A 3-point Derivation of Dominant Tree Height Equations

—Th is paper describes a new approach for deriving height-diameter (H-D) equations from limited information and a few assumptions about tree height. Only three data points are required to fi t this model, which can be based on virtually any nonlinear function. Th ese points are the height of a tree at diameter at breast height (d.b.h.), the predicted height of a 10-inch d.b.h. tree from an existing H-D model, and the height at species maximum d.b.h., estimated from a linear regression of big trees. Dominant sweetgum (Liquidambar styracifl ua L.) from the Arkansas region and yellow-poplar (Liriodendron tulipifera L.) from across the southeastern United States were used to estimate height at species maximum d.b.h. A composite of these fi eld-measured heights and site index trees from the U.S. Forest Service’s Forest Inventory and Analysis (FIA) database were used to compare the 3-point equations (fi t to the Chapman-Richards model) with the Forest Vegetation Simulator (FVS) default H-D models. Because of the limited range of diameters in the FIA site trees, the Chapman-Richards equations developed from site trees underpredicted large tree heights for both species. For the sweetgum, the 3-point equation was virtually identical to the FVS default model. However, the 3-point equation noticeably improved dominant height predictions for yellow-poplar. 1Research Forester, Southern Research Station, U.S. Forest Service, P.O. Box 3516 UAM, Monticello, AR 71656. To contact, call (870) 367-3464 or email at [email protected]. INTRODUCTION Simulation models are increasingly used to project forest dynamics over large spatial and temporal scales. Th e Forest Vegetation Simulator (FVS), for example, now encompasses virtually the entire continental United States, as well as parts of Alaska and Canada (Dixon 2009). Most of these models incorporate several mathematical relationships to defi ne the nature of simulated trees and stands, usually in the form of regression equations derived from fi eld-sampled data. One of the best examples of these models can be found in heightdiameter (H-D) models, which use any of a number of functions to describe the trend between total tree height and (typically) diameter at breast height (d.b.h.). Numerous H-D models have been developed for North American tree species (for example, Huang and others 1992, 2000; Lootens and others 2007; Zhang 1997). However, it is unusual for H-D models to be derived across the size range of a given taxon, primarily because few data sets include very large trees. Centuries of lumbering, land clearing, and catastrophic disturbance have greatly reduced the number of big trees, making their presence rare in most inventories. Some have sought to improve upon existing allometric relationships by expanding the range of data via the incorporation of champion-sized trees (for instance, Bragg 2008b, Shifl ey and Brand 1984). Th is approach has some limitations, including sensitivity to the individual chosen as the champion tree and the possibility that the specimen selected may not adequately represent the maximal expression of height and diameter, especially for open-grown champions (Bragg 2008b).