Allometric scaling theory applied to FIA biomass estimation

—Tree biomass estimates in the Forest Inventory and Analysis (FIA) database are derived from numerous methodologies whose abundance and complexity raise questions about consistent results throughout the U.S. A new model based on allometric scaling theory (“WBE”) offers simplified methodology and a theoretically sound basis for improving the reliability and usefulness of biomass estimation for all tree species. Although a complete test of the WBE theory is beyond the scope of this paper, implications of the theory are explored from results of another study consistent with WBE theory. Two interesting results were found: (1) a simplified approach using 10 generalized equations is within 10 to 40 percent of FIA county-scale biomass estimates, and (2) of the two methods, FIA’s methodology appears more inconsistent from State to State. The largest application of current biomass methodology in the U.S. is found in the Forest Inventory and Analysis (FIA) database. FIA biomass estimates are calculated either from conversion functions of merchantable volume to total tree biomass or from species-specific biomass equations. Because so many different equations and techniques are used, there is concern about equation bias confounding FIA biomass results. For example, Hansen (this volume, table 5) compared 67 tree species common to four eastern FIA regions and found that biomass estimates differed by an average of 25 to 30 percent among regions for trees of the same size and species. The test did not include a control for “known” biomass, but methodology differences among FIA regions seem a likely explanation for the observed differences among equations for the same species. Improving FIA biomass estimates by constructing new equations would be a huge and costly undertaking because there is no theory to guide the process other than statistically subsampling for new biomass data, which would need to represent all tree species in all locations throughout the entire U.S. However, allometric scaling theory offers a possible area of research to simplify the process. 1 Forester, Forest Inventory Research, Enterprise Unit; USDA Forest Service; 1115-VMPR; 1400 Independence Avenue, SW; Washington, DC 20250-1115. Phone (703) 605-5262; fax: (703) 605-5133; email: dchojnacky@fs.fed.us. Allometric scaling is an old idea in biology—linking an organism’s size to its energy balances and structural dimensions (Niklas 1994, Peters 1983, Schmidt-Nielsen 1984)—that is being revisited with new theoretical explanation (Enquist and Niklas 2001; Enquist and others 1998, 1999, 2000; West and others 1997, 1999a, 1999b). The logarithmic model currently used for many tree biomass and volume equations (Schumacher and Hall 1933, Whittaker and Woodell 1968) is related to allometric scaling theory. However, the widespread use of the logarithmic model is generally based on empirical evidence resulting from the fitting of regression data rather than on any firm theoretical basis. The objective of this paper is to explore devising new biomass estimators through greater use of the allometric scaling theory. First, tree biomass estimation is discussed based on recent work (Jenkins and others 2003), in which we surveyed the literature of all published biomass equations for U.S. tree species and summarized results into 10 equations based on diameter at breast height (d.b.h.). The synthesis into so few equations is consistent with allometric scaling theory or what we call the “WBE allometric-scaling model,” where WBE stands for the developers—West, Brown, and Enquist. Next, to hypothesize about the usefulness of the WBE model for FIA biomass estimation, the 10 equations were compared to FIA biomass in the Eastern U.S. (Hansen and others 1992). Because neither the 10 equations nor the FIA biomass estimates offer a satisfying measure for “true” biomass, the paper concludes with a fuller discussion of the WBE model that might be tested for improved biomass estimators. 96 A b o v e g ro u n d B io m a s s ( k g )