Estimating Pinus palustris tree diameter and stem volume from tree height,crown area and stand-level parameters

Accurate and efficient estimation of forest growth and live biomass is a critical element in assessing potential responses to forest management and environmental change. The objective of this study was to develop models to predict longleaf pine tree diameter at breast height （dbh） and merchantable stem volume （V） using data obtained from field measurements. We used longleaf pine tree data from 3,376 planted trees on 127 permanent plots located in the U.S. Gulf Coastal Plain region to fit equations to predict dbh and V as functions of tree height （H） and crown area （CA）. Prediction of dbh as a function of H improved when CA was added as an additional independent variable. Similarly, predic- tions of V based on H improved when CA was included. Incorporation of additional stand variables such as age, site index, dominant height, and stand density were also evaluated but resulted in only small improvements in model performance. For model testing we used data from planted and naturally-regenerated trees located inside and outside the geographic area used for model fitting. Our results suggest that the models are a robust alternative for dbh and V estimations when H and CA are known on planted stands with potential for naturally-regenerated stands, across a wide range of ages. We discuss the importance of these models for use with metrics derived from remote sensing data.

Innovative deep learning artificial intelligence applications for predicting relationships between individual tree height and diameter at breast height

Background:Deep Learning Algorithms(DLA)have become prominent as an application of Artificial Intelligence(Al)Techniques since 2010.This paper introduces the DLA to predict the relationships between individual tree height(ITH)and the diameter at breast height(DBH).Methods:A set of 2024 pairs of individual height and diameter at breast height measurements,originating from 150 sample plots located in stands of even aged and pure Anatolian Crimean Pine(Pinus nigra J.F.Arnold ssp.pallasiana(Lamb.)Holmboe)in Konya Forest Enterprise.The present study primarily investigated the capability and usability of DLA models for predicting the relationships between the ITH and the DBH sampled from some stands with different growth structures.The 80 different DLA models,which involve different the alternatives for the numbers of hidden layers and neuron,have been trained and compared to determine optimum and best predictive DLAs network structure.Results:It was determined that the DLA model with 9 layers and 100 neurons has been the best predictive network model compared as those by other different DLA,Artificial Neural Network,Nonlinear Regression and Nonlinear Mixed Effect models.The alternative of 100#neurons and 9#hidden layers in deep learning algorithms resulted in best predictive ITH values with root mean squared error(RMSE,0.5575),percent of the root mean squared error(RMSE%,4.9504%),Akaike information criterion(AIC,-998.9540),Bayesian information criterion(BIC,884.6591),fit index(Fl,0.9436),average absolute error(AAE,0.4077),maximum absolute error(max.AE,2.5106),Bias(0.0057)and percent Bias(Bias%,0.0502%).In addition,these predictive results with DLAs were further validated by the Equivalence tests that showed the DLA models successfully predicted the tree height in the independent dataset.Conclusion:This study has emphasized the capability of the DLA models,novel artificial intelligence technique,for predicting the relationships between individual tree height and the diameter at breast height that can be required information for the management of forests.

Accuracy assessment and error analysis for diameter at breast height measurement of trees obtained using a novel backpack LiDAR system

Background: The LiBackpack is a recently developed backpack light detection and ranging(LiDAR) system that combines the flexibility of human walking with the nearby measurement in all directions to provide a novel and efficient approach to LiDAR remote sensing, especially useful for forest structure inventory. However, the measurement accuracy and error sources have not been systematically explored for this system.Method: In this study, we used the LiBackpack D-50 system to measure the diameter at breast height(DBH) for a Pinus sylvestris tree population in the Saihanba National Forest Park of China, and estimated the accuracy of LiBackpack measurements of DBH based on comparisons with manually measured DBH values in the field. We determined the optimal vertical slice thickness of the point cloud sample for achieving the most stable and accurate LiBackpack measurements of DBH for this tree species, and explored the effects of different factors on the measurement error.Result: 1) A vertical thickness of 30 cm for the point cloud sample slice provided the highest fitting accuracy(adjusted R2= 0.89, Root Mean Squared Error(RMSE) = 20.85 mm);2) the point cloud density had a significant negative, logarithmic relationship with measurement error of DBH and it explained 35.1% of the measurement error;3) the LiBackpack measurements of DBH were generally smaller than the manually measured values, and the corresponding measurement errors increased for larger trees;and 4) by considering the effect of the point cloud density correction, a transitional model can be fitted to approximate field measured DBH using LiBackpackscanned value with satisfactory accuracy(adjusted R2= 0.920;RMSE = 14.77 mm), and decrease the predicting error by 29.2%. Our study confirmed the reliability of the novel LiBackpack system in accurate forestry inventory, set up a useful transitional model between scanning data and the traditional manual-measured data specifically for P.sylvestris, and implied the applicable substitution of this new approach for more species, with necessary parameter calibration.

Modelling joint distribution of tree diameter and height using Frank and Plackett copulas

Bivariate distribution models are veritable tools for improving forest stand volume estimations.Their accuracy depends on the method of construction.To-date,most bivariate distributions in forestry have been constructed either with normal or Plackett copulas.In this study,the accuracy of the Frank copula for constructing bivariate distributions was assessed.The effectiveness of Frank and Plackett copulas were evaluated on seven distribution models using data from temperate and tropical forests.The bivariate distributions include:Burr III,Burr XII,Logit-Logistic,Log-Logistic,generalized Weibull,Weibull and Kumaraswamy.Maximum likelihood was used to fit the models to the joint distribution of diameter and height data of Pinus pinaster(184 plots),Pinus radiata(96 plots),Eucalyptus camaldulensis(85 plots)and Gmelina arborea(60 plots).Models were evaluated based on negative log-likelihood(-ΛΛ).The result show that Frank-based models were more suitable in describing the joint distribution of diameter and height than most of their Plackett-based counterparts.The bivariate Burr III distributions had the overall best performance.The Frank copula is therefore recommended for the construction of more useful bivariate distributions in forestry.

Ecoregional height-diameter models for Scots pine in Turkiye

Ecoregion-based height-diameter models were developed in the present study for Scots pine(Pinus sylves-tris L.)stands in Turkiye and included several ecological factors derived from a pre-existing ecoregional classification system.The data were obtained from 2831 sample trees in 292 sample plots.Ten generalized height–diameter models were developed,and the best model(HD10)was selected according to statistical criteria.Then,nonlinear mixed-effects modeling was applied to the best model.The R2 for the generalized height‒diameter model(Richards function)modified by Sharma and Parton is 0.951,and the final model included number of trees,dominant height,and diameter at breast height,with a random parameter associated with each ecoregion attached to the inverse of the mean basal area.The full model predictions using the nonlinear mixed-effects model and the reduced model(HD10)predictions were compared using the nonlinear sum of extra squares test,which revealed significant differences between ecore-gions;ecoregion-based height–diameter models were thus found to be suitable to use.In addition,using these models in appropriate ecoregions was very important for achieving reliable predictions with low prediction errors.

Optimization models of stand structure and selective cutting cycle for large diameter trees of broadleaved forest in Changbai Mountain

The optimum models of harvesting yield and net profits of large diameter trees for broadleaved forest were developed, of which include matrix growth sub-model, harvesting cost and wood price sub-models, based on the data from Hongshi Forestry Bureau, in Changbai Mountain region, Jilin Province, China. The data were measured in 232 permanent sample plots. With the data of permanent sample plots, the parameters of transition probability and ingrowth models were estimated, and some models were compared and partly modified. During the simulation of stand structure, four factors such as largest diameter residual tree （LDT）, the ratio of the number of trees in a given diameter class to those in the next larger diameter class （q）, residual basal area （RBA） and selective cutting cycle （C） were considered. The simulation results showed that the optimum stand structure parameters for large diameter trees are as follows： q is 1.2, LDT is 46cm, RBA is larger than 26 m^2 and selective cutting cycle time （C） is between 10 and 20 years.

An approach to estimate tree height using PolInSAR data constructed by the Sentinel-1 dual-pol SAR data and RVoG model

We estimate tree heights using polarimetric interferometric synthetic aperture radar(PolInSAR)data constructed by the dual-polarization(dual-pol)SAR data and random volume over the ground(RVoG)model.Considering the Sentinel-1 SAR dual-pol(SVV,vertically transmitted and vertically received and SVH,vertically transmitted and horizontally received)configuration,one notes that S_(HH),the horizontally transmitted and horizontally received scattering element,is unavailable.The S_(HH)data were constructed using the SVH data,and polarimetric SAR(PolSAR)data were obtained.The proposed approach was first verified in simulation with satisfactory results.It was next applied to construct PolInSAR data by a pair of dual-pol Sentinel-1A data at Duke Forest,North Carolina,USA.According to local observations and forest descriptions,the range of estimated tree heights was overall reasonable.Comparing the heights with the ICESat-2 tree heights at 23 sampling locations,relative errors of 5 points were within±30%.Errors of 8 points ranged from 30%to 40%,but errors of the remaining 10 points were>40%.The results should be encouraged as error reduction is possible.For instance,the construction of PolSAR data should not be limited to using SVH,and a combination of SVH and SVV should be explored.Also,an ensemble of tree heights derived from multiple PolInSAR data can be considered since tree heights do not vary much with time frame in months or one season.

Stress-strain-acoustic responses in failure process of coal rock with different height to diameter ratios under uniaxial compression

Residual coal pillars play an important role in mining the adjacent coal seam safely,managing the gobs and maintaining the stability of abandoned coal mines.The height to diameter ratio(H/D)affects the stability of residual coal pillars.In this study,uniaxial compressive tests of coal specimens with five H/D(2.0,1.5,1.0,0.8 and 0.6)were performed,and the stress,strain and acoustic emission(AE)were monitored.Results show that the uniaxial compressive strength(UCS)and peak strain increase with H/D decreasing.An empirical equation is proposed to calculate the UCS based on the H/D.The AE activities during coal failure process can be separated into four periods.The span of quiet period and rapid decline period shorten with H/D decreasing.The smaller the H/D is,the more complicated the failure characteristics of coal will be.The failure form of coal with H/D of 2.0,1.5,and 1.0 is primarily shear failure,while splitting failure along the axial direction is the mainly mode when H/D is 0.8 or 0.6.The initiation,expansion,aggregation and connection of micro-cracks can be reflected by the real-time spatial evolution of AE event points.

Stand structure and height-diameter relationship of a degraded Populus euphratica forest in the lower reaches of the Tarim River, Northwest China

Understanding stand structure and height-diameter relationship of trees provides very useful information to establish appropriate countermeasures for sustainable management of endangered forests. Populus euphratica, a dominant tree species along the Tarim River watershed, plays an irreplaceable role in the sustainable development of regional ecology, economy and society. However, as the result of climate changes and human activities, the natural riparian ecosystems within the whole river basin were degraded enormously, particularly in the lower reaches of the river where about 320 km of the riparian forests were either highly degraded or dead. In this study, we presented one of the main criteria for the assessment of vitality of P. euphrafica forests by estimating the defoliation level, and analyzed forest structure and determined the height-diameter （height means the height of a tree and diameter means the diameter at breast height （DBH） of a tree） relationship of trees in different vitality classes （i.e. healthy, good, medium, senesced, dying, dead and fallen）. Trees classified as healthy and good ac- counted for approximately 40% of all sample trees, while slightly and highly degraded trees took up nearly 60% of total sample trees. The values of TH （tree height） and DBH ranged from 0-19 m and 0-125 cm, respectively. Trees more than 15 m in TH and 60 cm in DBH appeared sporadically. Trees in different vitality classes had different distribution patterns. Healthy trees were mainly composed more of relatively younger trees than of degraded tress. The height-diameter relationships differed greatly among tress in different vitality classes, with the coefficients ranging from 0.1653 to 0.6942. Correlation coefficients of TH and DBH in healthy and good trees were higher than those in trees of other vitality classes. The correlation between TH and DBH decreased with the decline of tree vitality. Our results suggested that it might be able to differentiate degraded P. euphratica trees from healthy trees by determining the height-diameter correlation coefficient, and the coefficient would be a new parameter for detecting degradation and assessing sustainable management of floodplain forests in arid regions. In addition, tree vitality should be taken into account to make an accurate height-diameter model for tree height prediction.

Trees with Given Diameter Minimizing the Augmented Zagreb Index and Maximizing the ABC Index

Let G be a simple connected graph with vertex set V（G） and edge set E（G）.The augmented Zagreb index of a graph G is defined asAZI（G） =∑uv∈E（G）(d;d;/（d;+ d;-2）);,and the atom-bond connectivity index（ABC index for short） of a graph G is defined asABC（G） =∑uv∈E（G）(（d;+ d;-2）/d;d;),where d;and d;denote the degree of vertices u and v in G,respectively.In this paper,trees with given diameter minimizing the augmented Zagreb index and maximizing the ABC index are determined,respectively.

On the Spectral Radius of Trees with the Given Diameter d

Let T denote a tree with the diameter d(d≥2) and order n. Let Pd,r,n-d-1 denote the tree obtained by identifying the rth vertex of path Pd+1 and the center of star K1,n-d-1, where r = r(d) is the integer part about d+2/2. Then p(T) ≤p(Pd,r,n-d-1),and equality holds if and only if T≌ Pd,r,n-d-1

THE CUTWIDTH OF TREES WITH DIAMETER AT MOST 4

The cutwidth problem for a graph G is to embed G into a path P n such that the maximum number of overlap edges (i.e., the congestion) is minimized. It is known that the problem for general graphs is NP-hard while it is polynomially solvable for trees. This paper presents an exact formula for the cutwidth of trees with diameter at most 4. A relation with the bandwidth is discussed as well.

On the Maximum Spectral Radius of (m,n)-trees with Given Diameter

Let （V, U） be the vertex-partition of tree T as a bipartite graph. T is called an （m, n）-tree if ｜V｜ = m and ｜U｜ = n. For given positive integers m, n and d, the maximum spectral radius of all （m, n）-trees on diameter d are obtained, and all extreme graphs are determined.

Incorporating shape constraints in generalized additive modelling of the height-diameter relationship for Norway spruce

Background： Measurements of tree heights and diameters are essential in forest assessment and modelling. Tree heights are used for estimating timber volume, site index and other important variables related to forest growth and yield, succession and carbon budget models. However, the diameter at breast height （dbh） can be more accurately obtained and at lower cost, than total tree height. Hence, generalized height-diameter （h-d） models that predict tree height from dbh, age and other covariates are needed. For a more flexible but biologically plausible estimation of covariate effects we use shape constrained generalized additive models as an extension of existing h-d model approaches. We use causal site parameters such as index of aridity to enhance the generality and causality of the models and to enable predictions under projected changeable climatic conditions. Methods： We develop unconstrained generalized additive models （GAM） and shape constrained generalized additive models （SCAM） for investigating the possible effects of tree-specific parameters such as tree age, relative diameter at breast height, and site-specific parameters such as index of aridity and sum of daily mean temperature during vegetation period, on the h-d relationship of forests in Lower Saxony, Germany. Results： Some of the derived effects, e.g. effects of age, index of aridity and sum of daily mean temperature have significantly non-linear pattern. The need for using SCAM results from the fact that some of the model effects show partially implausible patterns especially at the boundaries of data ranges. The derived model predicts monotonically increasing levels of tree height with increasing age and temperature sum and decreasing aridity and social rank of a tree within a stand, The definition of constraints leads only to marginal or minor decline in the model statistics like AIC An observed structured spatial trend in tree height is modelled via 2-dimensional surface fitting. Conclusions： We demonstrate that the SCAM approach allows optimal regression modelling flexibility similar to the standard GAM but with the additional possibility of defining specific constraints for the model effects. The longitudinal character of the model allows for tree height imputation for the current status of forests but also for future tree height prediction.

Modeling of the height–diameter relationship using an allometric equation model:a case study of stands of Phyllostachys edulis

Understanding the relationship between tree height （H） and diameter at breast height （D） is vital to forest design, monitoring and biomass estimation. We developed an allometric equation model and tested its applicability for unevenly aged stands of moso bamboo forest at a regional scale. Field data were collected for 21 plots. Based on these data, we identified two strong power relationships： a corre- lation between the mean bamboo height （Hm） and the upper mean H （Hu）, and a correlation between the mean D （Din） and the upper mean D （Du）. Simulation results derived from the aUometric equation model were in good agreement with observed culms derived from the field data for the 21 stands, with a root-mean-square error and relative root-mean-square error of 1.40 m and 13.41%, respectively. These results demonstrate that the allometric equation model had a strong predictive power in the unevenly aged stands at a regional scale. In addition, the estimated average height-diameter （H-D） model for South Anhui Province was used to predict H for the same type of bamboo in Hunan Province based on the measured D, and the results were highly similar. The allometric equation model has multiple uses at the regional scale, including the evaluation of the variation in the H- D relationship among regions. The model describes the average H-D relationship without considering the effects caused by variation in site conditions, tree density and other factors.

Survivorship, attained diameter, height and volume of three Paulownia species after 9 years in the southern Appalachians, USA

Little is known of the tree and stand dynamics of varied species of planted Paulownia left unmanaged until harvest in the southeastern United States.We sought to remedy this lack of information needed by land managers to make informed decisions by investigating diff erences in survivorship,attained diameter breast height(DBH),diameter at ground level,total height,tree volume and standlevel volume yields of planted P.elongata,P.fortunei,and P.tomentosa in the cool-moist environment of the southern Appalachian Mountains.After 9 years,combined-species survivorship was only 27.3%.Low survivorship was likely related to several inclement weather events.P.fortunei was signifi cantly smaller in DBH and total height.Three combined-species stem(bole)volume models were developed as functions of(1)DBH squared,(2)the product DBH squared and total height,and(3)the product diameter ground line squared and total height.Mean total volume production of unmanaged stands was greatest for P.elongata and P.fortunei 4 years after planting;by the 9th year,total volume of P.elongata was greater than the other two species.Results of our study provide managers information on productivity of three species of Paulownia that can be used for estimating plantation yields.

Results on energies for trees with a given diameter having perfect matching

Let Γd2nbe the set of trees with a given diameter d having a perfect matching,where 2n is the number of vertex.For a tree T in Γd2n,let Pd＋1be a diameter of T and q = d m,where m is the number of the edges of perfect matching inPd＋1.It can be found that the trees with minimal energy in Γd2nfor four cases q = d 2,d 3,d 4,[d2],and two remarks aregiven about the trees with minimal energy in Γd2nfor2d 33q d 5 and [d2] ＋ 1 q2d 33 1.

New approach to calculating tree height at the regional scale

Background:Determining the spatial distribution of tree heights at the regional area scale is significant when performing forest above-ground biomass estimates in forest resource management research.The geometric-optical mutual shadowing(GOMS)model can be used to invert the forest canopy structural parameters at the regional scale.However,this method can obtain only the ratios among the horizontal canopy diameter(CD),tree height,clear height,and vertical CD.In this paper,we used a semi-variance model to calculate the CD using high spatial resolution images and expanded this method to the regional scale.We then combined the CD results with the forest canopy structural parameter inversion results from the GOMS model to calculate tree heights at the regional scale.Results:The semi-variance model can be used to calculate the CD at the regional scale that closely matches(mainly with in a range from-1 to 1 m)the CD derived from the canopy height model(CHM)data.The difference between tree heights calculated by the GOMS model and the tree heights derived from the CHM data was small,with a root mean square error(RMSE)of 1.96 for a 500-m area with high fractional vegetation cover(FVC)(i.e.,forest area coverage index values greater than 0.8).Both the inaccuracy of the tree height derived from the CHM data and the unmatched spatial resolution of different datasets will influence the accuracy of the inverted tree height.And the error caused by the unmatched spatial resolution is small in dense forest.Conclusions:The semi-variance model can be used to calculate the CD at the regional scale,together with the canopy structure parameters inverted by the GOMS model,the mean tree height at the regional scale can be obtained.Our study provides a new approach for calculating tree height and provides further directions for the application of the GOMS model.

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

Background： Generalized height-diameter curves based on a re-parameterized version of the Korf function for Norway spruce （Piceo abies （L.） Karst.）, Scots pine （Pinus sylvestris L.） and silver birch （Betula pendula Roth） in Norwa 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 imputatio in forest inventories as well as future tree height predictions in growth and yield scenario simulations. Methods： Generalized 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 ag 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 （scare） were fit tc incorporate expert knowledge and intrinsic relationships by enforcing certain effect patterns like monotonicity. Results： Model 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. / two-dimensional spatially structured effect of UTM-coordinates accounts for the potential effects of large scale spatial 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. Conclusions： In 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, scare may provide methodological improvements in several applications by combining the flexibility of additive models with expert knowledge.

Predicting the Growth in Tree Height for Building Sunshine in Residential District

Residential greening constitutes a significant portion of the urban environment. Trees, as the largest entities in the tree-shrub-herb greening system, are the best choice for residential afforestation. Hence, tree arrangement in green space between buildings is significant, for which may exert negative impact on building sunshine. This study takes He Qingyuan residential area in Beijing as a case study to predict the growth in tree height between buildings to meet good sunshine requirements. The procedures were draw as follows: 1) models including building layout and trees were built using computer-aided design (Auto CAD). Afterwards, according to tree crown shape, tree height limits were determined for the same building layout;2) and after that, the growth in tree height was predicted using the nonlinear height-diameter functions to meet the good sunshine requirements. The results allow us to determine which trees to plant between buildings in that the designers can predict the effects of future tree growth on building sunshine.