Combining taper functions and critical height sampling for unbiased stand volume estimation

1987 ◽  
Vol 17 (11) ◽  
pp. 1416-1420 ◽  
Author(s):  
Paul C. Van Deusen
Keyword(s):  
Variance Reduction ◽  
Volume Growth ◽  
Volume Estimation ◽  
Critical Height ◽  
Stand Volume ◽  
Point Sampling ◽  
Taper Function ◽  
Unbiased Estimates ◽  
Sampling Procedures ◽  
Horizontal Point Sampling

New estimators have been developed for critical height sampling that allow any taper function to be used as a variance reduction mechanism. The new estimators are compatible with current horizontal point sampling procedures and will lead to unbiased estimates of cubic volume and cubic volume growth. It is proposed that critical height sampling should replace horizontal point sampling when one upper stem measurement can be made, because horizontal point sampling relies on predicted tree volumes and the assumption that resulting stand volume predictions are unbiased.

Variance reduction in Ueno's method and cylinder sampling for forest volume estimation

1995 ◽  
Vol 25 (11) ◽  
pp. 1783-1794 ◽  
Author(s):  
Thomas B. Lynch
Keyword(s):  
Computer Simulation ◽  
Variance Reduction ◽  
Volume Estimation ◽  
Critical Height ◽  
Volume Estimate ◽  
Individual Tree ◽  
Stand Volume ◽  
Reduction Techniques ◽  
Antithetic Variates ◽  
Volume Equation

Three basic techniques are proposed for reducing the variance of the stand volume estimate provided by cylinder sampling and Ueno's method. Ueno's method is based on critical height sampling but does not require measurement of critical heights. Instead, a count of trees whose critical heights are less than randomly generated heights is used to estimate stand volume. Cylinder sampling selects sample trees for which randomly generated heights fall within cylinders formed by tree heights and point sampling plot sizes. The methods proposed here for variance reduction in cylinder sampling and Ueno's method are antithetic variates, importance sampling, and control variates. Cylinder sampling without variance reduction was the most efficient of 12 methods compared in computer simulation that used estimated measurement times. However, cylinder sampling requires knowledge of a combined variable individual tree volume equation. Of the three variance reduction techniques applied to Ueno's method, antithetic variates performed best in computer simulation.

New and composite point sampling estimates

2010 ◽  
Vol 40 (11) ◽  
pp. 2234-2242 ◽  
Author(s):  
John Paul McTague
Keyword(s):  
Sampling Method ◽  
Sampling Methods ◽  
Basal Area ◽  
Population Parameters ◽  
Critical Height ◽  
Sampling Methodology ◽  
Stand Volume ◽  
Point Sampling ◽  
Repeated Sampling ◽  
Angle Count Sampling

A new estimator for basal area is introduced that is based on the concepts of angle count and angle summation sampling. Using the ratio of the angle count basal area factor and the angle summation (borderline) factor, it is possible to estimate stand volume without measuring the diameters and distances of the trees included in the sample. Employing simulation of repeated sampling in a 40 ha forest of known population parameters, it is demonstrated that the new sampling methodology is unbiased and weakly correlated with conventional angle count sampling. Hence, considerable gains in efficiency are made by combining the two sampling methods with composite estimators. Two applications are explored with the new composite point sampling estimates, including the use of the big basal area factor sampling method and critical height sampling using a Max and Burkhart taper formulation.

Stratified space angle-count sampling for an estimation of stand volume

2004 ◽  
Vol 34 (2) ◽  
pp. 507-508 ◽  
Author(s):  
Masahiko Nakagawa
Keyword(s):  
Basal Area ◽  
Critical Height ◽  
Easy Method ◽  
Indicator Variable ◽  
Stand Volume ◽  
Point Sampling ◽  
Stratified Space ◽  
Space Angle ◽  
Space Point ◽  
Angle Count Sampling

Stratified space angle-count sampling is a newly proposed method for estimating stand volume. This new method includes the theory and all the premises of space point sampling, as well as the following: (i) all trees taper, (ii) the box-like sampling space imagined in space point sampling is divided into several strata with the same vertical distances, (iii) the diameter of expanded tree stems in each stratum is represented at the middle of the vertical distance in each stratum. Stand volume is calculated using the following equation: V (m3/ha)=kH/Z Σ[Formula: see text] λi, where V is volume (m3/ha), k is basal area factor (m2/ha), H is the maximum tree height in the stand, Z is the number of strata in the sampling space, N is the number of trees in the stand, and λi is an indicator variable that takes the value 1 or 0, depending on whether the tree stem is in the sample or not. Since this method does not require a measurement or an estimation of a critical height, it could be an easy method for estimating stand volume.

scholarly journals Developing Growth Models of Stand Volume for Subtropical Forests in Karst Areas: A Case Study in the Guizhou Plateau

Forests ◽  
2021 ◽  
Vol 12 (1) ◽  
pp. 83
Author(s):  
Yuzhi Tang ◽  
Quanqin Shao ◽  
Tiezhu Shi ◽  
Guofeng Wu
Keyword(s):  
Growth Models ◽  
Volume Growth ◽  
Site Quality ◽  
Rocky Desertification ◽  
Stand Volume ◽  
Subtropical Forests ◽  
Karst Areas ◽  
Growth Equations ◽  
Global Carbon ◽  
Guizhou Plateau

Forest stand volume is one of the key forest structural attributes in estimating and forecasting ecosystem productivity and carbon stock. However, studies on growth modeling and environmental influences on stand volume are still rare to date, especially in subtropical forests in karst areas, which are characterized by a complex species composition and are important in the global carbon budget. In this paper, we developed growth models of stand volume for all the dominant tree species (groups) (DTSG) in a subtropical karst area, the Guizhou Plateau based on an investigation of the effects of various environmental factors on stand volume. The Richards growth function, space-for-time substitution and zonal-hierarchical modeling method were applied in the model fitting, and multiple indices were used in the model evaluation. The results showed that the climatic factors of annual temperature and precipitation, as well as the site factors of stand origin, elevation, slope gradient, topsoil thickness, site quality degree, rocky desertification type and rocky desertification degree, have significant influences on stand volume, and the topsoil thickness and site quality degree have the strongest positive effect. A total of 959 growth equations of stand volume were fitted with a five-level stand classifier (DTSG–climatic zone–site quality degree–stand origin–rocky desertification type). All the growth equations were qualified, because all passed the TRE test (≤30%), and the majority of the R2 ≥ 0.50, above 70% of the RMSE were between 5.0 and 20.0, and above 80% of the P ≥ 75%. These findings provide updated knowledge about the environmental effect on the stand volume growth of subtropical forests in karst areas, and the developed stand volume growth models are convenient for forest management and planning, further contributing to the study of forest carbon storage assessments and global carbon cycling.

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 Early response of Nothofagus antarctica forests to thinning intensity in northern Patagonia

2020 ◽  
Author(s):  
Matias G. Goldenberg ◽  
Marcos Nacif ◽  
Facundo Oddi ◽  
Lucas Garibaldi
Keyword(s):  
Forest Type ◽  
Volume Growth ◽  
Early Response ◽  
Annual Increment ◽  
Basal Diameter ◽  
Stand Volume ◽  
Thinning Intensity ◽  
Northern Patagonia ◽  
Silvicultural Treatments ◽  
Nothofagus Antarctica

Nothofagus antarctica (G. Forst.) Oerst. stands of northern Patagonia (Argentina) have great potential to provide multiple ecosystem services. Nonetheless, the lack of basic information limits the application of silvicultural treatments to this forest type. This study reports the early response to three systematic strip thinning treatments (30, 50, and 70%) carried out during 2013 in a 30-year N. antarctica stand, where control plots (i.e. no thinning) were also established. Subplots were located within each plot. Basal diameters (BD) of all retained stems were measured in the non-vegetative season (winter) of 2016, 2017 and 2018, to calculate basal diameter annual increment (BDI), and stand volume growth. BDI ranged from 1.9 mm year-1 in the control plots to 2.7 mm year-1 at 70% thinning. Relative BDI also responded positively to thinning intensity. Stand volume growth decreased non-linearly with thinning intensity, from 3.36 m3 ha-1 year-1 in the control plots, and 0.71 m3 ha-1 year-1 when thinning was 70%. Smaller differences were observed between control plots, 30% thinning and 50% thinning. Our results show that Nothofagus antarctica forests, in the stem exclusion stage, respond to strip thinning. Thus, silviculture based on this management system could favor the development of retained trees without losing productivity if it remains under 50% intensity. This outcome represents an important incremental contribution to the design of silvicultural interventions in northern Patagonia.

scholarly journals Increased Individual Tree Growth Maintains Stand Volume Growth after B-Level Thinning and Crop-Tree Management in Mature Oak Stands

2019 ◽  
Vol 65 (6) ◽  
pp. 784-795
Author(s):  
Jeffrey S Ward ◽  
Jessica Wikle
Keyword(s):  
Tree Growth ◽  
Growth Response ◽  
Volume Growth ◽  
Diameter Growth ◽  
Red Oak ◽  
Individual Tree ◽  
Stand Volume ◽  
Tree Management ◽  
Individual Tree Growth ◽  
Partial Release

AbstractSix study areas were established in 80–125-year-old upland oak stands on average sites to compare stand and individual tree growth response following two active treatments (B-level thinning, crop tree) with an unmanaged control. Initial stocking of 104 percent was reduced to 62 percent and 60 percent on the B-level and crop-tree-management plots, respectively. Approximately 7,200 board feet per acre (International ¼) were harvested on the actively managed plots with upland oaks accounting for 81 percent of pre- and 86 percent of residual stand. Eleven-year diameter and volume growth of oak sawtimber trees was greater on actively managed plots. Growth response increased with degree of release and was maintained for the length of the study. Because of the increased individual tree growth of oaks in response to release, stand volume growth of oak sawtimber did not differ between treatments. In contrast to an 11-year decline of poletimber stocking on unmanaged plots, poletimber stocking increased on managed plots as diameter growth increased in response to partial release. This may increase difficulty of regenerating oak in the future. For those mature red oak stands where traditional regeneration prescriptions will not be implemented or will be delayed, commercial harvests can be conducted without compromising stand volume growth of oak.

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.

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