Sampling Strategies for Efficient Estimation of Tree Foliage Biomass

Conifer crowns can be highly variable both within and between trees, particularly with respect to foliage biomass and leaf area. A variety of sampling schemes have been used to estimate biomass and leaf area at the individual tree and stand scales. Rarely has the effectiveness of these sampling schemes been compared across stands or even across species. In addition, sample size estimates for achieving a certain level of precision have rarely been given. This simulation study used extensive branch and tree foliage biomass data sets for Douglas-fir (Pseudotsuga menziesii var. menziesii [Mirb.] Franco) and ponderosa pine (Pinus ponderosa Dougl ex. Laws.) to compare alternative sampling schemes and sample sizes. The use of auxiliary information at the estimation phase resulted in a more cost-efficient sampling scheme than when auxiliary information was used at the design phase. However, using auxiliary information at the design phase resulted in more precise estimates than using the same at the estimation phase for the same sample size. For both species, systematic sampling with ratio estimation provided the most efficient estimate of individual tree foliage biomass. In Douglas-fir, stratifying by branch type (i.e., whorl versus interwhorl) resulted in a marginal gain in precision. For Douglas-fir, on average, root mean square error decreased by 43.1% when sample size increased from 6 to 12 branches per tree, with a further decrease of 24.3% when sample size increased from 12 to 18 branches per tree. For ponderosa pine, on average, the root mean square error decreased by 44.4 and 23.9% when the sample size was increased from 6 to 12 and from 12 to 18 branches per tree, respectively. Additional work is needed to understand the appropriate sampling techniques for older conifer tree crowns and sampling multileader deciduous crowns. FOR. SCI. 57(2):153–163. SAMPLING INDIVIDUAL TREE CROWNS to measure foliage biomass or leaf area index is a common approach for estimating the foliar biomass and leaf area index of the entire crown. Tree foliage biomass (mass of dry foliage) is a common response variable in analyzing the impact of silvicultural treatments such as fertilization and thinning. However, direct tree foliage biomass estimation is tedious, laborious, and costly. As a result, tree foliage biomass is typically estimated using regression or allometric relationships between foliage biomass and other easily measured attributes such as diameter outside bark at breast height (Baldwin 1989, Catchpole and Wheeler 1992, Jenkins et al. 2003), cross-sectional sapwood area at breast height (Waring et al. 1982), cross-sectional sapwood area at the base of the live crown (i.e., using the pipe model theory) (Maguire and Hann 1987), diameter at stump height (diameter outside bark at 0.3 m aboveground) (Helgerson et al. 1988), the ratio of live crown length to total tree height (Loomis et al. 1966), the distance from breast height to the base of live crown (Dean and Long 1986), or the proportion of light that passes through the canopy (Martens et al. 1993). Models or allometric equations are developed using data collected from a specific forest population (e.g., a particular tree species at a specific location) (e.g., Temesgen et al. 2003). The underlying models need to be valid, and a strong relationship between the response variable and the predictor variable(s) should exist. The development of such regression requires measuring foliar biomass on a sample of trees. Despite numerous attempts to quantify foliage biomass, accurate and efficient estimation of biomass continues to be problematic. The high withinand between-tree crown variation has prevented the development of efficient protocols. In this article, we focused on evaluating the performance of selected sampling strategies to estimate tree foliage mass. Estimating foliar biomass from a tree typically requires selecting a sample of branches and collecting and weighting the leaves on the branch. Many sampling designs have been used to select the sample, from very simple approaches that do not require additional measurements or only easily measured information such as counting and identifying branches to sampling protocols that require detailed auxiliary information about branch characteristics. Examples of simple designs include simple random sampling, systematic sampling, and stratified random sampling. Examples of sampling designs that require detailed auxiliary information include randomized branch sampling and probability proportional to branch size sampling. However, if auxiliary information (e.g., branch diameter or position) is available, it can be used to design an efficient sampling scheme (design phase) but can also be used to improve the efficiency of estimators after samples are drawn (estimation phase), regardless of the sampling design used. Comparing sampling strategies and, in particular, comparing strategies Hailemariam Temesgen, Oregon State University, Forest Resources, 237 Peavy Hall, Corvallis, OR 97331-5703—Phone: (541) 737-8549; Fax: (541) 737-4613; [email protected]. Vicente Monleon, Forest Inventory and Analysis—[email protected]. Aaron Weiskittel, The University of Maine—[email protected]. Duncan Wilson, Oklahoma State University—[email protected]. Acknowledgments: We thank Drs. John Kershaw, Don Stevens, Jeremy Groom, Sean Garber, and Bianca Eskelson for comments on earlier drafts, and two anonymous reviewers for their constructive feedback. We thank Mark Vomocil of Starker Forests, Inc. (Corvallis OR), for his insights and comments on an earlier draft. The Oregon State University Swiss Needle Cast Cooperative and its supporting members provided the funding for the collection of the Douglas-fir data. Thanks to the Deschutes National Forest for providing access to the ponderosa pine sample trees. Manuscript received May 31, 2009, accepted August 11, 2010 Copyright © 2011 by the Society of American Foresters Forest Science 57(2) 2011 153 that use auxiliary information during the design or estimation phases is the primary objective of this article. Some sampling designs use unequal probability sampling, typically selecting branches with probability proportional to a measure of their size. Larger branches are selected more often, which results in more precise estimates. However, it also means more effort to collect, handle, and measure branch biomass. Some sampling designs, such as probability proportional to branch size sampling, randomized branch sampling, and importance sampling are timeconsuming and cumbersome to apply in the field, because the diameter of each branch has to be measured and recorded, which might also contribute to measurement errors. For example, Cancino and Saborowski (2005) found conventional randomized branch sampling to be imprecise because its sampling variance exceeded the population variance by almost 30% in determining the foliage biomass of three different species. Temesgen (2003) summarized various sampling strategies that have been used to estimate crown attributes. Using Monte Carlo simulation techniques, Temesgen (2003) found that stratified random sampling resulted in the lowest mean square error values, followed by ellipsoidal, two-stage systematic, and simple random sampling, and then by twostage unequal probability sampling for estimating total tree leaf area. Although previous studies have provided a general framework for sampling tree crowns (e.g., Gregoire et al. 1995, Temesgen 2003, Cancino and Saborowski 2005), several fundamental questions still remain. First, how robust are these sampling techniques when there are differences in branching patterns among or between tree species? For example, Temesgen (2003) based his conclusions on a limited sample of only 12 trees of hybrid spruce (Picea engelmannii Parry Picea glauca [Moench] Voss Picea sitchensis [Bong.] Carr) across three stands. Furthermore, just the four tallest trees in each stand were sampled rather than multiple crown classes. Second, are the most efficient crown sampling schemes species-specific? Finally, how many branches per tree should be sampled to estimate total foliage biomass of individual tree crowns? We used a simulation study based on extensive branch and tree foliage biomass data sets for Douglas-fir (Pseudotsuga menziesii var. menziesii [Mirb.] Franco) (Weiskittel et al. 2006) and ponderosa pine (Pinus ponderosa Dougl. ex Laws.) (Wilson and Maguire 2009) in Oregon to examine those questions. The Douglas-fir data set was collected across a wide gradient of crown classes, stand ages, and severity of Swiss needle cast disease, a fungal disease caused by (Phaeocryptopus gaeumannii [T. Rohde] Petr.). The ponderosa pine data set was collected in midrotation, pure, even-aged ponderosa pine stands across a soil productivity gradient in central Oregon. Specific objectives of this study were to examine the statistical efficiency and amount of dry biomass that needs to be measured to achieve a given precision using selected sampling alternatives and to compare the use of auxiliary information (e.g., branch diameter) at either the design or estimation phase in estimating tree foliage biomass. Methods