the likelihood of an increase >10% was 34.4%.

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Generalized nonlinear height–diameter models for a <i>Cryptomeria fortunei</i> plantation in the Pingba region of Guizhou Province, China

Web Ecology ◽

10.5194/we-18-29-2018 ◽

2018 ◽

Vol 18 (1) ◽

pp. 29-35 ◽

Cited By ~ 2

Author(s):

Zongzheng Chai ◽

Wei Tan ◽

Yuanyuan Li ◽

Lan Yan ◽

Hongbo Yuan ◽

...

Keyword(s):

Model Performance ◽

Forest Growth ◽

Performance Criteria ◽

Forest Monitoring ◽

Growth And Yield ◽

Guizhou Province ◽

Biomass Estimation ◽

Multiple Model ◽

Nonlinear Growth ◽

The Relationship

Abstract. The relationship between height and diameter (H-D) is an important component in forest growth and yield models, and a better understanding of the relationship will improve forest monitoring, management, and biomass estimation. Sixteen nonlinear growth functions were fitted to H-D data for 1261 trees from a Cryptomeria fortunei plantation in the Pingba region of Guizhou Province, China. Of the 1261 trees, 80 % were randomly selected for model calibration, while the remaining trees were reserved for model validation. All models were evaluated and compared by means of multiple-model performance criteria. Although all 16 models showed a good fit to the dataset and each of them accounted for more than 75 % of the total variation in height, a large difference in asymptotic estimates was observed. The Chapman–Richards, Weibull, and Näslund models were recommended for C. fortunei plantations, due to their satisfactory height prediction and biological interpretability.

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Ecological and environmental indicators of Brazil Nut Tree (Bertholletia excelsa Bonpl.) in Flona do Jamari, Rondônia

Revista Ibero-Americana de Ciências Ambientais ◽

10.6008/cbpc2179-6858.2020.007.0056 ◽

2020 ◽

Vol 11 (7) ◽

pp. 740-751

Author(s):

Nilson Reinaldo Fernandes dos Santos Júnior ◽

Diogo Martins Rosa ◽

José Das Dores de Sá Rocha ◽

Marta Silvana Volpato Sccoti ◽

Scheila Cristina Biazatti ◽

...

Keyword(s):

Spatial Distribution ◽

Distribution Pattern ◽

Geographic Location ◽

Distribution Patterns ◽

Environmental Indicators ◽

Diameter Distribution ◽

Brazil Nut ◽

Productive Potential ◽

Morisita Index ◽

Individual Trees

Mapping Brazil nut trees in the Amazon is essential for indicating its distribution patterns within different ecosystems, while also being useful to estimate the species productive potential. This study aimed to evaluate the spatial distribution of Brazil nut trees in Flona do Jamari – RO, considering its environmental and topographic conditions. A census was performed for all individual trees sized ≥ 35 cm in diameter at 1.30 m breast height (DBH) above the ground of six Annual Production Units (APU) in Forest Management Unit III (FMU-III), a 11,011.2 ha area of Flona do Jamari, RO. DBH and geographic location (GPS) were collected for each tree. Structure and diameter distribution were evaluated by abundance, density, dominance, and frequency. The Morisita index was used to identify the spatial distribution pattern. The environment was defined by the local relative height found along the drainage network, by the digital model Height Above the Nearest Drainage (HAND). Most trees were among DBH intermediate classes (60 to 140 cm), and only a few were young trees (DBH < 50 cm). Brazil nut trees present a random spatial distribution and a predominant distribution pattern of 'terra-firme (solid ground)'. Such information on the species structural, spatial, and ecological patterns serve as key elements for further studies on production potential.

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Predicting Future Diameter Distributions Given Current Stand Attributes

Canadian Journal of Forest Research ◽

10.1139/cjfr-2021-0216 ◽

2022 ◽

Author(s):

Quang V. Cao

Keyword(s):

Prediction Method ◽

Diameter Distribution ◽

Tree Level ◽

Individual Tree ◽

Distribution Parameters ◽

Level Model ◽

Novel Method ◽

Quadratic Mean Diameter ◽

Stand Attributes ◽

Individual Trees

This study discussed four methods to project a diameter distribution from age A1 to age A2. Method 1 recovers parameters of the distribution at age A2 from stand attributes at that age. Method 2 uses a stand-level model to grow the quadratic mean diameter, and then recovers the distribution parameters from that prediction. Method 3 grows the diameter distribution by assuming tree-level survival and diameter growth functions. Method 4 first converts the diameter distribution at age A1 into a list of individual trees before growing these trees to age A2. In a numerical example employing the Weibull distribution, methods 3 and 4 produced better results based on two types of error indices and the relative predictive error for each diameter class. Method 4 is a novel method that converts a diameter distribution into a list of individual-trees, and in the process, successfully links together diameter distribution, individual-tree, and whole stand models.

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