Voronoi polygons quantify bias when sampling the nearest plant

The design bias in the sample mean obtained from sampling the trees nearest to points randomly and uniformly distributed over a forested area can be exactly quantified in terms of the Voronoi polygons (V polygons) surrounding each tree in the forest of interest. For this sampling method, the V polygon for a prospective sample tree is its inclusion zone. The sides of such polygons are perpendicular to a line joining adjacent trees and equidistant from these trees. For any individual tree attribute Y, the design bias in such a sample mean for estimating the population mean of Y will be equal to the covariance between Y and V-polygon area V divided by the mean V-polygon area. The bias as a percent of the population mean of Y is the product of the correlation coefficient between Y and V and the coefficients of variation for Y and V multiplied by 100. This implies that attempts to estimate the means of commonly measured individual tree variables such as DBH, basal area, and crown diameter or the area from sampling trees nearest to randomly located points will likely be positively biased, and the magnitude of that bias will depend on the strength of the linear relationship to the V-polygon area, as well as the variability among the V-polygon areas and the variable of interest. It is not obvious whether increment core data will be positively or negatively biased, because this depends on the characteristics of the forest of interest. The main conclusion of the study is that the bias formula derived for unweighted estimation from sampling the tree nearest to a point indicates that bias in the range of 5%–10% or greater can occur in many forest populations.

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Using double-sampling techniques to reduce the number of measurement trees during forest inventories

REFORESTA ◽

10.21750/refor.3.04.28 ◽

2017 ◽

pp. 31

Author(s):

Curtis L. VanderSchaaf ◽

Gordon Holley ◽

Joshua Adams

Keyword(s):

Loblolly Pine ◽

Basal Area ◽

Strong Relationship ◽

Sampling Techniques ◽

Sampling Point ◽

Individual Tree ◽

Variable Radius ◽

Sampling Schemes ◽

Forest Inventories ◽

Sample Tree

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.

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Dendrochronological study of Cedrus deodar Grown at Kumrat valley Dir Upper KPK, Pakistan: Evaluation of Tree Age and Increment Based on Increment Core

Jurnal Ilmu Pertanian Indonesia ◽

10.18343/jipi.26.2.201 ◽

2021 ◽

Vol 26 (2) ◽

pp. 201-208

Author(s):

Sajad Sajad ◽

Jawad Jawad ◽

Ikram Ul Haq

Keyword(s):

Tree Rings ◽

Basal Area ◽

Basal Area Increment ◽

Tree Age ◽

Annual Increment ◽

Increment Core ◽

Sample Tree ◽

Strong Positive Relationship ◽

Volume Increment ◽

Mean Annual Increment

The present research was conducted for tree-rings study in a mixed stand of Himalayan Species Credur deodar in Kumrat valley Dir Upper KPK, Pakistan. Tree-rings analysis was related to the counting of tree ring. Random sampling method was used, and 70 sample trees were selected, tree heights and diameters were measured, and increment cores were collected from each sample-tree diameter at the height at breast point to be analyzed and studied in the laboratory. The objectives of the study were to determine the exact age of tree and to evaluate total and mean annual increment in the basal area and tree volume based on the increment cores. Regression models revealed the impacts of tree age on the basal area and tree-volume increment. Results showed the minimum basal-area increment was 0.0028 m2 at the age of 10 years, the maximum basal-area increment was 2.658 m2 at the age of 60 years, with mean was 0.95±0.677 m2 at the age of 36 years and R2 was 0.9593. The maximum tree-volume increment was 1.42 m3 at the age of 60 years, the minimum tree-volume increment was 0.010 m3 at the age of 10 years, with mean was 1.35±0.96 m3 at the age of 36 years and R2 was 0.9167. The minimum mean annual-basal area increment was 0.0027 m2, the maximum mean annual-basal area increment was 0.048 m2, and the average increment was 0.022±0.010 m2. The maximum mean-annual increment in tree volume was 0.068 m3 at the age of 60 years, the minimum mean-annual increment was 0.0039 m3 at the age of 10 years, with mean was 0.032±0.014 m3 at the age of 36 years and R2 was 0.8903. Results showed a strong positive relationship of tree age with area and volume increment. Keywords: Basal area, increment, tree age, volume

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An antithetic variate to facilitate upper-stem height measurements for critical height sampling with importance sampling

Canadian Journal of Forest Research ◽

10.1139/cjfr-2013-0279 ◽

2013 ◽

Vol 43 (12) ◽

pp. 1151-1161 ◽

Cited By ~ 6

Author(s):

Thomas B. Lynch ◽

Jeffrey H. Gove

Keyword(s):

Importance Sampling ◽

Basal Area ◽

Cross Sectional Area ◽

Sample Point ◽

Sectional Area ◽

Critical Height ◽

Cross Sectional ◽

Individual Tree ◽

Sample Tree ◽

The Cross

Critical height sampling (CHS) estimates cubic volume per unit area by multiplying the sum of critical heights measured on trees tallied in a horizontal point sample (HPS) by the HPS basal area factor. One of the barriers to practical application of CHS is the fact that trees near the field location of the point-sampling sample point have critical heights that occur quite high on the stem, making them difficult to view from the sample point. To surmount this difficulty, use of the “antithetic variate” associated with the critical height together with importance sampling from the cylindrical shells integral is proposed. This antithetic variate will be u = (1 − b/B), where b is the cross-sectional area at “borderline” condition and B is the tree’s basal area. The cross-sectional area at borderline condition b can be determined with knowledge of the HPS gauge angle by measuring the distance to the sample tree. When the antithetic variate u is used in importance sampling, the upper-stem measurement will be low on tree stems close to the sample point and high on tree stems distant from the sample point, enhancing visibility and ease of measurement from the sample point. Computer simulations compared HPS, CHS, CHS with importance sampling (ICHS), ICHS and an antithetic variate (AICHS), and CHS with paired antithetic varariates (PAICHS) and found that HPS, ICHS, AICHS, and PAICHS were very nearly equally precise and were more precise than CHS. These results are favorable to AICHS, since it should require less time than either PAICHS or ICHS and is not subject to individual-tree volume equation bias.

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Biomass estimates derived from sector subsampling of 360° spherical images

Forestry An International Journal of Forest Research ◽

10.1093/forestry/cpab023 ◽

2021 ◽

Author(s):

Xiao Dai ◽

Mark J Ducey ◽

Haozhou Wang ◽

Ting-Ru Yang ◽

Yung-Han Hsu ◽

...

Keyword(s):

Basal Area ◽

Sampling Errors ◽

Eastern Canada ◽

Individual Tree ◽

Inventory Costs ◽

Standard Error Estimation ◽

The Mean ◽

Biomass Ratio ◽

Spherical Images ◽

Additional Level

Abstract Efficient subsampling designs reduce forest inventory costs by focusing sampling efforts on more variable forest attributes. Sector subsampling is an efficient and accurate alternative to big basal area factor (big BAF) sampling to estimate the mean basal area to biomass ratio. In this study, we apply sector subsampling of spherical images to estimate aboveground biomass and compare our image-based estimates with field data collected from three early spacing trials on western Newfoundland Island in eastern Canada. The results show that sector subsampling of spherical images produced increased sampling errors of 0.3–3.4 per cent with only about 60 trees measured across 30 spherical images compared with about 4000 trees measured in the field. Photo-derived basal area was underestimated because of occluded trees; however, we implemented an additional level of subsampling, collecting field-based basal area counts, to correct for bias due to occluded trees. We applied Bruce’s formula for standard error estimation to our three-level hierarchical subsampling scheme and showed that Bruce’s formula is generalizable to any dimension of hierarchical subsampling. Spherical images are easily and quickly captured in the field using a consumer-grade 360° camera and sector subsampling, including all individual tree measurements, were obtained using a custom-developed python software package. The system is an efficient and accurate photo-based alternative to field-based big BAF subsampling.

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Adjudicating Perspectives on Forest Structure: How Do Airborne, Terrestrial, and Mobile Lidar-Derived Estimates Compare?

Remote Sensing ◽

10.3390/rs13122297 ◽

2021 ◽

Vol 13 (12) ◽

pp. 2297

Author(s):

Jonathon J. Donager ◽

Andrew J. Sánchez Meador ◽

Ryan C. Blackburn

Keyword(s):

Ponderosa Pine ◽

Laser Scanning ◽

Canopy Cover ◽

Basal Area ◽

Tree Height ◽

Absolute Error ◽

Forest Monitoring ◽

Individual Tree ◽

Structural Configurations ◽

Individual Trees

Applications of lidar in ecosystem conservation and management continue to expand as technology has rapidly evolved. An accounting of relative accuracy and errors among lidar platforms within a range of forest types and structural configurations was needed. Within a ponderosa pine forest in northern Arizona, we compare vegetation attributes at the tree-, plot-, and stand-scales derived from three lidar platforms: fixed-wing airborne (ALS), fixed-location terrestrial (TLS), and hand-held mobile laser scanning (MLS). We present a methodology to segment individual trees from TLS and MLS datasets, incorporating eigen-value and density metrics to locate trees, then assigning point returns to trees using a graph-theory shortest-path approach. Overall, we found MLS consistently provided more accurate structural metrics at the tree- (e.g., mean absolute error for DBH in cm was 4.8, 5.0, and 9.1 for MLS, TLS and ALS, respectively) and plot-scale (e.g., R2 for field observed and lidar-derived basal area, m2 ha−1, was 0.986, 0.974, and 0.851 for MLS, TLS, and ALS, respectively) as compared to ALS and TLS. While TLS data produced estimates similar to MLS, attributes derived from TLS often underpredicted structural values due to occlusion. Additionally, ALS data provided accurate estimates of tree height for larger trees, yet consistently missed and underpredicted small trees (≤35 cm). MLS produced accurate estimates of canopy cover and landscape metrics up to 50 m from plot center. TLS tended to underpredict both canopy cover and patch metrics with constant bias due to occlusion. Taking full advantage of minimal occlusion effects, MLS data consistently provided the best individual tree and plot-based metrics, with ALS providing the best estimates for volume, biomass, and canopy cover. Overall, we found MLS data logistically simple, quickly acquirable, and accurate for small area inventories, assessments, and monitoring activities. We suggest further work exploring the active use of MLS for forest monitoring and inventory.

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Largest-Crown-Width Prediction Models for 53 Species in the Western United States

Western Journal of Applied Forestry ◽

10.1093/wjaf/19.4.245 ◽

2004 ◽

Vol 19 (4) ◽

pp. 245-251 ◽

Cited By ~ 28

Author(s):

William A. Bechtold

Keyword(s):

United States ◽

Prediction Models ◽

Basal Area ◽

Stem Diameter ◽

Western United States ◽

Quadratic Term ◽

Crown Width ◽

Coefficients Of Variation ◽

Bioclimatic Index ◽

Minor Improvement

Abstract The mean crown diameters of stand-grown trees 5.0-in. dbh and larger were modeled as a function of stem diameter, live-crown ratio, stand-level basal area, latitude, longitude, elevation, and Hopkins bioclimatic index for 53 tree species in the western United States. Stem diameter was statistically significant in all models, and a quadratic term for stem diameter was required for some species. Crown ratio and/or Hopkins index also improved the models for most species. A term for stand-level basal area was not generally needed but did yield some minor improvement for a few species. Coefficients of variation from the regression solutions ranged from 17 to 33%, and model R2 ranged from 0.15 to 0.85. Simpler models, based solely on stem diameter, are also presented. West. J. Appl. For. 19(4):245–251.

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A New Index Representing Individual Tree Competitive Status

Canadian Journal of Forest Research ◽

10.1139/x73-073 ◽

1973 ◽

Vol 3 (4) ◽

pp. 495-500 ◽

Cited By ~ 46

Author(s):

James A. Moore ◽

Carl A. Budelsky ◽

Richard C. Schlesinger

Keyword(s):

Spatial Distribution ◽

Strong Correlation ◽

Basal Area ◽

Tree Size ◽

Competition Index ◽

Individual Tree ◽

Silvicultural Practices ◽

Basal Area Growth ◽

Hardwood Species ◽

Area Growth

A new competition index, modified Area Potentially Available (APA), was tested in a complex unevenaged stand composed of 19 different hardwood species. APA considers tree size, spatial distribution, and distance relationships in quantifying intertree competition and exhibits a strong correlation with individual tree basal area growth. The most important characteristic of APA is its potential for evaluating silvicultural practices.

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Using tree rings to assess the potential of thinning to alleviate drought stress in a dry forest of western Canada

10.5194/egusphere-egu21-13182 ◽

2021 ◽

Author(s):

David Montwé ◽

Audrey Standish ◽

Miriam Isaac-Renton ◽

Jodi Axelson

Keyword(s):

Tree Ring ◽

Tree Rings ◽

Basal Area ◽

Dry Forest ◽

Tree Level ◽

Severe Drought ◽

Western Canada ◽

Drought Event ◽

Individual Tree ◽

Potential Benefits

Increasing frequency of severe drought events under climate change is a major cause for concern for millions of hectares of forested land. One practical solution to improving forest resilience may be thinning. There may be several potential benefits, chief of which is that drought tolerance could be improved in the remaining trees due to lower competition for resources and increased precipitation throughfall. By improving resilience to drought, this may increase productivity of the remaining trees while lowering risks of mortality. Such potential benefits can effectively be quantified with data from statistically-sound, long-term field experiments, and tree rings provide a suitable avenue to compare treatments. We work with an experiment that applied different levels of tree retention to mature interior Douglas fir (Pseudotsuga menziesii var. glauca) in a dry ecosystem of western Canada. The treatments were applied in the winter of 2002/2003, coinciding with the aftermath of a severe natural drought event in 2002. We used tree-rings to quantify the extent to which thinning improves recovery and resilience of treated trees as compared to non-thinned controls. Tree-ring samples as well as height and diameter data were obtained from 83 trees from 8 treatment units of the randomized experimental design. Indicators for resilience to drought were calculated based on basal area increments. Thinning substantially increased basal area increments at the individual tree level, but more importantly, led to significantly higher recovery and resilience relative to the control. The results of this tree-ring analysis suggest that thinning may be a viable silvicultural intervention to counteract effects of severe drought events and to maintain tree cover.

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