Predicting Diameter Distributions for Young
Longleaf Pine Plantations in Southwest Georgia
Lichun Jiang and John R. Brooks
Parameter prediction equations for the Weibull distribution function were developed based on four percentile functions and a parameter recovery method for
longleaf pine (Pinus palustris Mill.) in Southwest Georgia. Four percentiles were expressed as functions of stand-level characteristics based on stepwise regression
and seemingly unrelated regression. Using a percentile-based parameter recovery method (PCT), estimated diameter distributions were obtained from available
stand-level variables. The PCT method was also compared with a cumulative distribution function (CDF) regression method. The PCT method produced consistently
better goodness-of-fit statistics than the CDF method. The results indicate that diameter distribution in longleaf pine stands can be successfully characterized
with the Weibull function.
Keywords: longleaf pine, Weibull distribution, parameter recovery, stepwise and seemingly unrelated regression
T
he Weibull probability density function has been widely
used in forestry applications to describe the diameter distri-
bution of trees. The ultimate purpose of modeling diameter
distributions is to develop yield systems that provide volume esti-
mates by diameter class. The Weibull function was introduced to
forestry by Bailey and Dell (1973). Weibull parameters were initially
predicted using empirical functions of whole stand characteristics
(Smalley and Bailey 1974, Schreuder et al. 1979). Subsequently, the
parameter recovery method replaced the parameter prediction ap-
proach (Lohrey and Bailey 1976, Matney and Sullivan 1982, Burk
and Newberry 1984, McTague and Bailey 1987, Bailey et al. 1989,
Brooks et al. 1992, Knowe et al. 1997, Lee and Coble 2006). Re-
cently, Cao (2004) evaluated different methods for estimating
Weibull parameters and found that the cumulative distribution
function (CDF) regression method was better than the PCT
method (Cao 2004). This approach was later applied by Newton
and Amponsah (2005), Nord-Larsen and Cao (2006), and Palahí et
al. (2006). The objective of this study was to compare the two
methods (PCT and CDF) for estimating the diameter frequency
distributions of longleaf pine plantations using commonly mea-
sured stand variables.
Study Description
The longleaf pine data are part of a growth and yield study based
on 15 stands located in Lee, Worth, Mitchell, and Baker counties in
southwest Georgia. Seventeen rectangular fixed area plots were es-
tablished at different dates and have been remeasured annually;
thus, the number of measurements available per plot ranges from
two to nine. A total of 100 plot remeasurements are available for this
study with age ranging from 3 to 20 years old and stand density
ranging from 273 to 857 trees/ac and from 47 to 140 ft
2
of basal area
(BA) per acre (Table 1).
At each measurement date, dbh was measured with a diameter
tape and recorded for every tree to the nearest 0.1 in. Total tree
height was measured with a height pole (height, less than 15 ft)
and an Impulse laser (height, 15 ft or more) and recorded to the
nearest 0.1 ft. Initially, crown class was recorded for just the older
stands (more than12 years) but they incorporated for all trees,
regardless of age. The traditional definition of crown class was
slightly modified to assign crown class to the younger stands. The
younger plantations generally have a wider initial planting spac-
ing and thus all trees receive full sunlight. The dominant and
codominant crown classes were defined as those trees that make
up the main crown canopy while intermediate and suppressed
classes were assigned to those trees visually shorter (and usually
less vigorous) than the trees that constitute the average crown
height. Additional data set from 14 plots are available for
validation.
Received September 4, 2007; accepted December 19, 2008.
Lichun Jiang (jlichun@yahoo.com), Northeast Forestry University, Harbin, China. John Brooks (jrbrooks@mail.wvu.edu), Division of Forestry, Forest Biometrics, West Virginia
University, 322 Percival Hall, PO Box 6125, Morgantown, WV 26506. Appreciation is extended to Dr. Lindsay Boring of the Joseph W. Jones Ecological Research Center for his support
of this project.
Copyright © 2009 by the Society of American Foresters.
Table 1. Descriptive statistics of stand variables for young long-
leaf pine plantations in southwest Georgia.
Variable Mean SD Minimum Maximum
Fit data set
PS 0.13 0.03 0.09 0.19
A 11.88 4.69 3.00 20.00
HT 29.83 11.45 8.63 49.69
BA 69.24 38.13 47.4 140.74
N 509.93 193.17 273.49 857.9
Validation data set
PS 0.13 0.04 0.09 0.19
A 14.28 4.89 6.00 20.00
HT 37.08 9.21 19.41 49.92
BA 90.39 33.11 34.93 147.69
N 467.60 199.86 273.49 787.51
PS, plot size (ac); A, plantation age (yr); HT, average height of dominant and codominant trees
(ft); BA, basal area per acre (ft
2
); N, trees per acre.
SOUTH. J. APPL.FOR. 33(1) 2009 25
ABSTRACT
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