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

2003 ◽  
Vol 33 (8) ◽  
pp. 1587-1590 ◽  
Author(s):  
J H Gove
Keyword(s):  
Size Distribution ◽  
Graphical Representation ◽  
Basal Area ◽  
Distribution Theory ◽  
Harmonic Mean ◽  
Quadratic Mean ◽  
Point Sampling ◽  
The Relationship ◽  
Horizontal Point Sampling ◽  
Biased Distribution

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.

scholarly journals Vertical Point Sampling with a Camera

2011 ◽  
Vol 28 (2) ◽  
pp. 61-65 ◽  
Author(s):  
Mark J. Ducey ◽  
John A. Kershaw
Keyword(s):  
Basal Area ◽  
Stand Density ◽  
Double Sampling ◽  
Point Sampling ◽  
Field Techniques ◽  
Potential Applications ◽  
Stand Density Index ◽  
Detectable Bias ◽  
Horizontal Point Sampling

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.

scholarly journals Economic Impacts of Projecting Horizontal Angles to the Wrong Height When Conducting Point Sampling

2011 ◽  
Vol 35 (1) ◽  
pp. 33-38
Author(s):  
Curtis L. VanderSchaaf ◽  
Lewis Jordan
Keyword(s):  
Economic Impacts ◽  
Basal Area ◽  
Point Sampling ◽  
Breast Height ◽  
Area Estimate ◽  
Nonsampling Error ◽  
Taper Equation ◽  
Individual Trees ◽  
Horizontal Point Sampling ◽  
Stand Conditions

Abstract Horizontal point sampling selects sample trees by projecting horizontal angles. In many inventories, angles are to be projected to dbh, or the diameter at 4.5 ft, but because of user error, angles are often projected to heights other than breast height. Thus, errors are made as to which trees should be sampled, probabilities of sampling individual trees are incorrect, and the basal area estimate does not truly correspond to dbh. The objective of this study was to determine the potential economic impacts of projecting angles at heights other than breast height when breast height is the desired height. Projections for two planting densities (400 and 1,000 seedlings per acre) and two ages (20 and 30) were used to establish virtual plantations, and sampling was conducted using 10 and 20 basal area factor prisms by projecting horizontal angles to four heights, 4.5, 5.0, 5.5, and 6.0 ft. A taper equation was used to estimate changes in diameter along the stem. For the stand conditions examined in this study, incorrectly projecting angles to heights other than breast height reduced timber appraisals by as much as $190/ac. Across many acres and stands, this type of nonsampling error can result in serious errors in valuing stumpage.

Aspects of statistical bias due to the forest edge: horizontal point sampling

1981 ◽  
Vol 11 (2) ◽  
pp. 335-342 ◽  
Author(s):  
Gary W. Fowler ◽  
Loukas G. Arvanitis
Keyword(s):  
Spatial Distribution ◽  
Edge Effect ◽  
Unbiased Estimator ◽  
Basal Area ◽  
Forest Edge ◽  
Mean Square ◽  
Statistical Bias ◽  
Point Sampling ◽  
Mean Square Errors ◽  
Horizontal Point Sampling

A tree-concentric procedure is presented to eliminate edge effect statistical bias for horizontal point sampling. For known forest populations, the exact mean of the unbiased (adjusted for edge effect) and biased (unadjusted for edge effect) estimators of a forest characteristic can be determined along with the exact bias. Edge-effect bias is investigated for three forests that vary in area, four basal area factors (BAF), and three forest characteristics. Exact and estimated results based on 5000 random points were compared. Edge effect bias increases as the BAF decreases and varies with forest size, size and spatial distribution of trees, percentage of edge trees, and forest characteristic. The variance of the biased estimator was always smaller than the variance of the unbiased estimator. Using mean square errors, the biased estimator was found to be, in general, more accurate and the distortion of probability statements caused by the bias negligible for small to moderate sample sizes, especially for larger BAF's and certain forest characteristics.

scholarly journals Deriving Tree Size Distributions of Tropical Forests from Lidar

2021 ◽  
Vol 13 (1) ◽  
pp. 131
Author(s):  
Franziska Taubert ◽  
Rico Fischer ◽  
Nikolai Knapp ◽  
Andreas Huth
Keyword(s):  
Size Distribution ◽  
Spatial Scales ◽  
Basal Area ◽  
Tree Height ◽  
Tree Size ◽  
Diameter Distribution ◽  
Forest Inventories ◽  
Allometric Relations ◽  
Lidar Measurements ◽  
Derived Data

Remote sensing is an important tool to monitor forests to rapidly detect changes due to global change and other threats. Here, we present a novel methodology to infer the tree size distribution from light detection and ranging (lidar) measurements. Our approach is based on a theoretical leaf–tree matrix derived from allometric relations of trees. Using the leaf–tree matrix, we compute the tree size distribution that fit to the observed leaf area density profile via lidar. To validate our approach, we analyzed the stem diameter distribution of a tropical forest in Panama and compared lidar-derived data with data from forest inventories at different spatial scales (0.04 ha to 50 ha). Our estimates had a high accuracy at scales above 1 ha (1 ha: root mean square error (RMSE) 67.6 trees ha−1/normalized RMSE 18.8%/R² 0.76; 50 ha: 22.8 trees ha−1/6.2%/0.89). Estimates for smaller scales (1-ha to 0.04-ha) were reliably for forests with low height, dense canopy or low tree height heterogeneity. Estimates for the basal area were accurate at the 1-ha scale (RMSE 4.7 tree ha−1, bias 0.8 m² ha−1) but less accurate at smaller scales. Our methodology, further tested at additional sites, provides a useful approach to determine the tree size distribution of forests by integrating information on tree allometries.

scholarly journals Particle Size Distribution Based Occurrence Features of Organic Components in Printing and Dyeing Wastewater Under a Treatment Process

2019 ◽  
Vol 118 ◽  
pp. 04009
Author(s):  
Yuan Li ◽  
Jie Liu ◽  
Yibiao Yu ◽  
Hao Zhu ◽  
Zheng Shen ◽  
...  
Keyword(s):  
Particle Size ◽  
Particle Size Distribution ◽  
Size Distribution ◽  
Reverse Osmosis ◽  
Treatment Process ◽  
Dyeing Wastewater ◽  
Wastewater Treatment Process ◽  
Printing And Dyeing Wastewater ◽  
Sedimentation Tank ◽  
The Relationship

A more detailed occurrence features of organic matters in the printing and dyeing wastewater, based on its particle size distribution (PSD) and along with a wastewater treatment process, was conducted to provide a support for advanced treatment. Results suggested that, (1) In the dyeing wastewater, the occurrence characteristic of COD was: soluble>supra colloidal>colloidal>settleable; However, for protein, the supra colloidal was dominant, followed by the soluble. The feature of the polysaccharide was consistent with COD’s. In the wastewater, 29.66% of COD could be attributed to proteins and 3.45% of the COD could be attributed to polysaccharides. (2) The relationship among the forms of COD in the primary sedimentation tank, aerobic tank, secondary sedimentation tank, and reverse osmosis-treated concentrated effluent was consistent, that was: soluble>colloidal>supra colloidal>settleable. (3) In the primary sedimentation tank, the settleable COD was almost completely removed; In the aerobic tank, the residual super colloidal COD was not much; After MBR-RO treatment, the COD in the reverse osmosis concentrated water was almost dissolved and only a little presented in other forms.

scholarly journals Experimental-numerical studies of the effect of cell structure on the mechanical properties of polypropylene foams

e-Polymers ◽  
2020 ◽  
Vol 20 (1) ◽  
pp. 713-723
Author(s):  
Wei Gong ◽  
Tuan-Hui Jiang ◽  
Xiang-Bu Zeng ◽  
Li He ◽  
Chun Zhang
Keyword(s):  
Mechanical Properties ◽  
Size Distribution ◽  
Cell Size ◽  
Cell Structure ◽  
Structure Parameters ◽  
Cell Size Distribution ◽  
Numerical Studies ◽  
Polypropylene Foam ◽  
The Impact ◽  
The Relationship

AbstractThe effects of the cell size and distribution on the mechanical properties of polypropylene foam were simulated and analyzed by finite element modeling with ANSYS and supporting experiments. The results show that the reduced cell size and narrow size distribution have beneficial influences on both the tensile and impact strengths. Decreasing the cell size or narrowing the cell size distribution was more effective for increasing the impact strength than the tensile strength in the same case. The relationship between the mechanical properties and cell structure parameters has a good correlation with the theoretical model.

The effect of spatially variable overstory on the understory light environment of an open-canopied longleaf pine forest

2002 ◽  
Vol 32 (11) ◽  
pp. 1984-1991 ◽  
Author(s):  
Michael A Battaglia ◽  
Pu Mou ◽  
Brian Palik ◽  
Robert J Mitchell
Keyword(s):  
Spatial Variation ◽  
Spatial Patterns ◽  
Longleaf Pine ◽  
Light Availability ◽  
Canopy Structure ◽  
Basal Area ◽  
Pinus Palustris ◽  
Pine Forest ◽  
Large Group ◽  
The Relationship

Spatial aggregation of forest structure strongly regulates understory light and its spatial variation in longleaf pine (Pinus palustris Mill.) forest ecosystems. Previous studies have demonstrated that light availability strongly influences longleaf pine seedling growth. In this study, the relationship between spatial structure of a longleaf pine forest and spatial pattern of understory light availability were investigated by comparing three retention harvest treatments: single-tree, small-group, large-group, and an uncut control. The harvests retained similar residual basal area but the spatial patterns of the residual trees differed. Hemispherical photographs were taken at 300 stations to calculate gap light index (GLI), an estimate of understory light availability. Stand-level mean, variation, and spatial distribution of GLI were determined for each treatment. By aggregating residual trees, stand mean GLI increased by 20%, as well as its spatial variation. Spatial autocorrelation of GLI increased as the size of the canopy gaps increased and the gaps were better defined; thus, the predictability of GLI was enhanced. The ranges of detrended semivariograms were increased from the control to the large-group harvest indicating the spatial patterns of understory GLI became coarser textured. Our results demonstrated that aggregated canopy structure of longleaf pine forest will facilitate longleaf pine seedling regeneration.

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