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Using a Large-Angle Gauge to Select Trees for Measurement in Variable Plot Sampling

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Using a Large-Angle Gauge to Select Trees for Measurement in Variable Plot Sampling 840 Using a large-angle gauge to select trees for measurement in variable plot sampling David D. Marshall, Kim Iles, and John F. Bell Abstract: Variable plot sampling has been widely used for many years. It was recognized, early in its application, that the process of getting stand volume could be divided into two components, counting trees to get basal area per unit area and measuring trees to get volume/basal area ratios (VBARs). It was further recognized that these two components had different amounts of variation and therefore should be sampled at different intensities. The fact that basal area per unit area is almost always more variable than the VBARs of individual trees has led to the widespread practice of counting trees on all plots and subsampling trees for VBAR measurements, typically by measuring all the trees on every third or fourth plot. This article presents an alternative, the “big BAF method,” which uses a larger basal-area-factor angle gauge to do a second sweep of each plot to select the trees to be measured for VBAR. This procedure spreads the tree measure- ments throughout the stand and is thus more statistically efficient. The method is simple to apply, requires no additional computations, and is easy to audit. Two case-study examples are used to demonstrate the method. Résumé : La place-échantillon à superficie variable a été largement utilisée depuis plusieurs années. Dès le début de son utilisation, il a été reconnu que le processus pour obtenir le volume sur pied pouvait être séparé en deux compo- santes: le décompte des arbres pour obtenir la surface terrière par unité de surface et la mesure des arbres pour obtenir le rapport du volume sur la surface terrière (RVST). Il a de plus été reconnu que ces deux composantes varient diffé- remment et devraient donc être échantillonnées suivant différentes intensités. Le fait que la surface terrière par unité de surface soit presque toujours plus variable que le RVST des arbres individuels, a engendré la pratique courante qui consiste à compter les arbres dans toutes les places-échantillons et de sous-échantillonner les arbres pour la mesure du RVST, typiquement en mesurant tous les arbres à toutes les 3e ou 4e places-échantillons. Une méthode alternative, ap- pelée méthode du grand facteur de prisme, utilise un plus grand facteur de prisme pour faire un second balayage de la place-échantillon et sélectionner les arbres à mesurer pour le RVST. En répartissant la mesure des arbres dans l’en- semble du peuplement, cette méthode est statistiquement plus efficace. Elle est simple d’application, n’exige aucun cal- cul additionnel et est facile à vérifier. Deux études de cas sont utilisées pour illustrer la méthode. [Traduit par la Rédaction] Marshall et al. 845 Introduction [1b] Volume per unit area = basal area per unit area Variable plot sampling (also called point, horizontal point, × average VBAR angle-count, prism, or Bitterlich sampling) is widely used for where BAF is the basal-area factor (m2/ha) of the angle forest inventory. Bitterlich (1948) developed the idea of using gauge used; and VBAR is the average ratio of tree volume/ a horizontal angle gauge for estimating basal area per unit of tree basal area (also known as a mean-of-ratios estimator). land area by simply counting trees with diameters that sub- Bitterlich (1984) provided a detailed description of the tend angles larger than the horizontal angle gauge. Grosen- method and its development. baugh (1952, 1958) introduced this idea to North American Bell and Alexander (1957) showed how the standard error foresters and extended it to provide estimates of volume and in percent (SE%) of the estimated volume could be com- other stand variables from measured trees. The basic approach puted by combining the SEs for basal area (tree count) and can be expressed in the following two formulas: VBARs and using the formula that is commonly known as [1a] Basal area per unit area = average tree count “Bruce’s method” (Goodman 1960): =+22 × BAF [2] SEcombined%% SE TC SE VBAR % This formula assumes that the tree counts and VBARs are Received 7 May 2003. Accepted 7 October 2003. Published statistically independent, and it is simplified by dropping a on the NRC Research Press Web site at http://cjfr.nrc.ca on small, negative third term (SE %2 ×SE %2). The as- 19 April 2004. TC VBAR sumption of independence is commonly made in this appli- D.D. Marshall.1 Pacific Northwest Research Station, cation and has proven an adequate approximation for most 3625 93rd Avenue SW, Olympia, WA 98512, USA. cruise planning and reporting needs. In addition, the com- K. Iles. Kim Iles & Associates, 412 Valley Place, Nanaimo, bined SE% of a typical cruise will tend to be conservatively BC V9R 6A6, Canada. large, as systematic sampling is almost always used for for- J.F. Bell. John Bell & Associates, P.O. Box 1538, Corvallis, est inventory sampling, but computations are done as if it OR 97339, USA. were a random sample. Bruce (1961) pointed out that the 1Corresponding author (e-mail: [email protected]). variability for basal area is usually higher than for VBAR Can. J. For. Res. 34: 840–845 (2004) doi: 10.1139/X03-240 © 2004 NRC Canada Marshall et al. 841 and demonstrated that one can make a greater reduction in some messy bookkeeping, particularly if the selection ratio the combined SE% by reducing that larger component. is different between species. Bruce gave the following example to demonstrate this prin- In this article, we suggest an alternative way to subsample ciple: the trees to be measured for VBAR: using an additional large BAF angle gauge. The method is applied in two steps. =+=22 SEcombined%%%10 2 10.198 % First, the usual BAF angle gauge is used to get a tree count to estimate basal area at each sample point. Second, another =+=22 SEcombined%%%52 5.385% angle gauge, usually with a much larger BAF, is used to se- lect the trees to be subsampled and measured for VBAR. For =+=22 SEcombined%%%10 1 10.050 % example, if the desire is to select roughly every fifth tree to measure for VBAR, an angle gauge with a BAF five times This clearly shows that reducing the larger SE% (as could be larger than the one used to obtain tree counts would be used. done through additional fieldwork) from 10% to 5% makes a Husch et al. (1982) suggested using a larger BAF to select a greater impact on the overall combined SE% than reducing subsample of trees to increment core for growth measure- the smaller value from 2% to 1%. In the case of variable plot ment but did not extend this to measuring VBAR. The “big samples in which the larger SE% is almost always associ- BAF method” we are suggesting is easy to apply, requires no ated with basal area, this would suggest the desirability of computational changes, and is easily adjusted to optimally taking many plots where just basal area is estimated from subsample trees for VBAR measurement. The first written tree counts and measuring only a subsample of those trees to description of this particular method of “distributed VBARs” determine the average VBAR. Bruce (1961) pointed this out seems to be Bell et al. (1983), with a more developed de- and suggested that one way to do this would be to measure scription provided by Iles (1989). In this article, we give two the trees on every third or fourth plot where a tree count was case-study examples of the use of the big BAF method and made to estimate basal area. The idea of subsampling tree discuss the application and benefits of the method. measurements was also discussed by Johnson (1961), Palley and Horwitz (1961), and Beers and Miller (1964). The pro- Selecting sample sizes cedure of measuring all the trees on a subsample of the Selecting the sample size required for estimating basal count plots has been practised for about 40 years in the Pa- area using variable plot sampling requires the use of an cific Northwest. It has also been referred to as “point double appropriate-sized BAF angle gauge. The BAF to use for tree sampling” (Oderwald and Jones 1992). counts can be computed by dividing the stand’s expected This process of measuring all trees at every third or fourth basal area per unit area by the desired average number of point is a form of cluster sampling. The advantage of a clus- “in” trees on each plot. A common target for the desired av- ter sample is that it may be more economical to take mea- erage number of “in” trees is 4–10 per plot. Experience has surements at one location, rather then distributing them. A shown that plots with smaller tree counts have excessive disadvantage of this approach is that when the individuals variability and require more effort to get a desired SE, and within the cluster are similar, more measurements in the plots with larger tree counts tend to be subject to increasing cluster will not proportionately improve the precision of the personal error from missing trees and edge effects (Iles average. This is a problem whether the cluster is selected 1989). If applied correctly, the choice of any BAF will give with a fixed radius or a variable-radius plot is used. If the unbiased estimates of basal area, so it becomes a question of trees that are near each other have similar VBARs, it would what can be applied most correctly and most efficiently (in be more statistically efficient to distribute the measurements that order).
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