Taper Equations Research Articles

Models for Tree Taper Form: The Gompertz and Vasicek Diffusion Processes Framework

In this work, we employ stochastic differential equations (SDEs) to model tree stem taper. SDE stem taper models have some theoretical advantages over the commonly employed regression-based stem taper modeling techniques, as SDE models have both simple analytic forms and a high level of accuracy. We perform fixed- and mixed-effect parameters estimation for the stem taper models by developing an approximated maximum likelihood procedure and using a data set of longitudinal measurements from 319 mountain pine trees. The symmetric Vasicek- and asymmetric Gompertz-type diffusion processes used adequately describe stem taper evolution. The proposed SDE stem taper models are compared to four regression stem taper equations and four volume equations. Overall, the best goodness-of-fit statistics are produced by the mixed-effect parameters SDEs stem taper models. All results are obtained in the Maple computer algebra system.

Особливості моделювання твірної поверхні стовбурів дуба звичайного

Узагальнено досвід дослідження форми стовбурів дерев, який дав змогу зробити висновок про переваги математичного моделювання твірної поверхні для аналізу збігу стовбурів. На основі дослідного матеріалу, зібраного в дубових насадженнях Придніпровського правобережного Лісостепу на 17 тимчасових пробних площах, проаналізовано залежність форми стовбурів дуба звичайного (Quercus robur L.) від висоти та діаметра на висоті 1,3 м. За допомогою графічного аналізу та t-тесту середніх значень коефіцієнтів форми Шиффеля на 5 %-му рівні значущості виявлено відмінність у формі стовбурів дуба різних груп діаметрів. За розрядами висот статистично значущої різниці, за характером збігу не встановлено. Виконаний аналіз дав змогу обґрунтувати доцільність моделювання збігу стовбурів дуба звичайного незалежно від висоти, але в межах 3-х груп діаметрів: 20-28 см, 32-40 см та 44-64 см. Як моделі твірної поверхні стовбурів апробовано показниково-степеневі математичні рівняння A. Kozak (1988) і R. Newnham (1992). Підбір параметрів рівнянь виконано для вибірки з 171 модельного дерева в середовищі R за допомогою функції nls − нелінійна мінімізація суми квадратів відхилень. Систематична помилка обох рівнянь виявилася близькою до нуля (0,9-1,7 %), що дало змогу прийняти їх для моделювання твірної поверхні стовбурів різної форми для встановлених груп діаметрів. Розроблені моделі дають змогу прогнозувати діаметри стовбурів дуба на будь-якій висоті зі стандартною помилкою 1,5-3,2 см. Все ж аналіз розподілу залишків математичних моделей засвідчив переваги моделі A. Kozak (1988), яку рекомендовано використовувати надалі для моделювання розмірно-якісної структури стовбурів дуба звичайного.

Evaluation of potential modeling approaches for Scots pine stem diameter prediction in north-eastern Turkey

Critical forest management decisions are strongly supported by the knowledge of forest ecosystems and their features. There is a growing trend towards using models to predict the most accurate yield projections for forest management. In this research area, features of standing trees, such as diameters along the tree bole, are of much interest. This paper is focused on the construction and evaluation of potential modeling approaches for Scots pine stem diameter prediction in north-eastern Turkey, including (1) fixed-effects, (2) mixed-effects, (3) three and five quantile regression, and (4) an artificial neural network modeling techniques. Nonlinear fixed-effects, mixed-effects, and both quantile regression models were based on a variable exponent taper equation, while the Levenberg-Marquardt algorithm was investigated for the artificial neural network (LMANN) models construction. Parameters of the tested models were calibrated by the use of several stem diameter measurements obtained at relative height positions, with models’ superior performances in diameter predictions when the information of the additional diameter measured at 60% of total height, was included. Evaluation statistics show that both quantile regression and mixed-effects models improved results as compared to fixed-effects model. Overall, LMANN models achieved the best performance with higher accuracy for the Scots pine stem diameter prediction for the whole tree as well as for sections within the tree based on the ten relative height classes. Similarly to previous findings, the results of this study support that the use of mixed-effects modeling increases flexibility and efficiency of taper equations for stem diameter prediction. Moreover, the LMANN modeling approach was evaluated as superior according to its adequacy in predicting diameters along the tree stem. Therefore, the usage of the LMANNs for the tree stem diameter prediction can be a very useful tool in forest management practice and thus worth consideration.

Estimating stem volume using stem taper equation for Quercus mongolica in South Korea

This study was conducted to develop a stem volume table for Quercus mongolica in Korea by using Kozak’s stem taper equation. A total of 958 Quercus mongolica sample trees were collected around the country and a growth performance was investigated through compiling data of diameters by stem height and stem analysis. Fitness Index (FI), Bias, and Mean Absolute Deviation (MAD) were used to test the stem taper equation’s fitness. The fitness of the equation was estimated at 98%, bias as −0.0024, and MAD turned out as 0.6814. Furthermore, there was a statistically significant volume difference between the current volume table and the new volume table (p < .005). The result indicates that using the new volume table which reflects the actual forest will reduce a loss when assessing wood resources and also improve the accuracy of forest statistics at national and local governments. A stem volume table, the main result of this research which is utilized by estimated stem taper equation, will provide growth information of Quercus mongolica, one of the main broadleaf species in Korea and furthermore, work as a management indicator for rational forest management.

STEM TAPER ESTIMATIONS WITH ARTIFICIAL NEURAL NETWORKS FOR MIXED ORIENTAL BEECH AND KAZDAĞI FIR STANDS IN KARABÜK REGION, TURKEY

ABSTRACT Development of artificial neural network (ANN) models to estimate stem tapers of individual trees in mixed Fagus orientalis and Abies nordmanniana subsp. Equi-trojani stands distributed in Karabuk region of Turkey, and comparison of the ANN models with stem taper equations were aimed in this study. The measurements were obtained from 516 sample trees (238 for Oriental beech and 278 for Kazdagi fir) in mixed stands of Karabuk region. The measurements included diameter at breast height, tree height, diameter at stump height, and diameters at intervals of 1 m along the stem. In total, 45 ANN models and four stem taper equations were developed. Estimation performances of ANN models and stem taper equations were compared using relative rankings according to seven goodness-of-fit criteria. As a result, the ANN models were more successful in estimation of stem taper for both tree species. The most successful ANN model structures were (i) the model using logistic function in hidden layer with 10 nodes and hyperbolic tangent function in output layer for Fagus orientalis, and (ii) the model using logistic function in hidden layer with 10 nodes and linear function in output layer for Abies nordmanniana subsp. Equi-trojani.

STEM TAPER EQUATION WITH EXTENSIVE APPLICABILITY TO SEVERAL AGE CLASSES OF Pinus taeda L

The aim of this study was to develop stem taper equations for trees of Pinus taeda L. inside and outside bark with extensive applicability to several age classes. Data were obtained from 631 trees of P. taeda, ranging from 4 to 31 years of age, in different stands distributed in several counties of the Midwest region of the state of Santa Catarina, Brazil. The taper models of Biging (1984), Schöpfer (1966), and Kozak et al. (1969) were tested. These models were fitted in their simplest formulation as well as by varying their coefficient linear functions of stand age with the procedure PROC NLIN in the software SAS® University Edition. There were no significant differences in accuracy and precision in the estimates between the simplest formulation of the Schöpfer (1966) model and the variation of its coefficient b linear function of age, and thus, the simplest formulation was chosen. Among all taper models tested, the Schöpfer (1966) model presented greater accuracy and precision to estimate diameters inside and outside bark, throughout the stem of Pinus taeda, in the Midwest region of the state of Santa Catarina, Brazil.

¿Cómo corregir la heterocedasticidad y autocorrelación de residuales en modelos de ahusamiento y crecimiento en altura?

En la modelación del ahusamiento y del crecimiento en altura dominante con datos de series de tiempo, es muy común la presencia de heterocedasticidad y autocorrelación de los errores. Funciones de varianza (varFunc) y estructuras de correlación (corStruct) para corregir la heterocedasticidad y modelar dependencia de los errores, respectivamente. Estas fueron combinadas y evaluadas en ecuaciones de ahusamiento y crecimiento en altura de Pinus teocote en Durango, México. La base de datos se obtuvo de 51 análisis troncales con 768 observaciones de ahusamiento y 634 de altura. Las varFunc utilizadas fueron: 1) función de potencia (varPower); 2) función exponencial (varExp); 3) función constante y de potencia (varConstPower); y 4) función combinada de potencia y exponencial (varComb). Las corStruct incluyeron: simetría compuesta (corCompSymm), autorregresiva de orden 1 (corAR1), autorregresiva continua (corCAR1), autorregresiva de media móvil (corARMA2-0), corARMA1-1, corARMA2-1, corARMA2-2, corARMA3-1 y corARMA3-2. Las ecuaciones se ajustaron por mínimos cuadrados generalizados no lineales; y se evaluaron con un sistema de calificación con los estadísticos de ajuste: RMSE, R2, AIC, BIC, LogLik, CV y sesgo promedio. Con base en la calificación, las mejores combinaciones para el ahusamiento y crecimiento en altura fueron 1-9, 2-5, 3-8 y 4-6 y 1-6, 2-9, 3-7 y 4-4, respectivamente. En el ahusamiento solo la combinación 2-5 fue homocedástica con residuales independientes al igual que las ecuaciones de altura seleccionadas y las varFunc y corStruct presentaron influencia en la trayectoria de las curvas de índice de sitio construidas.

The conic-paraboloid formulae for coarse woody material volume and taper and their approximation

The conic-paraboloid volume equation is receiving increased use with downed coarse woody material (CWM), but the consequences for taper have not been identified mathematically. Requiring that subdivision of a conic-paraboloid yields two smaller conic-paraboloids leads to an exact taper equation intermediate between those of cones and second-order paraboloids. This exact taper equation does not have an explicit inverse, however. An alternative, naive approach does have an explicit inverse, but subdivision does not yield two conic-paraboloids. The exact conic-paraboloid is closely approximated by Fermat’s paraboloid with exponent 7/5. The exact and naive conic-paraboloids match in volume; differences in taper are ≤2.2% of large-end cross-sectional area and ≤5.9% of large-end diameter, while differences in inverse taper are ≤3.7% of total length. Fermat’s paraboloid is always within 1.2% of total volume; differences in taper are ≤0.8% of large-end cross-sectional area and ≤2.0% of large-end diameter, while differences in inverse taper are ≤1.1% of total length. Such differences are negligible given the variety of CWM shapes and practical measurement challenges. Either the exact conic-paraboloid or the corresponding Fermat’s paraboloid provides appropriate equations for estimating the volume and taper of CWM that is intermediate between conical and ordinary paraboloid frusta.

Modeling taper and volume of Sal (Shorea robusta Gaertn. f.) trees in the western Terai region of Nepal

Volume and taper equations are used for estimating timber volume and biomass of a tree. Despite their usefulness, precise and site specific equations are still lacking for commercially important tree species in Nepal. The study was carried out at Chandak Chatiya Mahila Community Forest in Bardia district and Lumbini Collaborative Forest of Saljhandi in Rupandehi district in western Terai of Nepal. A destructive sampling method was used and selected fifteen Sal trees (Shorea robusta Gaertn. f.) from Saljhandi (site 1) and eighteen trees from Bagnaha (site 2) randomly to calibrate an individual tree volume and a stem taper function. At first, a non-linear stem taper function was calibrated using stem diameters outside bark at different heights above ground as response variable and D (diameter at breast height), H (total height), h (height of interest) as predictors. Then, effect of crown characteristics on stem taper was evaluated. As stem HCB (height to crown base) was found to affect stem taper, its usefulness in existing stem volume equation was tested. Empirical relationships between V (stem volume) as a response variable and D, H, HCB and sites in Bardia and Rupandehi districts as predictors were established using a linear mixed modeling approach. Our result showed that, instead of H, use of HCB in stem volume equation increased model prediction accuracy and reduced prediction bias. Applicability of the suggested models for predicting individual S. robusta tree volume and stem taper is discussed. Banko JanakariA Journal of Forestry Information for Nepal Special Issue No. 4, 2018, Page: 76-83

Models for Predicting Specific Gravity and Ring Width for Loblolly Pine from Intensively Managed Plantations, and Implications for Wood Utilization

Loblolly pine (Pinus taeda L.) is increasingly grown on intensively managed plantations that yield high growth rates. Wood properties, including specific gravity (SG), change with cambial age, and thus intensively managed trees contain a high proportion of low density corewood when harvested because of reduced rotation lengths. This study was undertaken to develop models of ring-level properties (SG and width) in intensively managed loblolly pine plantations. Ninety-three trees from five stands aged from 24 to 33 years were harvested, and 490 disks were obtained from in between the 5.2-m logs that were cut, and at the merchantable top. The disks were cut into pith-to-bark radial strips that were scanned on an X-ray densitometer, and the resultant data analyzed using non-linear mixed-effects models. The fixed effects of the models, which included cambial age and for some models disk height and ring width, were able to explain 56, 46, 54, 16, and 46 percent of the within-tree variation for ring SG, ring width, latewood SG, earlywood SG, and latewood percent, respectively. To assess implications for wood utilization, a modeled tree was built by using height, diameter, and taper equations and these models were linked with the developed ring SG model to produce a tree properties map. The linked information was also used to generate tree and log SG and proportion of corewood values for different rotation ages. The results from this study are a step towards integrating wood quality models into growth-and-yield modeling systems that are important for loblolly pine plantation management.

Estimating upper stem diameters and volume of Douglas-fir and Western hemlock trees in the Pacific northwest

BackgroundVolume and taper equations are essential for obtaining estimates of total and merchantable stem volume. Taper functions provide advantages to merchantable volume equations because they estimate diameter inside or outside bark at specific heights on the stem, enabling the estimation of total and merchantable stem volume, volume of individual logs, and a height at a given diameter.MethodsUsing data collected from 1218 trees (1093 Douglas-fir (Pseudotsuga menziesii (Mirbel) Franco) and 125 western hemlock (Tsuga heterophylla)), we evaluated the performance of one simple polynomial function and four variable-exponent taper functions in predicting upper stem diameter. Sample trees were collected from different parts of the states of Oregon, Washington, and California. We compared inside-bark volume estimates obtained from the selected taper equation with estimates obtained from a simple logarithmic volume equation for the data obtained in this study and the equations used by the Forest Inventory and Analysis program in the Pacific Northwest (FIA-PNW) in the state of California and western half of the states of Oregon and Washington.ResultsVariable exponent taper equations were generally better than the simple polynomial taper equations. The FIA-PNW volume equations performed fairly well but volume equations with fewer parameters fitted in this study provided comparable results. The RMSE obtained from taper-based volume estimates were also comparable with the RMSE of the FIA-PNW volume equations for Douglas-fir and western hemlock trees respectively.ConclusionsThe taper equations fitted in this study provide added benefit to the users over the FIA-PNW volume equations by enabling the users to predict diameter at any height, height to a given diameter, and merchantable volume in addition to cubic volume including top and stump (CVTS) of Douglas-fir and western hemlock trees in the Pacific Northwest. The findings of this study also give more confidence to the users of FIA-PNW volume equations.

우리나라 소나무의 수간곡선식 추정에 의한 탄소저장량 및 흡수량 산정

This study was conducted to estimate carbon stocks of Pinus densiflora with drawing volume of trees in each tree height and DBH applying the suitable stem taper equation and tree specific carbon emission factors, using collected growth data from all over the country. Information on distribution area, tree age, tree number per hectare, tree volume and volume stocks were obtained from the 5th National Forest Inventory (2006∼2010) and Statistical yearbook of forest (2016), and method provided in IPCC GPG was applied to estimate carbon stock and uptake. Performance in predicting stem diameter at a specific point along a stem in Pinus densiflora by applying Kozak’s model, (수식 본문참조), which is well known equation in stem taper estimation, was evaluated with validations statistics, Fitness Index, Bias and Standard Error of Bias. Consequently, Kozak’s model turned out to be suitable in all validations statistics. Stem volume table of P. densiflora was derived by applying Kozak’s model and carbon stock tables in each tree height and DBH were developed with country-specific carbon emission factors (WD = 0.445 t/㎥, BEF = 1.445, R = 0.255) of P. densiflora. As the results of analysis in carbon uptake for each province, the values were high with Gangwon-do 9.4 tCO2/ha/yr, Gyeongsandnam-do and Gyeonggi-do 8.7 tCO₂/㏊/yr, Chungcheongnam-do 7.9 tCO₂/㏊/yr and Gyeongsangbuk-do 7.8 tCO₂/㏊/yr in order, and Jeju-do was the lowest with 6.8 tC/㏊/yr. Total carbon stocks of P. densiflora were 127,677 thousands tC which is 25.5% compared with total percentage of forest and carbon stock per hectare (ha) was 84.5 tC/㏊ and 7.8 tCO₂/㏊/yr, respectively.

Evaluation of stem taper models fitted for Japanese cedar (Cryptomeria japonica) in the subtropical forests of Jeju Island, Korea

ABSTRACTThis study was conducted to evaluate the performance of the five stem taper models in predicting the diameter over bark at any given height (d) and total volume of Japanese cedar (Cryptomeria japonica D.Don) in the subtropical forests of Korea. The four fit statistics used in this study were standard error of estimate (SEE), mean bias (), mean absolute bias (MAB), and coefficient of determination (R2). For the lack-of-fit statistics, SEE, MAB, and of the five models in predicting d in the different relative height classes and in predicting the total volume in the different diameter at breast height (D) classes were determined. Results of the model evaluation indicated that the Kozak88 stem taper model had the best performance in most of the fit statistics followed by Kozak02 stem taper model. The Kozak88 model also provided the best performance in the lack-of-fit statistics having the best SEE, MAB, and in predicting d in most of the relative height classes. This model consistently performed well in estimating the total volume of Japanese cedar in the different D classes as compared to other stem taper and volume models. These stem taper equations could serve as a management tool for forest managers to accurately predict the d, merchantable stem volumes, and total stem volumes of the standing trees of Japanese cedar in the southern plantation of Korea.

Deriving compatible taper functions from volume ratio equations based on upper-stem height

A very common model for prediction of tree stem volumes to upper-stem height or diameter limits is the use of a merchantable to total volume ratio function multiplied by a total stem volume function. Many users of these prediction systems also desire taper equations that can predict heights to upper-stem diameters. While taper equations compatible with volume ratio equations have been used for many years, compatible taper equations from volume ratio equations that are functions of upper-stem height have been used infrequently. Yet many studies have indicated that height-based ratio equations perform well and frequently have statistics of fit that are comparable with diameter-based volume ratio equations. Compatible taper equations derived from height-based ratio equations are presented here. The methodology that uses height-based merchantable to total volume ratios does not require the solution of a differential equation after differentiating the height-based volume ratio, as is necessary when using the method of deriving taper equations from diameter-based merchantable to total volume ratios. This could be an advantage depending on the complexity of the ratio function. Example taper equations fitted to loblolly pine (Pinus taeda L.) data from the southeastern USA and the state of Oklahoma, USA, indicate good fit to these data, whether fitted directly to taper data or implicitly by using parameters fitted to volume ratio data.

Stem taper equation analysis for Larix kaempferi species in the Central Region of South Korea

ABSTRACTTaper equation was developed to predict diameters at specific height for Larix kaempferi species in the Central Region of South Korea. The sampled trees that were collected through destructive sampling ranged from 0.60 to 47.90 cm DBH with total height ranging from 2.00 to 33.00 m. The dataset was randomly split into two: 80% for initial model fitting and 20% for model validation. The combined that means 100% dataset was used for final model fitting. Statistics of fit were used as criteria, including the coefficient of determination (R2), standard error of the estimate (SEE), bias (Ē), the absolute mean difference (AMD), and the Akaike information criterion (AIC) values and weight (AICw), with a rank analysis being applied. Initial model fitting utilized a total of nine taper equations, with the three segmented taper equations and another three non-segmented determined for model validation and final model fitting. Kozak02 equation, which had not yet been evaluated for L. kaempferi species, indicated the best performance for the species in the Central Region of South Korea. Upon comparison, the ability of this study to predict diameters at specific height and stem volume was better than the existing taper equation for L. kaempferi in South Korea.

VOLUME AND TAPER EQUATIONS FOR COMMERCIAL STEMS OF Nothofagus obliqua AND N. alpina

ABSTRACT Timber volume of standing trees is essential information for management decisions. The increasing need to optimize the potential capacity of forests maintaining their conservation, requires the quantification of the different potential possible timber products. The aim was to adjust taper equations to determine volumes of different timber products for commercial stems of Nothofagus alpina and N. obliqua. Trees of both species were randomly selected in harvesting areas of Lanin National Park (Argentina). Trees were felled and cut into commercial logs, measuring diameter with bark at different heights up to the beginning of the crown, and for each tree the diameter at breast height and total height. Five taper equations were selected and non-linear regression processes were employed for the fittings. We obtained the volume through the integration of the stem profile equation and the rotation in the space thereof through solid of revolution. The Bennet and Swindel (1972) model was selected for both Nothofagus species, obtaining similar equation parameters and differences were observed at the top of the stems of larger trees. For this the use of an integrated model is not recommended. With the obtained equations it is possible to: (i) estimate volume at different heights and for different commercial diameters, and (ii) predict the height at which both species reach to a certain diameter. The model presented some statistical limitations (e.g. multicollinearity), however, the fitting of the equation and the easy understanding of the outputs support it as a useful tool in a broad range of forest applications.

Stem taper and volume models for natural cedar and Taurus fir mixed stands in Bucak District

Abstract: In this study, we assessed the performance of different types of taper equations for predicting tree diameters at specific heights and total stem volumes for mixed stands of Taurus cedar ( Cedrus libani A. Rich.) and Taurus fir ( Abies cilicica Carr.). We used data from mixed stands containing a total of 131 cedar and 124 Taurus fir trees. We evaluated six commonly used and well-known forestry taper functions developed by a variety of researchers (Biging (1984), Zakrzewski (1999), Muhairwe (1999), Fang et al. (2000), Kozak (2004), and Sharma and Zhang (2004)). To address problems related to autocorrelation and multicollinearity in the hierarchical data associated with the construction of taper models, we used appropriate statistical procedures for the model fitting. We compared model performances based on the analysis of three goodness-of-fit statistics and found the compatible segmented model of Fang et al. (2000) to be superior in describing the stem profile and stem volume of both tree species in mixed stands. The equation used by Zakrzewski (1999) exhibited the poorest fitting results of the three taper equations. In general, we found segmented taper equations to provide more accurate predictions than variable-form models for both tree species. Results from the non-linear extra sum of squares method indicate that stem tapers differ among tree species in mixed stands. Therefore, a different taper function should be used for each tree species in mixed stands in the Bucak district. Using individual-specific taper equations yields more robust estimations and, therefore, will enhance the prediction accuracy of diameters at different heights and volumes in mixed stands. Keywords: Segmented model, compatible equation, stem form, merchantable volume, autocorrelation, F- test Received (Gelis): 08.02.2017 - Revised (Duzeltme): 17.03.2017 - Accepted (Kabul): 28.04.2017 Cite (Atif): Ozcelik, R., Dirican, O., 2017. Individual taper models for natural cedar and Taurus fir mixed stands of Bucak Region, Turkey. Journal of the Faculty of Forestry Istanbul University 67(2): 336-354. DOI: 10.17099/jffiu.290845

Taper equations based on nonlinear mixed effect modeling approach for Pinus nigra in Çank&amp;#305;r&amp;#305; forests

In this study, statistical nonlinear mixed effect models were used to model taper of individual trees in Pinus nigra stands distributed within the Cankiri Forests. The data from 210 trees that were felled from Pinus nigra stands were used in this study. Three tree taper equations were fitted and evaluated based on the sum square error (SSE), mean square error (MSE), root mean square error (RMSE) and the adjusted coefficient of determination (R²adj). The Jiang et al.'s equation was found to produce the most satisfactory fits with the SSE (4125.7), MSE (2.1771), RMSE (1.4755) and (0.976). The stem taper equation of Jiang et al. was used within the scope of mixed-effect model structures that involved both random and constant effect parameters. The nonlinear mixed-effect modeling approach for the stem taper equation of Jiang et al. with SSE (3254.8), MSE (1.71759), RMSE (1.3119) provided much better fitting and precise predictions than those produced by the nonlinear fixed effect model structures for this model. Within various sampling scenarios including different numbers of the sub-sample trees based on some sampling strategies from the validation data set, the sampling scheme with three top diameter sub-sample in a tree produced the best predictive results (SSE = 313.5321, MSE = 0.8637 and RMSE = 0.9345) in relation to the fixed effect predictions.

Estimativa do Afilamento do Fuste de Araucária Utilizando Técnicas de Inteligência Artificial

RESUMO O objetivo deste estudo foi comparar o desempenho de técnicas de inteligência artificial com funções de afilamento e avaliar a contribuição da idade nessa estimativa. O conjunto de dados foi composto por 135 observações, abrangendo as idades de 6, 12, 18, 24 e 43 anos de um povoamento de Araucaria angustifolia. As funções de afilamento ajustadas foram Kozak modificado, Schöepfer, Hradetzky e Garay. Os modelos de inteligência artificial utilizados foram: RNA e árvore modelo (M5P). Os vetores de entrada foram as mesmas variáveis utilizadas nas equações de afilamento e também o mesmo arranjo com a adição da idade. Foram utilizados 70% dos dados para ajuste e 30% para validação. A função de afilamento de Hradetzky forneceu o melhor ajuste. Dentre os modelos avaliados, a RNA propiciou as melhores estimativas, com destaque para a RNA com adição da variável idade. O desempenho da M5P foi satisfatório, porém, inferior às demais técnicas utilizadas.

Development and evaluation of teak (Tectona grandis L.f.) taper equations in northern Thailand

Taper refers to the general decrease in the regular outline of a solid body from its base to its tip. Taper models are used to estimate the volume and value of wood products from harvesting trees. Teak (Tectona grandis L.f.) is highly valued as one of the world's most preferred timbers and a teak taper equation is required to inform optimal harvesting strategies given the limited plantation resource available in Thailand. Teak taper equations were developed and evaluated based on 331 sample trees collected in 2014 from eight plantations in northern Thailand aged from 10 to 46 yr using two taper model formulations—the Kozak variable-exponent taper model and the Goodwin cubic polynomial model comprising hyperbolic and parabolic terms. Variants based on both model types were fitted using nonlinear regression analysis with diameter at breast height, total tree height and height of girth measurement as the independent variables to estimate diameter underbark at the nominated height. Goodness-of-fit and leave-one-out cross validation with lack-of-fit statistical testing combined with extensive graphical analysis of residuals were used to select the best model. A Goodwin model variant (named FIO-teak1 as the first plantation teak taper model known to be published in Thailand) provided the best estimates of volume and diameter underbark. A simple case study confirmed that FIO-teak1 in combination with the Farm Forestry Toolbox software package could assist teak plantation managers in decision making associated with optimizing log grade value based on standing tree inventory data.