Bottomland

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Bottomland Hardwoods Weights
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Physical Models

• Physical relationships size and density

• Taper
• Volume
• Weight

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• Types of Taper equations
• graphical
• polynomial
• segmented polynomial
• variable exponent (often polynomials)
• fixed-point segmented non-integer polynomial

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Tree Volume Estimation Trees volumes can be
estimated in a number of ways. Most methods
estimate different portions of the tree volume
using different formulas.
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Sections have different taper
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Tree Taper Estimation

• Taper equations provide
• estimates of inside bark diameter at any point
  along the stem
• estimates of merchantable height to any top
  diameter
• estimates of total stem volume
• estimates of volume from any stump height to any
  merchantable height
• estimates of individual log volumes of any length
  at any height from ground
• Consistency among estimates by exploiting
  physical models.

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Weight
Volume
Weight Density One measure of weight density is
defined as the pounds of green wood and bark per
cubic-foot of green wood. The following 3
segment segmented-quadratic polynomial model is
presented by an empirical model of weight
density as a function of height (h) from the
ground line (0) to the tip of a tree stem (H).
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Trees seem capable of assuming an infinite
variety of shapes
Two White Oaks, 15 DBH 80 H
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Segmented Taper Functions For Estimating
Tree Stem Volumes
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Model Development Requires Detailed Measurements
SRS Research Work Units Biomass Studies
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Segment and Join-point Selection
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Segment and Join-point Selection is Data Driven
Prediction is too close to zero
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Segmented polynomial has diameter prediction bias
at various heights
bias
bias
Short Trees systematic under-prediction
Tall Trees systematic over-prediction
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Reduced Bias Using Segmented Taper Models
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Bias inclination towards something, or a
partiality
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Accuracy - Precision - Bias

• Accuracy is how close a measured
• value is to the truth.

• Precision is how close the measured
• values are to each other.

• Bias is a systematic error which
• makes all measurements wrong by
• a certain amount.

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Magnitude of Volume Estimation Bias
Small lt 10 Direction Varies by Tree Size
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• Consistent with measured
• DBH
• Form Class
• Total Height

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Taper and Volume Prediction in Southern Tree
Species
Developed for USDA Forest Service September 22,
1999
Fixed-point segmented non-integer polynomial

• Consistent
• Varying parameters

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Model Derived Using Simple Segments

• that can be
• Inverted
• Integrated

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Fixed-point segmented non-integer polynomial
Accurate estimation almost everywhere
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Fixed-point segmented non-integer polynomial
Because parameters vary
bias reduced
bias reduced
Parameters and model forms associated with
Top q1(aq1bq1(tht)cq1dbh) a11/(1exp(-(aa1
ba1log(tht)ca1dbh))) q2(aq2.bq2(tht)cq2d
bh) a2(1/(1exp(-(aa2ba2log(tht)ca2dbh))))a
1 q3(aq3bq3(tht)cq3dbh) Parameters and
model form associated with Middle pexp(apbp(th
t)cpdbh) Parameters and model forms
associated with Bottom J1/(1exp(-(aJbJlog(tht
)cJdbh))) s(asbs(tht)csdbh) r(arbr(tht
)crdbh) c(acbclog(tht)ccdbh)
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SUMMARY OF TREES MEASURED FOR TAPER FUNCTION
DEVELOPMENT
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R8 National Forest System Timber Sales Felled Tre
e Measurements
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SRS Forest Inventory and Analysis Work Unit Stand
ing and Felled Tree Measurements
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Data Source - Geographic Region
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Prediction Invariant to Data Source - Geographic
Region
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Volume
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DEVELOPED SPECIES PROFILE FUNCTIONS FOR THE
FOLLOWING 26 SPECIES OF HARD HARDWOOD FOR POLE
AND SAWTIMBER TREES
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DEVELOPED SPECIES PROFILE FUNCTIONS FOR THE
FOLLOWING 21 SPECIES OF SOFT HARDWOODS FOR POLE
AND SAWTIMBER TREES
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DEVELOPED SPECIES PROFILE FUNCTIONS FOR THE
FOLLOWING 16 SPECIES OF SOFTWOOD FOR POLE AND
SAWTIMBER TREES
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GREEN AND DRY BIOMASS ESTIMATION
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GREEN AND DRY BIOMASS ESTIMATION
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STUMP AND CROWN GREEN AND DRY BIOMASS ESTIMATION
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Weight Density One measure of weight density is
defined as the pounds of green wood and bark per
cubic-foot of green wood. The following 3
segment segmented-quadratic polynomial model is
presented by an empirical model of weight
density as a function of height (h) from the
ground line (0) to the tip of a tree stem (H).
Weight
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Weight
Segmented polynomial density Integrated Over
Fixed-point segmented non-integer polynomial
taper
The only challenge Keep track of Join-points
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Weight Density One measure of weight density is
defined as the pounds of green wood and bark per
cubic-foot of green wood. The following 3
segment segmented-quadratic polynomial model is
presented by an empirical model of weight
density as a function of height (h) from the
ground line (0) to the tip of a tree stem (H).
Consider a situation in which there are two
distinct sections with constant weight densities
in each. This leads to weight density parameters
of a simpler form
Here is the pulpwood weight density and
is the difference in the sawlog and the
pulpwood densities. The indicator variable, ,
is equal to 1 when the height along the stem is
below the sawtimber top diameter ( is equal
to the height to the sawlog top diameter as a
proportion of total height).
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What More?
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Incorporate Bottomland Hardwoods Biomass Study
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Further Refinement
Define additional segments
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Applications Developed with Common Dynamic-Linked
Libraries