Biases in Volume Increment Estimates Derived from Successive Angle Count Sampling Chris S. Eastaugh and Hubert Hasenauer Abstract: Several large-scale forest inventories are now being conducted using angle count sampling, and the method is commonly used for timber cruising and corporate forest assessment. The calculation of basal area or volume increment from angle count sample data is not trivial, and three alternative methods are currently in common use: the difference method, the starting value method, and the end value method. This article develops the hypothesis that in various circumstances these methods are susceptible to bias as a result of measurement error and mis-sampling of trees. After reviewing prior work in angle count mathematics and developing the theoretical basis of our hypothesis, we present a supporting example based on a large permanent sampling plot at Hirschlacke in northern Austria. Our results suggest that the errors resulting from using calculation method- ologies susceptible to bias from measurement error may in practical circumstances be more than 10% of volume increment, which could have ramifications for sustainable forest management or carbon sequestration budgeting. FOR.SCI. ❚❚(❚):000 – 000. Keywords: point sample, angle count, sampling error, Bitterlich, inventory A CCURATE ASSESSMENTS OF FOREST volume incre- ment are becoming increasingly important within natural resource management. Apart from the ob- vious relevance to determining sustainable forest resource utilization, an increasing focus on using forest inventory data to assess the carbon sequestration potential of forests is taking forest growth assessment issues beyond the forest sector into a far wider policy environment. This suggests that consistent forest information is of increasing concern and any increment estimations derived from forest inven- tory data (e.g., timber volume, biomass, or carbon) that forest agencies provide to governments must therefore be as accurate and unbiased as possible to ensure their credibility and to allow support of rational policy development. Forest inventories in some form have been in place in some jurisdictions since the 15th century (Schadauer et al. 2007). Until recently, inventories were conducted solely as a means of determining what resource was present in a region, generally to determine its immediate extractive ca- pacity. Today, however, national forest inventories form an integral part of the way that many nations determine their national carbon balance, and inventories are used to esti- mate forest growth increment as a means of monitoring their value as a carbon sink. Since the early 1990s, regular forest inventories have been established in many countries, often using a permanent plot design to reduce the sampling error of the resulting increment calculations (Tomppo et al. 2010). The remea- surement interval ranges from 5 to 10 years, and a common sampling method in many jurisdictions is angle count sam- pling (Bitterlich 1948). Angle count samples, also referred to as sampling pro- portional to size, horizontal point samples, or Bitterlich plots, are considered to be an unbiased estimate of stand volume (Grosenbaugh 1958) and have been demonstrated to be a superior method of forest inventory under many cir- cumstances (Whyte and Tennent 1975, Scott 1990). In terms of increment assessment, they have high variance (Hradetzky 1995), although they are generally considered to be unbiased estimators of increment (Van Deusen et al. 1986). Three different methods for estimating volume in- crement from successive angle count samples are in com- mon use, attributed by Hradetzky (1995) to Van Deusen et al. (1986), Grosenbaugh (1958), and Roesch et al. (1989), respectively. 1. Difference method (Z D ). This method calculates incre- ment as the standing volume estimate at time 2 minus the volume estimate at time 1, plus the removals. 2. Starting value method (Z S ). This method selects only those trees present at both times and calculates stand increment as the increment of the selected trees mul- tiplied by the estimated number of trees of that size in the stand in time 1, plus new trees entering the stand. 3. End value method (Z E ). All trees present in time 2 are considered, and the stand increment as the increment of the selected trees multiplied by the estimated num- ber of trees of that size in the stand in time 2 is Manuscript received January 14, 2011; accepted September 28, 2011; published online February 9, 2012; http://dx.doi.org/10.5849/forsci.11-007. Chris S. Eastaugh, Universit¨ at f¨ ur Bodenkultur (BOKU), Peter Jordan Str. 82, A1190 Vienna, Austria—Phone: 43 (147) 654-4050; chris.eastaugh@ boku.ac.at. Hubert Hasenauer, Universita ¨t fu ¨r Bodenkultur (BOKU)— hubert.hasenauer@boku.ac.at. Acknowledgments: This work is part of the project “Comparing satellite versus ground driven carbon estimates for Austrian Forests” (MOTI). We are grateful for the financial support provided by the Energy Fund of the Federal State of Austria, managed by Kommunalkredit Public Consulting GmbH under Contract K10AC1K00050. We thank Prof. Hubert Sterba for comments on an earlier version of this manuscript and helpful review comments by the Associate Editor and two anonymous reviewers served to substantially improve the article. Copyright © 2012 by the Society of American Foresters. Forest Science ❚❚(❚) 2012 1