Using a large-angle gauge to select trees for measurement in variable plot sampling

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 ahnost 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 tQ apply, requires no additional computations, and is easy to audit. Two case-study examples are used to demonstrate the method. Resume : La place-echantillon a superficie variable a ete largement utilisee depuis plusieurs annees. Des le debut de son utilisation, il a ete reconnu que le processus pour obtenir le volume sur pied pouvait etre separe en deux compo­ santes: le decompte des arbres pour obtenir Ia surface terriere par unite de surface et Ia mesure des arbres pour obtenir le rapport du volume sur la surface terriere (RVST). Il a de plus ere reconnu que ces deux composantes varient diffe­ remment et devraient done etre echantillonnees suivant differentes intensites. Le fait que Ia surface terriere par unite de surface soit presque toujours plus variable que le RVST des arbres individuels, a engendre Ia pratique courante qui consiste a compter les arbres dans toutes les places-echantillons et de sous-echantillonner les arbres pour la mesure du RVST, typiquement en mesurant tous les arbres a toutes les 3e ou 4e places-echantillons. Une methode alternative, ap­ pelee methode du grand facteur de prisme, utilise un plus grand facteur de prisme pour faire un second balayage de la place-echantillon et selectionner les arbres a mesurer pour le RVST. En repartissant Ia mesure des arbres dans !'en­ semble du peuplement, cette methode est statistiquement plus efficace. Elle est simple d'application, n'exige aucun cal­ cui additionnel et est facile a verifier. Deux etudes de cas sont utilisees pour illustrer Ia methode. [Traduit par Ia Redaction] Introduction [lb] Volume per unit area = basal area per unit area x average VBAR Variable plot sampling (also called point, horizontal point, angle-count, prism, or Bitterlich sampling) is widely used for where BAF is the basal-area factor (m2/ha) of the angle David D. Marshall, Kim lies, and John F. Bell 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 "Bruce's method" (Goodman 1960): [Ia] Basal area per unit area = average tree count x BAF [2] SEcombined% = ~SETC%2 + SEVBAR% 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 (SErc%2 x SEvBAR%2). The as­ 19 April 2004. 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. Des. Kim lies & 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. Ben. 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