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.
Page 1
Page 2 Page 3
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 SRS101.
Asheville, NC: U.S. Department of Agriculture, Forest Service,
Southern Research Station: 2332. 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. 3843.
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 (50year 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 championsized 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 longterm 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. 2431
Many models to predict tree height from diameter have been
developed, but not all are equally useful. This study
compared a set of heightdiameter 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 (ChapmanRichards, modified logistic,
exponential, and CurtisArney) 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 3Point 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
57; Lexington, KY; Gen. Tech. Rep. NRSP78. Newtown Square,
PA: U.S. Department of Agriculture, Forest Service, Northern
Research Station. 678 p. CDROM. pp. 4150.
Abstract.—Th
is paper describes a new approach for deriving heightdiameter
(HD) 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 10inch d.b.h. tree from an existing HD 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 yellowpoplar (Liriodendron
tulipifera L.)
from across the southeastern United States were used to estimate
height at species maximum d.b.h. A composite of these
fieldmeasured heights and site index trees from the U.S. Forest
Service’s Forest Inventory and Analysis (FIA) database were used
to compare the 3point equations (fi t to the ChapmanRichards
model) with the Forest Vegetation Simulator (FVS) default HD
models. Because of the limited range of diameters in the FIA
site trees, the ChapmanRichards equations developed from site
trees underpredicted large tree heights for both species. For
the sweetgum, the 3point equation was virtually identical to
the FVS default model. However, the 3point equation noticeably
improved dominant height predictions for yellowpoplar.
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 SRS22, 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 forestgrown 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























