Height Growth Model Research Articles

Predicting fracture vertical growth containment using the width-induced net stress

The vertical growth of hydraulic fractures in layered formations is important from treatment-placement and well performance perspective. Most numerical fracture simulators generate fracture geometries by accounting for the in-situ stress and rock mechanical properties, along with key parameters related to fracturing fluids such as rheology and leakoff behavior, amongst various other critical parameters that can influence the outcome. Although the results from various simulators are generally reasonable, the fracture height estimates can vary significantly even for identical input data sets as shown in the literature. Because of the limitations of these simulators, some of the field observations, such as containment of fracture height growth across certain interfaces of contrasting material properties or weak interfacial bonding, are not replicated effectively, unless such an interface is pre-defined.In this study, the influence of fracture width on resultant stresses is incorporated in the calculation process while solving for vertical growth of hydraulic fractures. For this purpose, a modified equilibrium height growth model previously developed by the authors is used. The effects of viscous fluid movement in the fracture are also included in the calculation scheme.The outputs from the model were compared with the field-derived fracture heights that were inferred from micro seismic (MS) surveys conducted on various fracturing treatments that included both vertical and horizontal wells completed in layered formations. The analysis revealed a close agreement between the model-predicted and observed values of fracture height.While the authors acknowledge that predicting the containment of vertical growth of fracture across a plane is a challenging task given the complex nature of the problem, the paper discusses a method that offers a simpler approach to predicting the sites that may act as a constraint to the fracture growth during the stimulation treatments. This can aid in well-placement planning, perforation strategy, and hydraulic fracturing treatment design. The model can be readily deployed or incorporated in existing simulators.

Climate Effects on Black Spruce and Trembling Aspen Productivity in Natural Origin Mixed Stands

Forest managers need site productivity estimates for tree species growing in mixed stands. Models developed in the past are generally for pure stands and don’t factor in the effects of climate change on site productivity. Therefore, site index (SI) models were developed for black spruce (Picea mariana Mill. B.S.P.) and trembling aspen (Populus tremuloides Michx.) trees grown in natural origin mixed stands. For this, 186 trees (93 black spruce and trembling aspen each) were sampled from 31 even-aged natural mixed stands (sites) (3 trees/species/site) across Ontario, Canada. Stand height growth models were developed by incorporating climate variables during growth for each species. Stem analysis data collected from sampled trees were used to develop these models. A mixed effects modelling approach was used to fit the models. The relationship between SIs of black spruce and trembling aspen grown in mixed stands was analyzed by calculating correlation coefficients and plotting black spruce SIs against those of trembling aspen. Climate effects on site productivity were evaluated by predicting stand heights for 4 geographic areas of Ontario for the period 2021 to 2080. Three emissions scenarios reflecting different amounts of heat at the end of the century (i.e., 2.6, 4.5, and 8.5 watts m−2) were used in the stand height growth models developed here for evaluation. Climate effects were more pronounced for trembling aspen than black spruce only in the far west. The relationship between SIs of black spruce and trembling aspen trees grown in natural origin mixed stands could not be described using a linear/nonlinear mathematical function. The models developed here can be used to estimate stand height and SI of black spruce and trembling aspen trees grown in natural origin mixed stands in a changing climate. In the absence of climate data, models fitted without climate variables can be used to estimate SI of both species.

Assessment of suitable site for the long rotation management of Sugi stands, by developing a prediction model of height growth in Sugi stands at the regional-scale

Assessment of suitable site for the long rotation management of Sugi stands, by developing a prediction model of height growth in Sugi stands at the regional-scale

Modelling the Tree Height, Crown Base Height, and Effective Crown Height of Pinus koraiensis Plantations Based on Knot Analysis

Taking 1735 Pinus koraiensis knots in Mengjiagang Forest Farm plantations in Jiamusi City, Heilongjiang Province as the research object, a dynamic tree height, effective crown height, and crown base height growth model was developed using 349 screened knots. The Richards equation was selected as the basic model to develop a crown base height and effective crown height nonlinear mixed-effects model considering random tree-level effects. Model parameters were estimated with the non-liner mixed effect model (NLMIXED) Statistical Analysis System (SAS) module. The akaike information criterion (AIC), bayesian information criterion (BIC), −2 Log likelihood (−2LL), adjusted coefficient (Ra2), root mean square error (RMSE), and residual squared sum (RSS) values were used for the optimal model selection and performance evaluation. When tested with independent sample data, the mixed-effects model tree effects-considering outperformed the traditional model regarding their goodness of fit and validation; the two-parameter mixed-effects model outperformed the one-parameter model. Pinus koraiensis pruning times and intensities were calculated using the developed model. The difference between the effective crown and crown base heights was 1.01 m at the 15th year; thus, artificial pruning could occur. Initial pruning was performed with a 1.01 m intensity in the 15th year. Five pruning were required throughout the young forest period; the average pruning intensity was 1.46 m. The pruning interval did not differ extensively in the half-mature forest period, while the intensity decreased significantly. The final pruning intensity was only 0.34 m.

Weather-sensitive height growth modelling of Norway spruce using repeated airborne laser scanning data

Fluctuations in weather conditions, particularly precipitation and water availability, may strongly affect growth rate patterns and lead to interannual height growth variation. Consequently, height growth models developed using airborne laser scanning (ALS) data collected at short time intervals may over- or underestimate long-term height growth trends and finally result in different growth forecasts. The objective of this study was to develop height growth models for Norway spruce, including the effect of weather conditions. We used ALS-derived top height (TH) estimates and meteorological data from the research area collected for 2007-2012 and 2013-2018 to develop a weather-sensitive height growth model. The top height (TH) growth of Norway spruce was affected by the mean annual precipitation sum (APS) in the studied periods, and a higher APS resulted in faster TH growth. This study demonstrates the high potential of repeated ALS for detecting short-term variation in the tree height increment and the development of weather-sensitive height growth models.

Modeliranje višinske in debelinske rasti dominantnih dreves ter ocenjevanje indeksov produkcijske sposobnosti gozdnih rastišč

Modeling the height and diameter growth of trees is an important part of forest management. Growth models provide the basis for determining the thinning regime, target tree dimensions and optimal proportions of developmental phases of forest stands. We developed individual height growth models for dominant Norway spruce (Picea abies (L.) Karst) and European beech (Fagus sylvatica L.) in two forest types (sessile oak-European beech forests and pre-Alpine silver fir-European beech forests). Based on the models, the site productivity index (SPI), defined as the dominant tree height at a diameter of 45 cm, was determined for spruce and beech in both forest types. Based on the diameter increment of the dominant trees, the age of trees in regard to their diameter was calculated, which was the basis for Height-Age modeling. The site productivity index (SPI) of spruce in sessile oak-beech forests and pre-Alpine silver fir-European beech forests is higher than that of beech: 31.3 and 29.7 vs 28.7 and 27.9, respectively. Estimated site indices (SI; dominant tree height at the age of 100 years) in sessile oak- European beech forests and pre-Alpine silver fir-European beech forests were 33.4 and 32.0 for spruce, and 29.0 and 27.0 for beech, respectively. Using the described procedure, it is possible to determine indices of site productivity of spruce and beech (SI and SPI) in the selected forest habitat types. Testing the procedure in other forest types and for other tree species is suggested.

Dynamic Top Height Growth Models for Eight Native Tree Species in a Cool-Temperate Region in Northeast China

In this study, we developed dynamic top height growth models for the eight important Chinese tree species Larix gmelinii var. principis-rupprechtii, Pinus tabuliformis Carr., Pinus sylvestris var. mongolica Litv., Picea asperata Mast., Quercus mongolica Fisch. ex Ledeb, Betula platyphylla Suk., Betula dahurica Pall. and Populus davidiana Dode based on age-height relationships. For this purpose, commonly growth data from long-term observations of permanent experimental plots are used, which ideally cover all development stages from stand establishment to final harvest. As such data were not available in the research area of Hebei Province in Northeast China, we used stem analysis data as well as tree height and annual shoot length measurements. The dataset consisted of 72 stands, 233 dominant trees and 10,195 observations of stem discs and annual shoot length measurements. Five dynamic base-age invariant top height growth models were derived from four base models with the generalized algebraic difference approach and fitted to our age-height data using nested regression techniques. According to biological plausibility and model accuracy the Chapman–Richards model showed the best performance for Picea asperata. This selected model accounted for 99% of the total variance in age-height relationship with average absolute bias of 0.2322 m, root mean square error of 0.3337 m and Radj2 of 0.9979, respectively. The distribution of the residuals was scattered around 0 and without visible trends, indicating that the fitness of the models was good. All developed models are able to generate top height growth curves representing the analyzed height growth data and can be utilized for predicting height growth on the base of current height and age of dominant trees. Additionally, they are the base for calculating the development of other relevant stand attributes such as basal area and volume growth. The determination of potential site productivity by the use of top height growth curves is a practical and convenient method for a simplified presentation of complex growth processes in stands and helps to create growth models, which facilitate implementing sustainable forest management practices in Mulan Forest.

Regional height growth models for Scots pine in Poland

Site productivity remains a fundamental concern in forestry as a significant driver of resource availability for tree growth. The site index (SI) reflects the overall impact of all environmental factors that determine tree height growth and is the most commonly used indirect proxy for forest site productivity estimated using stand age and height. The SI concept challenges are local variations in climate, soil, and genotype-environmental interactions that lead to variable height growth patterns among ecoregions and cause inappropriate estimation of site productivity. Developing regional models allow us to determine forest growth and SI more appropriately. This study aimed to develop height growth models for the Scots pine in Poland, considering the natural forest region effect. For height growth modelling, we used the growth trajectory data of 855 sample trees, representing the Scots pine entire range of geographic locations and site conditions in Poland. We compared the development of regional height growth models using nonlinear-fixed-effects (NFE) and nonlinear-mixed-effects (NME) modelling approaches. Our results indicate a slightly better fit to the data of the model built using NFE approach. The results showed significant differences between Scots pine growth in natural forest regions I, II, and III located in northern Poland and natural forest regions IV, V, and VI in southern Poland. We compared the development of regional height growth models using NFE and NME modelling approaches. Our results indicate a slightly better fit to the data of the model built using the NFE approach. The developed models show differences in height growth patterns of Scots pines in Poland and revealed that acknowledgement of region as the independent variable could improve the growth prediction and quality of the SI estimation. Differences in climate and soil conditions that distinguish natural forest regions affect Scots pine height growth patterns. Therefore, extending this research to models that directly describe height growth interactions with site variables, such as climate, soil properties, and topography, can provide valuable forest management information.

Climate effects on jack pine and black spruce productivity in natural origin mixed stands and site index conversion equations

Forest managers need site productivity estimates for currently grown tree species as well as those that might be considered for future management on a given site. Existing models are generally for pure stands and don't factor in the effects of climate change on growth. Therefore, site index (SI) conversion equations were developed for jack pine (Pinus banksiana Lamb.) and black spruce (Picea mariana Mill. B.S.P.) trees grown in mixed natural stands. For this, 180 trees (90 jack pine and black spruce each) were sampled from 30 even-aged natural origin mixed stands (sites) (3 per species per site) across Ontario, Canada. Stem analysis data collected from these trees were used to develop stand height growth models that incorporate climate variables during growth for each species. A mixed effects modeling approach was used to fit the models. The SI conversion equations were then developed by regressing SI of one species against that of the other species and climate variables.To evaluate climate effects on site productivity, stand heights were predicted for 4 geographic areas of Ontario for the period 2021 to 2080 under 3 emissions scenarios reflecting different amounts of heat at the end of the century (i.e., 2.6, 4.5, and 8.5 W m −2) using the stand height growth models developed here. Climate effects were more pronounced for black spruce than for jack pine and varied among locations.The models developed here can be used to estimate stand height and SI of jack pine and black spruce trees grown in natural origin mixed stands in a changing climate. Using SI conversion equations, the SI of one species can be estimated in terms of the SI of the other species and climate variables. In the absence of climate data, models can be used to estimate SI of both species.

Hybrid height growth and survival model for juvenile Eucalyptus globoidea (Blakely) and E. bosistoana (F. Muell) in New Zealand

Juvenile plantation forest dynamics are complex but understanding and predicting early growth and survival enables effective management. Information provided by traditional growth and yield models is an essential input in decision-making processes for managing planted forests. They are generally fitted using permanent sample plot data, thus they are robust and simple. However, the introduction of explanatory factors affecting tree development (e.g. wetness index, morphometric protection index etc.) not only to improve the quality of predictions but also to add useful information underpinning forest management decisions (e.g. species choice, silvicultural practice etc.). In this study, three different hybrid growth and yield approaches for modelling height growth and survival were tested, culminating in models being developed for Eucalyptus globoidea and E. bosistoana by integrating climatic, edaphic and topographic factors. Permanent sample plot data (n = 84) were used to develop these models. The results showed that inclusion of topographic and climatic factors alongside potentially usable light sum (PULS) slightly improved both height and survival prediction of both species compared to time-based models (TA). The ranking and alignment of coefficient of determination for height models were PULS = 0.79 > 0.77 > TA = 0.75 and survival models were PULS = −0.47 > TA = −0.45, respectively. Both of the species were site-sensitive, especially to soil moisture and wind speed. This sensitivity also indicated the optimal requirements for height growth and survival for these species. All three modelling approaches can be applied for juvenile Eucalyptus plantations in any given site-specific case, based on available information and management demands. The models developed in this study can help forest managers make better decisions for new plantation establishment and management.

Tree Barrier Prediction of Power lines based on Tree Height Growth Model

Aiming at the problem that the hidden trouble of tree barrier seriously threatens the safe operation of power lines, the typical tree species in the corridor of power lines in Guangdong area are investigated and studied. Firstly, a tree height growth prediction model based on Richard’s equation is established. The correlation deviation test results show that the model can accurately predict the tree height. The hidden trouble of tree barrier under line and the hidden trouble caused by wind deviation of wire are analyzed. Finally, the model for predicting the clearance distance from tree to power lines is established. By predicting the clearance distance between wire and tree, the functions of real-time detection of hidden trouble of tree barrier and risk assessment and prediction of tree barrier are realized. It avoids the flashover fault caused by the excessive growth of trees, and ensures the safe and stable operation of power lines.

Site index models with density effect for hybrid aspen (Populus tremula L. × P. tremuloides Michx.) plantations in southern Finland

This study was conducted to examine the characteristics of dominant height growth and develop site index models for clonal hybrid aspen plantations in southern Finland. Data were obtained from repeatedly measured clonal hybrid aspen trials with varying initial spacing: 2.5 m × 2.5 m (1600 trees ha−1), 3.0 m × 3.0 m (1200 trees ha−1), 3.5 m × 3.5 m (800 trees ha−1), and 5.0 m × 5.0 m (400 trees ha−1). The total number of data points in the analysis was 389 for the age of 3–20. Within the range of observed data, the dominant height grew linearly over age and was significantly different due to the initial planting density; growth was higher when the planting was denser. Using the initial density effect, dominant height growth models were developed based on the Chapman-Richards function through nonlinear mixed-effects modelling. The density variable was found to be statistically the best variable when modifying only the shape parameter of the Chapman-Richards function. All fixed-effects were significant for both models, with and without the density effect. The residual plots of the model did not show any bias over the predicted value, stand age or planting density. The predicted dominant height was higher with increasing initial density. The predicted dominant height increment was faster with higher planting densities until the age of 14 years. The anamorphic site index curves were presented with base age of 20 years including the planting density effect. The overall pattern of site index curves was consistent with those observed in previous studies. The models developed in this study can be used to estimate the dominant height and site index of hybrid aspen plantations in southern Finland.

Modeling forest site productivity using climate data and topographic imagery in Pinus elliottii plantations of central Argentina

To be useful for silvicultural and forest management practices, the models of Site Index (SI) should be based on accessible predictor variables. In this study, we used spatially explicit data obtained from digital elevation models and climate data to develop SI prediction models with high local precision. Predicting tree growth and yield is a key component to sustainable forest management and depends on accurate measures of site quality. The aim of this study was to develop both empirical models to predict site index (SI) from biophysical variables and a dynamic model of top height growth for plantations of Pinus elliottii Engelm. in Cordoba, Argentina. Site productivity described by SI was related to environmental characteristics, including topographic and climatic variables. Separate models were created from only topographic data and the combination of topographic and climate data. Although SI can be adequately predicted through both types of models, the best results were obtained when combining topographic and climate variables (R2 = 0.83, RMSE% = 7.02%, for the best-fitting model). The key factors affecting site productivity were the landscape position and the mean precipitation of the last 5 years before the reference age, both related to the amount of plant-available water in the soils. Furthermore, the top height growth models developed are fairly accurate, considering the proportion of variance explained (R2 = 98%) and the precision of the estimates (RMSE% < 8%). The models developed here are likely to have considerable application in forestry, since they are based on accessible predictor variables, which make them useful for silvicultural and forest management practices, particularly for non-forest areas and for the young or uneven-aged stands.

Modeling height growth for teak plantations in Colombia using the reducible stochastic differential equation approach

Teak (Tectona grandis L.f.) plantations are increasingly being established in tropical regions to meet a rising demand for its highly valued timber. Teak plantations have been established in the Atlantic Coastal Plain region of Colombia, a region climatically suitable for teak growth by having a monsoon climate with a unimodal precipitation pattern. Tree diameter at breast height (DBH, 1.3 m above ground) and mean top height, periodically measured over a 17-year period in 44 permanent sampling plots of size 0.06 and 0.10 ha, were used in this study. A stochastic differential equation (SDE), along with a Bertalanffy–Richards-type height growth model, was used to model and estimate top height growth of teak plantations in Colombia. Environmental noise and height measurement errors were explicitly considered as the main uncertainty sources of mean top height growth. The best model for estimating mean top height, based on statistical performance and biological rationale, had the asymptote defined as a local parameter and the growth rate and shape specified as global parameters. This model outperformed its counterpart that had the growth rate specified as a local parameter and asymptote and shape as global parameters. The selected model also outperformed alternative approaches such as the mixed-effects model, generalized algebraic difference approach, and the dummy variable method. Estimated trajectories for the mean top height of teak in Colombia are biologically sound based on the measured height series and previous studies in Latin America. Results suggest that most of the uncertainty associated with the mean top height growth of teak plantations in Colombia was largely explained by environmental noise. The best estimated model using the SDE approach can be useful for predicting height growth and evaluating site productivity of teak plantations in Colombia and in neighbouring countries with biophysical characteristics similar to those where teak has been planted in Colombia.

Assessing the sensitivity of site index models developed using bi-temporal airborne laser scanning data to different top height estimates and grid cell sizes

Site productivity and forest growth are critical inputs into projecting wood volume and biomass accumulation over time. Site productivity, which is determined most commonly using site index models is also the primary criterion to consider many forest management decisions. Most of the previous research utilizing the remote sensing data for assessment of site index with forest height are based on the existing site index models developed with traditional dendrometric methods. However, these traditional methods are both time-consuming and expensive. This study demonstrates how bi-temporal airborne laser scanning (ALS) data collected within the 8-year period can be used for the development of site index models for Scots pine. The accuracy of ALS-derived models was assessed by comparison to the reference site index model developed based on data from stem analysis of 174 felled Scots pine trees. We evaluated the effect of different height metrics and grid cell size on the trajectory of site index models developed from ALS-derived measurements. Four methods of estimating top height from ALS point clouds were evaluated: 95th, 99th and 100th percentiles of point clouds and an individual tree detection approach (ITD). The models were created for a range of grid cell sizes: 10 × 10 m, 30 × 30 m, and 50 × 50 m. The results indicate that bitemporal ALS data could substitute traditional methods that have been applied to date for stand growth modelling. It was found that top height increment can be estimated by using both ITD approach and the 100th percentile of point cloud giving an appropriate top height (TH) increment estimation. Observed growth curves of reference trees agreed best with the trajectories that were obtained based on TH calculated using ITD method (R2 = 0.892) and 100th percentile (R2 = 0.797). In case of TH obtained from 99th and 95th percentiles only weak correlation was found: R2 = 0.358 and R2 = 0.213, accordingly. The height growth models developed with 95th and 99th percentiles of point cloud were not compatible with the reference model. We also found that grid cell size did not affect the model height growth trajectories. Irrespective of the grid cell size, the obtained model trajectories for the given method of TH estimation are nearly identical for cells 10 × 10, 30 × 30 and 50 × 50 m.

Individual Tree Diameter and Height Growth Models for 30 Tree Species in Mixed-Species and Uneven-Aged Forests of Mexico

Lack of knowledge of individual tree growth in species-rich, mixed forest ecosystems impedes their sustainable management. In this study, species-specific models for predicting individual diameter at breast height (dbh) and total tree height (h) growth were developed for 30 tree species growing in mixed and uneven-aged forest stands in Durango, Mexico. Growth models were also developed for all pine, all oaks, and all other species of the genus Arbutus (strawberry trees). A database of 55,158 trees with remeasurements of dbh and h of a 5-year growth period was used to develop the models. The data were collected from 217 stem-mapped plots located in the Sierra Madre Occidental (Mexico). Weighted regression was used to remove heteroscedasticity from the species-specific dbh and h growth models using a power function of the tree size independent variables. The final models developed in the present study to predict dbh and total tree height growth included size variables, site factors, and competition variables in their formulation. The developed models fitted the data well and explained between 98 and 99% and of the observed variation of dbh, and between 77 and 98% of the observed variation of total tree height for the studied species and groups of species. The developed models can be used for estimating the individual dbh and h growth for the analyzed species and can be integrated in decision support tools for management planning in these mixed forest ecosystems.

Modelling the effects of climate on site productivity of white pine plantations

Ninety-three dominant or co-dominant white pine (Pinus strobus L.) trees were sampled from 93 plots (one tree per plot) in even-aged monospecific plantations at 31 sites (three plots per site) across Ontario, Canada. Stem analysis data collected from these trees were used to develop and evaluate stand height models. The effects of site and climate on site productivity were examined by incorporating site and climate variables into a stand height model. Including climate variables improved the fit statistics of the stand height model for white pine. A covariance structure (AR(1)) was used to address autocorrelation in the data. Similarly, a variance function was used to account for heteroscedasticity. Stand heights were predicted for four areas (middle, easternmost, westernmost, and southernmost parts of Ontario where white pine were sampled) for the period 2021 to 2080 under two emissions trajectories known as representative concentration pathways (RCPs), with each reflecting different levels of heat at the end of the century (i.e., 2.6 and 8.5 W·m–2). At the end of the 2021 to 2080 growth period, projected heights were shorter by 7% for the southern parts and taller by 9.8% for the middle parts of Ontario under both climate change scenarios compared with those under a no change scenario. However, there was no pronounced difference in projected heights under both climate change scenarios and the no change scenario for the other two areas evaluated. The resulting height growth models can be used to estimate stand heights for white pine plantations in a changing climate. Using the same model, the site index of a plot or stand can be estimated by calculating height at a given base (index) age. In the absence of climatic data, the model fitted without climate variables can be used to estimate stand heights and site indices.

Axial variation of xylem conduits in the Earth’s tallest trees

In the Earth’s tallest tree species, axial variation in conduit size matches theoretical predictions minimizing the accumulation of hydraulic resistance with height growth, within a constraint of maximum conduit diameter. Hydraulic limitations to tree height can be mitigated by widening the conducting elements toward a tree’s base. However, size limits of tracheid and vessel dimensions may constrain this compensation mechanism as the water transport pathway elongates. Moreover, variation in conduit size is poorly described in tall trees even though their long transport paths have high potential for hydraulic resistance. Here, we evaluated whether axial variation in conduit diameter was uniquely structured, or matched theoretical predictions in Sequoia sempervirens, Sequoiadendron giganteum, and Eucalyptus regnans that were 86–105 m tall and exceeded 85% of the maximum height for each species. Across Sequoia and Sequoiadendron, tree top tracheids maintained constant width, whereas tree base tracheids in the outermost ring were 20% wider in taller trees, suggesting maintenance of basipetal conduit widening with height growth. In all trees, the observed widening decreased at a rate per unit path length that fitted well to a power function with an exponent consistent with hydraulic compensation. However, below about 60 m from the tree tops, conduit diameters approached an asymptote beneath the power function, indicating a limit to maximum conduit size. Quantifying the distribution of base-to-top hydraulic resistance suggested that the minimal hydraulic benefit gained with increasingly wider conduits near the tree base may trade off with other factors such as maintaining mechanical strength or reducing fluid volume. We summarize these results into an anatomical model of height growth that includes limits to axial variation in conduit diameter and is supported by many physiological and anatomical observations.

Development of Site Index Curves and Height-DBH Growth Model of Larix kaempferi for Deogyu Mountain in South Korea

In this study, we aimed to develop site index curves and a height growth model using forest data with the measured height, diameter at breast height (DBH), and age targeting a Larix kaempferi stand located on Mt. Deogyu in Muju, Jeollabuk-do. The site index estimation was calculated using Chapman-Richards equation. The coefficients were found to be α = 20.7837, β = 0.0566, γ = 1.6607, and MSE = 1.2034. The height growth model of the dominant trees depending on the DBH was determined to be α = 0.4872, β = 0.3687, and MSE = 1.8212 using the Petterson growth model. The Mean residual values for above two models were analyzed as 0.00004 and −0.00007, respectively. When comparing the skewness and kurtosis of the residual, the skewness values were 0.1659 and −0.1272, and the kurtosis values were −0.2310 and −0.5543. Therefore, the fitness was considered to be good because they were close to the normal distribution. The results of Shapiro-Wilk test showed P-values (0.77 for the height growth model and 0.62 for the height-DBH model) significantly higher than the alpha level of 0.05, and the residual form of the estimated values for the measured values showed uniform distribution indicating that the fitness of the two models was excellent.

Climatic Effects on Site Productivity of Red Pine Plantations

Climatic effects on site productivity of red pine (Pinus resinosa Aiton) plantations were examined. A stand height/site index equation with climate variables incorporated in the height growth model was developed from stem analysis data. These data were collected from 90 dominant or co-dominant red pine trees sampled from even-aged monospecific plantations located on 30 sites (3 trees per site) broadly distributed across Ontario, Canada. The stand height equation was fit using a nonlinear mixed-effects approach. Climatic effects on site productivity were examined by regressing site index against commonly reported climate variables. Three site-specific climate attributes explained 63% of the variability in observed site index. These climate variables were examined to be incorporated into the stand height growth models. However, only two climate variables—growing season total precipitation (GSTP) and growing season mean temperature (GSMT)—were significant in the model without random effects and autocorrelation. In the presence of random effects and autocorrelation, however, only GSMT remained significant in the model. Stand heights were predicted for three randomly selected locations (eastern, western, and southern Ontario) for the growth periods 2011 to 2040 and 2041 to 2070 under two (2.6 and 8.5 Watts/m2) emissions trajectories known as Representative Concentration Pathways (RCPs). At the end of both growth periods, projected heights were reduced under both climate change scenarios (compared to those under a no-climate-change scenario) at all locations. Under both scenarios, the decrease in height growth was more pronounced in the south than in the east or west. The developed height growth models can be used to estimate stand heights for red pine plantations in a changing climate. Using the same models, site index of a plot/stand can also be estimated by calculating height at a given base (index) age. In the absence of climate data, the model fitted without climate variables can be applied to estimate stand heights and site indices.