Line Sampling with Probability Proportional to The Geometrical Average Area Per Tree in The Stand

BackgroundIn fast-growing forests such as Eucalyptus plantations, the correct determination of stand productivity is essential to aid decision making processes and ensure the efficiency of the wood supply chain. In the past decade, advances in remote sensing and computational methods have yielded new tools, techniques, and technologies that have led to improvements in forest management and forest productivity assessments. Our aim was to estimate and map the basal area and volume of Eucalyptus stands through the integration of forest inventory, remote sensing, parametric, and nonparametric methods of spatial prediction.MethodsThis study was conducted in 20 5-year-old clonal stands (362 ha) of Eucalyptus urophylla S.T.Blake x Eucalyptus camaldulensis Dehnh. The stands are located in the northwest region of Minas Gerais state, Brazil. Basal area and volume data were obtained from forest inventory operations carried out in the field. Spectral data were collected from a Landsat 5 TM satellite image, composed of spectral bands and vegetation indices. Multiple linear regression (MLR), random forest (RF), support vector machine (SVM), and artificial neural network (ANN) methods were used for basal area and volume estimation. Using ordinary kriging, we spatialised the residuals generated by the spatial prediction methods for the correction of trends in the estimates and more detailing of the spatial behaviour of basal area and volume.ResultsThe ND54 index was the spectral variable that had the best correlation values with basal area (r = − 0.91) and volume (r = − 0.52) and was also the variable that most contributed to basal area and volume estimates by the MLR and RF methods. The RF algorithm presented smaller basal area and volume errors when compared to other machine learning algorithms and MLR. The addition of residual kriging in spatial prediction methods did not necessarily result in relative improvements in the estimations of these methods.ConclusionsRandom forest was the best method of spatial prediction and mapping of basal area and volume in the study area. The combination of spatial prediction methods with residual kriging did not result in relative improvement of spatial prediction accuracy of basal area and volume in all methods assessed in this study, and there is not always a spatial dependency structure in the residuals of a spatial prediction method. The approaches used in this study provide a framework for integrating field and multispectral data, highlighting methods that greatly improve spatial prediction of basal area and volume estimation in Eucalyptus stands. This has potential to support fast growth plantation monitoring, offering options for a robust analysis of high-dimensional data.

O plantio consorciado de eucalipto com leguminosas pode promover a melhoria da qualidade biológica do solo em áreas degradadas e também ser vantajoso para as espécies do consórcio. O objetivo deste trabalho foi avaliar a influência de sistemas de plantios (puros e consorciados) de Acacia mangium (AM), Sesbania virgata (SV) e Eucalyptus camaldulensis (EC), sobre o desenvolvimento das plantas em estudo (variáveis dendrométricas) e especificamente sobre a fauna da serapilheira e dos primeiros 5 cm do solo. Realizou-se um experimento, cujo delineamento utilizado foi o de blocos casualizados com seis tratamentos e três repetições. Os tratamentos utilizados para avaliação dos atributos dendrométricos foram: 100EC (100 % EC) e 100AM (100 % AM); 50EC:50AM (50 % EC + 50 % AM); 50EC:50SV (50 % EC + 50 % SV); e 50AM:50SV (50 % AM + 50 % SV). Para avaliação da fauna do solo foram: 100EC, 100AM, 100SV (100 % SV), 50EC:50SV e 50 AM:50SV. Aos 48 meses após o plantio, foram feitas medições de altura (H) e diâmetro à altura do peito (DAP) das espécies E. camaldulensis e A. mangium e estimativas da área basal (AB) e volume de madeira com casca por indivíduo (VCI). Na serapilheira e no solo (0-5 cm), foram avaliadas a abundância e diversidade da fauna edáfica. O E. camaldulensis quando cultivado em consórcio com as leguminosas apresentou maior DAP, AB e VCI. Em contrapartida, a A. mangium não teve essas variáveis influenciadas quando em consórcio com o E. camaldulensis e com a S. virgata. Plantios de E. camaldulensis e S. virgata em consórcio promoveram maior abundância total de organismos e maiores valores dos índices de diversidade de Shannon e Pielou, principalmente no que se refere ao compartimento serapilheira.

Abstract: Forest inventories were originally designed for the assessment of timber stocks over large areas. The large datasets gathered by these programs are becoming of increasing interest in other applications, particularly in ecosystem modeling. With inventory designs based on sampling proportional to size (angle-count plots) users should be cautious of using data pertaining to individual plots, as the plot-wise data is a statistical estimate rather than a true measurement. Estimates of per-plot basal area are mathematically unbiased, but the individual precision is extremely poor. Resampling of inventory datasets using multiple basal area factors can improve the precision of the estimates on single plots, thus providing better data for potential end users. Following two simulation studies to demonstrate our method we apply it to the sampling points of the Austrian National Forest Inventory, and show how the improved estimates of basal area give rise to more realistic estimates of basal area increment on individual points, reducing variance through the smoothing of extreme estimates. Our method will be useful in studies where angle count inventory data pertaining to individual plots is used to assess the precision of models or remote sensing methods.

Introduction. The current demands of society in precise and actual information on forest resources require improving methods of forest mensuration used in operational forest inventory in Ukraine. Prevailing ocular estimates during field examination of forest stands leads to biased estimation of growing stock volume. Thus, any improvement of current technology of forest survey requires reliable field data, usually collected in sample-based forest inventory relaying on predefined sampling design and accuracy. Nowadays, the technology of national forest inventory of Ukraine is under discussion therefore an analysis of different approaches for collecting data based on local case studies is of great importance. Analysis of recent research and publication. The modern technology of forest inventory has faced a gradual shift from sample unit of big size (strip sampling or rectangular plots) towards small plots typically having a form of circle. One good example of continuous advancement of methodology and application of different sampling approaches is multi-source national forest inventory of Finland. The circular form of sample units facilitates overcoming at least three problems: the shape of circle has the smallest area compared to its perimeter, so circular plot minimizes the number of bordering trees; the circular plot could be positioned using merely its center; to find the plot perimeter minimal time is needed as it defined by radius. By this time, there is no common plot size used in forest inventory. Many researchers think that optimal number of tally trees to be sampled per plot should not exceed 20–30 trees. Increasing plot size does not lead to improving the accuracy since some trees could be skipped during counting. From that point of view sampling with variable radius plots was developed. The studies had been conducted in Ukraine proved that optimal plot size includes in average 7 tally trees. The sample size for fixed radius plots depends on the area, but for angle counting plots it relies on basal area factor (BAF). The countries of Western and North Europe use the BAF from 1.5 to 4. If BAF > 1 is applied the number of bordering trees which diameters and distance from plot center should be checked decreases. To optimize field work, methods that combine fixed- and variable-area sampling were developed. The simplest way to improve the efficiency of field work is nested plot design. It refers to two or three circular plots of different radius so that thin trees are measured in plots of smaller area. Nested plots are widely used in many national forest inventories throughout of the world. Rather cost-efficient is also combination of fixed-area sampling and angle counting approach, so called “truncated angle sampling”. This technique is actively discussed in literature to optimize the combination of plot radius and BAF used for tree selection. Objective. The aim of the study is to investigate accuracy and efficiency of different plot configuration relied on two main methodological principles – tree selection with probabilities proportional to tree sizes and stand density. Methods. The study is based on empirical data collected within study area established in Kyiv region (Ukraine). The test polygon is located between longitudes 30° 00' E and 30° 12' E and latitudes 50° 12' N та 50° 20' N. We used systematic sampling by rectangular grid spacing 1՛ for both longitude and latitude to locate sample units within forested area. The forests are characterized by pine ( Pinus sylvestris L.) accompanied by several other tree species like oak ( Querqus robur L., Querqus rubra L.), birch ( Betula pendula Roth.), aspen ( Populus tremula L.) and alder ( Alnus glutinosa L.). We used Field-Map software for data collecting. Each tally tree within circular plot of 500 m 2 was mapped, afterwards a list of attributes has been measured including tree species and diameter at 1.3 m. For model trees (1/4 of total quantity) that were randomly selected among tally trees we also measured tree height. As an option, angle counting plots were established using BAF = 1. Mapping trees allowed us to calculate parameters of several additional plot configurations using diameters of trees and local coordinates defining their location within plot. We examined: 1) three nested plot configuration incorporating maximum radius of 12.62 m and three subplots radii – 3.98, 5.64, 7.98 m; 2) one nested plot design with maximum radius of 9.77 m and subplot radius of 5.64 m; 3) two truncated angle plot configurations with maximum radius of 12.62 m where BAF = 1 and BAF = 2 used; 4) two truncated angle plot configurations with BAF = 1 but having maximum radius 11.28 m and 9.77 m; 5) angle count plot with BAF = 1. In the study we focused on accuracy of estimation of basal areas and number of trees per hectare. As a reference, we used data obtained on fixed area plots of 500 m 2 . Results and discussion. Besides of common assumption that nested plot design is most suitable for natural forest with negatively J-shaped tree sizes distribution we outlined some advances of the configuration for the study area. The nested plots having maximum radius of 12.62 m were rather precise regardless of subplot radius. But, for practical use we would recommend establishing subplots having radius of 3.98 m since such design had least sample size and at the same time demonstrated good accuracy (standard deviation of basal area estimates did not exceed 0.5 m 2 ha -1 ). At the same time, we obtained biased estimates of basal area and stands density using nested plots with maximum radius of 9.77 m. The performance of truncated angle sampling was moderate if maximum radius was decreased or BAF = 2 was applied. The most accurate plot configuration was accepted which had maximum plot radius of 12.62 m and BAF = 1. The angle count approach was biased on average of 4 m 2 ‧ha -1 because of omission of some trees located a long distance from plot center.

Research Highlights: Studies on tree canopy dwelling species often require simple proxies of tree canopy volume estimated at a stand level. These include allometrically related tree crown parameters such as crown area and basal area, and canopy cover. Background and Objectives: In monoculture Scot’s pine and mixed pine/Norway spruce forest, we aimed to test the relationships between tree diameter at breast height (DBH) and tree crown volume at a tree level and between densitometer canopy closure estimates and tree crown volume at a stand level. Materials and Methods: The study was carried out in eastern Latvia (hemiboreal zone) in monoculture pine and mixed coniferous stands. On a subset of trees in 22 forest stands (88 100 m2 plots), we determined the best regression model that described the relationship between tree DBH and crown volume for spruce and pine. Tree crown volume at a stand level was determined from the individual tree volume estimates calculated from these regression models. On a stand level, we also calculated regression models for densitometer closure estimates versus total crown volume for pine and mixed stands. Results: Linear mixed effects models showed significant relationships between DBH and crown volume for pine (R2 = 0.63) and spruce (R2 = 0.40), indicating that basal area could be used as a predictor of crown volume at a stand level. Variance explained by a regression model of canopy closure versus tree crown volume at a stand level was R2 = 0.52. Conclusions: Tree basal area and crown closure can be used as proxies of tree crown volume at a stand scale in monoculture stands. In mixed stands estimates of crown volume based on basal area need to be calculated separately for each tree species, while canopy closure will provide an estimate of total crown volume.

Wood abundance in streams is an indicator of its likely geomorphological and ecological importance. However, wood volume estimates can be highly variable, due in part to natural variability and the methodology used to characterize it. We measured wood volume in streams of similar sizes and riparian forest conditions using extended field surveys and simulation modelling. We surveyed a total of 3·1 km along four tributary streams of New Zealand's Waihaha River to obtain an estimate of wood volume in streams with similar basin positions (second order), forest types (podocarp/hardwood forest), disturbance histories (post volcanic eruption of Taupo ca. 180 AD) and stream sizes (2–3 m bankfull width). A ‘sliding window’ analysis was conducted whereby the wood volume was calculated for a ‘window’ (i.e., reach survey of fixed length) that was progressively moved upstream in 10 m increments. The resulting frequency distributions of wood volume were bimodal and represented the range and relative proportion of reach volumes possible from the wood surveys. The wood volume based on all streams surveyed (23 m3/100 m) was equivalent to the 64th percentile of the sliding window distribution, suggesting that a randomly placed study reach would be likely to underestimate wood volume. The bimodal distribution was attributed to the inclusion/exclusion of relatively large (≥10 m3), but rare (0·3 logs/100 m) logs. We also examined the variability of reach‐level wood volume estimates (200 m and 400 m) for the Waihaha tributaries using the model OSU StreamWood. The volume frequency distributions from the simulations were similar to those from the empirical approach, except that they were unimodal. We attribute the unimodal distribution to the greater number of reach‐scale estimates used in the simulations (n = 2000). The two independent approaches characterized the variation of wood volumes possible for this forest type and stream width. Copyright © 2007 John Wiley & Sons, Ltd.

A new algorithm for stand table projection based on existing estimates of future basal area and survival is derived and demonstrated. An observed stand table is first projected by applying either an existing diameter growth equation or a growth equation derived from appropriate diameter distributional assumptions. The stand table is adjusted by an algorithm that equates the future stand table to existing estimate of basal area and survival. The algorithm does not use any species-specific parameters and can therefore be applied to any species for which future estimates of basal area and survival are available. This algorithm provides comparable estimates when the initial diameter distribution is close to the unimodal distribution assumed by parameter recovery procedures in diameter distribution growth and yield models. In fact, the algorithm reduces to the same future stand table when the initial stand table is actually generated by the diameter distribution derived by the parameter recovery procedure. However, if the observed stand table is multimodal, the prediction by this algorithm is better than predictions from the parameter recovery method alone. Favorable comparisons are also made with the stand table projection method introduced by Pienaar and Harrison (1988), for natural even-aged longleaf pine stands. For. Sci. 38(1):120-133.

This study aimed to analyze the applicability of the Bitterlich sampling in a fomented farm, populated with Eucalyptus grandis, in the southern state of Espirito Santo. To that end, were launched ten plots for the methods of Bitterlich, with different basal area factors, and fixed area, which were measured the diameter at breast height. The total height and volume was estimated by means of height-diameter relations and volumetric equations. From these data were estimated the volume and basal area per hectare, for further comparison by Student’s t-test. There was no statistically significant difference for the estimation of basal area and volume per hectare between the methods of fixed area and Bitterlich, independent of basal area factor used. To meet the same limit of error, the Bitterlich sampling requires a greater number of plots. This number of plots is greater with the increase in basal area factor used. Finally, it can be concluded that the methodology proposed by Bitterlich and fixed area presented the same accuracy in the estimation of average volume and basal area in the analyzed Eucalyptus grandis population.

RESUMO Objetivou-se, no presente trabalho, avaliar o método de quadrantes na estimativa da abundância (A), área basal (G) e volume comercial (V) de uma área de Floresta Ombrófila na Amazônia. Foram simuladas amostragens por dois processos (aleatório e sistemático) com diferentes tamanhos de amostra, variando de 100 a 200 pontos de amostragem. Os valores estimados pelas amostragens foram comparados com os valoreis reais das variáveis registradas no censo, considerando-se a população com DAP ≥ 40 cm em uma área de 1.000 ha de floresta, submetida ao plano de manejo sustentável. O método de quadrantes não atingiu o nível de exatidão desejado para as variáveis área basal e volume comercial, superestimando os seus valores reais registrados no censo. No entanto, a precisão de suas estimativas para abundância, área basal e volume comercial foi satisfatória para a aplicação do método em inventários florestais destinados a planos de manejo na Amazônia.

Variable-radius sampling techniques are commonly used during forest inventories. For each sample tree at a particular sampling point, diameter and height(s) are measured and then weight is estimated using established equations. Heights can require a fair amount of time to measure in the field. Separating the weight per acre estimate into two components; average basal area per acre and WBAR (individual tree weight-basal area ratio) across all points, can often lead to more efficient sampling schemes. Variable-radius sampling allows for a quick estimate of basal area per acre at a point since no individual tree measurements are needed. If there is a strong relationship between weight and basal area, then by knowing basal area you essentially know weight. Separation into two components is advantageous because in most cases there is more variability among basal area estimates per point then there is in WBAR. Hence, you can spend more resources establishing many points that only estimate basal area – often called “Count” points. “Full” points are those where individual tree measurements are also conducted. There is little published information quantifying the impacts on basal area, weight, etc., estimates among different “Full/Count” sample size ratios at the same site. Inventories were examined to determine this method’s applicability to loblolly pine plantations in southern Arkansas and northern Louisiana. Results show there is more variability among basal area estimates than WBAR and that the amount of trees being “intensively” measured is excessive. Based on these four plantations, a “Full” point could be installed ranging from every other point to every fifth point depending on site conditions and the desired variable.

Estimates of wood volume, either in even or uneven-aged forests, is necessary for planning forest management, studies concerning carbon sequestration and natural resources conservation, as well as energy planning in regions where wood is the primary fuel for power generation. Such purposes mainly involve analysis of large areas, which leads to challenges that can be solved through remote sensing. Using multispectral and microwave data, respectively, from the AVNIR-2 and PALSAR sensors, both on board in the ALOS satellite, the wood volume of a commercial eucalyptus plantation located in the state of Minas Gerais, Brazil was estimated using artificial neural. Neural networks emerged as a powerful machine learning technique, capable of modeling intrinsically nonlinear relationships that are present in the data. Thus, the obtained estimates for wood volume in the eucalyptus plantations showed a correlation coefficient with the corresponding observed volumes (forest inventory) of 0.99, a square root of the quadratic error (RQEM) of 0.3% and errors with amplitude between -1 to 1%. The efficiency of artificial neural networks for estimating wood volume in homogeneous plantations has been proven. The multilayer perceptron neural network was efficient in modeling the complex relationships that exist between multispectral, microwave and wood volume data, producing highly accurate estimates. Only a small amount of plots was sufficient to train the artificial neural networks in order to estimate volume. In addition, the fast convergence obtained by the BFGS algorithm allowed a comprehensive data analysis.

Addressing management practices of private forests by remote sensing and open data: A tentative procedure

Compatible estimates of basal area and basal area growth have the growth estimate equal to the difference in successive basal area estimates. The compatible growth estimator associated with the usual basal area estimator has a high variance; a noncompatible growth estimator with less variance is usually preferred. A new compatible estimator is proposed for use with trees selected by the usual Bitterlich sampling procedure. This estimator, which requires some additional measurements, results in an increased variance for basal area estimation and a greatly reduced variance for growth estimation compared to the usual compatible estimation procedure; the latter variance approaches that of the noncompatible growth estimator. A purely random distribution of trees is assumed and deterministic formulas are used to calculate variances. Extensions to volume estimation are discussed. Forest Sci. 27:191-203.

BackgroundA new variance estimator is derived and tested for big BAF (Basal Area Factor) sampling which is a forest inventory system that utilizes Bitterlich sampling (point sampling) with two BAF sizes, a small BAF for tree counts and a larger BAF on which tree measurements are made usually including DBHs and heights needed for volume estimation.MethodsThe new estimator is derived using the Delta method from an existing formulation of the big BAF estimator as consisting of three sample means. The new formula is compared to existing big BAF estimators including a popular estimator based on Bruce’s formula.ResultsSeveral computer simulation studies were conducted comparing the new variance estimator to all known variance estimators for big BAF currently in the forest inventory literature. In simulations the new estimator performed well and comparably to existing variance formulas.ConclusionsA possible advantage of the new estimator is that it does not require the assumption of negligible correlation between basal area counts on the small BAF factor and volume-basal area ratios based on the large BAF factor selection trees, an assumption required by all previous big BAF variance estimation formulas. Although this correlation was negligible on the simulation stands used in this study, it is conceivable that the correlation could be significant in some forest types, such as those in which the DBH-height relationship can be affected substantially by density perhaps through competition. We derived a formula that can be used to estimate the covariance between estimates of mean basal area and the ratio of estimates of mean volume and mean basal area. We also mathematically derived expressions for bias in the big BAF estimator that can be used to show the bias approaches zero in large samples on the order of frac {1}{n} where n is the number of sample points.

Simultaneous growth and yield equations were developed for predicting basal area growth and cubic-foot volume growth and yield in thinned stands of yellow-poplar. A joint loss function involving both volume and basal area was used to estimate the coefficients in the system of equations. The estimates obtained were analytically compatible, invariant for projection length, and numerically equivalent with alternative applications of the equations. Given estimates of basal area and cubic-foot volume from these equations, board-foot volumes can also be calculated. As an adjunct to the stand-level equations, compatible stand tables were derived by solving for the parameters of the Weibull distribution from attributes predicted with the stand-level equations. This procedure for estimating the parameters of the diameter distributions of the stands before thinning gave reasonable estimates of number of trees, basal area, and cubic-foot volume per acre by diameter class. The thinning algorithm removes a proportion of the basal area from each diameter class and produces stand and stock tables after thinning from below that are consistent with those generated before thinning.