Parameter Recovery Method Research Articles

ALGORITHM FOR THE PROJECTION OF FOREST GROWTH AND PRODUCTION

The modeling of forest growth and production is an essential tool for forestry management because it allows us to perform simulations and project forest biometric variables in the future, thus assisting in stock planning and economic analyses. In this work, a growth and production model by diameter distribution was proposed with the application of the Weibull function based on the recovery of parameters through simplified functions between the forest attributes and the parameters of the Weibull function. The algorithm was developed in Excel’s VBA language. Validation was performed with data from the Continuous Forest Inventory (CFI) in a stand of Khaya grandifoliola and in rows of Eucalyptus spp. in the ILPF system, which were ordinarily organized into seven date combinations, from the most distant from to the closest to the projection date. The results were evaluated by the percentage standard error (SE%) applied to the projected and observed volumes and by the Kolmogorov‒Smirnov test applied to the diameter distributions to verify adherence. It was possible to identify an exact relationship for parameter c of the Weibull function as a function of the percentiles and for parameter b, improving the parameter recovery method. Another methodological improvement was the use of maximum diameter and maximum height for age to adjust the hypsometric function. The algorithm presented results for total volume with errors up to 20% in 85% of the tests.

Constraint Shock in Diameter Distribution Models: The Cost of Ignoring Negative Bounds

Abstract Diameter distributions are invariably fitted with constrained zero or positive lower bounds to prevent negative diameters. Goodwin (2021) found that the bound for the 3-parameter Weibull could be negative for negatively skewed data, and that constraining it to zero reduced model accuracy. The loss of model accuracy due to a bound constraint is referred to here as constraint shock. This article shows that the 4-parameter Kumaraswamy and Johnson’s SB distributions can also have negative lower bounds and exhibit constraint shock. A 3-step parameter recovery method was used to fit these distributions to plots in unthinned mixed species eucalypt plantations and results were compared with the less flexible Weibull. Based on Kolmogorov-Smirnov statistics, mean and maximum constraint shock for the 4-parameter distributions were 19% and 62%, respectively, compared with 19% and 51% for the Weibull, which indicated that constraint shock was not affected by model flexibility. Constraint shock was largely avoided by truncating and normalizing distributions with negative bounds. This work introduces a paradigm shift in diameter distribution modelling and adds clarity to a field that has not previously recognized the existence of constraint shock. Study Implications: Constraint shock is the loss of accuracy incurred by constraining the negative lower bound of a distribution to a nonnegative value. For a plantation eucalypt dataset in which 83% of plot diameters were negatively skewed, maximum constraint shock was 62% for the Kumaraswamy and Johnson’s SB distributions, and 51% for the less flexible 3-parameter Weibull, based on Kolmogorov-Smirnov statistics. Using distribution expectations of kurtosis, skewness, maximum diameter, and minimum diameter—all independent of bound parameters—a tractable 3-step parameter recovery method is described for unconstrained, constrained, and truncated 3- and 4-parameter distributions. This work introduces a paradigm shift in the treatment of distribution bounds that will result in substantial model improvements for negatively skewed data.

Developing a new model for predicting the diameter distribution of oak forests using an artificial neural network

The parameters of the probability density function (PDF) may be estimated using the parameter prediction method (PPM) and the parameter recovery method (PRM). However, these methods can suffer from accuracy issues. We developed and evaluated the prediction accuracy of two PPMs (stepwise regression model and dummy variable model) and an artificial neural network (ANN) to predict diameter distribution using data collected from 188 oak forest plots. The results demonstrated that the Weibull distribution performed well in fitting the diameter distribution. Compared with the stepwise regression model, the PPM model with stand type as a dummy variable reduced the predictional errors in estimating the parameters b and c of the Weibull distribution, but the prediction accuracy of the diameter distribution showed no significant improvement. Compared with the two PPM models, the ANN model with diameter class (C), average diameter (D) and stand type (T) as input variables decreased the RRMSE by 2.9% and 4.33% in estimating diameter distribution, respectively. The satisfactory prediction accuracy and simple model structure indicated that an ANN worked well for the prediction of the diameter distribution with few requirements and high practicality.

Climate-sensitive diameter distribution models of larch plantations in north and northeast China

Tree diameter distribution models are important tools for forest management decision making. Climate change will affect tree growth and thus diameter distribution. However, there is lack of diameter distribution models describing the effects of climate. The paper developed a climate-sensitive diameter distribution model based on 193 sample plots of larch plantations in north and northeast China. Weibull distribution model was modified by a compatible simultaneous system and the percentile-based parameter recovery method with the inclusion of climate variables. The results showed that showed BIO10 (mean temperature of warmest quarter) andBIO14 (precipitation of driest month) are key climatic factors which shape the diameter distribution of Larch plantations. Compared with parameter estimation models without climate variables, the adjusted R2 was improved (5.03% for β, and 3.32 % for γ), RMSE (73.12% for β, and 2.89 % for γ)and TRE (92.16% for β, and 5.57% for γ) decreased. The models with climate factors are significantly different from that without climate factors by F test. The models with climate factors are improved and could be applied for diameter distribution projection under future climate change.

Modelling resin production distributions for Pinus pinaster Ait. stands in NW Spain

Pine resin, a viscous material secreted as a defensive response to biotic or abiotic damage, is a highly valuable non-wood forest product with multiple uses in the industrial sector. Resin production can be induced by tapping live trees, but not all pine species produce resin of suitable quality and/or in profitable quantities. Maritime pine (Pinus pinaster Ait.) is currently the only species tapped in Spain, where resin tapping activity has been recovered in the last few decades. Most studies on resin production focus on the mean production per tree or per area, and less attention is given to determining how the production is distributed across individuals or production classes. We modelled the distribution of resin production in Pinus pinaster stands in Galicia (NW Spain) by using the Weibull function and the moment-based parameter recovery method. We observed a high level of variance in resin production between plots (different sites, stimulants used, tapping method or year) and within plots, between trees. All resin production distributions modelled using the arithmetic mean resin production (x¯) and the variance of the distribution (σ2) per plot satisfied the Kolmogorov-Smirnov (KS) test, in which critical values were obtained by Monte Carlo simulation. The variance of the distribution (σ2) was positively correlated with x¯, and the relationship was described by an exponential model. When resin production distributions were modelled using x¯ and estimated variance (σˆ2), 7% of the distributions (corresponding to trees in which chemical stimulants were not used) did not satisfy the KS test. The mean production (x¯) can be easily determined by dividing the stand production by the number of trees. However, x¯ could also be estimated before commercial tapping by sampling a representative number of trees. We conclude that in order to estimate x¯, a minimum sample of 50–60 trees should be tapped, to yield a relative standard error (RSE) below 10%; 10–15 trees should be considered for RSE < 20% and 5–10 for RSE < 30%.

Estimation and calibration of stem diameter distribution using UAV laser scanning data: A case study for larch (Larix olgensis) forests in Northeast China

Diameter frequency distributions provide essential information for estimating timber assortment, monitoring carbon stocks, and formulating forest management measures. In this study, we estimated diameter distribution utilizing unmanned aerial vehicle laser scanning (ULS) data by applying three Weibull distribution modeling methods: (1) parameter prediction method (PPM); (2) moment-based parameter recovery method (PRMM); and (3) percentile-based parameter recovery method (PRMP). The variables used in Weibull distribution modeling methods were combined with stand density as response groups to be modeled with ULS metrics. Considering the hierarchical structure of ULS data and the autocorrelation among sub-models, mixed-effects seemingly unrelated regression (SURM) were applied to take into account both spatial and cross-model correlations. The experiments were conducted for 11 sites of larch plantations using leave-one-out cross-validation (LOOCV). The diameter distribution was estimated and calibrated by the observed stand density considering the correlations of sub-models' random-effects. The results demonstrated that applying a relatively small number of plots (1 to 6) and estimated best linear predictor (EBLUP) for local calibration could improve the prediction performance. The optimal results were obtained from PRMM with six calibrated plots, and the average Reynolds error index was 45.30. Furthermore, simulation applications with different pulse densities were applied and suggested that calibration could also improve the estimation performance but brought little improvement on estimation stability, far lesser than the impact of point cloud density. This study provides an improved approach for diameter distribution estimation and benefits for operational forest applications using remote sensing data.

Modeling diameter distribution of Aleppo pine (Pinus halepensis Mill.) natural forest in the Aures (Algeria) using the Weibull, Beta and Normal distributions with parameters depending on stand variables

230 temporary plots located in Aleppo pine ( Pinus halepensis Mill.) stands in the Aures (Algeria) were used for modeling its structure with three theoretical distributions, i.e., the Weibull; the normal and the Beta one. Parameters of the Weibull distribution were estimated using two methods: the maximum likelihood and the method of moments. Diameter distribution models were obtained by estimation of each distribution parameters and by their prediction using stand variables. Results revealed the efficiency of the Weibull distribution estimated with the method of moments. The parameter estimation method is more accurate compared to parameter recovery method despite the existence of strong correlations between parameters of the theoretical distributions and some population variables such as arithmetic or quadratic mean diameter and dominant height. Plot characteristics revealed the existence of several distribution shapes: symmetrical; dissymmetrical with left asymmetry and reverse I or J -shaped distributions.

Comparison of two parameter recovery methods for the transformation of Pinus sylvestris yield tables into a diameter distribution model

• Key message We successfully transformed Pinus sylvestris yield tables into diameter distribution models. The best results were obtained with the parameter recovery method based on both mean and quadratic mean diameter, which explained 70% of the variability of frequencies by diameter classes and provided better results in the analysis of errors. On the other hand, the method based on stand density, dominant diameter and quadratic mean diameter explained less variability of frequencies by diameter classes (64.4%). • Context Old datasets used to develop yield table models can be recovered to transform those yield tables into diameter distribution models that provide a more detailed description of size variability and forest structure. • Aims We used archived measurements collected to develop yield table models for Pinus sylvestris L in central Spain, to transform those yield tables into a diameter distribution model by using parameter recovery methods. • Methods We compared two different parameter recovery methods, one based on both mean and quadratic mean diameter and another one based on dominant diameter, stand density and quadratic mean diameter and used a set of 104 even aged plots to analyze the performance of the said methods for the transformation of Pinus sylvestris L yield tables in central Spain into a diameter distribution model. • Results The parameter recovery method based on both mean and quadratic mean diameter explained 70% of the variability of frequencies by diameter classes and provided better results than the method based on stand density, dominant diameter and quadratic mean diameter that explained 64.4% of the variability of frequencies by diameter classes. However, more important than the method itself were the errors that propagated from the models predicting the different variables used in the parameter recovery. • Conclusion Based on the results from the analysis of errors by diameter classes, the method using both mean and quadratic mean diameter outperformed the method using dominant diameter, stand density and quadratic mean diameter and is the best option to transform P. sylvestris yield tables into diameter distribution models.

Models for diameter distribution and tree height in hybrid aspen plantations in southern Finland

Hybrid aspen ( L. × Michx.) is known with outstanding growth rate and some favourable wood characteristics, but models for stand management have not yet been prepared in northern Europe. This study introduces methods and models to predict tree dimensions, diameter at breast height (dbh) and tree height for a hybrid aspen plantation using data from repeatedly measured permanent sample plots established in clonal plantations in southern Finland. Dbh distributions using parameter recovery method for the Weibull function was used with Näslund’s height curve to model tree heights. According to the goodness-of-fit statistics of Kolmogorov-Smirnov and the Error Index, the arithmetic mean diameter () and basal area-weighted mean diameter () provided more stable parameter recovery for the Weibull distribution than the median diameter () and basal area-weighted median diameter (), while showed the best overall fit. Thus, Näslund’s height curve was modelled using with Lorey’s height (), age, basal area (), and tree dbh (Model 1). Also, Model 2 was tested using all predictors of Model 1 with the number of trees per ha (). All predictors were shown to be significant in both Models, showing slightly different behaviour. Model 1 was sensitive to the mean characteristics, and , while Model 2 was sensitive to stand density, including both and as predictors. Model 1 was considered more reasonable to apply based on our results. Consequently, the parameter recovery method using and Näslund’s models were applicable for predicting tree diameter and height.Populus tremulaP. tremuloidesDDGDMDGMDGDGHGBATPHDGHGBATPHDG

On the use of the Weibull distribution in modeling and describing diameter distributions of clonal eucalypt stands

Weibull distributions have been widely used to describe tree stem diameter distributions. However, there is a scarcity of studies that suggest the best Weibull formulation. The parameters of the Weibull distribution are usually predicted by either the parameter prediction method (PPM) or the parameter recovery method (PRM), although other methods have been proposed. Thus, this study aimed to evaluate the performance of eight Weibull formulations and compare methods of parameter prediction to describe diameter distributions of clonal eucalypt stands in Brazil. Data originated from remeasurements of 56 plots at ages 3, 5, and 6 years. Weibull distributions were fitted using the maximum likelihood method and evaluated in a goodness-of-fit indicators ranking. The right-truncated two-parameter formulation showed the best results and was used to evaluate the methods of parameter prediction. Stand attributes showed a strong relationship with shape and scale parameters. Regression models were developed and resulted in accurate estimates using PPM. PRM used a growth and yield system to estimate the stand attributes, followed by the moment-based method. The modified cumulative distribution function regression (CDFR) approach was also evaluated, and it presented the poorest results. Although the PPM showed excellent results, PRM is recommended in older stands with inventory because it implicitly promotes compatibility among stand attributes.

Performances of different methods of estimating the diameter distribution based on simple stand structure variables in monospecific regular temperate European forests

Using the three characteristic points of a forest stand, dg (mean quadratic diameter), dmin (diameter of the smallest tree) and dmax (diameter of the largest tree), appears informative enough to determine the parameters of the whole diameter distribution and, hence, the standing volume, with an accuracy of 2–3%. This is related principally with a particular feature of the Weibull distribution function, and the empirical dependency of the main scale parameter α + β from the mean quadratic diameter (dg): This allows the prediction of the parameter β with an unexpectedly high likelihood. This feature could be used for growth modelling as well as inventory purposes, at least for monospecific and even-aged stands and, maybe more, because this feature is proper to the function itself. One of the most appealing applications of diameter distribution functions is to predict compliant stand diameters without needing to tally all stems, but in determining the function parameters only on the base of simple stand characteristics. This can be applied for yield model construction or inventory purposes. The aim of this paper is to compare different methods of estimating the Weibull distribution parameters, partly based on parameter recovery method (PRM). They use a remarkable, empiric property of the Weibull function. Their performances are assessed in comparison to real distributions from a wide database of permanent Swiss yield plots repeatedly measured (time series) for Norway spruce (Picea abies (L.) Karst.) and European beech (Fagus sylvatica L.). The Weibull distribution offers the advantage of simple but reliable estimation procedures. One of these is the main (scale) parameter β being given at a remarkable point of the function free, i.e. independent from the shape parameter γ. Because dg lies very close to this point, it correlates empirically very tightly with this parameter and thus allows for a trustful simple estimation. We compare, with appropriate statistic tests, real distribution with such obtained with the usual maximum likelihood estimation (MLE) of the Weibull parameters and those obtained with these new procedures. The results obtained from a set of 800 yield plots of regular spruce stands and 596 of beech in Switzerland illustrate the good performances of the two much simpler procedures. The accuracy of estimating the standing volume is about 1.4% for beech and 2.8% for spruce when the site index (SI) is known. The three considered characteristic stand attributes (dg, dmin and dmax) appear robust enough for determining the diameter distribution with a respectable accuracy. This is enough reason for a revival of the old, but very ingenious, method of angle count sampling of Walter Bitterlich (1947).

Temperature and anisotropy effects in the application of the hindered diffusion model to composite laminates

The one-dimensional hindered diffusion model was applied to gravimetric moisture uptake data for a six-ply high-temperature quartz-fiber-reinforced bismaleimide laminate. Diffusion behavior was evaluated as a function of specimen geometry and temperature to determine the effect on both diffusivity and the binding and unbinding probabilities of diffusing water molecules predicted by the model. Pre-equilibrium experimental uptake data were used to recover model parameters, including equilibrium moisture content, for specimens designed with intentionally-low planar surface-to-edge area ratios of 20, 12.5, and 5. Gravimetric uptake data for fully-immersed laminates at 25°C, 37°C, and 50°C was used to determine diffusion parameters and characterize the temperature and geometry-dependent behavior of the laminate. A parameter recovery method employing least-squares regression was used to determine best-fit parameters of the hindered diffusion model, including diffusivity (DZ), equilibrium moisture content (M∞), ...

Effect of Stand Structure and Number of Sample Trees on Optimal Management for Scots Pine: A Model-Based Study

This study presents an attempt to discover the effect of sample size on the financial outcome derived by stand-level optimization with individual tree modeling. The initial stand structure was altered to reflect sparse, average, and dense Scots pine (Pinus sylvestris L.) stands. The stands had varying numbers of stems but identical weighted median diameters and stand basal areas. The hypothetical Weibull diameter distributions were solved according to the parameter recovery method. The trees were systematically sampled with respect to the tree basal area corresponding to sample sizes of 10, 20, or 40 trees. We optimized the stand management with varying numbers of sample trees and with varying stand structures and compared the optimal solutions with respect to the objective function value (maximum net present value) and underlying management schedule. The results for the pine stands in southern and central Finland indicated that the variations in the objective function value relating to sample size were minor (&lt;2.6%) in the sparse and average stand densities but exceeded 3% in the dense stands. Generally, the stand density is not always known, and thus, we may need to generalize the average density for all cases in question. This assumption, however, resulted in overestimations with respect to the optimal rotation period and financial performance in this study. The overestimations in the net present value decreased along with the increasing sample size, from 22% to 14% in the sample sizes of 10 and 40 trees, respectively.

Modeling diameter distributions in radiata pine plantations in Spain with existing countrywide LiDAR data

We evaluated the use of low-density airborne laser scanning data to estimate diameter distributions in radiata pine plantations. The moment-based parameter recovery method was used to estimate the diameter distributions, considering LiDAR metrics as explanatory variables. The fitted models explained more than 77% of the observed variability. This approach can be replicated every 6 years (temporal cover planned for countrywide LiDAR flights in Spain). The estimation of stand diameter distribution is informative for forest managers in terms of stand structure, forest growth model inputs, and economic timber value. In this sense, airborne LiDAR may represent an adequate source of information. The objective was to evaluate the use of low-density Spanish countrywide LiDAR data for estimating diameter distributions in Pinus radiata D. Don stands in NW Spain. The empirical distributions were obtained from 25 sample plots. We applied the moment-based parameter recovery method in combination with the Weibull function to estimate the diameter distributions, considering LiDAR metrics as explanatory variables. We evaluated the results by using the Kolmogorov–Smirnov (KS) test and a classification tree and random forest (RF) to relate the KS test result for each plot to stand-level variables. The models used to estimate average (dm) and quadratic (dg) mean diameters from LiDAR metrics, required for recovery of the Weibull parameters, explained a high percentage of the observed variance (77 and 80%, respectively), with RMSE values of 3.626 and 3.422 cm for the same variables. However, the proportion of plots accepted by the KS was low. This poor performance may be due to the strictness of the KS test and/or by the characteristics of the LiDAR flight. The results justify the assessment of this approach over different species and forest types in regional or countrywide surveys.

A stand table projection system for interior Douglas-fir in British Columbia, Canada

Abstract This study developed a stand table projection system for interior Douglas-fir (Pseudotsuga menziesii (Mirb.) Franco var. glauca (Beissn.) Franco) in British Columbia, Canada. Simulation data, obtained by running PrognosisBC (with 150 year projections) using input derived from 140 permanent sample plots, were utilized for model construction. First, a whole-stand attributes (number of trees per ha, quadratic mean diameter, and arithmetic mean diameter) prediction model was constructed. Weibull parameters for the diameter distribution of the future stand were estimated from the predicted stand attributes using two parameter prediction methods (via seemingly unrelated regression and the cumulative distribution function) and one parameter recovery method. The future stand table was projected with the estimated Weibull parameters and compared with two stand diameter distribution adjustment algorithms, yielding a total of nine parameter estimation-diameter adjustment combinations. The outputs from the stand table projection model were evaluated with repeated measures data covering 20 years from 18 independent plots, as well as compared with the outcomes predicted by PrognosisBC for those plots. The diameter class adjustment procedure applying tree mortality prior to growth, combined with the cumulative distribution parameter prediction method, performed best among the nine combinations we compared. The stand table projection system yielded similar results to PrognosisBC on the evaluation data and is expected to be a useful tool for managing forests sustainably and effectively.

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.

Stand Diameter Distribution Modelling and Prediction Based on Richards Function

The objective of this study was to introduce application of the Richards equation on modelling and prediction of stand diameter distribution. The long-term repeated measurement data sets, consisted of 309 diameter frequency distributions from Chinese fir (Cunninghamia lanceolata) plantations in the southern China, were used. Also, 150 stands were used as fitting data, the other 159 stands were used for testing. Nonlinear regression method (NRM) or maximum likelihood estimates method (MLEM) were applied to estimate the parameters of models, and the parameter prediction method (PPM) and parameter recovery method (PRM) were used to predict the diameter distributions of unknown stands. Four main conclusions were obtained: (1) R distribution presented a more accurate simulation than three-parametric Weibull function; (2) the parameters p, q and r of R distribution proved to be its scale, location and shape parameters, and have a deep relationship with stand characteristics, which means the parameters of R distribution have good theoretical interpretation; (3) the ordinate of inflection point of R distribution has significant relativity with its skewness and kurtosis, and the fitted main distribution range for the cumulative diameter distribution of Chinese fir plantations was 0.4∼0.6; (4) the goodness-of-fit test showed diameter distributions of unknown stands can be well estimated by applying R distribution based on PRM or the combination of PPM and PRM under the condition that only quadratic mean DBH or plus stand age are known, and the non-rejection rates were near 80%, which are higher than the 72.33% non-rejection rate of three-parametric Weibull function based on the combination of PPM and PRM.

Evaluation of Methods to Predict Weibull Parameters for Characterizing Diameter Distributions

Compared with other distribution functions, the Weibull distribution has been more widely used in describing diameter distributions because of its flexibility and relative simplicity. Parameters of the Weibull distribution are generally predicted either by the parameter prediction method or by the parameter recovery method. The coefficients of the regression equations for predicting Weibull parameters, moments, or percentiles are often estimated by use of different approaches such as ordinary least squares, seemingly unrelated regression (SUR), or cumulative distribution function regression (CDFR). However, there is no strong rationale for preferring one method over the other. We developed and evaluated different methods of predicting parameters of Weibull distribution to characterize diameter distribution using data from the Southwide Seed Source Study. The SUR and the CDFR approaches were applied to 10 different parameter prediction and parameter recovery methods. A modified CDFR approach was developed by modifying the CDFR technique such that the CDF is computed using information from diameter classes instead of individual trees as in the CDFR approach. These methods were evaluated based on four goodness-of-fit statistics (Anderson-Darling, Kolmogorov-Smirnov, negative log-likelihood, and error index). The CDFR approach provided better results than the SUR approach for all methods. The modified CDFR approach consistently provided better results than the SUR approach and was superior to the CDFR approach in all evaluation statistics but the Anderson-Darling statistic. FOR .S CI. 59(2): 243-252.

Parameter recovery vs. parameter prediction for the Weibull distribution validated for Scots pine stands in Finland

The moment-based parameter recovery method (PRM) has not been applied in Finland since the 1930s, even after a continuation of forest stand structure modelling in the 1980s. This paper presents a general overview of PRM and some useful applications. Applied PRM provided compatibility for the included stand characteristics of stem number (N) and basal area (G) with either mean (D), basal area-weighted mean (DG), median (DM) or basal area-median (DGM) diameter at breast height (dbh). A two-parameter Weibull function was used to describe the dbh-frequency distribution of Scots pine stands in Finland. In the validation, PRM was compared with existing parameter prediction models (PPMs). In addition, existing models for stand characteristics were used for the prediction of unknown characteristics. Validation consisted of examining the performance of the predicted distributions with respect to variation in stand density and accuracy of the localised distributions, as well as accuracy in terms of bias and the RMSE in stand characteristics in the independent test data set. The validation data consisted of 467 randomly selected stands from the National Forest Inventory based plots. PRM demonstrated excellent accuracy if G and N were both known. At its best, PRM provided accuracy that was superior to any existing model in Finland – especially in young stands (mean height < 9 m), where the RMSE in total and pulp wood volumes, 3.6 and 5.7%, respectively, was reduced by one-half of the values obtained using the best performing existing PPM (8.7–11.3%). The unweighted Weibull distribution solved by PRM was found to be competitive with weighted existing PPMs for advanced stands. Therefore, using PRM, the need for a basal area weighted distribution proved unnecessary, contrary to common belief. Models for G and N were shown to be unreliable and need to be improved to obtain more reliable distributions using PRM.

Modeling the Distribution of Marketable Timber Products of Private Teak (&amp;lt;i&amp;gt;Tectona grandis&amp;lt;/i&amp;gt; L.f.) Plantations

Management of marketable products of private plantations will not be sustainable without class girth being identifiable readily. Modeling marketable products is a key to obtain good fitness between observed and theoretical girth distribution. We determine the best parameter recovery method with the Weibull function for two sylvicultural regimes (coppice and high forest). Data on stand variables were collected from 1101 sample plots. The three Weibull function parameters were estimated with three parameters recovery methods: the maximum likelihood method, the method of moments and the method of percentiles. Stepwise regression and the simultaneously re-estimated parameter using the Seemingly Unrelated Regression Estimation were applied to model each parameter. The results indicated that the three methods successfully predicted girth size distributions within the sample stands. The method of moments was the best one with lowest values of Reynolds error index and Kolmogorov-Smirnov statistic however the sylvicultural regimes. The Weibull parameter distribution model developed for each of the two sylvicultural regimes was quite reliable.