Generalized Height-diameter Models Research Articles

New generalized height-diameter models for birch in European Russia

Height and diameter at breast height are basic variables that are measured in a forest inventory. Generalized models do not require measuring tree heights or number of measurements is minimal. The purpose of this study was to obtain 24 new generalized height-diameter models based on simple basic models, compare them with 9 generalized models selected from other studies, and develop an appropriate height-diameter model for birch in the European Russia. To select models which better describe the relationship between the heights and diameters of the trees, six metrics were used – root mean square error (RMSE), mean absolute percentage error (MAPE), coefficient of determination (R2), adjusted coefficient of determination (R2-adj.), Akaike information criterion (AIC) and Bayesian information criterion (BIC). Results show that there are slight differences between all models. The performance statistics showed that model M24 is the most suitable and recommended for predicting the height-diameter relationships for birch trees in this study area. The predicting variables for applying developed generalized models to estimate total tree height require less sampling effort and are derived from conventional forest inventory data which allows to reduce costs and time consumption in field work.

A generalized nonlinear mixed-effects height–diameter model for Norway spruce in mixed-uneven aged stands

Tree height measurements are laborious and require more time and effort compared to tree diameter measurements. That being the case, height-diameter (H-D) models are usually used to predict individual tree heights, which are necessary for estimating the tree volume and the site index, as well as for projecting the stand development over time. Using a permanent sampling network (400x400m) from Retezat National Park in Romania, twenty-one (H-D) functions were evaluated for their fit performance, sensitivity to outliers and prediction ability for Norway spruce in mixed uneven aged stands. A set of twenty-three stand variables, both spatial and non-spatial, were used to describe the stand structure, species inter-mingling and competition, in order to be used as stand predictors in a generalized H-D model. Nonlinear mixed effects model was used in modelling the H-D relationship of Norway spruce. We developed the first generalized height-diameter model in Romania using three stand predictors as measures of the stand vertical structure, density and competition. Random and fixed effects calibration techniques were compared, testing various sampling designs in order to improve the height prediction accuracy of the model on a new dataset. Measuring six trees around the median and the thickest tree gave the best result in calibrating both fixed and random effects. On average, the best calibration design increased the accuracy of the prediction by 50 cm compared to the fixed effects prediction. The use of the estimated coefficients and the calibration design will significantly decrease the amount of work done by forest management planners, while ensuring high accuracy and reducing costs.

Mixed-effects generalized height–diameter model for young silver birch stands on post-agricultural lands

The purpose of creating regression equations is often to predict unmeasured features based upon more easily obtainable ones. Species-specific height–diameter (H–D) models of trees are an example of this situation and can be defined as either simple or generalized. Simple H–D models express height as a function of tree diameter at the breast height. They are easily applicable without additional measurement but do not take properly into account the variability in H-D relationship between stands. Meanwhile, generalized models also include stand-level predictors. The H-D data sets are often characterized by a grouped structure. The mixed-effects modeling approach is a mainstream method employed for these types of forestry data. In this study, we created a mixed-effects generalized H–D model for young silver birch stands on post-agricultural lands in central Poland. This model was chosen from among 11 simple nonlinear models based on the goodness of fit and residual behavior. We accounted for two stand-level predictors that did not require additional measurements beyond tree diameter at the breast height: quadratic mean diameter at the breast height and basal area. Fixed- and random-effect predictions were then calculated to illustrate that increases in the number of measured trees improves height predictions. Moreover, the gain in predictive power is the largest if extreme trees (i.e., from the extrema of the diameter range) are used for random-effect prediction.

A Mixed-effects Height-Diameter Model for Pinus kesiya in Malawi

A Mixed-effects Height-Diameter Model for Pinus kesiya in Malawi A height-diameter model was developed in order to predict the total height of individual trees in Pinus kesiya in Malawi. Six generalized height-diameter models were fitted and evaluated based on data set consisting of 18156 tree heights and corresponding diameters at breast height. The data were collected during three inventories of 332 permanent plots located in Chongoni, Malawi. A model including the diameter at breast height of the tree, stand age, site index, and basal area as independent variables was selected as the best model. To deal with the problem of among-unit variability, a non-linear mixed effects modelling approach was used to fit the selected model. The mixed model included a random parameter that affected the model and provided realistic height predictions. The equation developed represents a new tool for evaluation and management of Pinus kesiya stands in the region.

Nonlinear fixed and random generalized height–diameter models for Portuguese cork oak stands

The objective of the research was to develop a generalized height–diameter model for Quercus suber L. in Portugal, which can be applied both to undebarked and debarked trees, with diameter at breast height over cork larger than 2.5 cm. A nonlinear fixed effects model (NLFEM) and a nonlinear mixed effects model (NLMEM) approaches were used. Parameters estimates were obtained using the SAS macro NLINMIX, which uses a linear approximation to the marginal likelihood function by expanding it with a first-order Taylor series on the random effects. The option of expanding on the random effects at their current empirical best linear unbiased predictors (EBLUP) was used. The fitted models were evaluated using an independent data set, together with an existing model specific for undebarked trees. To obtain subject specific predictions with the NLMEM, a conventional and an improved calibration procedures were applied, considering four different tree sub-sampling designs. Both proposed models included dominant height and stand density as covariates to explain plot variability. Validation indicated that, even in the situations where the NLMEM calibration is not possible, this model should be preferred. The differences between the validated models, which were more evident for young stands, were considered. No large differences in predictive accuracy were found between the calibrated NLMEM using the conventional or the improved calibration procedures, for all the considered sub-sampling designs.

Generalized height-diameter models for Populus tremula L. stands

Using permanent sample plot data, selected tree height and diameter functions were evaluated for their predictive abilities for Populus tremula stands in Turkey. Two sets of models were evaluated. The first set included five models for estimating height as a function of individual tree diameter; the second set also included six models for estimating height as a function of individual tree diameter and some stand-level-attributes. The inclusion of the stand-level-attributes (basal area, dominant height, dominant diameter, number of trees) and BAL index (which simultaneously indicates the relative position of a tree and stand density) into the base height-diameter models increased the accuracy of prediction for P. tremula. As a result, the second set models gave high performance than the first models. On average, by including stand level attributes, root mean square values were reduced by 21 cm. In the second set, the best results were obtained by the Schnute’s function. In this function, dominant diameter and dominant height independent variables in addition to tree diameter were found significant at 0.01 significant level (R2= 0.949, , 0.01). Root mean square was reduced 35 cm Schnute’s function alone. Thus, a generalized height-diameter model based on Schnute’s function was developed for P. tremula L. stands in Turkey. Based on the residual plots and fit statistics, the model can be recommended for estimating tree heights for P. tremula L. in Turkey. The model coefficients are documented for future use. Key words: Schnute’s function, h-d models, Populus tremula L.

Generalized Height-Diameter Models for Acacia mangium willd. Plantations In South Sumatra

The aim of this study was to develop a generalized height-diameter model for predicting tree height of A caci a mangium plantations in South Sumatra that could account for the variability of site and stand conditions. Six commonly used non-linear growth functions (i.e. Gompertz, Chapman-Richards, Lundqvist-Korf, Weibull, modified logistic, and exponential) were selected as candidate base models and were fitted to individual tree’s height-diameter data of A . ma n g i u m plantations. A total of 13,302 trees collected from permanent sample plots with various spacing , stand age, and site quality were available for this study. The data were split into two sets: one set being the majority (75%) was used to estimate model parameters and the remaining data set (25%) was used to validate the models. The results showed that the six base models produced almost identical fits with a relatively high root mean squared error (± 3.4 m) and a relatively low proportion of the total variation in obser ved tree height (52.5 - 53.4%). The Lundqvist-Korf (LK) model performed slightly better than the other models based on the goodness of fit as well as bias and standard errors of the predictions. This LK model can be fitted easily and provided more satisfactory fit when additional variables were included into the model, hence was selected as the base model. Introducing stand variables into the selected base model resulted in a significant improvement of the accuracy for predicting heights. The root mean squared error decreased by the value between 0.5564 and 1.4252 m and the proportion of variation explained by the model increased by the value between 13.88 and 33.21%. The best improvement based on fit and model validation was achieved by the generalized height-diameter model with inclusion of stand age and site index.

A generalized nonlinear mixed-effects height–diameter model for Eucalyptus globulus L. in northwestern Spain

A generalized height–diameter model was developed for Eucalyptus globulus Labill. stands in Galicia (northwestern Spain). The study involved a variety of pure stands ranging from even-aged to uneven-aged. Data were obtained from permanent circular sample plots in which trees were sampled within different radii according to their diameter at breast height. A combination of weighted regression, to take into account the unequal selection probabilities of such an inventory design, and mixed model techniques, to accommodate local random fluctuations in the height–diameter relationship, were applied to estimate fixed and random parameters for several models reported in the relevant literature. The models that provided the best results included dominant height and dominant diameter as fixed effects. These models explained more than 83% of the observed variability, with mean errors of less than 2.5 m. Random parameters for particular plots were estimated with different tree selection options. Height–diameter relationships tailored to individual plots can be obtained by calibration of the height measurements of the three smallest trees in a plot. An independent dataset was used to test the performance of the model with data not used in the fitting process, and to demonstrate the advantages of calibrating the mixed-effects model.

A generalized height-diameter model with random coefficients for uneven-aged stands in El Salto, Durango (Mexico)

Summary A generalized height – diameter ( h - d ) model was developed in order to predict the total height of individual trees in uneven-aged stands in the region of El Salto, Durango (Mexico). Seven generalized h-d equations were evaluated and the equation proposed by Sharma and Parton, which includes the diameter at breast height of the tree and the quadratic mean diameter and the dominant height of the stand as independent variables, was selected as the best model. In order to address the among-plot variability, a non-linear mixed-effects modelling approach was used to fi t the selected model for all the species or groups of species. The mixed model included a random parameter that affected the model asymptote. Calibration of the obtained h-d model for a particular species or group of species in a plot of interest was carried out with only a single randomly selected tree from the species or group of species within the plot. The stochastic component added to the mixed-effects model enabled the observed natural variability in heights within diameter classes for the same stand to be mimicked, thereby providing more realistic predictions. The equation developed represents a new tool for evaluation and management of uneven-aged stands in the region.

A generalized height–diameter model including random components for radiata pine plantations in northwestern Spain

A generalized height–diameter ( h– d) model based on Schnute's function was developed for radiata pine ( Pinus radiata D. Don) plantations in Galicia (northwestern Spain). The study involved the estimation of fixed and random parameters by mixed-model techniques. The hierarchical structure of the data set, trees within plots, justifies the application of mixed-effects modelling. Techniques for calibrating the generalized height–diameter model for a particular plot of interest were also applied. For the experimental data analyzed, calibration can be used to obtain h– d relationships tailored to individual plots after measuring the height of only the three smallest trees in a plot. The main reason for the high predictive ability using this subsample of trees is that the dominant height of each plot was already considered as a fixed-effect in the height–diameter model formulation; therefore, heights corresponding to the largest trees did not provide much more additional information for calibrations. The model also included an unstructured random component to mimic the observed natural variability in heights within diameter classes for the same plot. This is an important aspect because the model will be applied to fill in the missing height measurements, subsequently used for assessing variables (e.g., volume, biomass, etc.) that depend on the estimated heights.

Generalized height–diameter models—an application for major tree species in complex stands of interior British Columbia

Using permanent sample-plot data, selected tree height and diameter functions were evaluated for their predictive abilities for major tree species in complex (multiple age, size and species cohort) stands of interior British Columbia (BC), Canada. Two sets of models were evaluated. The first set included five models for estimating height as a function of individual tree diameter, the second set also included five models for estimating height as a function of individual tree diameter and other stand-level attributes. The inclusion of the BAL index (which simultaneously indicates the relative position of a tree and stand density) into the base height–diameter models increased the accuracy of prediction for all species. On average, by including stand level attributes, root mean square values were reduced by 30.0 cm. Based on the residual plots and fit statistics, these models can be recommended for estimating tree heights for major tree species in complex stands of interior BC. The model coefficients are documented for future use.