Horizontal Point Sampling Research Articles

Determination of optimal tree height models and calibration designs for Araucaria araucana and Nothofagus pumilio in mixed stands affected to different levels by anthropogenic disturbance in South-Central Chile

Key messageHere, we present a workflow for determining the optimal tree height model and calibration design for forests affected to varying degrees by anthropogenic disturbance. For mixed Araucaria-Nothofagus forests, tree height predictions in newly surveyed stands are most accurate and effective when the height of up to five random trees is measured to recalibrate predefined nonlinear mixed-effects models.ContextAraucaria-Nothofagus forests in Chile are affected by anthropogenic disturbances such as intentional forest fires, grazing, and seed harvesting, causing forest structure to become more heterogeneous. This also challenges tree height predictions, which are required for yield estimations, carbon accounting, and forest management, since height measurements of standing trees are often considered too costly, difficult, and imprecise.AimsHow does the structure of these forests vary by different levels of anthropogenic disturbance? Which models for estimating tree height of Araucaria araucana and Nothofagus pumilio are most reliable and generally usable? And considering their application in stands they have not been fitted to, which calibration design is optimal for these models?MethodsTwelve stands were surveyed and classified into four different intensities of anthropogenic disturbance. In 25 to 36 plots per stand, horizontal point sampling measurements of stem diameter as well as of height of selected trees were carried out. Different quantitative stand-level properties were calculated to determine forest structure, which was compared among stands by cluster analysis. To identify the optimal height-diameter (H–D) model, simple models including diameter only as well as generalized models including stand variables were tested, each additionally extended by a nonlinear mixed-effects (NLME) modeling framework accounting for nested and random effects. To further determine tree height in new stands, the optimal model calibration design was identified involving the empirical best unbiased predictor technique.ResultsForest structure greatly varied among stands affected by different levels of anthropogenic disturbance, which challenged the development of tree height prediction models. Of all the simple H–D models considered, the Gompertz model was the best for A. araucana and the Näslund model for N. pumilio. The models progressively improved by adding stand variables and using NLME techniques. However, our final model comparisons indicate that a calibrated simple NLME model without stand variables should be preferred. It was further found that the optimal calibration design is to use five randomly selected trees.ConclusionAlthough anthropogenic disturbances can have a complex effect on height-diameter relationships, the same H–D model can be used for stands representing different anthropogenic disturbance levels and recalibrated by cost-effective measurements.

Normal and Bootstrap Confidence Intervals in Bitterlich Sampling

The Bitterlich Sampling (horizontal point sampling) is a common method in forest inventories. By this method, the Horvitz-Thompson estimator is used in a number of independent sampling points for the estimation of overall tree volume in a forest area/stand. In this paper, confidence intervals are constructed and evaluated using the normal approach and two bootstrap methods; the percentile method (Cα) and the bias-corrected and accelerated method (BCα). The simulation results show that the normal confidence interval has better coverage of true value at sample size 10. At sample sizes 20 and 30, it seems that there are no substantial differences in coverage between confidence intervals, although it could be noted a small superiority of BCα method. At sample size 40, the coverage of the three confidence intervals is higher than the nominal coverage (95%).

EQUAÇÕES PARA ESTIMAR ESTOQUE DE CARBONO POR HECTARE NOS FUSTES DAS ÁRVORES DE FLORESTA ESTACIONAL SEMIDECIDUAL

Este trabalho teve por objetivo ajustar equações para estimar o estoque de carbono por hectare nos fustes das árvores, em função de variáveis da floresta obtidas por meio da amostragem por ponto horizontal (método de Bitterlich). Foram amostrados 55 pontos, com um fator de área basal igual a 1, em fragmentos de floresta estacional semidecidual, no município de Viçosa, Minas Gerais. Após o ajuste e a avaliação de diferentes modelos de regressão lineares e não lineares, verificou-se que as equações referentes ao modelo 8 (não linear) foram as mais precisas para estimar o estoque de carbono por hectare nos fustes das árvores.

Efficiency of alternative forest inventory methods in partially harvested stands

Forest inventory is vital to all aspects of forest management and inventory methods can vary greatly in their accuracy, precision, efficiency and cost. In Maine, much of the forestland base has been managed using partial harvesting methods over the past two decades. These partial harvesting methods generally produce highly heterogeneous stand structures and composition. Consequently, it is currently unclear which inventory methods are best given the distinct spatial and structural heterogeneity that is created. We compared efficiency and stand-level inventory estimates using horizontal point, fixed area and horizontal line sampling measurement methods in 16 partially harvested stands across northern and central Maine. Some stand-level variables were sensitive to measurement method (e.g., volume, quadratic mean diameter and small stem density and basal area), while others were less sensitive (e.g., overall basal area and stem density). Efficiency, defined as a combination of precision of volume estimates and measurement time, varied among measurement methods at lower stand basal area values but was similar at higher basal area, with the exception of the fixed area method. Overall, horizontal line sampling proved to be a viable method in post-partial harvest stand conditions. Our results illustrate the trade-offs between precision and time costs involved in several measurement methods under a range of heterogeneous stand conditions.

Practical Implications of Projecting a Horizontal Angle in a Nonhorizontal Manner to Diameter at Breast Height

Horizontal-point sampling is commonly applied during forest inventories. A problem widely known is the error associated with probabilities of selection when projecting horizontal angles along the slope of a site. However, the consequences of the slope created by projecting a horizontal angle to dbh from another height, such as eye height when it differs from 4.5 ft—whereby the angle is no longer horizontal—have not been widely appreciated. Although trivial in many cases, as basal area factor (BAF) increases, dbh decreases, the angle vertex height difference from dbh increases, and the length of the angle from the point to the tree decreases, the reductions in selection probabilities can become meaningful.

Evaluation of <I>n</I>-Tree Distance Sampling for Inventory of Headwater Riparian Forests of Western Oregon

n-Tree distance sampling (NTDS), also known as k-tree sampling and point-to-tree sampling, has been promoted as a practical method for forest inventory. This simulation study evaluated the performance of three NTDS estimators, as compared with fixed plot sampling and horizontal point sampling, for estimating density and basal area in headwater riparian forests of western Oregon. Bias of at least one NTDS estimator was low for both density and basal area when at least six trees were captured at each sample point, but performance of NTDS for density estimation was poor on stem maps exhibiting a clustered pattern. We close with some comments regarding the statistical efficiency of NTDS for riparian area inventory in similar forest conditions.

Vertical Point Sampling with a Camera

Abstract Vertical point sampling has seen relatively little use in practical forestry, in part because existing field techniques are difficult. We show how vertical point sampling can be implemented quickly and easily using a camera. We give tables and equations for calculating the height-squared factor, which plays a role similar to that of the basal area factor in horizontal point sampling. Some suggestions for choosing a height-squared factor are discussed, along with potential applications for further exploration. We illustrate the technique using a case study in southern Maine. Direct estimates with no statistically detectable bias were obtained using height-squared factors greater than 3. The results also suggested that the technique could be used as a correlate in double sampling for variables such as cubic volume, stand density index, and biomass, and possibly board foot volume as well.

Utilization and Modification of Point Sampling and Line Sampling in the Forestry Survey

Problem statement: In the practice of conventional point sampling and line sampling methods in the forestry survey, we often encounter problems such as boundary and hole problems. These problems could introduce bias in the results of forest sampling. Proper modifications are needed. Approach: This study developed novel probability computation approaches in the utilization and modification of horizontal point sampling and line sampling in the forestry inventory. It reviewed conventional point sampling and line sampling methods, identifies specific problems associated with actual forest sampling and provides modification solutions using probability computations. Results: By modifying the original point sampling and line sampling procedures, this study proposed novel solutions to these problems and provides better sampling methods with reduced bias in the forestry survey. Conclusion: In this study, only horizontal gauging for point sampling and line sampling was discussed. For the corresponding problems encountered in vertical gauging, the solutions are similar to the ones for the horizontal gauging sampling. These modifications had been presented with varying levels of complexity. To maintain a balance between precision and costs, modifications with an appropriate level of complexity may be selected.

Rapid Assessment of Relative Density in Mixed-Species Stands of the Northeastern United States

Basal area has shortcomings as a measure of stand density, but it is often preferred for operational assessments because it is easy to measure. Previous work has demonstrated that an additive version of Reineke's stand density index can be estimated by a simple tree count using a modified horizontal point sampling technique. We show that this technique can be extended further to estimate a mixed-species density measure that has been developed for complex stands in the northeastern United States, using wood specific gravity to harmonize the density contributions of different species. The sampling technique provides design-unbiased estimates of stand density from a weighted tree count, where the weights depend on specific gravity but not on diameter. Rounding the specific gravity values for different species in the calculation of estimates introduces a trivial amount of bias but streamlines the procedure for rapid use in the field.

Sampling trees with probability nearly proportional to biomass

It is a truism in the sampling literature that sampling is most efficient when it is conducted with probability proportional to the variable of interest. Variable probability sampling methods have long been applied to trees. The most familiar approach is horizontal point sampling (HPS) which samples trees with probability proportional to basal area. Here, I introduce a generalization of horizontal point sampling (GHPS). GHPS is a simple practical technique for sampling trees with probability proportional to an approximate equation for biomass. The technique requires construction of a gauge, but the gauge need not be complicated. In principle, GHPS should be more efficient than ordinary HPS. This hypothesis was tested with a field trial. Somewhat surprisingly, GHPS was only marginally superior to HPS in terms of sampling variance and efficiency. However, GHPS took no longer to perform, and was not associated with detectable non-sampling error. Results suggest that a well-designed subsampling approach, used in conjunction with GHPS, might lead to appreciable improvements.

Area-Independent Sampling for Total Basal Area

Abstract An unbiased direct estimator of total basal area for a stand is presented; stand area need not be known. Sampling can use horizontal point samples or fixed-area plots distributed on a regular grid or randomly selected. The sample space extends beyond the stand boundary. The estimator for basal area makes no distinction between plots whose centers are interior to the stand boundary and plots whose centers are outside. Only trees within the stand boundary are tallied. For horizontal point sampling, the estimator is the product of the sample tree count, the basal area factor, and the area per grid point, with the latter being derived from grid spacing. This method avoids the complexities associated with most other estimators designed to minimize or eliminate edge bias. The proposed method may require more sample points to achieve the same level of precision as competing estimators. FOR. SCI. 50(4):512–517.

A note on the relationship between the quadratic mean stand diameter and harmonic mean basal area under size-biased distribution theory

This note seeks to extend the utility of size-biased distribution theory as applied to forestry through two relationships regarding the quadratic mean stand diameter. First, the quadratic mean stand diameter's relationship to the harmonic mean basal area for horizontal point sampling, which has been known algebraically from early on, is proved under size-biased distribution theory. Second, a new result, which may prove most valuable in viewing the graphical representation of assumed distributions, is also derived. The results are also shown to apply to the basal area – size distribution, providing a unique duality between the two means.

Comparação de métodos de amostragem para análise estrutural de florestas ineqüiâneas

O presente trabalho foi realizado em um povoamento florestal ineqüiâneo, pertencente à Universidade Federal de Viçosa-MG, objetivando comparar estimativas do número de árvores por hectare, volume por hectare, área basal por hectare, diâmetro médio e altura média do povoamento e número de espécies, utilizando parcelas de área fixa (método I) e amostragem por ponto horizontal (método de Bitterlich), com fatores de área basal K=1, K=2 e K=4 (métodos II, III e IV, respectivamente). Após análises, constatou-se que: a) para atender a um determinado erro de amostragem, há a necessidade de maior número de pontos de amostragem, em comparação ao número de parcelas de área fixa; b) não houve diferença estatística entre as estimativas de volume por hectare, área basal por hectare, diâmetro médio e altura média do povoamento, obtidas nas parcelas de área fixa e nos pontos de amostragem, independentemente do fator de área basal; c) a amostragem por ponto horizontal (método de Bitterlich) poderá ser utilizada para caracterização da composição florística se houver aumento de intensidade amostral ou se a floresta apresentar baixa diversidade de espécies; e d) houve diferença estatística entre o número de árvores por hectare e por classe de diâmetro para os métodos de amostragem estudados. Os métodos II, III e IV subestimaram o número de árvores nas maiores classes de dap (diâmetro à altura do peito) e superestimaram-no nas menores.

Point Relascope Sampling: A New Way to Assess Downed Coarse Woody Debris

Abstract This article presents a practical review of one of two recently developed methods for sampling downed coarse woody debris in forest stands. The method discussed here, point relascope sampling, is closely related to the familiar horizontal point sampling and this relationship is demonstrated throughout. Formulas, worked examples, and guidelines for the field implementation of the technique are presented.

Comparison between sampling methods

This research was carried out in a giant Chinaberry tree (Melia azedarach var. gigantea) plantation located in the Province of Santiago del Estero, Argentina. At seven years of age, the plantation had reached the stage of high forest, with an original spacing of 4 m X 4 m. Fixed area plots are already installed for a study on growth and yield. Measurements were conducted on these plots by using two sampling methods of probability proportional to size (PPS), i.e., horizontal point sampling and horizontal line sampling, with variable size plots. Basal area factors K=1 and K=2 of the Bitterlich relascope were used in order to select the trees which made up the sample. Basal area, volume, and number of trees per hectare were estimated for each method. The resulting data were assorted by diameter class and subjected to analysis of variance in a random block design, where diameter classes were considered as blocks, basal area factors, as treatments, and fixed area plot sampling methods as controls. The relative efficiency of each method was also calculated. No significant difference among treatments was found at the one percent probability level. The horizontal point and the horizontal line sampling estimates are as accurate as those obtained with the control, whereas the relative efficiency of the PPS methods was greater than that of the control.

Some observations on fitting assumed diameter distributions to horizontal point sampling data

This paper revisits the link between assumed diameter distributions arising from horizontal point samples and their unbiased stand-based representation through weighted distribution theory. Examples are presented, which show that the assumption of a common shared parameter set between these two distributional forms, while theoretically valid, may not be reasonable in many operational cases. Simulation results are presented, which relate the conformity (or lack thereof) in these estimates to sampling intensity per point and the underlying shape of the population diameter distribution from which the sample point was drawn. In general, larger sample sizes per point are required to yield reliable parameter estimates than are generally taken for inventory purposes. In addition, a complimentary finding suggests that the more positively skewed the underlying distribution, the more trees per point are required for good parameter estimates.

Some observations on fitting assumed diameter distributions to horizontal point sampling data

This paper revisits the link between assumed diameter distributions arising from horizontal point samples and their unbiased stand-based representation through weighted distribution theory. Examples are presented, which show that the assumption of a common shared parameter set between these two distributional forms, while theoretically valid, may not be reasonable in many operational cases. Simulation results are presented, which relate the conformity (or lack thereof) in these estimates to sampling intensity per point and the underlying shape of the population diameter distribution from which the sample point was drawn. In general, larger sample sizes per point are required to yield reliable parameter estimates than are generally taken for inventory purposes. In addition, a complimentary finding suggests that the more positively skewed the underlying distribution, the more trees per point are required for good parameter estimates.

Minimizing the Rounding Error from Point Sample Estimates of Tree Frequencies

Abstract Three solutions are presented for estimating stems per acre when trees are tallied by diameter class with horizontal point sampling. The first solution is based on the arithmetic mean of the diameter-class limits. The second is based on the geometric mean of the diameter-class limits and is unbiased for uniform within-class diameter distributions. The third is a harmonic mean solution; it is derived from the ratio of the geometric mean squared and the arithmetic mean. If the within-class distribution is linear, then the solution based on the geometric mean is preferable. Any of these solutions may be adequate provided diameter-class widths are minimized, particularly for small trees. The geometric-mean solution is the recommended solution in instances where uniformity can be assumed within diameter classes. Observed frequencies in two stands, however, provided inconsistent results. In estimating tree frequency, errors resulting from grouping become smaller as tree diameter increases. For large trees, estimation of frequency can be obtained with much wider diameter limits than with small trees for a fixed level of grouping error. Rather than fixing diameter-class width, it may be advantageous to consider a narrower class width or exact measurement for trees in smaller diameter classes. West. J. Appl. For. 12(4):108-114.

Variable stocking version of Plonski's yield tables formulated

Plonski's yield tables have been used extensively in forest management, economic evaluation, and as a basis for management planning in Ontario. However, because these tables are based on site classes, they are not directly applicable to uneven-aged mixed-wood cover types. A four-parameter nonlinear model was employed to express various stand attributes as a function of stand age and recently developed basal area indices for the major species in Ontario. The resulting variable stocking yield functions will be applicable to even-aged stands as well as the boreal mixedwood. Basal area index proved superior to site index for estimating both merchantable basal area and volume for the James River/Marathon data set representing boreal mixed from Northcentral Ontario. In addition, stand basal area index may be determined easily and inexpensively via horizontal point sampling or prism cruising. Key word: Basal area index, sigmoidal growth curve, variable stocking

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.