Smalian's Formula Research Articles

A non-destructive approach to estimate buttress volume using 3D point cloud data

Buttressed trees provide mechanical support for themselves and offer essential ecological functions, such as nutrient acquisition, while being one of the largest sources of volume or biomass estimation variation in tropical forests. In this study, we collected 51 buttressed trees from (33) Democratic Republic of Congo, (12) Indonesia, and (6) Costa Rica, including (48) point clouds, and (3) destructive measurement. Specifically, we compared the performance of the Alpha Shape Algorithm (ASA) and the Slice Triangulation (ST) method on buttress volume estimation based on 30 point clouds with two species. Six point clouds from Costa Rica were used to validate the 3D surface reconstruction method. Meanwhile, we developed three allometric models based on 36 point clouds: a diameter above the buttress-based (DAB, 39 to 203 cm) model, a diameter computed from the non-convex area (Darea130) model, and the convex hull perimeter (Dconvex130) of the breast height model. The developed models were validated with independent data, including (6) point clouds and (3) destructive measurements, to highlight the broader contextualization and application of these methods. Volume estimated by the ASA and ST showed a high agreement with the reference volume acquired using the Smalian formula (relative RMSE of 0.07 and 0.11, respectively, regardless of species effect). ASA was also robust when modeling trees with more and shallower horizontal buttresses. Darea130 was the most accurate predictor to estimate buttress volume, with a lower Akaike information criterion (−66.25) than DAB (−59.55) and Dconvex130 (30.56); however, DAB and Darea130 (relative RMSE of 0.21 and 0.23, respectively) showed similar performance when validated with independent datasets. Our results indicate that the ASA approach performs better than both the ST and allometric models used in this study. Furthermore, the ASA method can help correct the bias in the present and past estimates of volume and biomass of large trees, which are foundational components for understanding biomass allocation and dynamics in tropical forests contemporary fields.

Further application of using a personal laser scanner and simultaneous localization and mapping technology to estimate the log’s volume and its comparison with traditional methods

The aim of this study was the development of a methodical processing line for estimating the log’s volume from scanning logs using a long-range high-speed personal laser scanner (PLS) GeoSLAM ZEB HORIZON and simultaneous localization and mapping (SLAM) technology in an open-source software framework of Cloud Compare. Additionally, the accuracy and precision of using PLS and the suggested method when measuring roundwood volume was examined compared to measurements made using a xylometer and estimations obtained from applying the formulae of Huber, Smalian and Newton. For this purpose, several parameters were measured in 50 logs of Norway spruce with an average length of 2.53 m and a mean diameter of 19.97 cm. Afterwards, the volume of these 50 logs was measured with a xylometer. The results of these measurements served as reference values. The same 50 logs were subsequently scanned with the PLS. The scans were converted into point clouds and were analyzed in Cloud Compare to estimate the volume of the scanned logs. Next, the root mean square error (RMSE) and the mean bias error (MBE) as well as their relative values were calculated for the volumes determined in Cloud Compare and estimated with the above mentioned formulae. The calculated RMSE (and relative RMSE) determined a deviation of the logs' volumes estimated in Cloud Compare from the xylometric volumes of 2.88 dm3 (3.54%) whereas the deviations of the log’s volumes calculated applying the formulae of Huber, Smalian and Newton from the xylometric volumes were respectively 9.63 dm3 (11.83%), 10.33 dm3 (12.69%) and 4.69 dm3 (5.76%). The calculated MBE (and relative MBE) showed that the estimated volumes in Cloud Compare and those using the formulae were overestimated, with the lowest overestimation of 0.10 dm3 (0.12%) in Cloud Compare and the highest, 5.50 dm3 (6.75%), using the Smalian formula. Therefore, it can be stated that results of suggested methodical processing line came closest to the logs' volumes obtained with the xylometer, i.e., they were more accurate and precise compared to the conventionally formulae for log’s volume estimation. The implementation of this method has the potential filling a gap towards a wall-to-wall complete digitization of the roundwood commercialization and ensure transparency and acceptance between the stakeholders involved in the wood supply chain.

Regression models for estimating stem volume of Aquilaria malaccensis (Lam.) in North East India

Aquilaria malaccensis Lam. (Agar), a Critically Endangered tree species native to the tropical rain forests of South and South East Asia, is known for eaglewood and its oil of medicinal and aromatic value. In order to develop stem volume prediction models for agar tree, an exercise was carried out with 441 trees selected in North East India, by non-destructive sampling. The required variables, such as, diameter at breast height (D), tree height (H) and fraction diameters at 1 m interval were physically measured for estimating the volume of each fraction using Smalian formula, and summing up the volumes of fractions to yield the volume of the tree. A comparison of different stem volume models showed that the power function V=aDb and the polynomial of degree-3 V=a+bDH+cD2H+dDH2were the best fitting models for single independent variable D and two independent variables D & H, respectively. The regression models shall be useful for farmers to optimize their income while selling the agar wood. These agar specific regression models will also be helpful to fix the quota for agar wood harvest and trade in the country, while implementing the Convention on International Trade in Endangered Species of Fauna and Flora (CITES).

Allometric Equations for Volume, Biomass, and Carbon in Commercial Stems Harvested in a Managed Forest in the Southwestern Amazon: A Case Study

Forests in the southwestern Amazon are rich, diverse, and dense. The region is of high ecological importance, is crucial for conservation and management of natural resources, and contains substantial carbon and biodiversity stocks. Nevertheless, few studies have developed allometric equations for this part of the Amazon, which differs ecologically from the parts of Amazonia where most allometric studies have been done. To fill this gap, we developed allometric equations to estimate the volume, biomass, and carbon in commercial trees with diameter at breast height (DBH) ≥ 50 cm in an area under forest management in the southeastern portion of Brazil’s state of Acre. We applied the Smalian formula to data collected from 223 felled trees in 20 species, and compared multiple linear and nonlinear models. The models used diameter (DBH) measured at 1.30 m height (d), length of the commercial stem (l), basic wood density (p), and carbon content (t), as independent variables. For each dependent variable (volume, biomass, or carbon) we compared models using multiple measures of goodness-of-fit, as well as graphically analyzing residuals. The best fit for estimating aboveground volume of individual stems using diameter (d) and length (l) as variables was obtained with the Spurr model (1952; logarithmic) (root mean square error (RMSE) = 1.637, R² = 0.833, mean absolute deviation (MAD) = 1.059). The best-fit equation for biomass, considering d, l, and p as the explanatory variables, was the Loetsch et al. (1973; logarithmic) model (RMSE = 1.047, R² = 0.855, MAD = 0.609). The best fit equation for carbon was the Loetsch et al. (1973; modified) model, using the explanatory variables d, l, p, and t (RMSE = 0.530, R² = 0.85, MAD = 0.304). Existing allometric equations applied to our study trees performed poorly. We showed that the use of linear and nonlinear allometric equations for volume, biomass, and carbon can reduce the errors and improve the estimation of these metrics for the harvested stems of commercial species in the southwestern Amazon.

Growth and survival of potential tree species for carbon-offset in degraded areas from southeast Brazil

Abstract Brazil must restore 12 million hectares of degraded areas by 2030 to meet its goal of the Paris Global Climate Agreement (PGCA). In view of this, the development of mixed planting projects related to carbon-offset in degraded areas is increasing, which demonstrates environmental and social responsibility of corporate and governmental organizations. Despite the great potential of mixed restoration plantations to mitigate climate change, Brazil must overcome major challenges in achieving the ratified goals of the PGCA as well as the effectiveness of its carbon-offset projects. In this context, this study has focused on the evaluation of the growth and survival of tree species in a carbon-offset plantation from a degraded area in southeastern Brazil. Five-hundred-and-nine seedlings (15 forest species) were planted in a completely randomized design. Diameter at the soil level and height of individuals were measured at 40 months. Three individuals of each species were selected and was scaling by a non-destructive method. Timber volume was estimated from the sum of the volume of the sections of the individuals, obtained by the Smalian formula. The average annual carbon increment of the individuals was estimated by the equation adjusted from the Schumacher & Hall model. The potential of carbon-offset of the tested plants was evaluated from the SP and μC analysis. The REML (Restricted Maximum Likelihood)/BLUP (Best Linear Unbiased Prediction) method was used to predict μC values for species ordering with carbon -offset potential. Survival was 47.54% at 40 months. The carbon stock of the planting was 2.60 ± 6.2 Kg C individual−1, and the average annual increase in carbon (AAIC) was 0.78 Kg C individual−1year−1. The AAIC value was lower than the average value stipulated for carbon-offset projects (6.0 Kg CO2 individual−1 year−1). Pioneer species contributed more to carbon storage than non-pioneer species.

EXATIDÃO DE DENDRÔMETROS ÓPTICOS PARA DETERMINAÇÃO DO VOLUME DE ÁRVORES EM PÉ

http://dx.doi.org/10.5902/1980509818458O objetivo desse trabalho é verificar a exatidão dos dendrômetros ópticos Criterion 400 e RC3H, estudando a qualidade das medidas de cubagem da árvore em pé pelo uso desses dendrômetros. O trabalho foi desenvolvido na Estação Experimental de Itatinga - SP que pertence à Universidade de São Paulo (ESALQ-USP). Amostraram-se no total 175 árvores em três parcelas de Eucalyptus grandis. O diâmetro do fuste das árvores em pé foi mensurado com os dois dendrômetros ópticos nas distâncias de 0,1; 0,4; 0,7; 1,0; 1,3; 2,0 m e a partir desse ponto, de metro em metro ao longo do tronco até os 8 m de altura. Após a cubagem em pé foram derrubadas as árvores e obtido o diâmetro nas diferentes posições com uma suta e trena nas mesmas posições em que se realizou a cubagem não destrutiva. De posse dos diâmetros foi calculado o volume por secção e por árvore individual pelo uso da fórmula de Smalian para posterior comparação dos métodos. Analisando as medidas do diâmetro do fuste e volume por árvore percebe-se que os dois dendrômetros forneceram medidas subestimadas de modo geral, porém, o Criterion foi o que resultou nas melhores estimativas. Para o diâmetro e volume por árvore, o Criterion demonstrou erros subestimados médios de aproximadamente 1 cm (10%), enquanto o RC3H resultou em erros superiores aos 5 cm (30%) em média. Portanto, quando se deseja maior confiabilidade e exatidão das variáveis observadas de forma não destrutiva, o Criterion apresentou melhores resultados.

Hacia una descripción de fuste para el Laurel Cordia alliodora en sistemas agroforestales en el Bosque Protector Sumaco, Ecuador

El Bosque Protector Sumaco esta caracterizado por extensas áreas de bosque secundario en la zona de amortiguamiento del Parque Nacional Sumaco-Napo-Galeras a una altitud de 1160 m y con una precipitación promedio de 4000 mm año-1. Un adecuado manejo de estas áreas requiere información básica sobre el crecimiento y producción dependiendo de la regeneración del Laurel Cordia alliodora en sistemas agroforestales. El presente estudio muestra los resultados sobre diferentes modelos para determinar el coeficiente de forma, volumen, perfil de fuste y desarrolla un sistema de ecuaciones matemáticamente y numéricamente consistente para Cordia alliodora bajo un sistema agroforestal en la comunidad indígena de Wamaní. Para la búsqueda de los parámetros de las funciones de volumen total, el cociente de forma, la descripción del perfil de fuste y la función de conicidad, un total de 308 árboles fueron medidos el diámetro a 1, 3, 2, 4, 6, 8, metros, a la mitad del árbol y la altura total en metros. Se presenta un modelo para determinar el volumen del Laurel en base al cociente de forma, diámetro y altura total. El modelo de perfil de fuste a través de la función Pain demuestra ser un modelo muy apropiado para describir este parámetro, así como también para calcular el volumen con mayor exactitud. En este estudio la consistencia algebraica y numérica para determinar el volumen y el diámetro a una establecida altura del fuste a través de la función de conicidad fue verificada. Todos estos modelos pueden ser utilizados en la práctica, constituyéndose estos en la esencia del negocio de la madera.

PREDICTION OF THE ERROR GENERATED BY SMALIAN'S AND HUBER'S FORMULAE IN VOLUME MEASUREMENTS OF Pinus caribaea (MORELET).

One of the common methods of volume estimation is the use of mathematical equations.Among such equations, Huber's, Smalian's and Newton's formulae are commonly usedand it is believed that Newton's formula which uses bottom, mid and top diameter of thelog and log length gives most precise volume estimations than Smalian's or Huber'sformulae. The latter two equations use only log length and end diameters and middiameter respectively. Usually for volume calculations Huber's formula is used due to theinvolvement of less measurements (mid diameter and log length)Present study was conducted in the 26 year old Pinus caribaea plantation in YagiralaForest Reserve situated in the low country wet zone of Sri Lanka. In order to representthe whole area of the forest, stratified random sampling method was used and one O.OShasample plot was laid in each stratum. Altogether 3 plots were selected.Each tree was divided into twelve one meter long sections using a ranging staff. Threediameters i.e., bottom, mid and top diameters of each section were measured using theSpiegel relascope. Other than section diameters, diameter at breast height (dbh) of thetree was measured using the diameter tape.Cumulative section volumes per each tree were calculated separately from Im to 12musing Huber's, Smalian's and Newton's formulae. other than the above method volumewas calculated using section lengths separately up to twelve meter long sections usingNewton's formula to test whether log length affect the Newton's volume. When testedthere was no significant difference between two volume types. However, for furtheranalysis Newton's volume calculated using the sectio•. length separately was used.For each cumulative volume (i.e., lm to 12m) calculated using different formulae werestatistically tested using one way ANOVA. According to the results 6m is the maximumlength for Huber's formula to predict the volume accurately. However it does not show asignificant difference between Smalian's and Newton's formulae up to twelve metersection length.Generally Huber's formula underestimates and Smalian's formula overestimates thevolume. Therefore it is recommended to use Huber's formula for volume calculations dueto it's ease of use, keeping the log length shorter than 6m.

RELATIONSHIP BETWEEN STEM BIOMASS AND VOLUME OF Pinus caribaea IN THE YAGIRALA FOREST RESERVE

The biomass is an important measurement in commercial forestry maintained to producepulp, paper, chips, fuel wood products etc. The estimation of the biomass of the tree is notan easy task and few studies were carried out so far.The present study was conducted in the 25 years old Pinus caribaea plantation in YagiralaForest Reserve, which is in the low country wet zone. According to the geographicaldifferences in the plantation, i.e., valley, slopes and ridge, stratified random sampling wascarried out and two 0.05 ha circular plots were established in each stratum. Altogether 6plots were used for the data collection.The diameter at breast height (dbh), total height were measured for all the trees in theseplots and after dividing the tree stem into several sections, the length and end and middiameters of each section was measured using the Spiegel relaskop.The volume of the stem was estimated by calculating section volumes. Smalian's andNewton's formula were used to estimate the section volumes except for the final section atthe top, which was assumed as a cone. In order to save time, one plot was measured forNewton's formula and the rest was measured for Smalian's formula. Then a relationshipwas build to estimate Newton's volume (Ne) using Smalian's volume (Sm) as theexplanatory variable (equation I). The R2value was 99.9%.Ne = 0.976 * Sm (1)Biomass of the tree was estimated by extracting core samples at the breast height and midheight of the tree. The density of the core samples were estimated using oven dry weightand the green volume of the core samples. When tested, there was no significant differenceof the density along the stem. Therefore stem biomass was estimated using the density atthe breast height, and the total stem volume. Also there was no significant densitydifferences between three sites.The regression analysis was used with the pooled data to find out the relationship betweenthe stem biomass (W) and the volume (V). Using variable of stem volume and the biomassand its tranformations developed the several models. The best model was selected bychecking the R2 value, standard residual distribution, modelling efficiency and bias. Thebest rclationshin for the hiOI1l;]SS :l1lrl YOIIl"lr ,,·:1< lhr rnll:l1;nn ') whir]' h·w 02 .... 1.. " nr

Volume Table of Raintree (Samanea Saman) in Bangladesh by Regression Technique

Raintree (Samanea saman) is a multipurpose village tree species grown in abundance at southern and northern regions of Bangladesh. Village people need to know estimation procedure for timber inventory of this useful tree species. Data on diameter at breast height (diameter) and total height (height) of 205 standing sample trees were collected by Spiegel relascope for the purpose. The sample trees with diameter ranging 21 cm - 91 cm and height ranging 10 m - 20 m were considered for measurement. Volumes (m3) of individual trees were computed by Smalian formula. A total of 10 linear models of volume on diameter and volume (V) on diameter (D) and height (H) were examined with the sample trees. A few statistics of F, t, mean square error, multiple correlation coefficient and Furnivall Index was computed and tested for investigation of best fitted models. The two models of In(V) = 8.3023 + 2.1746 In(D) and In(V) = –9.1864 + 1.85502 In(D) + 0.8234 In(H) were found to be best fitted models. They have been recommended to estimate volume of large scale standing Raintree trees.

Influence of section lengths on volume determination in eucalyptus trees

The aim of this work was to assess the influence of different section lengths on the determination of eucalyptus tree stem (with bark) volumes and its implications in forest inventory procedures. The 40 Eucalyptus grandis trees used, all from the municipality of Viçosa, Minas Gerais state, were 77 months old. The volume of the stems (with bark), whose maximum diameter was 3,0 cm, was obtained through the Smalian formula, with sections 1.0, 2.0 and 3.0 m long. Longer sections lead to overestimations of the volume of the trees' basal part and, consequently, of their total volume. Different statistical tests led to different conclusions regarding the similar volume estimates resulting from experiments using different section lengths4. Volumetric equations adjusted with longer sections may introduce bias errors in forest inventory procedures.

Estimativa do volume de madeira partindo do diâmetro da cepa em uma área explorada de Floresta Amazônica de Terra Firme.

O objetivo deste estudo foi estimar o volume de árvores de uma floresta tropical de terra firme, considerando apenas o diâmetro da cepa (d0) como variável independente. A área de estudo está localizada no município de Breu Branco, PA. Um total de 113 árvores com DAP ≥ 51 cm, pertencentes a diferentes espécies e classes de diâmetro, foram cubadas rigorosamente. A cubagem rigorosa foi feita pelo método de Hohenadl, considerando a divisão do tronco comercial em dez seções de comprimentos iguais e o cálculo do volume de cada seção da tora foi feito pela fórmula de Smalian. Equações de volume foram ajustadas para estimar o volume comercial das árvores em função de d0e também em função do DAP, para efeito de comparação. Os resultados mostraram que d0 apresentou boa relação com o volume comercial de árvores em floresta de terra firme, e pode ser utilizado no ajuste de modelos matemáticos visando a estimar o volume comercial de árvores. Não foi observada diferença significativa entre os valores reais de volume comercial de árvores e os volumes estimados, gerados partindo de uma equação linear ajustada em função de d0, demonstrando que é possível obter com precisão, informações de volume partindo de d0.

Estimating tree bole volume using artificial neural network models for four species in Turkey

Tree bole volumes of 89 Scots pine ( Pinus sylvestris L.), 96 Brutian pine ( Pinus brutia Ten.), 107 Cilicica fir ( Abies cilicica Carr.) and 67 Cedar of Lebanon ( Cedrus libani A. Rich.) trees were estimated using Artificial Neural Network (ANN) models. Neural networks offer a number of advantages including the ability to implicitly detect complex nonlinear relationships between input and output variables, which is very helpful in tree volume modeling. Two different neural network architectures were used and produced the Back propagation (BPANN) and the Cascade Correlation (CCANN) Artificial Neural Network models. In addition, tree bole volume estimates were compared to other established tree bole volume estimation techniques including the centroid method, taper equations, and existing standard volume tables. An overview of the features of ANNs and traditional methods is presented and the advantages and limitations of each one of them are discussed. For validation purposes, actual volumes were determined by aggregating the volumes of measured short sections (average 1 meter) of the tree bole using Smalian's formula. The results reported in this research suggest that the selected cascade correlation artificial neural network (CCANN) models are reliable for estimating the tree bole volume of the four examined tree species since they gave unbiased results and were superior to almost all methods in terms of error (%) expressed as the mean of the percentage errors.

Comparison of formulae for estimating tree bole volumes of Pinus sylvestris

Tree bole volumes of 103 Scots pine (Pinus sylvestris L.) were estimated using nine methods (paracone, centroid, control-variate with one and two measurement points, Huber's formula, antithetic method using importance sampling, standard volume table, local volume table, importance sampling using one and two measurement points, and a taper equation). These estimates were compared with “true” volume of each tree bole which was determined by aggregating the volumes of measured short sections (average 1m) using Smalian's formula. The antithetic method performed well in terms of mean square error and tolerance intervals, which indicate the precision of the estimates. For both importance and control-variate sampling, better precision of the estimate may be achieved by taking measurements at two positions along a stem. The results showed that the antithetic method, importance sampling and control-variate method with two measurement points, paracone and centroid methods are useful alternatives to local volume tables and other standard formulae and are recommended for tree bole volume estimations of Scots pine in Turkey. However, in practice, convenience and economics play an important a role in the decision whether to use given estimation methods. On that basic, the paracone or centroid method may be recommended for use in tree volume estimating, as these are the easiest methods to apply, are less time consuming than other methods and show very acceptable statistical performance.

Volume ratio models for prediction of merchantable volumes of Radiata pine in the Basque Country

Four volume ratio equations were fitted as part of a Pinus radiata yield tables updating project in plantations within the Basque Country. In this approach, volume ratio equation gives the proportion of merchantable volume to total volume using final diameter and breast height diameter as independent variables. For models fitting, data from 71 felled trees were used. Trees were cubed by the Smalian formula, obtaining from each one both, the total volume over bark and the merchantable volume over bark for 7, 10, 15, 20, 25 and 30 cm of final diameter. Despite the four models exhibited a high precision to estimate merchantable individual volume, the model 1 (Parresol) had the best performance. They are considered original for this species in Spain.

Tree Trunk Volume of Shorea Species Case Study in Darmaga and Haurbentes Research Forest in West Java Indonesia

Activities of forest management require a well planned, systematic and well directed handling, so that achieving maximal and beneficial results in terms of economic, ecological and social prospects. In relevant to data on trunk volume of available tree stands are required to set up a plan intended to produce sustainable timber. The research was conducted in the Darmaga and Haurbentes research forests of the Forest and Nature Conservation Research and Development Center located in West Java. The trunk volume model as conceived was based on the Smalian's formula employed to particular tree species (i.e. S h ore a bala ng gera n ; S. gu is so ; S . leprosula; S. mecistoptery x ; S . ova l is; S. p a le m ba n ic a; S. p i n a n g a; S. s e lani ca ; S. sem i nis and S . st e nopt e ra ) . This model could estimate the trunk volume with non-destructive sampling. In this way, therefore, the trunk volume can be estimated from the tree diameter on a single variable.

TOMRUK HACMİNİN TAHMİNİNDE KULLANILAN CENTROID METOD VE DÖRT STANDART FORMÜLÜN KARŞILAŞTIRILMASI

Centroid Sampling was terted on 20 logs of Pinus brutia (Pinus brutia Ten.) and 17 logs of Cedar (Cedrus libani A.Rich) all of which were measured in detail. The volume of each log was estimated using Huber's, Smalian's, Newton- Riecke's, Hossfeld's formulas and Centroid Sampling. These estimates were compared with “true” volume of each log which was determined by aggregating the volumes of measured short (10 cm) using Smalian's formula. According to the mean error of the Centroid estimates of the log volumes was not significant for Pinus brutia (Pinus brutia Ten.) and Cedar (Cedrus libani A.Rich) was less than those derived form Huber's, Smalian's, Newton-Riecke's, Hossfeld's formulas. Keywords: Centroid sampling, log volume, Taurus Cedar, Red Pine.

Comparison of Formulas for Estimating Volumes of Butt Logs of Appalachian Hardwoods

Abstract A database comprising measurements of over 700 trees and logs of Appalachian hardwoods was used to compare the performance of five formulas (Newton, Huber, Smalian, Bruce, and that of the centroid method)for estimating the volumes of butt logs. In terms of bias and precision, the centroid method was clearly superior to all other methods. Bruce's formula performed better than Smalian's formula and is recommended for use when only the ends of butt logs are accessible for measuring diameter, as in log stacks. North. J. Appl. For. 13(1): 5-7.

Use of a tree volume equation based on two lower-stem diameters to estimate forest volume from sample tree counts

A recently developed method of individual-tree volume prediction uses measurements of two lower-stem diameters, rather than the more traditional DBH and height measurements, to estimate stemwood. One form of the equation is linear with respect to volume between the two diameter measurements, as computed by Smalian's formula, and can be algebraically rearranged into the sum of two equations, one linear with respect to the square of the topmost lower-stem diameter, the other linear with respect to the square of the bottom lower-stem diameter. These two equations have the same form as local volume equations that are linear functions of the square of diameter. Because of this, a variation of horizontal point sampling can be used to select trees with probability exactly proportional to each of the equations. Forest volumes can be estimated from counts of trees obtained by comparing the point sampling gauge angle with individual tree diameters at the lower-stem diameter measurement points used by the individual-tree volume equation. To account for the negative intercept term in the linear equations, trees within a small fixed-radius plot are not included in the counts.

Upper stem volumes from stem analysis data: an overlapping bolts method

Studies to develop equations for upper stem taper, volume, and weight require observed values of upper stem volume. Tree volumes up to various upper stem diameters calculated using Smalian's formula throughout the stem length on 4- to 8-ft (1 ft = 0.30 m) bolts may overestimate true volumes by 1 to 4%. Calculating the butt bolt's volume with Newton's formula improves the estimates considerably. A new approach that uses Newton's formula on successive overlapping pairs of bolts produces even more improvement and still gives volume estimates for each bolt. The overlapping bolts method on 6-ft bolts is equally as precise as the conventional non-overlapping method on 4-ft bolts and would result in a 33.3% savings in sampling effort.