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.

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.

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.

Modelling height-diameter relationships in complex tropical rain forest ecosystems using deep learning algorithm

Modelling tree height-diameter relationships in complex tropical rain forest ecosystems remains a challenge because of characteristics of multi-species, multi-layers, and indeterminate age composition. Effective modelling of such complex systems required innovative techniques to improve prediction of tree heights for use for aboveground biomass estimations. Therefore, in this study, deep learning algorithm (DLA) models based on artificial intelligence were trained for predicting tree heights in a tropical rain forest of Nigeria. The data consisted of 1736 individual trees representing 116 species, and measured from 52 0.25 ha sample plots. A K-means clustering was used to classify the species into three groups based on height-diameter ratios. The DLA models were trained for each species-group in which diameter at beast height, quadratic mean diameter and number of trees per ha were used as input variables. Predictions by the DLA models were compared with those developed by nonlinear least squares (NLS) and nonlinear mixed-effects (NLME) using different evaluation statistics and equivalence test. In addition, the predicted heights by the models were used to estimate aboveground biomass. The results showed that the DLA models with 100 neurons in 6 hidden layers, 100 neurons in 9 hidden layers and 100 neurons in 7 hidden layers for groups 1, 2, and 3, respectively, outperformed the NLS and NLME models. The root mean square error for the DLA models ranged from 1.939 to 3.887 m. The results also showed that using height predicted by the DLA models for aboveground biomass estimation brought about more than 30% reduction in error relative to NLS and NLME. Consequently, minimal errors were created in aboveground biomass estimation compared to those of the classical methods.

Culm form analysis for bamboo, Phyllostachys pubescens

We investigated the culm form for one of the largest bamboo species, Phyllostachys pubescens Mazel ex Houz. in relation to the me- chanical constraint principles, i.e., elastic, stress and geometric similarity. The fine-resolution analysis of the culm taper indicated that the culm for P. pubescens consisted of three or four segments with various forms, except for the butt swell. This implied that the taper of the whole culm for P. pubescens could be expressed by neither of these principles. The regression slope between culm height and diameter at breast height on the double logarithmic coordinates was 0.629, which was significantly different from the values predicted from these principles. In conclusion, none of these mechanical constraint principles can express the culm taper and height-diameter relationship, and there may be a need for a more complicated model to express the culm form for P. pubescens.

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.

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.

Determination of the Observation Area for Metallographic Microstructure of GH4033 Superalloy in a Uniaxially Thermo-Mechanical Compression Experiment

Based on two-dimensional （2D） rigid-plastic finite element （FE） method, the optimum observation area for metallographic microstructure and the influence of the height-diameter ratio on which were analyzed for the cylindrical samples with the diameter of 8 mm and different heights from 8 to 16 mm in nonuniform compressive experiments. It is shown that the representative metallographic observation area relevant to the applied deformation condition is located at about 0.835 of the radius from the center of the sample to the solder joint between the sample and the thermocouples. At the same time, the microstructure in that area is more appropriate as the height of the sample is 12 mm. The related parameters of GH4033 superalloy were adopted in the FE analysis, and the validity of this analysis was verified by the compressive experiments.