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.

Stand volume estimation from tree counts in the context of vertical line sampling

1990 ◽  
Vol 20 (3) ◽  
pp. 274-279 ◽  
Author(s):  
Thomas B. Lynch
Keyword(s):  
Volume Estimation ◽  
Vertical Line ◽  
Individual Tree ◽  
Stand Volume ◽  
Variable Volume ◽  
Sample Tree ◽  
Line Sampling ◽  
Constant Form ◽  
Volume Equation ◽  
Line Sample

Stand volume estimators are developed in the context of vertical line sampling that depend on counts of sample trees only, rather than on measurements of sample tree dimensions. These estimators are based on three commonly used individual tree volume equations: the constant form factor volume equation, the combined variable volume equation with negative intercept, and the combined variable volume equation with positive intercept. Fieldwork for each of the estimators involves comparison of the squared dbh's of trees that would qualify for selection in an ordinary vertical line sample with numbers chosen randomly from the interval bounded by zero and a fixed maximum squared dbh. Two of the estimators choose sample trees with probability exactly proportional to an individual tree volume equation.

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.

Estimation of individual tree volume by importance sampling and antithetic variates from the cylindrical shells integral

1992 ◽  
Vol 22 (3) ◽  
pp. 326-335 ◽  
Author(s):  
Thomas B. Lynch ◽  
Shen-Then Chang ◽  
John P. Chandler
Keyword(s):  
Importance Sampling ◽  
Cylindrical Shells ◽  
Volume Estimation ◽  
Volume Integral ◽  
Volume Estimate ◽  
Cross Sectional ◽  
Individual Tree ◽  
Solid Of Revolution ◽  
Antithetic Variates ◽  
Tree Stem

A method of estimating individual tree volume by importance sampling is developed that is based on the cylindrical shells volume integral. The cylindrical shells volume integral conceptualizes a tree stem as being a solid of revolution comprising a collection of thin cylinders. Previous applications of importance sampling to individual tree volume estimation have been based on the method of slices integral, in which the tree stem is viewed as a solid of revolution comprising a collection of thin disks. Both approaches provide unbiased estimates of individual tree volume for any monotonic tree taper, if it can be assumed that the tree is circular in cross section. An advantage of the cylindrical shells approach is that total tree height need not be measured to accomplish the estimation process, as would be required when using importance sampling estimators based on the method of slices integral. Tree volume estimation via importance sampling based on the cylindrical shells integral requires measurement of stump cross-sectional area, which is usually more easily obtained than total or merchantable height measurements. Both approaches require one or more upper stem diameter measurements. Computer simulation shows that use of antithetic variates with importance sampling reduces the variance of the volume estimate significantly when a paraboloid is used as a proxy taper function.

Effects of measurement error on Monte Carlo integration estimators of tree volume: critical height sampling and vertical Monte Carlo methods

2015 ◽  
Vol 45 (4) ◽  
pp. 463-470 ◽  
Author(s):  
Thomas B. Lynch
Keyword(s):  
Monte Carlo ◽  
Measurement Error ◽  
Sampling Error ◽  
Monte Carlo Integration ◽  
Critical Height ◽  
Volume Estimate ◽  
Cross Sectional ◽  
Individual Tree ◽  
Control Variate ◽  
Multiplicative Measurement Error

The effects of measurement error on Monte Carlo (MC) integration estimators of individual-tree volume that sample upper-stem heights at randomly selected cross-sectional areas (termed vertical methods) were studied. These methods included critical height sampling (on an individual-tree basis), vertical importance sampling (VIS), and vertical control variate sampling (VCS). These estimators were unbiased in the presence of two error models: additive measurement error with mean zero and multiplicative measurement error with mean one. Exact mathematical expressions were derived for the variances of VIS and VCS that include additive components for sampling error and measurement error, which together comprise total variance. Previous studies of sampling error for MC integration estimators of tree volume were combined with estimates of upper-stem measurement error obtained from the mensurational literature to compute typical estimates of total standard errors for VIS and VCS. Through examples, it is shown that measurement error can substantially increase the total root mean square error of the volume estimate, especially for small trees.

An Equation for Estimating Total Volume of Both Stands and Single Trees of Black Spruce

1983 ◽  
Vol 59 (1) ◽  
pp. 26-29 ◽  
Author(s):  
F. Evert
Keyword(s):  
Picea Mariana ◽  
Black Spruce ◽  
Direct Reference ◽  
Individual Tree ◽  
Stand Volume ◽  
Volume Equation ◽  
The Individual ◽  
Individual Trees

A stand volume equation is presented for black spruce (Picea mariana (Mill.)B.S.P.), based on a sample of 785 felled trees. To ensure that the equation will provide accurate estimates of the volume of both variously stocked stands and of individual trees, stand volume was expressed as the sum of individual tree volumes without direct reference to the size of the area that the trees occupy. The equation will reduce the problem of forecasting stand volume to the simpler problem of forecasting separately the individual components in the stand-volume equation.

Compatible taper function for Scots pine plantations in northwestern Spain

2006 ◽  
Vol 36 (5) ◽  
pp. 1190-1205 ◽  
Author(s):  
Ulises Diéguez-Aranda ◽  
Fernando Castedo-Dorado ◽  
Juan Gabriel Álvarez-González ◽  
Alberto Rojo
Keyword(s):  
Scots Pine ◽  
Model Development ◽  
Individual Tree ◽  
Stand Volume ◽  
Taper Function ◽  
Northwestern Spain ◽  
Volume Equation ◽  
Taper Equation ◽  
Volume Equations

A compatible system for estimation of individual tree volume was developed for Scots pine (Pinus sylvestris L.) in northwestern Spain. The system comprises a merchantable volume equation, a total volume equation, and a taper function. The use of the volume equation allows rapid estimation of tree volume, and stand volume by summing individual tree volumes, which is equal to the volume obtained by integrating the taper equation. The volume equation is very easy to use and is therefore preferred when classification of the products by merchantable sizes is not required. Data from 228 destructively sampled trees were used for model development. Fourteen compatible volume equations were evaluated, 13 of these equations were taken from the available literature, and the other was developed in the present study. A modified second-order continuous autoregressive error structure was used to correct the autocorrelation of the hierarchical data used. The model developed by Fang et al. (Z. Fang, B.E. Borders, and R.L. Bailey. 2000. For. Sci. 46: 1–12) best described the data. There model is therefore recommended for the estimation of diameter at a specific height, merchantable volume, and total volume of Scots pine stems in the area of study.

scholarly journals Height Extraction and Stand Volume Estimation Based on Fusion Airborne LiDAR Data and Terrestrial Measurements for a Norway Spruce [Picea abies (L.) Karst.] Test Site in Romania

2016 ◽  
Vol 44 (1) ◽  
pp. 313-323 ◽  
Author(s):  
Bogdan APOSTOL ◽  
Adrian LORENT ◽  
Marius PETRILA ◽  
Vladimir GANCZ ◽  
Ovidiu BADEA
Keyword(s):  
Picea Abies ◽  
Norway Spruce ◽  
Volume Estimation ◽  
Airborne Lidar ◽  
Stem Volume ◽  
Lidar Data ◽  
Individual Tree ◽  
Stand Volume ◽  
Empirical Modelling ◽  
The Individual

The objective of this study was to analyze the efficiency of individual tree identification and stand volume estimation from LiDAR data. The study was located in Norway spruce [Picea abies (L.) Karst.] stands in southwestern Romania and linked airborne laser scanning (ALS) with terrestrial measurements through empirical modelling. The proposed method uses the Canopy Maxima algorithm for individual tree detection together with biometric field measurements and individual trees positioning. Field data was collected using Field-Map real-time GIS-laser equipment, a high-accuracy GNSS receiver and a Vertex IV ultrasound inclinometer. ALS data were collected using a Riegl LMS-Q560 instrument and processed using LP360 and Fusion software to extract digital terrain, surface and canopy height models. For the estimation of tree heights, number of trees and tree crown widths from the ALS data, the Canopy Maxima algorithm was used together with local regression equations relating field-measured tree heights and crown widths at each plot. When compared to LiDAR detected trees, about 40-61% of the field-measured trees were correctly identified. Such trees represented, in general, predominant, dominant and co-dominant trees from the upper canopy. However, it should be noted that the volume of the correctly identified trees represented 60-78% of the total plot volume. The estimation of stand volume using the LiDAR data was achieved by empirical modelling, taking into account the individual tree heights (as identified from the ALS data) and the corresponding ground reference stem volume. The root mean square error (RMSE) between the individual tree heights measured in the field and the corresponding heights identified in the ALS data was 1.7-2.2 meters. Comparing the ground reference estimated stem volume (at trees level) with the corresponding ALS estimated tree stem volume, an RMSE of 0.5-0.7 m3 was achieved. The RMSE was slightly lower when comparing the ground reference stem volume at plot level with the ALS-estimated one, taking into account both the identified and unidentified trees in the LiDAR data (0.4-0.6 m3).

Assessing the Accuracy of a Product-form Tree Volume Equation

1981 ◽  
Vol 57 (3) ◽  
pp. 119-122
Author(s):  
Peter Roebbelen ◽  
Victor G. Smith
Keyword(s):  
Volume Estimation ◽  
Red Pine ◽  
Product Form ◽  
Weighted Regression ◽  
Individual Tree ◽  
Form Class ◽  
Volume Equation ◽  
Individual Trees ◽  
Volume Equations

In a continuing investigation of product-form as a predicting variable in volume estimation, this study compares a product-form tree volume equation with two standard volume equations and the Dominion Forestry Service form-class 70 and 75 volume tables in their ability to estimate individual tree red pine volumes. Using weighted regression and measurements from 3607 individual trees, coefficients for the three equations were developed. Freese's test of accuracy was used as the criterion of choice in deciding which method proved most accurate in estimating the volumes of a set of test data.The product-form volume equation gave the most accurate estimates.

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