Abstract—Most hypsometers apply a mathematical technique that utilizes the tangent of angles and a horizontal distance to deliver the exact height of a tree under idealized circumstances. Unfortunately, these conditions are rarely met for hardwoods in the field. A “new” predictor based on sine and slope distance and discussed here does not require the same assumptions for accurate height determination. Case studies using a sycamore (Platanus occidentalis L.), a water oak (Quercus nigra L.), and a southern red oak (Q. falcata Michx.) from southern Arkansas are presented to emphasize the sensitivity of the tangent method to erroneous measurement procedures. When heights were measured properly and under favorable circumstances, the results obtained by the tangent and sine methods differed only by about 2 percent. Under more challenging conditions, however, errors ranged from 8 to 42 percent. These examples also highlight a number of distinct advantages of using the sine method, especially when exact tree height is required.

Available for download as part of the Native Tree Society Special Publication Series:  NTS SP #18

By adapting data from national and state champion lists and the predictions of an existing height model, an exponential function was developed to improve tree height estimation. As a case study, comparisons between the original and redesigned model were made with eastern white pine (Pinus strobus L.). For example, the heights predicted by the new design varied by centimeters from the original until the pines were more than 25 cm dbh, after which the differences increased notably. On a very good site (50-year base age site index [SI50]
27.4 m) at the upper end of the range of basal area (BA; 68.9 m2/ha) for the region, the redesigned model predicted a champion-sized eastern white pine (actual measurements: 97.0 cm dbh, 50.9 m tall) to be 51.3 m tall, compared with 38.8 m using the original formulation under the same conditions. The NORTHWDS Individual Response Model (NIRM) individual tree model further highlighted the influence of these differences with long-term simulations of eastern white pine height. On a moderate site (SI50
18.7 m) with intermediate (BA
15 m2/ha) stand density, NIRM results show that the original model consistently predicts heights to be 20 –30% lower for mature white pine.

Many models to predict tree height from diameter have been developed, but not all are equally useful.  This study compared a set of height-diameter models for loblolly (Pinus taeda) and shortleaf (Pinus echinata) pines from Ashley County, Arkansas.  Almost 560 trees ranging in diameter at breast height (DBH) from 0.3 cm (both species) to 91.9 cm (for shortleaf) or 108.2 cm (for loblolly) were chosen for measurement. Height equations were then fit to four different functions (Chapman-Richards, modified logistic, exponential, and Curtis-Arney) with weighted nonlinear least squares regression using DBH as the only predictor...

Abstract.—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. 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 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 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 (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.

Available for download as part of the Native Tree Society Special Publication Series: NTS SP #21