An approximate point-based alternative for the estimation of variance under big BAF sampling

Abstract Background A 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. Methods The 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. Results Several 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. Conclusions A 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 $\frac {1}{n}$ 1 n where n is the number of sample points.

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An Approximate Point-based Alternative for the Estimation of Variance under Big BAF Sampling

10.21203/rs.3.rs-135016/v1 ◽

2020 ◽

Author(s):

Thomas B. Lynch ◽

Jeffrey H Gove ◽

Timothy G Gregoire ◽

Mark J Ducey

Keyword(s):

Forest Inventory ◽

Variance Estimation ◽

Basal Area ◽

Simulation Studies ◽

Variance Estimator ◽

Forest Types ◽

Variance Estimators ◽

Computer Simulation Studies ◽

New Formula ◽

Estimation Of Variance

Abstract BackgroundA new variance estimator is derived and tested for big BAF (Basal Area Factor) sampling which is a forest inventory system that utilizes two BAF sizes, a small BAF for tree counts and a larger BAF on which tree measurements are made usually including \dbh s and heights needed for volume estimation.MethodsThe new estimator is derived using the \Dm\ 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 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 1/n where n is the number of sample points.

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A note on the estimation of variance for big BAF sampling

Forest Ecosystems ◽

10.1186/s40663-020-00272-x ◽

2020 ◽

Vol 7 (1) ◽

Author(s):

Jeffrey H. Gove ◽

Timothy G. Gregoire ◽

Mark J. Ducey ◽

Thomas B. Lynch

Keyword(s):

Variance Estimation ◽

Basal Area ◽

Estimation Procedure ◽

Delta Method ◽

Sampling Effort ◽

Individual Tree ◽

Variance Estimators ◽

Taylor Series Approximation ◽

The Mean ◽

Estimation Of Variance

Abstract Background The double sampling method known as “big BAF sampling” has been advocated as a way to reduce sampling effort while still maintaining a reasonably precise estimate of volume. A well-known method for variance determination, Bruce’s method, is customarily used because the volume estimator takes the form of a product of random variables. However, the genesis of Bruce’s method is not known to most foresters who use the method in practice. Methods We establish that the Taylor series approximation known as the Delta method provides a plausible explanation for the origins of Bruce’s method. Simulations were conducted on two different tree populations to ascertain the similarities of the Delta method to the exact variance of a product. Additionally, two alternative estimators for the variance of individual tree volume-basal area ratios, which are part of the estimation process, were compared within the overall variance estimation procedure. Results The simulation results demonstrate that Bruce’s method provides a robust method for estimating the variance of inventories conducted with the big BAF method. The simulations also demonstrate that the variance of the mean volume-basal area ratios can be computed using either the usual sample variance of the mean or the ratio variance estimators with equal accuracy, which had not been shown previously for Big BAF sampling. Conclusions A plausible explanation for the origins of Bruce’s method has been set forth both historically and mathematically in the Delta Method. In most settings, there is evidently no practical difference between applying the exact variance of a product or the Delta method—either can be used. A caution is articulated concerning the aggregation of tree-wise attributes into point-wise summaries in order to test the correlation between the two as a possible indicator of the need for further covariance augmentation.

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Evaluation of mapped-plot variance estimators across a range of partial nonresponse in a post-stratified national forest inventory

Canadian Journal of Forest Research ◽

10.1139/cjfr-2021-0159 ◽

2021 ◽

Author(s):

James A. Westfall ◽

Andrew J. Lister ◽

Charles T. Scott

Keyword(s):

Forest Inventory ◽

Variance Estimation ◽

Phase 1 ◽

National Forest Inventory ◽

Forest Area ◽

Variance Estimator ◽

Adjustment Factor ◽

Primary Methods ◽

Wide Range ◽

Variance Estimates

When conducting a forest inventory, sometimes portions of plots cannot be measured due to inaccessibility. Two primary methods have been presented to account for partial nonresponse in the estimation phase: 1) use a ratio-to-size estimator, or 2) apply an adjustment factor to all plot observations in proportion to the missing area. Both approaches provide identical estimates of the population mean, but the estimates of variance differ when partial nonresponse is present. Variance estimator performance was examined for a range of population forest area and partial nonresponse proportions in the sample. The ratio-to-size variance estimator performed unbiasedly with respect to simulation results, but the adjustment factor variance estimates were biased with the magnitude and direction dependent upon the forest area proportion and amount of partial nonresponse. The bias is relatively small when the partial nonresponse is small, which is often the case; however, the ratio-to-size method is preferred to ensure accurate variance estimation for a wide range of circumstances.

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Contribution to the automation of the calculations involving the forest inventory with the aid of an office computer

Silva Gandavensis ◽

10.21825/sg.v20i0.1001 ◽

1970 ◽

Vol 20 ◽

Author(s):

R. Goossens

Keyword(s):

Tree Species ◽

Forest Inventory ◽

Basal Area ◽

Annual Increment ◽

Mixed Stands ◽

Mean Values ◽

Standing Trees ◽

General Program ◽

Magnetic Card ◽

The Right

Contribution to the automation of the calculations involving the forest inventory with the aid of an office computer - In this contribution an attempt was made to perform the calculations involving the forest inventory by means of an office computer Olivetti P203. The general program (flowchart 1), identical for all tree species except for the values of the different parameters, occupies the tracks A and B of a magnetic card used with this computer. For each tree species one magnetic card is required, while some supplementary cards are used for the subroutines. The first subroutine (flowchart 1) enables us to preserve temporarily the subtotals between two tree species (mixed stands) and so called special or stand cards (SC). After the last tree species the totals per ha are calculated and printed on the former, the average trees occuring on the line below. Appendix 1 gives an example of a similar form resulting from calculations involving a sampling in a mixed stand consisting of Oak (code 11), Red oak (code 12), Japanese larch (code 24) and Beech (code 13). On this form we find from the left to the right: the diameter class (m), the number of trees per ha, the basal area (m2/ha), the current annual increment of the basal area (m2/year/ha), current annual volume increment (m3/year/ha), the volume (m3/ha) and the money value of the standing trees (Bfr/ha). On the line before the last, the totals of the quantities mentioned above and of all the tree species together are to be found. The last line gives a survey of the average values dg, g, ig, ig, v and w. Besides this form each stand or plot has a so-called 'stand card SC' on wich the totals cited above as well as the area of the stand or the plot and its code are stored. Similar 'stand card' may replace in many cases completely the classical index cards; moreover they have the advantage that the data can be entered directly into the computer so that further calculations, classifications or tabling can be carried out by means of an appropriate program or subroutine. The subroutine 2 (flowchart 2) illustrates the use of similar cards for a series of stands or eventually a complete forest, the real values of the different quantities above are calculated and tabled (taking into account the area). At the same time the general totals and the general mean values per ha, as well as the average trees are calculated and printed. Appendix 2 represents a form resulting from such calculations by means of subroutine 2.

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A note on design-based versus model-based variance estimation in stereology

Advances in Applied Probability ◽

10.1017/s000186780001171x ◽

2002 ◽

Vol 34 (03) ◽

pp. 484-490 ◽

Cited By ~ 1

Author(s):

Asger Hobolth ◽

Eva B. Vedel Jensen

Keyword(s):

Mathematical Model ◽

Original Problem ◽

Variance Estimation ◽

Point Of View ◽

Systematic Sampling ◽

Variance Estimator ◽

Shape Model ◽

Model Based ◽

Versus Model ◽

Special Case

Recently, systematic sampling on the circle and the sphere has been studied by Gual-Arnau and Cruz-Orive (2000) from a design-based point of view. In this note, it is shown that their mathematical model for the covariogram is, in a model-based statistical setting, a special case of the p-order shape model suggested by Hobolth, Pedersen and Jensen (2000) and Hobolth, Kent and Dryden (2002) for planar objects without landmarks. Benefits of this observation include an alternative variance estimator, applicable in the original problem of systematic sampling. In a wider perspective, the paper contributes to the discussion concerning design-based versus model-based stereology.

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Zur Auswirkung der Hangneigungskorrektur auf Schätzwerte im Schweizerischen Landesforstinventar (LFI) | Investigation of the effect of the slope correction method as applied in the Swiss National Forest Inventory of estimates

Schweizerische Zeitschrift fur Forstwesen ◽

10.3188/szf.2001.0215 ◽

2001 ◽

Vol 152 (6) ◽

pp. 215-225 ◽

Cited By ~ 4

Author(s):

Michael Köhl ◽

Peter Brassel

Keyword(s):

Forest Inventory ◽

Basal Area ◽

Correction Method ◽

National Forest Inventory ◽

National Forest ◽

Average Deviation ◽

Forest Inventories ◽

Slope Correction ◽

Number Of Stems ◽

Elliptical Area

For forest inventories on slopes, it is necessary to correct the test areas, because the circular areas, when projected, become elliptical. Based on 93 samples from the Swiss National Forest Inventory (FNI), it was determined whether the simplified method, which increases the radius to match that of the elliptical area, leads to a distortion of the results. An average deviation of 2% was found between the FNI estimated values and the actual values for the basal area and the number of stems. For estimations of smaller units, greater distortions of the results are expected.

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Regional Variability of the Romanian Main Tree Species Growth Using National Forest Inventory Increment Cores

Forests ◽

10.3390/f11040409 ◽

2020 ◽

Vol 11 (4) ◽

pp. 409

Author(s):

Gheorghe Marin ◽

Vlad C. Strimbu ◽

Ioan V. Abrudan ◽

Bogdan M. Strimbu

Keyword(s):

Mixed Models ◽

Forest Inventory ◽

Basal Area ◽

National Forest Inventory ◽

Forest Growth ◽

National Forest ◽

Sessile Oak ◽

Basal Area Growth ◽

Temporal Grouping ◽

Area Growth

In many countries, National Forest Inventory (NFI) data is used to assess the variability of forest growth across the country. The identification of areas with similar growths provides the foundation for development of regional models. The objective of the present study is to identify areas with similar diameter and basal area growth using increment cores acquired by the NFI for the three main Romanian species: Norway spruce (Picea abies L. Karst), European beech (Fagus sylvatica L.), and Sessile oak (Quercus petraea (Matt.) Liebl.). We used 6536 increment cores with ages less than 100 years, a total of 427,635 rings. The country was divided in 21 non-overlapping ecoregions based on geomorphology, soil, geology and spatial contiguousness. Mixed models and multivariate analyses were used to assess the differences in annual dimeter at breast height and basal area growth among ecoregions. Irrespective of the species, the mixed models analysis revealed significant differences in growth between the ecoregions. However, some ecoregions were similar in terms of growth and could be aggregated. Multivariate analysis reinforced the difference between ecoregions and showed no temporal grouping for spruce and beech. Sessile oak growth was separated not only by ecoregions, but also by time, with some ecoregions being more prone to draught. Our study showed that countries of median size, such as Romania, could exhibit significant spatial differences in forest growth. Therefore, countrywide growth models incorporate too much variability to be considered operationally feasible. Furthermore, it is difficult to justify the current growth and yield models as a legal binding planning tool.

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Predicting Growing Stock Volume of Eucalyptus Plantations Using 3-D Point Clouds Derived from UAV Imagery and ALS Data

Forests ◽

10.3390/f10100905 ◽

2019 ◽

Vol 10 (10) ◽

pp. 905 ◽

Cited By ~ 3

Author(s):

Guerra-Hernández ◽

Cosenza ◽

Cardil ◽

Silva ◽

Botequim ◽

...

Keyword(s):

Laser Scanning ◽

Basal Area ◽

Remote Sensing Data ◽

Tree Height ◽

Point Clouds ◽

Volume Estimation ◽

P Value ◽

Test Statistic ◽

Individual Tree ◽

Significant Difference

Estimating forest inventory variables is important in monitoring forest resources and mitigating climate change. In this respect, forest managers require flexible, non-destructive methods for estimating volume and biomass. High-resolution and low-cost remote sensing data are increasingly available to measure three-dimensional (3D) canopy structure and to model forest structural attributes. The main objective of this study was to evaluate and compare the individual tree volume estimates derived from high-density point clouds obtained from airborne laser scanning (ALS) and digital aerial photogrammetry (DAP) in Eucalyptus spp. plantations. Object-based image analysis (OBIA) techniques were applied for individual tree crown (ITC) delineation. The ITC algorithm applied correctly detected and delineated 199 trees from ALS-derived data, while 192 trees were correctly identified using DAP-based point clouds acquired from Unmanned Aerial Vehicles (UAV), representing accuracy levels of respectively 62% and 60%. Addressing volume modelling, non-linear regression fit based on individual tree height and individual crown area derived from the ITC provided the following results: Model Efficiency (Mef) = 0.43 and 0.46, Root Mean Square Error (RMSE) = 0.030 m3 and 0.026 m3, rRMSE = 20.31% and 19.97%, and an approximately unbiased results (0.025 m3 and 0.0004 m3) using DAP and ALS-based estimations, respectively. No significant difference was found between the observed value (field data) and volume estimation from ALS and DAP (p-value from t-test statistic = 0.99 and 0.98, respectively). The proposed approaches could also be used to estimate basal area or biomass stocks in Eucalyptus spp. plantations.

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SISTEMA DE INVENTÁRIO FLORESTAL PARA SERINGAL NATIVO

FLORESTA ◽

10.5380/rf.v32i1.2351 ◽

2002 ◽

Vol 32 (1) ◽

Author(s):

José de Arimatéa Silva ◽

Sylvio Péllico Netto

Keyword(s):

Forest Inventory ◽

Random Sampling ◽

Rubber Tree ◽

Basal Area ◽

Simple Random Sampling ◽

Inventory System ◽

Stratified Random Sampling ◽

Stage Number ◽

Second Stage ◽

Two Stages

Este trabalho teve como objetivo desenvolver um Sistema de Inventário Florestal para seringal nativo. Aplicou-se a Amostragem Inteiramente Aleatória (AIA), em dois estágios: colocação de seringa, no primeiro, e estrada de seringa, no segundo. Foram estimados: número de seringueiras por estrada (N), área basal das seringueiras da estrada (G) e volume da porção explorada do fuste (V). Realizou-se uma pós-estratificação, considerando-se estradas de centro e de margem, aplicando-se a Amostragem Estratificada (AE). Comparou-se a AIA com a AE, com base na eficiência relativa. Os resultados revelaram as seguintes estimativas para as médias estratificadas: N=100; G=19,00 m², V= 62,8 m³. Concluiu-se que a AE revelou-se mais eficiente que a AIA para estimar as variáveis analisadas. Propõe-se que um sistema de inventário para seringal nativo deve combinar: informações de um censo das colocações; um processo de amostragem estratificada; e um método de amostragem cuja unidade de amostra é a estrada de seringa. Forest Inventory System for Rubber Trees Abstract Forest Inventory System for rubber trees. This work had as objective to develop an Inventory System for native rubber tree areas. The Simple Random Sampling (SRS) was applied in two stages: the setting, in the first, and the rubber trees tracks, in the second stage. Number of rubber trees per track (N), basal area of the rubber trees track (G) and volume of the stem portion explored (V) were the parameters estimated. A post-stratification was become fulfilled, considering itself center tracks and river side tracks, applying itself it Stratified Random Sampling (STRS). It was compared SRS with the STRS, on the basis of the relative efficiency. The results showed the following estimates for the stratified means: N=100; G=19,00 m², V = 62,8 m³. It was concluded that the STRS showed more efficient than the SRS to estimate the analyzed variables. It is considered that an Inventory System for native rubber tree areas must match: information of a census of the settings; a process of Stratified Random Sampling; and a sampling method whose unit of sample is the rubber tree track.

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Effects of Basal Area Factor and Plot Size on Precision and Accuracy of Forest Inventory Estimates

Northern Journal of Applied Forestry ◽

10.1093/njaf/28.3.152 ◽

2011 ◽

Vol 28 (3) ◽

pp. 152-156 ◽

Cited By ~ 1

Author(s):

Peter Becker ◽

Tom Nichols

Keyword(s):

Forest Inventory ◽

Basal Area ◽

Cost Effective ◽

Sampling Errors ◽

Plot Size ◽

Accuracy And Precision ◽

Coefficients Of Variation ◽

Fixed Radius ◽

Tree Number ◽

Biased Estimates

Abstract We tested the effects of plot size (0.05-0.30 ac) and basal area factor (BAF) (5-30) on the accuracy and precision of per-acre estimates of tree number, basal area, biomass (all for trees ≥4.5 in. dbh), and sawtimber volume (for trees ≥11.6 in. dbh). Field sampling errors, such as missing in-trees, did not affect our tests. Virtual variable- and fixed-radius plots were randomly located within an artificial matrix of 130 real plots in well-stocked upland hardwood forests of sawtimber-sized trees in the Missouri Ozarks. Inventory parameters were essentially independent of plot size and BAF, whereas their coefficients of variation decreased with plot size and increased with BAF. Thus, our results for random plots agreed with sampling theory, unlike a previous study using concentric virtual plots in West Virginia forests. A very concentrated zone of high tree density around some plot centers apparently caused the biased estimates by concentric plots. Compared with the entire composite forest, inventory means were accurately estimated (to within 5%) and size class distributions were well represented for plots ≥0.1 ac or ≤15 BAF. Our procedures provide a basis for selecting an efficient and cost-effective sampling design suited to forest characteristics and the inventory's purpose.

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