ALBERT

Description: Individual tree growth and yield models precisely describe tree growth irrespective of stand complexity and are capable of simulating various silvicultural alternatives in the stands with diverse structure, species composition, and management history. We developed both age dependent and age independent diameter increment models using long-term research sample plot data collected from both monospecific and mixed stands of European beech (Fagus sylvatica L.) in the Slovak Republic. We used diameter at breast height (DBH) as a main predictor and other characteristics describing site quality (site index), stand development stage (dominant height and stand age), stand density or competition (ratio of individual tree DBH to quadratic mean diameter), species mixture (basal area proportion of a species of interest), and dummy variable describing stand management regimes as covariate predictors to develop the models. We evaluated eight versatile growth functions in the first stage using DBH as a single predictor and selected the most suitable one, i.e., Chapman-Richards function for further analysis through the inclusion of covariate predictors. We introduced the random components describing sample plot-level random effects and stochastic variations on the diameter increment, into the models through the mixed-effects modelling. The autocorrelation caused by hierarchical data-structure, which is assumed to be partially reduced by mixed-effects modelling, was removed through the inclusion of the parameter accounting for the autoregressive error-structures. The models described about two-third parts of a total variation in the diameter increment without significant trends in the residuals. Compared to the age independent mixed-effects model (conditional coefficient of determination, R c 2 = 0.6566; root mean square error, RMSE = 0.1196), the age dependent model described a significantly larger proportion of the variations in diameter increment ( R c 2 = 0.6796, RMSE = 0.1141). Diameter increment was significantly influenced differently by covariate predictors included into the models. Diameter increment decreased with the advancement of stand development stage (increased dominant height and stand age), increasing intraspecific competition (increased basal area proportion of European beech per sample plot), and diameter increment increased with increasing site quality (increased site index) and decreased competition (increased ratio of DBH to quadratic mean diameter). Our mixed-effects models, which can be easily localized with the random effects estimated from prior measurement of diameter increments of four randomly selected trees per sample plot, will provide high prediction accuracies. Our models may be used for simulating growth of European beech irrespective of its stand structural complexity, as these models have included various covariate variables describing both tree-and stand-level characteristics, thinning regimes, except the climate characteristics. Together with other forest models, our models will be used as inputs to the growth simulator to be developed in the future, which is important for decision-making in forestry.

Description: The objective of this study was to develop the models that predict both timber and branch volumes of Norway spruce (Picea abies/L./Karst.), the most abundant tree species in Europe, and determine the relationships among timber and branch volumes and various site and stand characteristics. The data used in this study come from 76 sample plots in the different stands and site conditions across Norway spruce forests in the Czech Republic. Timber volume was determined by Huber’s formula and branch volume (logging residue) was determined by drying and weighing of 10 samples from the 10-chipped trees on each sample plot, meaning that a total of 760 samples were analyzed. The results showed that timber volume was significantly positively correlated with branch volume, mean diameter at breast height (mean DBH) per sample plot, mean height per sample plot, slope of sample plot, and stand age, but negatively correlated with stand stocking. The branch volume was more significantly affected by stand stocking than timber volume. The timber-to-branch volume ratio (TBR) reached the mean value of 3.7 (±0.14 SE) and significantly increased with increasing elevation. The trees on the nutrient-rich sites were characterized by higher branch volume, while TBR reached higher values on the acid sites. Site quality class had a significant effect only on the branch volume production. Compared to the timber volume (root mean square error, RMSE = 3.6176; adjusted coefficient of determination, R2adj = 0.7310), the branch volume was relatively poorly described by the model (RMSE = 1.928; R2adj = 0.2517). The volume prediction models show that timber volumes increase with increasing slope and branch volume increases with decreasing site quality class. For effective forest management practice, the highest branch volume in favor of timber production is characterized for lowland forests with stand stocking ≤60% (TBR 1.5), while the highest share of timber volume (TBR 9.5) can be reached in the mountains with a full stand stocking.

Description: Forests, Vol. 9, Pages 555: Generalized Nonlinear Mixed-Effects Individual Tree Crown Ratio Models for Norway Spruce and European Beech Forests doi: 10.3390/f9090555 Authors: Ram P. Sharma Zdeněk Vacek Stanislav Vacek Tree crowns are commonly measured to understand tree growth and stand dynamics. Crown ratio (CR—crown depth-to-total height ratio) is significantly affected by a number of tree- and stand-level characteristics and other factors as well. Generalized mixed-effects CR models were developed using a large dataset (measurements from 14,669 trees of Norway spruce (Picea abies (L.) Karst.) and European beech (Fagus sylvatica (L.)) acquired from permanent research plots in various parts of the Czech Republic. Among several tree- and stand-level variables evaluated, diameter at breast height, height to crown base, dominant height, basal area of trees larger in diameter than a focal tree, relative spacing index, and variables describing the effects of species mixture and canopy height differentiation significantly contributed to CR variation. We included sample-plot-level variations caused by randomness in the data and other stochastic factors into the CR models using the mixed-effects modeling approach. The logistic function, which predicts the values between 0 and 1, was chosen to develop the generalized CR mixed-effects model. A large proportion of the CR variation (R2adj ≈ 0.63 (Norway spruce); 0.72 (European beech)) was described by generalized mixed-effects model without significant residual trends. Testing the CR model against a part of the model fitting dataset confirmed its high prediction precision. Our CR model can be useful for growth simulation using inventory databases that lack crown measures. Other potential implications of our CR models in forest management are mentioned in the article.

Description: Tree crowns are commonly measured to understand tree growth and stand dynamics. Crown ratio (CR—crown depth-to-total height ratio) is significantly affected by a number of tree- and stand-level characteristics and other factors as well. Generalized mixed-effects CR models were developed using a large dataset (measurements from 14,669 trees of Norway spruce (Picea abies (L.) Karst.) and European beech (Fagus sylvatica (L.)) acquired from permanent research plots in various parts of the Czech Republic. Among several tree- and stand-level variables evaluated, diameter at breast height, height to crown base, dominant height, basal area of trees larger in diameter than a focal tree, relative spacing index, and variables describing the effects of species mixture and canopy height differentiation significantly contributed to CR variation. We included sample-plot-level variations caused by randomness in the data and other stochastic factors into the CR models using the mixed-effects modeling approach. The logistic function, which predicts the values between 0 and 1, was chosen to develop the generalized CR mixed-effects model. A large proportion of the CR variation (R2adj ≈ 0.63 (Norway spruce); 0.72 (European beech)) was described by generalized mixed-effects model without significant residual trends. Testing the CR model against a part of the model fitting dataset confirmed its high prediction precision. Our CR model can be useful for growth simulation using inventory databases that lack crown measures. Other potential implications of our CR models in forest management are mentioned in the article.

Description: Height-to-diameter at breast height (DBH) ratio (HDR) is an important tree and stand stability measure. Several factors such as stand dynamics, natural and anthropogenic disturbances, and silvicultural tending significantly affect HDR, and, therefore, in-depth investigation of HDR is essential for better understanding of ecological processes in a forest. A nonlinear mixed-effects HDR model applicable to several tree species was developed using the Czech national forest inventory data comprising 13,875 sample plots and 348,980 trees. The predictive performance of this model was evaluated using the independent dataset which was originated from 25,146 trees on 220 research sample plots. Among various tree- and stand-level variables describing tree size, site quality, stand development stage, stand density, inter-tree spacing, and competition evaluated, dominant height (HDOM), dominant diameter (DDOM), relative spacing index (RS), and DBH-to-quadratic mean DBH ratio (dq) were identified as the most important predictors of HDR variations. A random component describing sample plot-specific HDR variations was included through mixed-effects modelling, and dummy variables describing species-specific HDR variations and canopy layer-specific HDR variations were also included into the HDR model through dummy variable modelling. The mixed-effects HDR model explained 79% of HDR variations without any significant trends in the residuals. Simulation results showed that HDR for each canopy layer increased with increasing site quality and stand development stage (increased HDOM) and increasing competition (increased RS, decreased DDOM and dq). Testing the HDR model on the independent data revealed that more than 85% of HDR variations were described for each individual species (Norway spruce, Scots pine, European larch, and European beech) and group of species (fir species, oak species, birch and alder species) without significant trends in the prediction errors. The HDR can be predicted with a higher accuracy using the calibrated mixed-effects HDR model from measurements of its predictors that can be obtained from routine forest inventories. To improve the prediction accuracy, a model needs to be calibrated with the random effects estimated using one to four randomly selected trees of a particular species or group of species depending on the availability of their numbers per sample plot. The HDR model can be applied for stand stability assessment and stand density regulation. The HDR information is also useful for designing a stand density management diagram. Brief implications of the HDR model for designing silviculture strategies and forest management planning are presented in the article.

Description: Forests, Vol. 9, Pages 267: Climate Change-Induced Shift of Tree Growth Sensitivity at a Central Himalayan Treeline Ecotone Forests doi: 10.3390/f9050267 Authors: Niels Schwab Ryszard J. Kaczka Karolina Janecka Jürgen Böhner Ram P. Chaudhary Thomas Scholten Udo Schickhoff Himalayan treelines are exposed to above average climate change impact, resulting in complex tree growth–climate relationships for Himalayan Silver Fir (Abies spectabilis (D. Don) Spach) at central Himalayan treelines. The majority of recent studies detected current tree growth sensitivity to dry conditions during pre-monsoon seasons. The aim of this study was to analyze growth–climate relationships for more than a century for a treeline ecotone in east-central Nepal and to test for Blue Intensity (BI; used as a surrogate of maximum late wood density) as climate proxy. We determined the relationships of Abies spectabilis radial tree growth and BI to climate by correlating both to temperature, precipitation and drought index data. The results showed a significantly unstable dendroclimatic signal over time. Climate warming-induced moisture deficits during pre-monsoon seasons became a major factor limiting radial tree growth during recent decades. Earlier in time, the dendroclimatic signal was weaker, predominantly reflecting a positive relationship of tree growth and summer temperature. Compared to radial tree growth, BI showed a different but strong climate signal. Temporally unstable correlations may be attributed to increasing effects of above-average rates of climate warming. An extended network of Himalayan tree-ring sites is needed to further analyze cause–effect relationships and to solve this attribution problem.

Description: Relationship of total height and diameter at breast height (hereafter diameter) of the trees is generally nonlinear, and therefore has complex characteristics, which can be accurately described by the height–diameter model developed using the back propagation (BP) neural network approach. The multiple hidden layered-BP neural network has several hidden layers and neurons, and is therefore considered more appropriate modeling approach compared to the single hidden layered-BP neural network approach. However, the former approach is not widely applied for tree height prediction due to absence of the effective optimization method, but it can be done using the BP neural network modeling approach. The poplar (Populus spp. L.) plantation data acquired from Guangdong province of China were used for evaluating the BP neural network modeling approach and compared its results with those obtained from the traditional regression modeling and mixed-effects modeling approaches. We determined the best BP neural network structure with two hidden layers and five neurons in each layer, and logistic sigmoid transfer functions. Relative to the Mitscherlich height–diameter model that had the highest fitting precision among the six traditional height–diameter models evaluated, coefficient of determination (R2) of the neural network height–diameter model increased by 10.3%, root mean squares error (RMSE) and mean absolute error (MAE) decreased by 12% and 13.5%, respectively. The BP neural network height–diameter model also appeared more accurate than the mixed-effects height–diameter model. Our study proposes the method of determining the optimal numbers of hidden layers, neurons of each layer, and transfer functions in the BP neural network structure. This method can be useful for other modeling studies of similar or different types, such as tree crown modeling, height, and diameter increments modeling, and so on.

Description: Forest degradation has been considered as one of the main causes of climate change in recent years. The knowledge of estimating degraded forest areas without the application of remote sensing tools can be useful in finding solutions to resolve degradation problems through appropriate restoration methods. Using the existing knowledge through literature review and field-based primary information, we generated new knowledge by combining the information obtained from multi-criteria decision analyses with an analytic hierarchy process, and this was then used to estimate degraded forest area. Estimation involves determining forest degradation index (FDI) and degradation threshold. Continuous inventory data of permanent sample plots collected from degraded forests, consisting of various forest types divided by dominant tree species in the Guangdong province and Tibet autonomous region of China, were used for the purposes. We identified four different forest degradation levels through the determination and comprehensive evaluation of FDI. The degraded forest area with broad-leaved species as dominant tree species in the Guangdong province was estimated to be 83.3% of a total forest area of 24,037 km2. In the same province, the degraded forest area with eucalyptus as a dominant tree species was 59.5% of a total forest area of 18,665 km2. In the Tibet autonomous region, the degraded forest area with spruce as a dominant tree species was 99.1% of a total forest area of 17,614 km2, and with fir as a dominant tree species, the degraded area was 98.4% of a forest area of 12,103 km2. A sampling accuracy of forest areas with national forest inventory was about 95% in both provinces. Our study concludes that the FDI method used has a certain scientific rationality in estimating degraded forest area. The forest provides a variety of tangible and intangible goods and services for humans. Therefore, forest management should focus on the improvement of its overall productivity, which is only possible with improving forest site quality. One of the important steps to improve the quality of a forest site is to resolve its degradation issues. The presented method in this article will be useful in finding the solutions to forest degradation problems. This method, which does not need any remote sensing tool, is simple and can be easily applied for estimating any degraded forest area and developing effective forest restoration plans.

Description: Individual tree growth and yield models precisely describe tree growth irrespective of stand complexity and are capable of simulating various silvicultural alternatives in the stands with diverse structure, species composition, and management history. We developed both age dependent and age independent diameter increment models using long-term research sample plot data collected from both monospecific and mixed stands of European beech (Fagus sylvatica L.) in the Slovak Republic. We used diameter at breast height (DBH) as a main predictor and other characteristics describing site quality (site index), stand development stage (dominant height and stand age), stand density or competition (ratio of individual tree DBH to quadratic mean diameter), species mixture (basal area proportion of a species of interest), and dummy variable describing stand management regimes as covariate predictors to develop the models. We evaluated eight versatile growth functions in the first stage using DBH as a single predictor and selected the most suitable one, i.e., Chapman-Richards function for further analysis through the inclusion of covariate predictors. We introduced the random components describing sample plot-level random effects and stochastic variations on the diameter increment, into the models through the mixed-effects modelling. The autocorrelation caused by hierarchical data-structure, which is assumed to be partially reduced by mixed-effects modelling, was removed through the inclusion of the parameter accounting for the autoregressive error-structures. The models described about two-third parts of a total variation in the diameter increment without significant trends in the residuals. Compared to the age independent mixed-effects model (conditional coefficient of determination, R c 2 = 0.6566; root mean square error, RMSE = 0.1196), the age dependent model described a significantly larger proportion of the variations in diameter increment ( R c 2 = 0.6796, RMSE = 0.1141). Diameter increment was significantly influenced differently by covariate predictors included into the models. Diameter increment decreased with the advancement of stand development stage (increased dominant height and stand age), increasing intraspecific competition (increased basal area proportion of European beech per sample plot), and diameter increment increased with increasing site quality (increased site index) and decreased competition (increased ratio of DBH to quadratic mean diameter). Our mixed-effects models, which can be easily localized with the random effects estimated from prior measurement of diameter increments of four randomly selected trees per sample plot, will provide high prediction accuracies. Our models may be used for simulating growth of European beech irrespective of its stand structural complexity, as these models have included various covariate variables describing both tree-and stand-level characteristics, thinning regimes, except the climate characteristics. Together with other forest models, our models will be used as inputs to the growth simulator to be developed in the future, which is important for decision-making in forestry.

Description: Tree height is a basic input variable in various forest models, such as growth and yield models, biomass models, and carbon budget models, which serve as very important tools for the informed decision-making in forestry. The height-diameter model is the most important component of the growth and yield models and forest simulators. We developed the nonlinear mixed-effects height-diameter model with the interaction effects of stand density and site index introduced using data from 765 Larix olgensis trees in Jingouling forest farm of the Wangqing Forest Bureau in northeast China. Among the various basic versatile functions evaluated, a simple exponential growth function fitted the data adequately well, and this was then expanded through the introduction of the variables describing the interaction effects of the stand density and site index on the height-diameter relationship. Sample plot-level random effects were included into this model through mixed-effects modeling. The results showed that the random effect of the stand density on the height-diameter relationship was substantially different at different classes of the site index, and the random effect of the site index was different for the different stand density classes. The nonlinear mixed-effects (NLME) height-diameter model coping with the interaction effects of the stand density and site index had a better performance than those of the NLME models with the random effect of the single variable of stand density or site index. To conclude, the inclusion of the interaction effects of stand density and site index could significantly improve the prediction accuracy of the height-diameter model for Larix olgensis Henry. The proposed model with the interactive random effects included can be applied for the accurate prediction of Larix olgensis tree height in northeast China.