Prediction Of Diameter Distribution Research Articles

Spatial Prediction of Diameter Distributions for the Alpine Protection Forests in Ebensee, Austria, Using ALS/PLS and Spatial Distributional Regression Models

A novel Bayesian spatial distributional regression model is presented to predict forest structural diversity in terms of the distributions of the stem diameter at breast height (DBH) in the protection forests in Ebensee, Austria. The distributional regression approach overcomes the limitations and uncertainties of traditional regression modeling, in which the conditional mean of the response is regressed against explanatory variables. The distributional regression addresses the complete conditional response distribution, instead. In total 36,338 sample trees were measured via a handheld mobile personal laser scanning system (PLS) on 273 sample plots each having a 20 m radius. Recent airborne laser scanning (ALS) data were used to derive regression covariates from the normalized digital vegetation height model (DVHM) and the digital terrain model (DTM). Candidate models were constructed that differed in their linear predictors of the two gamma distribution parameters. In the distributional regression approach, covariates can enter the model in a flexible form, such as via nonlinear smooth curves, cyclic smooths, or spatial effects. Supported by Bayesian diagnostics DIC and WAIC, nonlinear smoothing splines outperformed linear parametric slope coefficients, and the best implementation of spatial structured effects was achieved by a Gaussian process smooth. Model fitting and posterior parameter inference was achieved by using full Bayesian methodology and MCMC sampling algorithms implemented in the R-package BAMLSS. With BAMLSS, spatial interval predictions of the DBH distribution at any new geo-locations were enabled via straightforward access to the posterior predictive distributions of the model terms and by offering simple plug-in solutions for new covariate values. A cross-validation analysis validated the robustness of the proposed method’s parameter estimation and out-of-sample prediction. Spatial predictions of stem count proportions per DBH classes revealed that regeneration of smaller trees was lacking in certain areas of the protection forest landscape. Therefore, the intensity of final felling needs to be increased to reduce shading from the dense, overmature shelter trees and to promote sunlight for the young regeneration trees.

Predicting parameters of Weibull probability density function for diametric distributions in A. melanoxylon, E. camaldulensis, and E. nitens bioenergy plantation

Precise modeling of stand diameter distributions is required to provide accurate estimates of volume per diameter class and unit area. Therefore, it is necessary to obtain the most accurate probability density functions parameters estimates to predict stand diameter distribution in time. We evaluate two methods to estimate the parameters of the Weibull probability density function in the modeling of diameter distributions of bioenergy plantations. The methods considered a direct method of parameter prediction based on regression models (PPRM) and an indirect method of parameter recovery through the determination of percentiles (PRDP). Both methods are considered systems of linear equations and are adjusted through simultaneous estimation of parameters using stand variables. The greatest precision was obtained with PPRM. The PRDP method was not effective in the prediction of diameter distributions due to the high level of truncation of the observed distributions showing an overestimation of the distribution for the largest diameter classes. Estimated parameters of the Weibull PDF are directly related to mean height, quadratic mean diameter, and crop age; and are inversely related to stocking.

Prediction of diameter distributions in boreal forests using remotely sensed data

Prediction of diameter distributions in boreal forests using remotely sensed data

Fusing diameter distributions predicted by an area-based approach and individual-tree detection in coniferous-dominated forests

An area-based approach (ABA) is the most common method used to predict forest attributes with airborne laser scanning (ALS) data. Individual-tree detection (ITD) offers an alternative to ABA; however, few studies have examined the selection of these two alternatives for the prediction of diameter distributions. We predicted diameter distributions by applying ABA and ITD in coniferous-dominated boreal forests using ALS data and examined their predictive performance based on the shapes of the diameter distributions (Gaussian, bimodal, and reverse-J). We proposed an ABA–ITD fusion for diameter distribution prediction. Firstly, the fusion was optimized and its potential was evaluated using an error index. Secondly, we offer two alternatives to incorporate the fusion into ALS-based forest inventories. Our results indicate that ITD is more prone to errors than ABA and that the predictive performance of ITD is more sensitive than ABA to the shape of the diameter distribution. The results show that ITD outperforms ABA with Gaussian diameter distributions. In contrast, ABA was seen as preferable to ITD with bimodal- or reverse-J-shaped diameter distributions. The findings indicate that ABA–ITD fusion has potential for predicting diameter distributions, although the predictive capability of ITD is limited compared with that of ABA.

Prediction of diameter distributions and tree-lists in southwestern Oregon using LiDAR and stand-level auxiliary information

Diameter distributions and tree-lists provide information about forest stocks disaggregated by size and species and are key for informing forest management. Diameter distributions and tree-lists are multivariate responses, which makes the evaluation of methods for their prediction reliant on the use of dissimilarity metrics to summarize differences between observations and predictions. We compared four strategies for selection of k nearest neighbors (k-NN) methods to predict diameter distributions and tree-lists using LiDAR and stand-level auxiliary data and analyzed the effect of the k-NN distance and number of neighbors in the performance of the predictions. Strategies differed by the dissimilarity metric used to search for optimal k-NN configurations and the presence or absence of post-stratification. We also analyzed how alternative k-NN configurations ranked when tree-lists were aggregated using different DBH classes and species groupings. For all dissimilarity metrics, k-NN configurations using random-forest distance and three or more neighbors provided the best results. Rankings of k-NN configurations based on different dissimilarity metrics were relatively insensitive to changes on the width of the DBH classes and the definition of the species groups. The selection of the k-NN methods was clearly dependent on the choice of the dissimilarity metric. Further research is needed to find suitable ways to define dissimilarity metrics that reflect how forest managers evaluate differences between predicted and observed tree-lists and diameter distributions.

Prediction of Diameter Distributions with Multimodal Models Using LiDAR Data in Subtropical Planted Forests

Tree diameter distributions are essential for the calculation of stem volume and biomass, as well as simulation of growth and yield and to understand timber assortments. Accurate and reliable prediction of tree diameter distributions is critical for optimizing forest structure compositions, scheduling silvicultural operations and promoting sustainable management. In this study, we investigated the potential of airborne Light Detection and Ranging (LiDAR) data for predicting tree diameter distributions using a bimodal finite mixture model (FMM) and a multimodal k-nearest neighbor (KNN) model (compared to the unimodal Weibull model (UWM)) over a subtropical planted forest in southern China. To do so, we first evaluated the capability of various LiDAR predictions (i.e., the bimodality coefficient (BC) and Lorenz-based indicators) to stratify forest structural types into unimodal and multimodal stands. Once the best LiDAR prediction for the differentiation was determined, the parameters of UWM (in non-specific and species-specific models) and FMM (in structure-specific models) were estimated by LiDAR-derived metrics and the tree diameter distributions of stands were generated by the estimated LiDAR parameters. When KNN was applied for constructing diameter distributions, optimal KNN strategies, including number of neighbors k, response configurations and imputation methods (i.e., Most Similar Neighbor (MSN) and Random Forest (RF)) for different species were heuristically determined. Finally, the predictive performance of estimated LiDAR the parameters of UWM, FMM and KNN for predicting diameter distributions were assessed. The results showed that LiDAR-predicted Lorenz-based indicators performed best for differentiation. Parameters of UWM and FMM were predicted well and the species-specific models had higher accuracies than the non-specific models. Overall, RF imputation from KNN with an optimal response set (i.e., DBH) were was stable than MSN imputation when k = 5 neighbors. In addition, the inclusion of bimodal FMM for differentiated all plots generally produced a more accurate result (Mean eR = 40.85, Mean eP = 0.20) than multimodal KNN (Mean eR = 52.19, Mean eP = 0.26), whereas the UWM produced the lowest performance (Mean eR = 52.31, Mean eP = 0.26). This study demonstrated the benefits of multimodal models with LiDAR for estimating diameter distributions for supporting forest inventory and sustainable forest management in subtropical planted forests.

An Examination of Diameter Density Prediction with k-NN and Airborne Lidar

While lidar-based forest inventory methods have been widely demonstrated, performances of methods to predict tree diameters with airborne lidar (lidar) are not well understood. One cause for this is that the performance metrics typically used in studies for prediction of diameters can be difficult to interpret, and may not support comparative inferences between sampling designs and study areas. To help with this problem we propose two indices and use them to evaluate a variety of lidar and k nearest neighbor (k-NN) strategies for prediction of tree diameter distributions. The indices are based on the coefficient of determination (R2), and root mean square deviation (RMSD). Both of the indices are highly interpretable, and the RMSD-based index facilitates comparisons with alternative (non-lidar) inventory strategies, and with projects in other regions. K-NN diameter distribution prediction strategies were examined using auxiliary lidar for 190 training plots distribute across the 800 km2 Savannah River Site in South Carolina, USA. We evaluate the performance of k-NN with respect to distance metrics, number of neighbors, predictor sets, and response sets. K-NN and lidar explained 80% of variability in diameters, and Mahalanobis distance with k = 3 neighbors performed best according to a number of criteria.

The prediction of single-tree biomass, logging recoveries and quality attributes with laser scanning techniques

The precise knowledge of forest structural attributes, such as biomass, logging recoveries and quality of the available timber, play an essential role in decision-making, forest management procedure planning and in wood supply chain optimization. Remote sensing-aided mapping applications are used intensively to acquire required forest resource information. Laser scanning (LS) is one of the most promising remote sensing techniques, which can be used to estimate forest attributes at all levels, from single trees to global applications. The main objectives of the present thesis were to develop LS-based methodologies for mapping and measuring single trees. More specifically, new high-density LS-based models and methodologies were developed for the prediction of aboveground biomass (AGB), logging recovery, stem curve and external tree quality estimation. Multisource remote sensing methodologies were additionally introduced for the detailed next generation forest-inventory process. Substudies I and II concentrated on developing LS-based biomass models. Total AGB was estimated with the relative root mean squared errors (RMSE%) of 12.9% and 11.9% for Scots pine (Pinus sylvestris L.) and Norway spruce (Picea abies (L.) H.Karst.), respectively using terrestrial LS (TLS) -derived predictors in multiple regression modelling. TLS-based AGB models significantly improved the estimation accuracy of AGB components compared to state-of-the-art allometric biomass models. Airborne LS (ALS) resulted in slightly higher RMSE% values of 26.3% and 36.8% for Scots pine and Norway spruce compared to results obtained with TLS. The goal of substudies III and IV was to predict timber assortment and tree quality information using high-density LS data. Sawlog volumes were estimated with RMSE% of 17.5% and 16.8% with TLS and a combination of TLS and ALS, respectively. Tree quality is an important factor for accurate and successful timber assortment estimation. The use of TLS data showed high potential for tree quality assessment. Results in IV showed that trees could be successfully classified in different quality classes based on TLS-measured attributes with accuracies between 76.4% and 83.6% depending on the amount of quality classes. Substudies V and VI presented new automatic processing tools for TLS data and a multisource approach for the more detailed prediction of diameter distribution. Automatic processing of TLS data was demonstrated to be effective and accurate and could be utilized to make future TLS measurements more efficient. Accuracies of ~1 cm were achieved using the automatic stem curve procedure. The multisource single-tree inventory approach combined accurate treemaps produced automatically from the TLS data, and ALS individual tree detection technique for predicting forest preharvest information. Results from diverse forest conditions were promising, resulting in diameter prediction accuracies between 1.4 cm and 4.7 cm depending on tree density and main tree species. Each substudy (I–VI) presented new methods and results for single-tree AGB modelling, external tree quality classification, automatic stem reconstruction and multisource approaches.

A dynamic volume and biomass growth model system for even-aged downy birch stands in south-western Europe

This study develops some components to complete a management-oriented dynamic model system for simulating current and future volume and biomass of even-aged stands of managed downy birch (Betula pubescens Ehrh.) in Galicia (NW Spain). The specific components developed are a mortality equation, a basal area growth equation, a diameter distribution prediction system and equations for total and component biomass prediction. Functions to predict decreases in numberof trees per hectare and basal area growth were simultaneously fitted using Nonlinear Seemingly Unrelated Regression (NSUR) and a base-age invariant dummy variable method; critical errors of 19 and 16 per cent were obtained, respectively, when projections were made. The Weibull function modelled successfully all but four of the 198 diameter distributions examined, using the parameter recovery method through moments. To predict components and total aboveground biomass, a system of additive equations was simultaneously fitted using the generalized method of moments (GMM), which takes into account heteroscedasticity and inherent correlations among the biomass components. A two-step fitting procedure was used because of the different number of observations for the components considered. The biomass equations explained more than 85 per cent of the observed variability. The Galician birch stands which were surveyed were found to have grown by 3–10 m ha year in volume and by 2–8 Mg ha year in aboveground total biomass, with rotations between 30 and 60 years. The model system now forms an accessible decision support system for forest management and land development in the region.

Comparison of basal area and stem frequency diameter distribution modelling using airborne laser scanner data and calibration estimation

The diameter distribution of a forest stand is of primary importance for deriving various stand characteristics, but measuring the diameters of a tree stock is rather time-consuming, so theoretical diameter distribution models are usually employed. We examine here the prediction of diameter distribution using information obtained from airborne laser scanning (ALS). The aim is to compare the accuracy of ALS-based stem frequency and basal area diameter distribution models and the usability of calibration to adjust the predicted distributions to be compatible with the ALS based estimated stand volume. A network of 472 sample plots of 9 m radius was established in a typical managed boreal forest area in eastern Finland. ALS data were acquired from an altitude of 1500 m above ground level, which produced a sampling density of about 0.7 pulses per square metre. A two-parameter Weibull function was employed to determine field-measured stem frequency and basal area diameter distributions using maximum likelihood estimation, and these parameters together with the number of stems, basal area and stand volume were then regressed simultaneously using ALS-based characteristics as explanatory variables. Predicted basal area diameter distribution from each plot was scaled using the ALS-based estimate for the basal area, and the stem frequency diameter distribution was scaled using the ALS-based estimate for the stem number. Finally, the distributions were calibrated against volume, basal area and number of stems which were ALS data based model estimates. Without calibration estimation the accuracy of the volume prediction was almost equal for both distribution types (basal area and stem frequency). However, calibration estimation improved the accuracy of the volume estimates of both distribution types and also of the stem number estimates in the case of the basal area distribution.

The use of quantile trees in the prediction of the diameter distribution of a stand

This study deals with the prediction of the basal area diameter distribution of a stand without using a complete sample of diameters from the target stand. Traditionally, this problem has been solved by either the parameter recovery method or the parameter prediction method. This study uses the parameter prediction method and the percentile based diameter distribution with a recent development that makes it possible to improve these predictions by using sample order statistics. A sample order statistic is a tree whose diameter and rank at the plot are known, and is referred to in this paper as a quantile tree. This study tested 13 different strategies for selection of the quantile trees from among the trees of horizontal point sample plots, and compared them with respect to RMSE and the bias of four criterion variables in a dataset of 512 stands. The sample minimum was found to be the most promising alternative with respect to RMSE, even though it introduced a rather large amount of bias in the criterion variables. Other good and less biased alternatives are the second and third smallest trees and the tree closest to the plot centre. The use of minimum is recommended for practical inventories because its rank is probably easiest to determine correctly in the field.

Bayesian estimation of diameter distribution during harvesting

This research aims to combine two different data sets with Bayesian statistics in order to predict the diameter distribution of trees at harvest. The parameters of prior distribution are derived from the forest management plans supplemented by additional ocular information. We derive the parameters for the sample data from the first trees harvested, and then create the posterior distribution within the Bayesian framework. We apply the standard normal distribution to construct diameter (dbh) distributions, although many other theoretical distributions have been proved better with dbh data available. The methodology developed is then tested on nine mature spruce (Picea abies) dominated stands, on which the normal distribution seems to work well in mature spruce stands. The tests indicate that prediction of diameter distribution for the whole stand based on the first trees harvested is not wise, since it tends to give inaccurate predictions. Combining the first trees harvested with prior information seems to increase the reliability of predictions.

Localizing a Predicted Diameter Distribution Using Sample Information

Abstract This study presents a new method for predicting the diameter distribution of a stand, utilizing the percentile-based diameter distribution. The expected diameter percentiles are first predicted using stand measurements. Subsequently, the distribution is calibrated (localized) for the stand using sample order statistics, which consist of one or more diameters of sample trees and their ranks on the sample plot(s). These measurements can be quickly carried out in the field, because the rank can be assessed visually. The sample order statistics can be interpreted as measured sample percentiles. The expectations, variances, and covariances of the measured sample order statistics are derived using the theory of order statistics. Regression models are used to predict the conditional expectations of predefined percentiles, which are then combined with the measured percentiles using the best linear unbiased predictor. The method was tested in a real data set using simulated sample plots. The test showed that, even with a small number of sample measurements, the relative root mean square error and bias of volume per hectare could be decreased remarkably. Furthermore, increasing the number of measurements steadily improved the prediction. The proposed method seems to be a promising tool in the prediction of diameter distributions of various forms, including those found in complex stands. FOR. SCI. 51(4):292–303.

Basal Area and Diameter Distribution Prediction Equations for Young Douglas-Fir Plantations with Hardwood Competition: Coast Ranges

Abstract A stand-level modeling system for young Douglas-fir plantations applicable to the Coast Ranges of the Pacific Northwest was developed by using data from 84 growth-monitoring plots. Specific components of the system for predicting current size distributions of planted Douglas-fir include: dominant height and survival of planted Douglas-fir; a basal area projection equation for hardwoods; and diameter distribution percentile prediction functions for planted Douglas-fir. Prediction equations for height, crown width, and height to crown base of individual trees describe stand structure of the planted Douglas-fir. The stand- and tree-level equations include both direct and indirect effects of hardwood competition and site preparation, competition release, and precommercial thinning treatments. With the exception of minimum dbh, stand-level equations for planted Douglas-fir explained at least 92% of the observed variation. Basal area dynamics were simulated through plantation age 20 years for site preparation and competition release treatments of different effectiveness by varying hardwood basal area at plantation age 5 years. The simulations indicate that site preparation must reduce hardwood basal area at plantation age 5 years by 75% or more to realize an increase in Douglas-fir basal area and shift of the diameter distribution toward larger trees. This is due to increased growth of hardwoods that survive site preparation. In contrast, competition release treatments exhibited positive Douglas-fir response with 50% efficacy or more. Therefore, ineffective site preparation treatments need to be followed with competition release treatments having at least 50% efficacy to produce similar Douglas-fir basal area and diameter distributions at age 20 as in stands with no site preparation. West. J. Appl. For. 20(2):77–93.

Spatial prediction of diameter distribution models

The prediction of the diameter distribution of a stand is of great interest to forest managers for the evaluation of forest resources and scheduling the future silvicultural treatments. In the present paper, we present a geostatistical approach for the prediction of diameter distributions. The advantage of the proposed method over traditional prediction systems is that it is possible to estimate the diameter distribution at locations, where no secondary variables are measured. The Weibull and the Chaudhry–Ahmad probability density functions were fitted by maximum likelihood to the diameter distribution of 176 plots of pure, even aged stands of Pinus pinaster Ait. located in the province of Segovia of central Spain. Data were taken from the Second National Forest Inventory of Spain. The spatial “behaviour” of the parameters of the density functions was studied by variogram analysis and the results showed that all parameters were spatially correlated to some extent. Kriging was used for the interpolation of parameters of the diameter distributions over the study area. Cross-validation was performed separately for every parameter. Results showed that the Weibull function gave smaller relative bias in the prediction of the diameter sum. Additionally, the likelihood ratio was used to compare the fit of the density functions. This ratio was computed twice: firstly when parameters were estimated by maximum likelihood and secondly, when parameters were predicted by kriging-cross-validation. The Chaudhry–Ahmad function fitted better the actual diameter distributions when maximum-likelihood was used for parameter estimation. Nevertheless, the fit of the Weibull was much better when kriging was used for parameter prediction. The prediction of the diameter distribution was made using data from the National Forest Inventory, therefore predictions should be used for regional planning and estimation of forest resources at this spatial scale (national). For forest management purposes at a local scale, data sources taken at fine spatial scales should be preferred. The spatial discontinuities that the forest compartments introduce during kriging interpolation are finally discussed and some solutions are proposed.

Performance of percentile based diameter distribution prediction and Weibull method in independent data sets

Diameter distribution is used in most forest management planning packages for predicting stand volume, timber volume and stand growth. The prediction of diameter distribution can be based on parametric distribution functions, distribution-free parametric prediction methods or purely non-parametric methods. In the first case, the distribution is obtained by predicting the parameters of some probability density function. In a distribution-free percentile method, the diameters at certain percentiles of the distribution are predicted with models. In non-parametric methods, the predicted distribution is a linear combination of similar measured stands. In this study, the percentile based diameter distribution is compared to the results obtained with the Weibull method in four independent data sets. In the case of Scots pine, the other methods are also compared to k-nearest neighbour method. The comparison was made with respect to the accuracy of predicted stand volume, saw timber volume and number of stems. The predicted percentile and Weibull distributions were calibrated using number of stems measured from the stand. The information of minimum and maximum diameters were also used, for re-scaling the percentile based distribution or for parameter recovery of Weibull parameters. The accuracy of the predicted stand characteristics were also compared for calibrated distributions. The most reliable results were obtained using the percentile method with the model set including number of stems as a predictor. Calibration improved the results in most cases. However, using the minimum and maximum diameters for parameter recovery proved to be inefficient.

Incorporating the effects of interspecific competition and vegetation management treatments in stand table projection models for Douglas-fir saplings

A stand table projection system based on individual-tree and stand-level models for young Douglas-fir ( Pseudotsuga menziesii (Mirb.) Franco var. menziesii) plantations was developed from and evaluated with remeasurement data from sites in the Siskiyou Mountains of southwestern Oregon and in the Coast Ranges of Oregon and Washington. A projection equation was developed for relative tree size, defined as the ratio of individual-tree diameter at 15 or 30 cm above ground level (depending on the study location) to quadratic mean diameter. The relative size projection equation for the Coast Ranges study included the effect of total vegetation control, which indicated that diameters of Douglas-fir receiving total vegetation control tended to become more uniform over time in the Coast Ranges. An additional equation was developed to project quadratic mean diameter so that individual-tree diameters could be estimated from projected relative size. The effect of vegetation management treatments on projected quadratic mean diameters in the Siskiyou study was expressed as an interaction between proportion of cover removed by treatments (intensity) and dominant height of Douglas-fir at time of treatment relative to current dominant height. In 1- and 2-year projection periods, the stand table projection system performed similarly to a diameter distribution prediction system based on a Weibull distribution function. However, the difference between projected and predicted diameter distributions became more pronounced as the projection period increased to 5 years.

A Bivariate Distribution Approach to Modeling Forest Diameter Distributions at Two Points in Time

SUMMARY A procedure for predicting diameter distribution at two points in time in single-species forest stands was developed based on the bivariate SB distribution model. The future diameter distribution is determined from an initial distribution and a specified initial-future diameter relationship. The model developed is theoretically appealing and it performed as well as, and in some cases better than, the established methods of forest diameter distribution prediction such as parameter recovery, percentile prediction, and parameter prediction. Although developed for forest diameter distribution prediction, the methods presented here should be useful in a wide array of problems where initial and future distributions of some size characteristic are needed.

A Markov Chain Approach to the Prediction of Diameter Distributions in Uneven-aged Forest Stands

A simple stochastic model to predict future diameter distributions, number of survivor trees, number of mortality trees, and number of harvested trees is developed from conventional continuous forest inventory data over two measurement periods. The length of the prediction period is limited to multiples of the remeasurement period. Data used to construct the model and test its predictive ability came from 19 consecutive years of C.F.I, measurements collected in Washington County, Wisconsin. Results indicate that number of survivor trees can be predicted with very good accuracy; predictions of diameter distributions, number of mortality trees, and number of harvested trees are less accurate.