This 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 fit this model, which can be based on virtually any nonlinear function. These 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 styraciflua
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 field-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 (fit 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 under-redicted 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.
Bragg, Don C. 2011. A 3-point derivation of dominant tree height equations. In: Fei, Songlin; Lhotka, John M.; Stringer, Jeffrey W.; Gottschalk, Kurt W.; Miller, Gary W., eds. Proceedings, 17th central hardwood forest conference; 2010 April 5-7; Lexington, KY; Gen. Tech. Rep. NRS-P-78. Newtown Square, PA: U.S. Department of Agriculture, Forest Service, Northern Research Station: 41-50.