Height-diameter Curves Research Articles

New Coupled Canopy–Light Model (CCLM) to Improve Visual Polymorphism Simulation of Fir Morphology

Environmental factors substantially influence the growth of trees. The current studies on tree growth simulation have mainly focused on the effect of environmental factors on diameter at breast height and tree height. However, the influence of environmental factors, especially light, on canopy morphology has not been considered, hindering the accurate understanding of the range of characteristics of tree morphology that occur due to environmental changes. To solve this problem, this study investigated the influence of light on the changes in canopy morphology and constructed a coupled canopy–light model (CCLM) to visually simulate the polymorphism of fir morphology. Using the Huangfengqiao Forestry Farm in You County, Hunan Province, China, as the study area, we selected a typical sample plot. Field surveys of the fir trees in the sample plot were conducted for three consecutive years to obtain longitudinal data of fir tree canopy shape. We constructed the canopy curves using a cubic uniform B-spline to construct 3D models of the fir trees in different years. The topographic and spatial location distribution data of the fir trees were used to construct a 3D scene of the sample plot in the UE4 3D engine, and the light distribution for each part of the canopy was calculated in a 3D scene by using the annual average photosynthetically active radiation (PAR) as the light parameter, which we combined with the ray-tracing algorithm. This study constructed the CCLM from the fir diameter using the breast-height growth model (BDGM) and the height–diameter curve model (HDCM), the fir trees’ canopy shape description from two years, and the light distribution data. We compared the canopy data obtained from canopy simulations using the CCLM with those obtained using a growth model based on spatial structure (GMBOSS) and those obtained from field surveys to identify any difference in the effectiveness of the canopy simulations using the CCLM and GMBOSS. Based on the BDGM and HDCM, we constructed the CCLM of firs with a determination coefficient (R2) of 0.829, combining data on canopy shape descriptions obtained from two years of field surveys and the light distribution data of each part of the canopy obtained through the ray-tracing algorithm. The Euclidean distance between the canopy description data obtained using the CCLM and the canopy description data obtained from the field survey was 15.561; that between the GMBOSS and the field survey was 23.944. A virtual forest stand environment was constructed from the survey data, combining ray-tracing algorithms to construct the CCLM model of fir in a virtual forest stand environment for growth visualization and simulation. Compared with the canopy description data obtained using the GMBOSS, the canopy description data obtained using the CCLM better fit the canopy description data obtained from the field survey, and the Euclidean distance decreased from 23.944 to 15.561.

General regularities of height-diameter curves in Hungarian oak, sessile oak and Turkey oak high forests

The height-diameter curves of natural even-aged Hungarian oak, sessile oak and Turkey oak forests in the regions of Staro Oryahovo, Sherba, Tsonevo and Aytos Forestry Districts have been studied. In order to explore the shape of the curves and, in particular, their steepness, the steepness index SI of Douhovnikov (“the method of natural indicators”) was applied. The curves were divided into three groups according to it: flat curves, medium steep curves and steep curves. Both the traditional height-diameter curves and the corresponding relative curves of Tyurin were studied. Consideration of the traditional height-diameter curves gives a certain ground for investigating to-gether the height-diameter curves of Hungarian oak and sessile oak, disregarding the tree species. This inference was confirmed by comparing the relative height-diameter curves for Hungarian oak, sessile oak and Turkey oak with Tyurin’s uniform curve of relative heights. For these comparisons we used the Willcoxon test. A statistically significant great proximity in their shapes was found. As a uniform average curve of relative heights has been established for all tree species, this proximity indicates a possibility of creating a single fan of height-diameter curves for high Hungarian, sessile and Turkey oak.

A multi-temporal dataset of forest mensuration of reforestations: a case study in peri-urban Rome, Italy

The dataset supplied in this article provides data from continuous forest inventory carried out in the Castel di Guido estate, located in the Italian Tyrrhenian coast. The reforestation project started over 30 years ago using native and non-native species: 29 forested plot areas have been surveyed in 1997, 2000, 2003, 2006, 2011, 2013 and 2017 where information about species and stem diameters have been collected for a total of 2’215 tree stems. The dataset also contains height-diameter curves modelled for 1997, 2006 and 2017 years to let the user to estimate growing stock and total biomass easily. These data can be exploited to assess net primary productivity, pollutant uptake, and as comparisons with other European artificial reforestations programs with similar species. The database is finalized to narrow the knowledge gap on long-term growth pattern of urban and peri-urban reforestations, providing comparative data on different species performances, grown in pure and mixed stands. Dataset and metadata here presented are available at https://doi.org/10.5281/zenodo.2633972 .

The structure of forest stands in the Tatra National Park: The results of 2016–2017 inventory

Abstract The composition and structure of forest stands in the Tatra National Park were examined using data gathered in 2016 and 2017 from 617 circular sample plots (0.05 ha each). The diameter at breast height of all living trees, standing dead trees, snags, and wind throws was measured along with diameters and lengths of fallen logs within the plot boundaries. Tree height was measured for all living trees within the core (0.01 ha) of the sample plots. Using the obtained data, height-diameter curves were calculated for all major tree species and in the case of spruce, the height-diameter relationships were also calculated separately for each of the three elevation zones (up to 1200 m, between 1200 and 1400 m, above 1400 m). For each elevation zone and park protection zone, we also determined the volumes of live and dead trees. The volume of living trees in the Tatra National Park amounted to 259 m3/ha, which was higher than the volume of dead trees (176 m3/ha). Snags constituted the largest part of the dead wood whilst over 97% of the standing dead trees were spruce Picea abies. Among living trees, the share of spruce ranged from 81% in the low elevation zone to 98% in the middle zone. Other significant species in the lower zone were Abies alba (11%) and Fagus sylvatica (4.5%), while in the middle and upper elevation zones only Sorbus aucuparia occurred in significant numbers. Furthermore, in the lower elevation zone, Fagus sylvatica was the only species displaying significantly higher volumes in the ‘strict protection’ zone compared to the other park areas. In the ‘landscape protection’ zone, Picea abies was the most dominant species and the share of other species in the lowest elevation zones calculated based on tree density was smaller than calculated based on tree volume, indicating problems with stand conversion from spruce monoculture to mixed forest.

Defining Deforestation Patterns Using Satellite Images from 2000 and 2017: Assessment of Forest Management in Miombo Forests—A Case Study of Huambo Province in Angola

A few studies have recently been published on changes in land use/land cover (LU/LC) of Angolan Miombo forests, however, none have attempted to offer forest management solutions for degraded Miombo forests. Landscapes are witness to past and present natural and social processes influencing the environment, where each period in the past leaves footprints on the landscape’s development, which can be described by a continual decrease in forest area over time. The expansion of degraded areas from 2000 to 20017 began near urban areas where many Miombo forests have been eliminated or highly degraded, particularly in the southwest and northeast of the Huambo province. Large areas of degraded forests were observed along the Benguela railway (Caminho de ferro de Benguela). Our detailed analysis of the landcover map suggests that the impact has been devastating and there is no form of forest protection, which leads to unregulated exploitation. Descriptions of the Miombo forest dynamics are explained using height–diameter curves developed for different vegetation types that provide important insights about forest structures in the management zones. The height–diameter models differed for all vegetation types, and four management zones (MZ) were created based on a set of particular attributes. The vegetation types differed in each management zone, which included agricultural land and bare soil (MZ–E), grassland or savanna (MZ–C), open Miombo forests (MZ–B), and closed Miombo forests (Miombo forests). The four management zones were easily identified on the available maps and the height–diameter models developed represent a fundamental tool for future studies on forest planning.

Longitudinal height-diameter curves for Norway spruce, Scots pine and silver birch in Norway based on shape constraint additive regression models

BackgroundGeneralized height-diameter curves based on a re-parameterized version of the Korf function for Norway spruce (Picea abies (L.) Karst.), Scots pine (Pinus sylvestris L.) and silver birch (Betula pendula Roth) in Norway are presented. The Norwegian National Forest Inventory (NFI) is used as data base for estimating the model parameters. The derived models are developed to enable spatially explicit and site sensitive tree height imputation in forest inventories as well as future tree height predictions in growth and yield scenario simulations.MethodsGeneralized additive mixed models (gamm) are employed to detect and quantify potentially non-linear effects of predictor variables. In doing so the quadratic mean diameter serves as longitudinal covariate since stand age, as measured in the NFI, shows only a weak correlation with a stands developmental status in Norwegian forests. Additionally the models can be locally calibrated by predicting random effects if measured height-diameter pairs are available. Based on the model selection of non-constraint models, shape constraint additive models (scam) were fit to incorporate expert knowledge and intrinsic relationships by enforcing certain effect patterns like monotonicity.ResultsModel comparisons demonstrate that the shape constraints lead to only marginal differences in statistical characteristics but ensure reasonable model predictions. Under constant constraints the developed models predict increasing tree heights with decreasing altitude, increasing soil depth and increasing competition pressure of a tree. A two-dimensional spatially structured effect of UTM-coordinates accounts for the potential effects of large scale spatially correlated covariates, which were not at our disposal. The main result of modelling the spatially structured effect is lower tree height prediction for coastal sites and with increasing latitude. The quadratic mean diameter affects both the level and the slope of the height-diameter curve and both effects are positive.ConclusionsIn this investigation it is assumed that model effects in additive modelling of height-diameter curves which are unfeasible and too wiggly from an expert point of view are a result of quantitatively or qualitatively limited data bases. However, this problem can be regarded not to be specific to our investigation but more general since growth and yield data that are balanced over the whole data range with respect to all combinations of predictor variables are exceptional cases. Hence, scam may provide methodological improvements in several applications by combining the flexibility of additive models with expert knowledge.

インドネシア東部ジャワのファルカタ人工林の樹高・直径関係式について : 相対化した樹高曲線の適用

インドネシア東部ジャワのファルカタ人工林の樹高・直径関係式について : 相対化した樹高曲線の適用

Comparison of height-diameter models based on geographically weighted regressions and linear mixed modelling applied to large scale forest inventory data

Aim of the study: The main objective of this study was to test Geographically Weighted Regression (GWR) for developing height-diameter curves for forests on a large scale and to compare it with Linear Mixed Models (LMM).Area of study: Monospecific stands of Pinus halepensis Mill. located in the region of Murcia (Southeast Spain).Materials and Methods: The dataset consisted of 230 sample plots (2582 trees) from the Third Spanish National Forest Inventory (SNFI) randomly split into training data (152 plots) and validation data (78 plots). Two different methodologies were used for modelling local (Petterson) and generalized height-diameter relationships (Cañadas I): GWR, with different bandwidths, and linear mixed models. Finally, the quality of the estimated models was compared throughout statistical analysis. Main results: In general, both LMM and GWR provide better prediction capability when applied to a generalized height-diameter function than when applied to a local one, with R2 values increasing from around 0.6 to 0.7 in the model validation. Bias and RMSE were also lower for the generalized function. However, error analysis showed that there were no large differences between these two methodologies, evidencing that GWR provides results which are as good as the more frequently used LMM methodology, at least when no additional measurements are available for calibrating.Research highlights: GWR is a type of spatial analysis for exploring spatially heterogeneous processes. GWR can model spatial variation in tree height-diameter relationship and its regression quality is comparable to LMM. The advantage of GWR over LMM is the possibility to determine the spatial location of every parameter without additional measurements. Keywords: Spatial analysis; Pinus halepensis Mill; forest modelling.Abbreviations: GWR (Geographically Weighted Regression); LMM (Linear Mixed Model); SNFI (Spanish National Forest Inventory).

The construction of diameter-height models based on nonlinear mixed effect regression equations for oriental spruce located in mixed oriental spruce-scotch pine stands at Trabzon Forest District

Because of hard-working and time-consuming measurements for tree height, heights for all tree in sample plots can't be measure in many forest applications. These unmeasured tree heights can be predicted by height-diameter models relating tree height and diameters. In modeling the relationships between tree height and diameter, autocorrelation or serially correlations can be occurred in nested sampling systems for tree data measuring forest ecosystems. In this study, it is proposed to predict Nonlinear Mixed Effect Regression Models to alleviate these autocorrelation problems for constructing stand height-diameter curves in Oriental spruce (Picea orientalis (L.) Link) trees growing admixtures with scotch pine (Pinus sylvestris L.). The Schnute (1981), Huang et al. (2009), Wykoff et. al. (1982) nonlinear mixed effect model structure were predicted and compared for model height-diameter relationships in this study. In comparing these models, The Schnute (1981)'s nonlinear mixed effect model produced the best prediction results based on accuracy statistics. The Akaike (AIC) and Bayesian (BIC) Information Criterion were calculated as 15242 and 15257 and Schnute (1981) model predicted the % 95 percent of variability for height (R2=0.95). Schnute (1981) model with significant explanatory at variability of height and without serial correlation in diameter and height data will be use reliably to obtain predictions for oriental spruce tree heights. Keyword: Relationships between height and diameter, Oriental spruce, Nonlinear mixed effect regression model

文化財建造物を構成する大径長大材に適用できるヒノキ天然林の森林資源評価

This study aims to obtain information of the potential supply of natural forest resources of Japanese cypress required to maintain the wooden heritage buildings. Prescribed conditions to maintain important cultural buildings are strict and require using the same building technique as well as using the same tree species of the same quality. To investigate the potential to ensure sustainable materials, it is necessary to estimate the forest resources that reflect the information on demand-side. A case study of Donjon of Ozu castle in Ehime prefecture, we calculated the necessary forest resources to build a Donjon based on height-diameter curve equation and taper curve equation of methodology technique of forest measurement. As a result, it is estimated that the construction of Donjon requires about 53.6ha forest resources. In addition, the required area could be 5 times larger than the estimation if we took account of the cutting ratio in forestry management.

A Height–Diameter Curve for Longleaf Pine Plantations in the Gulf Coastal Plain

Abstract Tree height is a critical component of a complete growth-and-yield model because it is one of the primary components used in volume calculation. To develop an equation to predict total height from dbh for longleaf pine (Pinus palustris Mill.) plantations in the West Gulf region, many different sigmoidal curve forms, weighting functions, and ways of expressing height and diameter were explored. Most of the functional forms tried produced very similar results, but ultimately the form developed by Levakovic was chosen as best. Another useful result was that scaling diameters by the quadratic mean diameter on a plot and height by the average height of dominant and codominant trees in the target stand resulted in dramatically better fits than using these variables in their raw forms.

Shifts of the height-diameter curve in a stand and an application of the modified HENRICKSEN equation

Shifts of the height-diameter curve in a stand and an application of the modified HENRICKSEN equation

Estimation of stand attributes in Cryptomeria japonica and Chamaecyparis obtusa stands using QuickBird panchromatic data

This study aims to estimate stand density and stand volume in Cryptomeria japonica and Chamaecyparis obtusa stands from high-resolution satellite data and verify the reliability and uncertainty of the data. Sixty circular sample plots of 0.04 ha each were established. Their stand densities were estimated from the number of tree crowns derived from high-resolution satellite data using the watershed method. Stand densities derived from field surveys in the sample plots were compared with those obtained from high-resolution satellite data by stand age class. As a result, there was a positive correlation between them for sample plots of 41 years of age and over (R = 0.82); however, there was no correlation between them for sample plots of 40 years and under. Individual diameters at breast height (DBH) were estimated from crown areas obtained from high-resolution satellite data for the two species. Using the estimated DBH, individual tree heights were predicted from the height–diameter curves. Stand volumes were estimated from the sum of individual volumes, which were derived from volume formulas having two variables, i.e., DBH and height. Stand volumes derived from the field survey were compared with those obtained from high-resolution satellite data. The correlation coefficient between them for stands of 41 years of age and over was 0.78.

Analysis of the height-diameter curve of Japanese cedar even-aged pure forest stands using an allometric equation A simple method of estimating coefficients of the equation.

Analysis of the height-diameter curve of Japanese cedar even-aged pure forest stands using an allometric equation A simple method of estimating coefficients of the equation.

Allometric model of the height—diameter curve for even-aged pure stands of Japanese cedar (Cryptomeria japonica)

We derived an allometric model of the height–diameter curve for even-aged pure stands, which was a modification of the earlier model proposed by Inoue (2000a). An individual-dependent allometric equation was used as the height–diameter curve. Using the discriminant analysis method, all trees composed of a stand were stratified into upper and lower trees. It was assumed that both relationships between mean tree height Hm and upper tree height Hu and between mean DBH Dm and mean DBH of upper trees Du could be described by the time-dependent allometric power equations. The height–diameter curve showed an average relationship between tree height and DBH of a given stand at a given time, and hence it could be assumed that the height–diameter curve contained two points (Dm, Hm) and (Du, Hu). With these assumptions, we derived an allometirc model of height–diameter curve, which allowed the coefficients of the curve to be estimated from mean tree height and mean DBH. The proposed model was fitted to Japanese cedar (Cryptomeria japonica D. Don) data. The error ratio of the allometric model ranged from 2.254% to 13.412% (mean = 6.785%), which was significantly smaller than that of the earlier model. When the error of mean tree height was ±1.0 m or less, the effect of the error of mean tree height on the error ratio was comparatively small. This suggested that the error of ±1.0 m in mean tree height could be accepted in the estimation of height–diameter curve using the allometric model. These features enable us to combine the allometric model with Hirata's vertical angle-count sampling or growth models. In conclusion, the allometric model would be one of the most practical and convenient approaches for estimating the height–diameter relationship of even-aged pure stands.

Practical approaches to calibrating height–diameter relationships for natural sugar maple stands in Ontario

Abstract The efficiency of a random parameter approach for calibrating a height–diameter model of trees in natural sugar maple Acer saccharum (Marsh.) stands in Ontario was compared with that of a fixed parameter approach. From a practical point of view, both methods were equally efficient. However, the random parameter model has a theoretical advantage, mostly because random deviations from the mean function can be predicted with known precision levels. The study also produced parameter estimates that can be used for localizing height–diameter curves in natural undisturbed sugar maple stands in southern Ontario. The models had negligible bias. The root mean square of the residuals for tree height, computed for an independent validation data set, was in the order of 1.5 m. The coefficient of determination for the validation data set was around 0.95.

Estimation of height–diameter curves through multilevel models with special reference to even-aged teak stands

The use of a multilevel model for estimation and prediction of height–diameter curves in planted teak stands is discussed in the context of analyzing data from a stratified two-stage sample survey. Plantations selected randomly from different age groups within each Territorial Division in the State of Kerala, India, served as first stage units; circular plots along a transect within each selected plantation formed the second stage units. Girth at breast-height was measured on all the trees within the selected plots and height was measured on a sub-sample of trees within each selected plot. Plantations, plots within plantations, and trees within plots formed the three levels in the multilevel model for the height–diameter relation. The overall height–diameter model included fixed effects of age and mean diameter of the stands and also random effects on the deviations of the expected values of the parameters of the height–diameter curve at the plantation and plot levels. Differences in the height–diameter curves among the different Territorial Divisions were also investigated. The age along with the mean diameter of the stands could explain only a small part of the variation in the height–diameter curves. Random plantation and plot effects were prominent, but predictable using height measurements on a few sample trees from plots in individual plantations. The models are useful in generating accurate (localized) predictions of tree height which would eventually lead to better tree volume predictions and evaluation of site quality.

Curvas de altura-diâmetro de acácia negra (Acacia Mearnsii de Wild)

No presente estudo, a relação altura-diâmetro de Acacia mearnsii foi analisada em três diferentes regiões do Rio Grande do Sul, Brasil, em povoamentos com idades de oito, nove e dez anos, plantados com espaçamentos de 3 x 1,33m. Entre os modelos de regressão utilizados, foi selecionado o modelo de PRODAN, que apresentou um coeficiente de determinação (R²) de 0,98 e um erro padrão da média (Sxy%) menor que 9%. Foi aplicada a análise de covariância para testar o paralelismo das curvas de altura-diâmetro dos diferentes povoamentos, nas respectivas regiões. As relações das curvas de altura-diâmetro mostraram mesma inclinação nos diferentes povoamentos para toda a região, permitindo o uso de uma curva única para reestimar o coeficiente de intercepto para cada novo ponto de observação na respectiva região.

The process-based stand growth model Formix 3-Q applied in a GIS environment for growth and yield analysis in a tropical rain forest.

Managing tropical rain forests is difficult because few long-term field data on forest growth and the impact of harvesting disturbance are available. Growth models may provide a valuable tool for managers of tropical forests, particularly if applied to the extended forest areas of up to 100,000 ha that typically constitute the so-called forest management units (FMUs). We used a stand growth model in a geographic information system (GIS) environment to simulate tropical rain forest growth at the FMU level. We applied the process-based rain forest growth model Formix 3-Q to the 55,000 ha Deramakot Forest Reserve (DFR) in Sabah, Malaysia. The FMU was considered to be composed of single and independent small-scale stands differing in site conditions and forest structure. Field data, which were analyzed with a GIS, comprised a terrestrial forest inventory, site and soil analyses (water, nutrients, slope), the interpretation of aerial photographs of the present vegetation and topographic maps. Different stand types were determined based on a classification of site quality (three classes), slopes (four classes), and present forest structure (four strata). The effects of site quality on tree allometry (height-diameter curve, biomass allometry, leaf area) and growth (increment size) are incorporated into Formix 3-Q. We derived allometric relations and growth factors for different site conditions from the field data. Climax forest structure at the stand level was shown to depend strongly on site conditions. Simulated successional pattern and climax structure were compared with field observations. Based on the current management plan for the DFR, harvesting scenarios were simulated for stands on different sites. The effects of harvesting guidelines on forest structure and the implications for sustainable forest management at Deramakot were analyzed. Based on the stand types and GIS analysis, we also simulated undisturbed regeneration of the logged-over forest in the DFR at the FMU level. The simulations predict slow recovery rates, and regeneration times far exceeding 100 years.

Height-diameter curves with random intercepts and slopes for trees growing on drained peatlands

Models for predicting tree height were constructed for Scots pine ( Pinus sylvestris), Norway spruce ( Picea abies) and pubescent birch ( Betula pubescens). The data consisted of two separate sets of permanent sample plots forming a representative sample of drained peatland stands in the whole country. A logarithmic height-diameter curve with one nonlinear parameter specific to each tree species was applied. It was assumed that the intercept and slope of the curve would vary randomly from stand to stand. Stand characteristics were used to predict the mean intercept and slope. A nonhomogeneous variance of the residual error was modelled as a function of tree diameter. A mixed linear model technique was applied to fit the models. The diameter of the tree of the median basal area, stand basal area, geographical location of the stand, and site quality were used as fixed independent variables in explaining the variation in the intercept. The diameter of the tree of the median basal area and the stand basal area were used in explaining the variation in the slope.