Special Publications of the Native Tree Society

The Native Tree Society also publishes a series of Special Publications on an irregular basis as appropriate material become available.  The first in the series is the Tree Measuring Guideline of the Eastern Native Tree Society by Will Blozan.

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NTS SP #17
The Sine Method as a More Accurate Height Predictor for Hardwoods
by Don C. Bragg, In: Buckley, David S.; Clatterbuck, Wayne K. (eds.). Proceedings of the 15th Central Hardwood Forest Conference. General Technical Report SRS-101.
Asheville, NC: U.S. Department of Agriculture, Forest Service, Southern Research Station: 23-32. Published in April 2007.

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 #17

NTS SP #18
An Improved Tree Height Measurement Technique Tested on Mature Southern Pines
by Don C. Bragg. SOUTH. J. APPL. FOR. 32(1) 2008, pp. 38-43.

Virtually all techniques for tree height determination follow one of two principles: similar triangles or the tangent method. Most people apply the latter approach, which uses the tangents of the angles to the top and bottom and a true horizontal distance to the subject tree. However, few adjust this method for ground slope, tree lean, crown shape, and crown configuration, making errors commonplace. Given documented discrepancies exceeding 30% with current methods, a reevaluation of height measurement is in order. The sine method is an alternative that measures a real point in the crown. Hence, it is not subject to the same assumptions as the similar triangle and tangent approaches. In addition, the sine method is insensitive to distance from tree or observer position and can not overestimate tree height. The advantages of the sine approach are shown with mature southern pines from Arkansas.

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

NTS SP #19
Practical Extension of a Lake States Tree Height Model
by Don C. Bragg, NORTH. J. APPL. FOR. 25(4) 2008, pp. 186- 194

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.

Available for download as part of the Native Tree Society Special Publication Series:  NTS SP #19

NTS SP #20
A Comparison of Pine Height Models for the Crossett Experimental Forest
by D. Bragg.  Journal of the Arkansas Academy of Science, Vol. 62, 2008, pp. 24-31

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...

Available for download as part of the Native Tree Society Special Publication Series:  NTS SP #20

NTS SP #21
A 3-Point Derivation of Dominant Tree Height Equations
by Don C. Bragg, In: Fei, Songlin; Lhotka, John M.; Stringer, Jeffrey W.; Gottschalk, Kurt W.; Miller, Gary W., eds. 2011. 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. 678 p. CD-ROM. pp. 41-50.

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

NTS SP #22
The Sine Method: An Alternative Height Measurement Technique
by Don C. Bragg, Lee E. Frelich, Robert T. Leverett, Will Blozan, and Dale J. Luthringer.  United States Department of Agriculture Forest Service, Southern Research Station Research Note SRS-22, December 2011, 12 p.

Height is one of the most important dimensions of trees, but few observers are fully aware of the consequences of the misapplication of conventional height measurement techniques. A new approach, the sine method, can improve height measurement by being less sensitive to the requirements of conventional techniques (similar triangles and the tangent method).  We studied the sine method through a couple of comparisons. First, we demonstrated the validity of the sine method under idealized conditions by comparing tangent and sine measurements on a stationary object of a known height. Then, we compared heights collected via climbing and lowering a tape from the highest point of a number of forest-grown trees with heights measured with the sine method. The sine method offers a viable, cost effective alternative to traditional measurement approaches, especially for large or leaning trees, and for trees with broadly spreading crowns.

Available for download as part of the Native Tree Society Special Publication Series:  NTS SP #22