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thesis entitled

VALIDATION OF TWO GROWTH AND YIELD MODELS ON
RED PINE PLANTATIONS IN MICHIGAN

presented by

ERIN E. SMITH—MATEJA

has been accepted towards fulfillment
of the requirements for the

MS. degree in Forestry

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6/01 cJCIRC/DatoDuopGS—p. 1 5

VALIDATION OF TWO GROWTH AND YIELD MODELS ON RED PINE
PLANTATIONS TN MICHIGAN

By

Erin E. Smith-Mateja

A THESIS
Submitted to
Michigan State University
in partial fitlfillment of the requirements
For the degree of

MASTER OF SCIENCE
Department of Forestry

2003

ABSTRACT

VALIDATION OF TWO GROWTH AND YIELD MODELS ON RED PINE
PLANTATIONS IN MICHIGAN

By

Erin E. Smith-Mateja

Two red pine thinning study sites were used to validate two different forest
grth and yield computer models, the Forest Vegetation Simulator (FVS) Lakes States
variant, an individual tree model and Red Pine Al Lundgren (RPAL), a stand level model.
Both study sites had been established as red pine plantations in the 1930’s and became
thinning study sites in the 1960’s. Approximately every five to ten years (between 1964,
1965 through 1991 , 1992) the stands were thinned and individual tree measurements
were taken on every tree in the study. Both growth models “grew” the data from the
second inventory date through the last inventory. The simulated estimates of diameter at
breast height (dbh) for FVS, trees per acre, and basal area were compared to the actual
measurements. Two types of simulations were projected using FVS; with diameter
growth calibration and without diameter growth calibration. One type of RPAL
simulation was run.

FVS predicted more accurate results than RPAL for trees per acre but not
necessarily for basal area per acre. F VS predicted more accurately dbh and basal area per
acre with dbh growth calibration turned on, it had little to no effect on more accurately
estimating mortality on either site. With calibration turned on FVS predicted up to

twenty- seven years of growth with an absolute mean error less than 1.0 inch.

ACKNOWLEDGEMENTS

There are friends and a few family members that I need to thank, most important,
my mentor Dr. Carl W. Ramm who started me out on this project. With out his guidance
and support this project would not have been undertaken. Dr. Ramm was an excellent
teacher and biometrician, he was also a friend. He was taken from us much earlier than
we all could have imagined, and he is dearly missed.

I must say thank you to my family. To my parents for raising us with out thinking
there were limits to our success, to my sister Meghan who pushed me forward, my sister
Ryan who quietly with force pulled me along and to my husband Brian who reminded me
to relax and smell the flowers.

Thank you to my graduate committee, Dr. Karen Potter-Witter, Dr. Larry Leefers,
and Dr. J ianguo Liu. Your input and expertise helped make this a success. Karen thanks
for stepping in and letting me know the project could be finished.

Thanks to the Vegetation Simulator Group at the USDA Forest Service in Fort
Collins, Colorado who always had an answer. To the guys at the Kellogg Experimental
Forest for letting me use the ‘gator’ and always having a good story to tell.

The Mclntire-Stennis Cooperative Forestry Research funded much of this work,

and with out that support this project would not have been undertaken.

iii

TABLE OF CONTENTS

LIST OF TABLES ............................................................................................................... v
LIST OF FIGURES ........................................................................................................... vi
INTRODUCTION ............................................................................................................... 1
Objectives ........................................................................................................................ 5
LITERATURE REVIEW .................................................................................................... 6
METHODS ......................................................................................... . .............................. 12
Data Description ............................................................................................................ 12
Growth Simulations ....................................................................................................... l4
Validation ...................................................................................................................... 16
RESULTS .......................................................................................................................... 19
Diameter at Breast Height Error .................................................................................... 19
Basal Area Error ............................................................................................................ 23
Trees per acre Error ....................................................................................................... 27
DISCUSSION .................................................................................................................... 31
FVS Options and Defaults ............................................................................................. 31
RPAL Options and Defaults .......................................................................................... 32
Model Performance ....................................................................................................... 32
CONCLUSION .................................................................................................................. 36
APPENDICES ................................................................................................................... 47
BIBLIOGRAPHY .............................................................................................................. 51

iv

LIST OF TABLES
Table 1. Hiawatha National Forest thinning study treatments ......................................... 13

Table 2. WK. Kellogg Forest Thinning Treatments ........................................................ 14

Table 3 . Hiawatha site and Kellogg site absolute mean error for all treatments by cycle
length. ........................................................................................................................ 20

Table 4. Hiawatha mean error (E) and standard deviation (5) of mean error for estimated
diameter at breast height by treatment and projection length for the two types of
simulation. Error expressed as predicted value minus observed value ..................... 21

Table 5. Kellogg mean error (6) and standard deviation (5) of mean error for estimated
diameter at breast height by treatment and projection length for the two types of
simulation. Error expressed as predicted value minus observed value ..................... 22

Table 6. Hiawatha mean error (E) and standard deviation (3) of mean error for estimated
basal area by treatment and projection length for three types of simulation. Error
expressed as predicted value minus observed value .................................................. 24

Table 7. Kellogg mean error (e) and standard deviation (3) of mean error for estimated
basal area by treatment and projection length for three types of simulation. Error
expressed as predicted value minus observed value .................................................. 26

Table 8. Hiawatha mean error (E) and standard deviation (3) of mean error for estimated
trees per acre by treatment and projection length for three types of simulation. Error
expressed as predicted value minus observed value. ................................................. 28

Table 9. Kellogg mean error (E) and standard deviation (5) of mean error for estimated
trees per acre by treatment and projection length for three types of simulation. Error
expressed as predicted value minus observed value. ................................................. 30

LIST OF FIGURES

Figure 1. Diagram of the cycle boundaries at which bias was calculated for the Hiawatha
and Kellogg sites ........................................................................................................ 18

Figure 2. Hiawatha site mean error for estimated diameter at breast height by treatment
and prjection length for the FVS with out DBH growth calibration (NA). (Error
expressed as predicted value minus observed value.) ............................................... 39

Figure 3. Hiawatha site mean error for estimated diameter at breast height by treatment
and projection length for the FVS with growth calibration (AD). (Error expressed as
predicted value minus observed value.) ..................................................................... 39

Figure 4. Kellogg site mean error for estimated diameter at breast height by treatment
and projection length for the F VS with out DBH growth calibration (NA). (Error
expressed as predicted value minus observed value.) ............................................... 40

Figure 5. Kellogg site mean error for estimated diameter at breast height by treatment
and projection length for the FVS with growth calibration (AD). (Error expressed as
predicted value minus observed value.) ..................................................................... 40

Figure 6. Hiawatha site mean error for estimated basal area per acre by treatment and
projection length for the F VS with out DBH growth calibration (NA). (Error
expressed as predicted value minus observed value.) ............................................... 41

Figure 7. Hiawatha site mean error for estimated basal area per acre by treatment and
projection length for the F VS with growth calibration (AD). (Error expressed as
predicted value minus observed value.) ..................................................................... 41

Figure 8. Hiawatha site error for estimated basal area per acre by treatment and
projection length for RPAL . (Error expressed as predicted value minus observed
value.) ........................................................................................................................ 42

Figure 9. Kellogg site mean error for estimated basal area per acre by treatment and
projection length for the FVS with out DBH growth calibration (NA). (Error
expressed as predicted value minus observed value.) ............................................... 42

Figure 10. Kellogg site mean error for estimated basal area per acre by treatment and
projection length for the FVS with growth calibration (AD). Error expressed as
predicted value minus observed value. ...................................................................... 43

Figure 11. Kellogg site mean error for estimated basal area per acre by treatment and

projection length for RPAL. (Error expressed as predicted value minus observed
value.) ........................................................................................................................ 43

vi

Figure 12. Hiawatha site mean error for estimated trees per acre by treatment and
projection length for the F VS with out DBH growth calibration (NA). (Error
expressed as predicted value minus observed value.) ............................................... 44

Figure 13. Hiawatha site mean error for estimated trees per acre by treatment and
projection length for the F VS with growth calibration (AD). (Error expressed as
predicted value minus observed value.) ..................................................................... 44

Figure 14. Hiawatha site mean error for estimated trees per acre by treatment and
projection length for RPAL. (Error expressed as predicted value minus observed
value.) ........................................................................................................................ 45

Figure 15. Kellogg site mean error for estimated trees per acre by treatment and
projection length for the FVS with out DBH growth calibration (NA). (Error
expressed as predicted value minus observed value.) ............................................... 45

Figure 16. Kellogg site mean error for estimated trees per acre by treatment and
projection length for the FVS with growth calibration (AD). (Error expressed as
predicted value minus observed value.) ..................................................................... 46

Figure 17. Kellogg site mean error for estimated trees per acre by treatment and
projection length for RPAL. (Error expressed as predicted value minus observed
value.) ........................................................................................................................ 46

vii

INTRODUCTION

Red pine or Norway pine, Pinus resinosa, is commonly regarded as Michigan’s
most significant commercial sofiwood species, and with good reason. In 1992 red pine
production was valued at $25.3 million (Potter-Witter 1995). Red pine covers 897,200
acres of Michigan timberland, 641,200 acres in the Lower Peninsula, and 256,000 acres
in the Upper Peninsula (Leatherberry and Spencer 1996). Average net annual growth
(1980-1992) was 78,310 thousand ft3 and removals were 15,980 thousand ft3
(Leatherberry and Spencer 1996). In 1994 timber industries in Michigan produced over
93,261 MBF of sawlogs, approximately 56,040 cords of pulpwood and almost 3,053
MCF of industrial fuelwood from red pine (Hackett and Pilon, 1997). Red pine has been
managed since the turn of the 20th century (Eyre and Zehngraff 1948). Numerous
research articles have been written on the best way to manage red pine in the Lake States.
Research results (or advice) vary depending on the desired timber products, site quality
and location, and initial densities.

Considering the value of the resource and the body of work on red pine growth
and yield, resource managers need some way to compare alternate management regimes
which will allow them to pick the best management scenario to meet their objective for

their site. Growth models are an excellent way to do this. However how does a resource

manager evaluate what model is best to use? In the Lake States there are presently two
main PC based computer models that can be used to predict red pine growth and yield;
the Forest Vegetation Simulator- Lakes States variant (FVS-LS) or RPAL (REDPIN E —
Allen Lundgren). Validating a model’s performance is an essential part of model
development and revision. Previously, the only sub-regional (using only Michigan tree
data) validation of FVS-LS was done on hardwood stands on 5 and 10-year growth
(Canavan and Ramm 2000, Guertin and Ramm 1996). RPAL was based on unpublished
equations and no validation study has been published. Given the importance of red pine
in the Lake States it is necessary that land managers have a model that correctly predicts
growth to compare alternative management treatments, whether the objective is timber
volume, wildlife habitat or recreational area.

This paper explores FVS-LS prediction of individual tree and stand level
attributes and RPAL prediction of stand level attributes. The validation project uses two
long-term thinning-study sites in lower and upper Michigan. These study sites have had
repeated measurements taken approximately every five to ten years for the past 27 years,
which make them an excellent resource to test growth models. In addition to testing the
models prediction accuracy over time, at different sites and densities, the study also tests
how much better FVS predicts using diameter calibration. Diameter calibration is a
unique function of the FVS program. It allows the users to include dbh increment cores or
past diameter measurement (at least five measurements for each species), which FVS
uses to scale its own growth equations to more closely represent past growth on the site.

Previous validation studies of Lakes States growth and yield models use at least

three variables to test the model performance, diameter at breast height, trees per acre and

basal area per acre (Holdaway and Brand 1983, Kowalski and Gertner 1989, Guertin and
Ramm 1996, Canavan and Ramm 2000). These three variables are good descriptors of a
stand’s growth and mortality. “An analysis of dbh predictions provides an indication of
the predictive ability of individual tree growth equations functions. The accuracy of
predicted TPA reflects the effectiveness of the mortality model at simulating mortality
due to stand composition. BA predictions, which can be viewed as a combination of the
growth and mortality models, provide a measure of overall model performance”
(Canavan and Ramm 2000). Once a model can be “trusted” to give accurate results of
diameter or basal area grth and mortality, then it can used to predict more specific and
management oriented variables, such as volume or percent canopy cover.

The models performance was measured by how well it predicted stand growth and
mortality to the stand’s actual growth and mortality. This is called bias, the difference
between the observed measurement and the predicted measurement. This difference is
used to calculate two statistics which give a description of the error; the mean error (the
average difference between the predicted and observed values) and the standard deviation
(the variability of the error estimate). These statistics are often referred to as accuracy and
precision. “Accuracy is an expression of how close something is to the correct
answer. . ..Precision, on the other hand, is just a consequence of repeatability” (Iles 2003).
These two concepts are essential when testing a model. It is imperative to know how
close the prediction is to the correct answer and how much variability there is in the
predictions. The classic textbook example of this is throwing a dart at a bullseye.
Accuracy is how close the darts land to the bullseye, while precision describes how close

the darts are to each other. The objective of this study is to test how close the predicted

answer is to the observed and how reliable that estimate is under varying conditions.
Standards for accuracy and precision can vary greatly in natural resource planning and
projects. Large scale forest projects covering millions of acres, over a long time frame
may not require a highly accurate model. On the other hand a manager setting up a 10-
year thinning project for a private landowner’s woodlot would want a model with very
high accuracy and low variability. When considering the information most land managers
are interested in they tend not to be just trees per acre and basal area, but other variables
which are calculated from these base stand structure components, such as percent canopy
cover, down woody debris and volume estimates. Validation should first occur on this
base component. In FVS these equations are diameter growth and mortality. In RPAL

these equations are basal area growth and mortality.

Objectives

The objectives of this research are to:

1.

Compare the ability of the Forest Vegetation Simulator Lakes States variant
(FVS-LS) to accurately predict red pine diameter growth, basal area growth, and
mortality over varying time intervals up to 27 years for two Michigan plantation
sites.

Compare the ability of REDPINE -Allen Lundgren (RPAL) to accurately predict
red pine basal area growth and mortality over varying time intervals up to 27

years for two Michigan plantation sites.

. Compare the effects of including past diameter measurements in the F VS-LS

inputs on the accuracy and precisions of diameter growth, basal area growth, and
mortality.
Compare the ability of F VS-LS and RPAL to accurately predict growth under

varying thinning densities.

LITERATURE REVIEW

Red pine has been managed in the Lake States since the start of the 20‘h century
(Eyre and Zehngraff 1948). Many of the early management studies are from Minnesota
and deal with different methods of regenerating or thinning natural stands. Buckman’s
(1962) study of permanent plots in Minnesota initiated the move from normal yield tables
to stand-level models for red pine. Some of the models developed by Buckman,
including a three dimensional response surface, are still in use today (Ramm 1997).
Buckman and Lundgren (1962) looked at growth response to removing hardwood
competition from three red pine plantations planted by the Civilian Conservation Corps
(CCC) in northern Minnesota. Lundgren (1963) used a modified soil expectation value to
analyze the economic returns from releasing these plantations. Lundgren (1965) also
examined land expectation values and return rates for a range of thinning intensities and
rotation ages and recommended regular thinnings to 90 fi/acre. This work was later
expanded to a series of tables and worksheets for estimating income, costs, and rate of
return from growing red pine for pulp and sawtimber (Lundgren 1966). Lundgren
assembled a number of published and unpublished stand-level growth and yield models
into a mainframe computer program called REDPINE. The program was used to evaluate

the effect of initial density and different levels of thinning intensity on yield (Lundgren

1981) and prepare graphical guidelines. Using REDPINE, Lundgren (1983) found that
normal yield tables underestimated cubic foot yield for both thinned and unthinned stands
on average sites. REDPINE was adopted from the mainframe to the personal computer
in 1984 and named RPAL for REDPINE -Allen Lundgren (Ramm 1990).

In Michigan, early work focused on quantifying the response to different thinning
intensities. Day and Rudolph (1971) used residual spacing or percent height as a thinning
guide in a red pine plantation at the Dunbar Forest in Michigan’s Eastern Upper
Peninsula (UP). They found significant differences in basal area (BA) and cubic foot
volume production between thinning intensities, and used stumpage prices and costs to
determine total value production over 15 years. Rudolph et al. (1982) collected data from
a red pine plantation in Michigan’s Upper Peninsula and from a plantation in the Lower
Peninsula to evaluate competition quotient as a guide for thinning. Rudolph et al. (1984)
summarized results fiom three thinning studies in Michigan and compared growth, yield,
changes in stand structure, and value of residual stands for a wide variety of thinning
treatments. Marty (1988) analyzed the results of a 18 year thinning study in northern
lower Michigan and recommended that managers interested in red pine sawtimber start at
lower densities (200 - 500 TPA) than generally used.

DeNaurois and Buongiomo (1986) compared red pine pulpwood production to
pulp and sawtimber production across a range of sites in Wisconsin using soil expectation
values and internal rate of return. Dual management was deemed superior, and the
authors found that plantation density of 680 TPA with heavy thinning every 15 years

until rotation at 45 years maximized returns'. Harms et al. (1990) evaluated the potential

 

' Grossman and Potter-Witter (1991) later found that the TWlGS economic algorithm that DeNaurois and
Buongiorno used incorrectly calculated the rate of returns.

market for red pine utility poles in Wisconsin, where pole production was minor, along
with the regional market. Grossman and Potter-Witter (1991) used the TWIGS
projection system (Miner et al. 198 8) and data from the Kellogg Experimental Forest in
southwest Michigan and Petawawa Forest in Ontario to determine that management
strategies including utility poles maximized returns. They recommended plantation
densities of 890 trees per acre and thinning intensities above 110 ftZ/acre basal area.
Marty and Potter-Witter (1992) used Forest Survey data from recent Michigan
inventories, along with empirical yield tables developed for Michigan (Hahn and Stelman
1984) to predict that current rates of red pine production could not be maintained in the
future without significant increases in planting.

There have been a number of studies on red pine growth and yield in the Lake
States. Martin and Bk (1984) discovered that simple empirical models provided the best
fit for diameter and height growth for 20-58 year old plantations in Wisconsin. . Reed et
al. (1986) developed compatible equations for red pine, allowing estimation of cubic foot
volume to any upper stem diameter. Zamoch et al. (1982) used the Weibull probability
density fimction to model changes in stand structure over time. In the 1990’s, red pine
growth and yield information was compiled into an expert system (Rauscher et al. 1990),
survival was modeled using an artificial neural network (Guan and Gertner 1991), and an
interactive program was developed to produce optimal thinning schedules through
dynamic programming (Rose and Chen 1995). Erickson (1996) summarized height and
diameter growth over 59 years for one plot in a 1.4 acre site in northern Minnesota. In
contrast, Fowler (1997) measured over 3,500 tree from 27 red pine stands across

Michigan to develop new individual tree volume equations.

Given the number of studies on red pine, do resource managers have an easy way
to compare alternate thinning treatments? Resource managers can choose among three
projection systems for red pine in the Lake States; all of which originated with the USDA
Forest Service. The Woodsman’s Ideal Growth Projection System (TWIGS) is an
individual tree, distance-independent growth and yield simulator developed by the USDA
Forest Service’s North Central Forest Experiment Station to simulate growth of mixed
species stands (Miner et al. 1988). The regional models in Lake States TWIGS were
calibrated with 80,000 trees from over 1,500 plots in Wisconsin, Michigan, and
Minnesota (Miner et al. 1988). Lake States TWIGS has been superseded by the Forest
Vegetation Simulator (FVS), also developed by the USDA Forest Service (Bush and
Brand 1995). FVS began as PROGNOSIS, an individual tree, distance-independent
growth and yield projection system developed for the Inland Empire area of Idaho and
Montana. The file input and output format used in PROGNOSIS was adopted as the
standard for all grth and yield projection systems used by the USDA Forest Service.

The Lake States TWIGS variant of the Forest Vegetation Simulator (FVS-LS) uses this
standard file input and output and uses the growth and mortality functions based on Lake
States TWIGS and can be run stochastically or deterministically. One important difference
is that Lake States TWIGS uses annual increments, while FVS-LS calculates 10 year
gowth by multiplying the annual increment by 10 and then scaling back if the growth
period is less than 10 years (Bush and Brand 1995). Predicted individual tree and stand-
level attributes, including both stand tables and volume tables, can be obtained for any
year in a projection. FVS-LS can simulate a wide range of silvicultural prescriptions and

provide economic analyses of the prescriptions.

There have been two sub-regional validations of TWIGS and later F VS-LS, both
using hardwood stands in the northern Lower Peninsula. The TWIGS study (Guertin and
Ramm 1996) showed that the precision was quite variable, five-year diameter growth was
predicted within : 0.3 inches for the five species studied. Mean errors for basal area
projections were within i 5 ftZ/acre for all species and mean error for trees per acre
(TPA) was within : 20 TPA for all species but other red oak. A follow-up study five
years later found that FVS-LS consistently overestimated 10-year diameter growth across
seven hardwood species (Canavan 1997).

RPAL (Ramm 1990) is a deterministic, interactive program based on stand-level
models of grth and yield for red pine plantations. The user provides information on
stand site index, stand age, density in basal area (BA) and trees per acre (TPA), desired
residual BA, and the thinning interval. The residual BA and the projection period may be
unique for each thinning interval. The stand is described before and after each thinning;
through stand age, quadratic mean diameter at breast height (dbh), average height of
dominant and codominant trees, basal area per acre and trees per acre. Total volume in
cunits per acre and merchantable volume in standard cords per acre or thousand board feet
(MBF) per acre, (International l/4-inch rule), are shown for the stand before and after
thinning. The volume removed during thinning is also given. RPAL does not provide any
financial analysis. Hyldahl and Grossman (1994) filled this gap with a financial
spreadsheet RPGROWS that incorporated the models used in RPAL.

RPAL was initially based on row-thinning but was extended to other thinning
regimes. Stand growth is driven by two different basal area growth models. The growth

model for stands less than 25 years old was developed by Lundgren using data from

10

unthinned red pine plantations in Michigan, Minnesota and Wisconsin (Wambach 1967).
The growth model for stands over 25 years old predicts average annual BA grth (in
square feet per acre) as a simple quadratic function of BA, stand age, and site index
(Buckman 1962). Total cubic foot volume per acre is estimated using a stand level model
with stand BA and average stand height (Buckman 1962). Volume is then allocated

between size classes using a ratio based on quadratic stand diameter (QSD).

ll

METHODS
Data Description

The validation data were collected from two-long term study sites in Michigan,
the Hiawatha National Forest in the eastern Upper Peninsula (Hiawatha site) and the W.
K. Kellogg Experimental Forest (Kellogg site) in the southwestern Michigan. The
Kellogg site is owned and managed by Michigan State University’s Department of
Forestry.

The Hiawatha site was planted in 1938 with approximately six by six foot
spacing. It is located in the Sault Ste. Marie district near Trout Lake on level area where
East Lake, Rubicon and Rousseau fine sands are present. In 1962 it became a thinning
study established as a randomized complete block design (RCBD) with four blocks
(Rudolph et al.1984). Each block contained 16 treatments, with each being a 0.10 acre in
size. This study examined 12 of the treatments (Table 1), four of the treatments were
taken out of this study because the initial thinning method was the percent of height
method and the researchers felt this method was no longer commonly used to manage red
pine. The percent of height thinning method is set up so the average spacing between
residual trees is a specified percent of the average dominant and codominant stand height
(Rudolph et al.1984). On each 0.10 acre treatment plot diameter at breast height for each

tree was measured along with the height of three to five trees on the plot. These

12

measurements were taken in 1962, 1965, 1969, 1976, 1982, and 1992 and the blocks
were thinned in 1962, 1969, 1976, 1982 and 1992, except for a few plots for which basal
areas were too low to thin in 1982 and 1992. The researchers then calculated the basal
area per acre and trees per acre for the years that measurement or thinning occurred.

Table l. Hiawatha National Forest thinning study treatments

 

Treatment: Description of treatment

BAr30: Initial thinning to a residual BA of 30 ft2/acre
BAr45: Initial thinning to a residual BA of 45 ft2/acre
BAr60: Initial thinning to a residual BA of 60 ft2/acre
BAr80: Initial thinning to a residual BA of 80 fi2/acre
BAr100: Initial thinning to a residual BA of 100 ftZ/acre
BArl30: Initial thinning to a residual BA of I30 ft2/acre
BArl 60: Initial thinning to a residual BA of 160 ft2/acre
Row2nd: Initial thinning removed every other row
Row3rd: Initial thinning removed every third row
Row4_2: Initial thinning removed every fourth row; at second thinning removed center row
Row4th: Initial thinning removed every fourth row
Control: Control - no thinning

 

The Kellogg study site was planted in 1936 and 1937 with spacing of
approximately seven by eight feet. This site was planted on rolling hills with Oshtemo
loamy sand. In 1960 it became a thinning study with nine thinning treatments applied in a
randomized complete block design with four replications of each treatment (Rudolph et a1
1984). These treatments (Table 2) were also 0.10 acres in size. On each 0.10 acre
treatment plot diameter at breath height for each tree was measured along with the height
on three to five trees on the plot. Measurement and thinning occurred in 1960, 1964,
1967, 1972, 1980, 1985 and 1991. The author then calculated the basal area per acre and

trees per acre for these years.

13

Table 2. WK. Kellogg Forest Thinning Treatments

 

Treatment- Description of treatment

Row2nd: Initial thinning removed every 2nd row

Row3rd: Initial thinning removed every 3rd row

Row4th: Initial thinning removed very 4th row

Row4_2: Initial thinning removed every 4th row, at second thinning removed center row
BAr90: Initial thinning to a residual BA of 90 fi2/acre

BAr70: Initial thinning to a residual BA of 70 ft2/acre

BArl 10: Initial thinning to a residual BA of 110 ft2/acre

BArl30: Initial thinning to a residual BA of 130 ft2/acre

Control: Control — no thinning

 

The researchers on this project did not set up the thinning studies or take the
measurements, and thus did not have a choice on what measurements were taken, the size
of the plots or how and when the stands were thinned. However a data set of this type is
not common in forestry, because of the completeness of the experimental design (RCBD)
and the span in years of the repeated measurements. In forestry it is more common to find
data sets which cover a large spatial distribution (across a state or National Forest),
however rarely do they have permanent plots with repeated measurements over a decade.
The uniqueness of this data and foresight of the designers of the experiment, make this

data an excellent choice to test the basic equations in a forest growth and yield model.

Growth Simulations

Three types of growth simulations were run for validation. The first used RPAL,
which is a stand level program. The data needed for input were stand age, basal area,
trees per acre, desired residual basal area after thinning and the length of the projection.
For the Hiawatha site, stand age (28 years in 1965), BA at age 28, TPA at age 28, site

index at a base age of 50 years, the desired residual BA, and the specified projection

14

interval ending in 1969, 1976, 1982, 1992 were used. For the Kellogg site, stand age (27
years in 1964), BA at age 27, TPA at age 27, site index at a base age of 50 years, the
desired residual BA and the projection lengths ending in 1964, 1967, 1972, 1980, 1985,
1991. The residual basal area of the plots was entered at the beginning of each projection
cycle for Hiawatha and Kellogg sites to match the actual residual basal area, while trees
per acre was only entered at the start of the program, either 1965 or 1964.

Two types of FVS-LS simulations were run for each block of each treatment; with
FVS diameter calibration turned off, the other with diameter calibration turned on. This
was to compare how well FVS predicted tree growth without past diameter information.
The simulations that did not include past diameter measurements were abbreviated ‘NA’
for no ancillary data. The simulations that included past diameter measurements were
abbreviated ‘AD’. All runs included plot name, age, site index (base age 50 years), dbh
(1965: Hiawatha, 1964: Kellogg), height if measured, and the specific year the tree was
cut. The AD simulations also included diameter growth, which was calculated from the
diameter from the simulation start date minus the previous diameter measurement. The
Hiawatha grth measurements were from age 25 to 28, and Kellogg grth
measurements were from age 27 to 31. The Hiawatha site had a three year growth
measurement and the Kellogg site had a four year growth measurement period that F VS
used to scale or calibrate the growth equations to more closely match the growth that was
occurring in the plantation at that time. In the FVS tree list all trees were coded with the
species code “RP” indicating red pine plantation trees and the model was run

deterrninistically.

15

Validation

The validation examined twelve treatments on the Hiawatha National Forest
(Table 1) and nine treatments on the Kellogg Forest (Table 2). Basal area and trees per
acre error were calculated for the RPAL simulations. Basal area, trees per acre, and
diameter at breast height error were calculated for FVS-LS simulations. Other studies of
Lakes States growth and yield models use at least three variables to test the model
performance, diameter at breast height, trees per acre and basal area per acre (Holdaway
and Brand 1983, Kowalski and Gertner 1989, Guertin and Ramm 1996, Canavan and
Ramm 2000). Testing trees per acre evaluates the mortality equations in both models.
Since RPAL is a stand level model evaluating basal area estimates tests the models base
growth equations and overall estimates of growth and mortality. In FVS, testing the
diameter growth equations evaluates individual tree growth equations and evaluating
basal area provides an over all estimate of how FVS is predicting growth and mortality.
Mean error and standard deviations were the statistics chosen to display the error because
this is what other Lake States validation studies have used and most professionals
understands these statistics with little to no explanation needed for interpreting the
results.

Mean error and standard deviation were calculated from the bias; where the bias
is defined as the error between actual and predicted measurement for each treatment.
Error was calculated as predicted value minus observed value, to be consistent with the
other Lake States validation studies (Holdaway and Brand 1983, Holdaway and Brand
1986, Guertin and Ramm 1996, Canavan and Ramm 2000). Overestimates therefore were

positive numbers.

16

The formula used to calculate mean error and standard deviation were:

I:

20‘“ - Yi)
Mean Error (6) = 1:]

Il

 

“ (er - E)’
Standard Deviation of the error = z n 1
i=1 —

where y, is the predicted TPA, BA, DBH
yi is the actual TPA, BA, DBH

6i = (9i - Yi)

n = sample size

The Hiawatha simulations projected growth from 1965 through 1992, with
cycle boundaries at 1969, 1976, 1982 and 1992. The Kellogg simulations
projected growth from 1964 through 1991, with cycle boundaries at 1967, 1972,
1980, 1985 and 1991. For example a 0.10 acre treatment plot on Hiawatha site
would be “grown” from 1965 to 1969 (4 years). The simulated tree or stand
conditions were checked against the actual tree or stand conditions for 1969 and
bias was calculated. The stand then continued to “grow” another seven years and
the simulated tree or stand conditions were compared to the actual conditions in
1976 and bias was calculated. This process continued so that at every cycle
boundary the simulated tree or stand conditions were compared to the actual
conditions. From the bias at each cycle boundary, mean error and standard
deviations were calculated. The mean errors and standard deviation calculated at

each cycle boundary for stand level measurements (TPA and BA) had a sample

size of four (for each treatment). The sample size for DBH error decreased over

17

time as trees were cut and was dependant on the type of treatment. Treatments
that had a high residual basal area (less trees cut per acre) had a larger sample size
then those with low residual basal area treatments.

Figure 1. Diagram of the cycle boundaries at which bias was calculated for the
Hiawatha and Kellogg sites.

 

Hiawatha site

 

 

simulation 0 4 1 l 17 27
length (years)

I I I I I
cycle
boundaries 1965 1969 1976 1982 1992

Kellogg site

 

simulation 0 3 8 l 6 21 27
length (years)

I I I I I I
cycle
boundaries 19641967 1972 1980 1985 1991

 

18

RESULTS

Diameter at Breast Height Error

Only FVS-LS runs were used to predict dbh error because RPAL, a stand level
model, does not predict individual tree diameters.

Hiawatha - FVS-LS, on average predicted diameter grth with better accuracy
for the AD (calibrated) simulations than for the NA (not calibrated) simulations (Table 3).
For both types of simulations F VS-LS over-predicted diameter growth, except in
treatments with low residual basal areas. In the last cycle (27 years) five of the twelve
treatments had errors greater than 1.0 inches in the NA simulation and only one of the
twelve treatments in the AD simulations had an error greater than 1.0 inches (Table 4).
When absolute mean error was calculated, averaged over the treatments the absolute
mean error over the 27 year growth projection was 0.4 inches (AD) and 0.8 inches (NA)
(Table 3). No treatment had an error greater than 1.78 inches in dbh. Absolute mean
error increased as the length of the projection increased.

Kellogg - Unlike the Hiawatha results, FVS did not necessarily predict diameter
growth with better accuracy for the AD simulations than for the NA simulations (Table
5). FVS-LS over—predicted growth for all trees in the NA projections except for the thin
every 4th row treatment (Row 4’“) where grth was under-predicted. In both runs as

projection length increased so did the error. Almost all of the simulations had an error of

19

less than one inch, except for the longer projection lengths in the control, thin every 4th
row, and 70 fiZ/acre thinnings. Only treatments thin every 2nd row and thin to a basal area
of 90 fiz/acre of the NA simulation had error of more than 2.0 inches. These errors
occurred in the 27 -year interval. Absolute mean error for the AD simulation showed an
error less than 1.0 inches up to the 27 years of growth, while the NA simulation only

showed an absolute mean error of less than 1.0 inch up to eight years of growth (Table3).

Table 3 . Hiawatha site and Kellogg site absolute mean error for all treatments by cycle

length.

 

 

 

 

Hiawathg site NA AD RPAL
DBH 4 years 0.3 0.2
11 years 0.5 0.3
17 years 0.7 0.4
27 years 0.8 0.4
BA 4 years 12.3 5.8 2.0
11 years 18.9 6.7 5.9
17 years 19.1 8.5 5.4
27 years 24.2 11.4 17.9
TPA 4 years 3.2 2.8 3.8
11 years 5.6 4.7 36.4
17 years 8.1 7.3 40.6
27 years 24.1 23.9 37.5
Kellogg site NA AD RPAL
DBH 3 years 0.1 0.1
8 years 0.4 0.3
16 years 1.0 0.5
21 years 1.3 0.6
27 years 1.5 0.8
BA 3 years 2.4 7.4 3.2
8 years 8.3 10.4 6.2
16 years 18.1 13.2 18.9
21 years 19.6 16.0 7.6
27 years 30.0 19.5 18.9
TPA 3 years 10.0 9.4 10.1
8 years 21.6 20.5 57.3
16 years 37.9 36.3 84.2
21 years 44.1 42.4 58.2
27 years 52.3 50.5 59.3

 

20

Table 4. Hiawatha mean error (E) and standard deviation (5) of mean error for estimated
diameter at breast height by treatment and projection length for the two types of
simulation. (Error expressed as predicted value minus observed value.)

 

 

 

- - NA Simulation - - - - AD Simulation - -
treatment projection cycle age OM D. n t': s E s
BAr30 65-69 = 4yrs 32 8.7 59 -0.52 0.23 -0.47 0.27
65-76 = Ilyrs 39 10.9 30 -0.77 0.30 -O.78 0.51
65-82 = 17yrs 45 12.9 21 -0.99 0.45 -097 0.74
65-92 = 27yrs 55 15.0 21 -0.59 0.62 0.58 1.02
BAr45 65-69 = 4yrs 32 8.2 85 -0.28 0.25 -0.44 0.73
65-76 = Ilyrs 39 10.4 46 -0.48 0.50 -0.37 0.49
65-82 = 17yis 45 12.6 29 -0.91 0.62 -0.80 0.61
65-92 = 27yrs 55 14.8 29 -0.26 2.59 -0.11 2.56
BAr60 65-69 = 4yrs 32 7.8 121 -0.05 0.57 -0.04 0.56
65-76 = Ilyrs 39 9.9 71 -0.26 0.97 -0.29 0.96
65—82 = 17yrs 45 l 1.8 47 -0.54 1.40 -0.60 1.42
65-92 = 27yrs 55 13.7 47 -0.30 1.72 -0.41 1.76
BAr80 65-69 = 4yrs 32 7.1 173 0.13 0.22 0.05 0.21
65-76 = Ilyrs 39 8.9 1 10 0.07 0.40 -0.15 0.36
65-82 = 17yrs 45 10.5 73 -0 26 0.47 -0.56 0.45
65-92 = 27yrs 55 12.5 58 -0.24 0.63 -0.65 0.59
BAr100 65-69 = 4yrs 32 6.9 220 0.19 0.17 0.12 0.17
65-76 = Ilyrs 39 8.3 146 0.28 0.31 0.08 0.34
65-82 = I7yrs 45 9.5 105 0.33 0.77 0.04 0.82
65-92 = 27yrs 55 11.2 84 0.62 1.51 0.22 1.55
BAr130 65-69 = 4yrs 32 6.4 302 0.29 0.38 0.17 0.38
65-76 = Ilyrs 39 7.6 218 0.51 0.58 0.18 0.58
65-82 = l7yrs 45 8.7 162 0.53 0.97 0.08 0.98
65-92 = 27yrs 55 10.1 130 0.68 1.25 0.08 1.27
BArI60 65-69 = 4yrs 32 6.0 395 0.38 0.54 0.20 0.54
65-76 = Ilyrs 39 6.9 305 0.73 0.71 0.31 0.72
65-82 = l7yrs 45 7.7 241 0.89 1.00 0.32 1.03
65-92 = 27yrs 55 8.7 200 1.27 1.37 0.53 1.41
Row2nd 65-69 = 4yrs 32 6.5 231 0.19 0.29 0.08 0.29
65-76 = Ilyrs 39 8.3 138 0.26 0.53 -0.03 0.53
65-82 = 17yrs 45 9.6 96 0.21 0.73 -0. 19 0.73
65-92 = 27yrs 55 1 1.4 79 0.56 1.54 0.00 1.53
Row3rd 65-69 = 4yrs 32 6.0 332 0.31 0.23 0.13 0.23
65-76 = Ilyrs 39 7.5 212 0.56 0.47 0.10 0.49
65-82 = l7yrs 45 8.6 158 0.61 0.67 -0.03 0.72
65-92 = 27yrs 55 10.0 129 1.16 2.12 0.32 2.13
Row4_2 65-69 = 4yrs 32 6.1 331 0.36 0.46 0.19 0.45
65-76 = Ilyrs 39 7.0 224 0.71 1.09 0.28 1.10
65-82 = l7yrs 45 8.4 159 0.97 1.75 0.36 1.80
65-92 = 27yrs 55 10.2 129 1.55 2.60 0.73 2.69
Row4th 65-69 = 4yrs 32 5.9 366 0.35 0.40 0.16 0.41
6576 = Ilyrs 39 7.4 218 0.69 0.82 0.17 0.87
65—82 = l7yrs 45 8.6 161 0.71 1.15 0.00 1.23
65-92 = 27yrs 55 10.3 118 1.06 1.92 0.10 2.03
Control 65-69 = 4yrs 32 5.9 466 0.36 0.33 0.18 0.34
(no thin) 65-76 = Ilyrs 39 6.3 463 0.76 0.49 0.38 0.52
65-82 = 17yrs 45 6.6 454 0.95 0.77 0.54 0.81
65-92 = 27yrs 55 7.3 378 1.78 2.25 1.51 2.26

 

* QMD: The plots actual quadratic mean diameter at the end of the measurement cycle (start of the next
cycle, before thinning.)

21

Table 5. Kellogg mean error (6) and standard deviation (3) of mean error for estimated
diameter at breast height by treatment and projection length for the two types of
simulation. (Error expressed as predicted value minus observed value.)

 

 

 

- — NA Simulation - - - - AD Simulation - -
treatment Drm'tLCtion cycle age OMD“ n E s E s
BAr70 6467 = 3yrs 31 7.3 150 0.16 0.76 -0.35 0.77
64-72 = 8yrs 36 7.9 150 0.31 1.64 -0.52 1.87
64-80 = 16yrs 44 10.8 77 1.01 3.18 -1.29 3.31
64-85=21_vrs 49 11.9 69 1.13 3.68 -1.15 3.48
64-91 = 27yrs 55 12.9 69 1.63 4.20 -1.67 4.39
BAr90 64-67 = 3yrs 31 7.5 168 0.21 1.46 0.00 1.48
64-72 = 8yr‘s 36 9.0 115 0.94 2.98 0.41 2.72
64-80 = 16yrs 44 11.0 91 1.77 3.86 0.85 3.92
64-85 = 21yrs 49 12.1 83 1.92 4.40 0.84 4.48
64-91 = 27yrs 55 12.7 83 2.17 4.68 0.97 4.77
BAr110 64-67 = 3yrs 31 7.3 205 0.08 1.01 -0.10 1.02
64-72 = 8yrs 36 8.8 135 0.26 1.68 -0.23 1.71
64-80 = l6yrs 44 10.7 104 1.23 3.45 0.36 3.49
64-85 = 21yrs 49 12.0 93 1.59 4.19 0.59 4.24
64-91 = 27yrs 55 12.5 93 1.98 4.56 0.85 4.61
BAr130 6467 = 3yrs 31 7.1 255 0.18 1.14 0.01 1.14
64-72 = 8yrs 36 8.2 184 0.61 2.10 0.18 2.09
64-80 = 16yrs 44 9.7 147 1.61 3.54 0.85 3.53
64-85 = 21yrs 49 11.0 131 1.81 4.05 0.92 4.06
64-91 = 27yrs 55 11.6 131 1.94 4.32 0.96 4.34
Row2nd 64-67 = 3yrs 31 7.2 159 0.18 1.35 -0.08 1.35
64-72 = 8yrs 36 7.8 159 0.70 2.34 0.23 2.35
64-80 = 16yrs 44 10.2 106 1.38 3.55 0.27 3.72
64-85 = 21yrs 49 11.5 85 1.64 4.37 0.35 4.48
64-91 = 27yrs 55 12.3 85 2.08 4.62 0.63 4.87
Row3rd 64-67 = 3yrs 31 7.2 194 0.02 0.64 -0.25 0.64
64-72 = 8yrs 36 8.6 122 0.07 0.97 -0.65 0.97
64-80 = 16yrs 44 10.4 98 0.83 2.85 -0.47 2.90
64-85 = 21yrs 49 11.7 81 1.34 4.02 -0.22 4.05
64-91 = 27yrs 55 12.6 81 1.49 4.30 -0.30 4.34
Row4_2 64-67 = 3yrs 31 6.8 250 0.06 0.69 -0.18 0.69
64-72 = 8yrs 36 7.8 171 0.62 1.93 0.03 1.94
64-80 = l6yrs 44 9.9 123 1.09 3.02 0.00 3.09
64-85 = 21yrs 49 11.2 109 1.22 3.51 -0.07 3.61
64-91 = 27yrs 55 12.0 109 1.40 4.12 -0.04 3.86
Row4th 64-67 = 3yrs 31 7.0 232 -0. 10 0.27 -0.21 0.19
64-72 = Syrs 36 8.1 158 —0. 18 0.74 —0.47 0.56
64—80 = 16yr‘s 44 10.0 110 -0.42 1.21 -0.97 0.74
64-85 = 21yrs 49 11.3 86 -0.75 1.45 -1.39 0.73
64-91 = 27yrs 55 12.0 86 -0.53 2.27 -1.23 1.72
Control 64-67 = 3yrs 31 6.8 289 0.18 0.69 -0.06 0.70
(no thin) 64-72 = 8yrs 36 7.3 288 0.45 0.80 -0.10 0.82
64-80 = 16yrs 44 8.0 269 1.09 1.57 0.25 1.64
64-85 = 21yrs 49 8.5 253 1.51 2.19 0.60 2.27
64-91 = 27yrs 55 9.0 234 1.96 2.76 1.04 2.83

 

* QMD: The plots actual quadratic mean diameter at the end of the measurement cycle (start of the next
cycle, before thinning.)

22

Basal Area Error

Basal area mean error and standard deviation were calculated for the four plots for
each treatment and projection length (Table 6 and Table 7). Error was calculated for all
three simulations types, FVS-LS (NA and AD) and RPAL.

Hiawatha-AD simulations projections were more accurate than the NA
simulations. The absolute mean error was two to three times as great is the NA as in the
AD simulations. As with the dbh mean error projections, the AD simulations were more
likely to under-predict in treatments with low residual basal areas, and tended to over
predict in treatments with high residual basal areas. RPAL predicted stands with high
residual basal areas with lower mean errors. In all but the two lightest thinning treatments
the mean error was less than 10 l’tZ/acre up to a 17 year projection cycle. In treatments
with low residual basal area by the last cycle (27 years), the model over-predicted basal
area up to 40 fiZ/acre (Table 6). With all three projection types, as time increased so did

the error (Table 3).

23

Table 6. Hiawatha mean error (E) and standard deviation (3) of mean error for estimated
basal area by treatment and projection length for three types of simulation. (Error
expressed as predicted value minus observed value.)

 

 

 

-----BA NA ---------- BA A1) ---------- BA RPAL-"-
treatment protection length age BA" E s e s E s
BAr30 65—69 = 4yrs 32 60 -7.06 2.44 -6.46 3.19 -0.67 2.88
65-76 = Ilyrs 39 48 -675 1.92 -6.69 4.51 16.18 2.10
65-82 = 17yrs 45 47 -7.20 1.76 -6.97 4.52 13.20 2.19
65-92 = 27yrs 55 65 -5.48 3.38 -5.22 8.14 38.70 6.63
BAr45 65-69 = 4yrs 32 78 -5.32 1.71 -4.02 1.14 -1.35 2.54
65-76 = Ilyrs 39 67 -6.32 1.73 -5.03 0.62 12.55 2.97
65-82 = 17yrs 45 63 -9.17 2.83 -8.12 1.57 10.90 1.65
6592 = 27yrs 55 83 -6.50 5.90 -4.85 4.48 40.23 4.85
BAr60 65-69 = 4yrs 32 99 -2.25 2.62 -2.05 1.65 -1.35 2.20
65-76 = Ilyrs 39 91 -6.38 4.92 -6.91 4.12 5.70 3.07
65-82 = 17yrs 45 86 -10.01 3.83 -10.83 5.23 6.50 2.74
65-92 = 27yrs 55 116 —8.57 7.15 -10.32 10.21 26.33 6.18
BAr80 65-69 = 4yrs 32 120 4.45 2.25 1.96 0.71 0.53 2.47
65-76 = Ilyrs 39 116 1.22 5.18 -4.38 1.29 5.88 3.20
65-82 = 173/18 45 109 -5.87 3.55 ~11.87 1.40 0.88 2.19
65-92 = 27yrs 55 124 -5.68 5.29 -13.36 2.29 14.90 6.08
BAr100 65-69 = 4yrs 32 143 7.01 3.98 3.09 1.56 -0.25 2.33
65-76 = Ilyrs 39 138 8.92 4.51 2.46 6.43 0.55 6.68
65-82 = ”yrs 45 128 6.94 3.81 -2.11 7.99 4.65 7.42
65-92 = 27yrs 55 141 11.63 7.34 1.75 14.33 14.55 6.61
BAr130 65-69 = 4yrs 32 172 14.33 2.06 7.55 1.66 2.38 1.21
65-76 = ”yrs 39 169 21.75 4.71 6.67 2.42 2.18 3.46
65-82 = l7yrs 45 164 17.55 4.07 .005 3.63 -0.70 2.06
65-92 = 27yrs 55 179 20.09 4.79 -1.74 7.34 4.90 2.87
BAr160 65-69 = 4yrs 32 193 22.74 4.87 10.83 3.55 5.43 3.49
65-76 = llyrs 39 194 40.34 5.60 14.23 9.06 2.78 4.85
6582 = l7yrs 45 191 41.40 10.75 10.65 15.08 -0.27 4.42
65-92 = 27yrs 55 201 53.92 18.01 16.45 22.81 6.05 8.49
Row2nd 65-69 = 4yrs 32 130 6.70 1.36 2.08 0.87 -1.48 2.73
65-76 = Ilyrs 39 126 6.80 6.07 -2.15 5.18 6.05 4.16
65-82 = l7yrs 45 119 3.64 9.68 —6.47 8.45 3.88 4.40
65-92 = 27yrs 55 136 9.25 13.25 —4.45 10.91 15.63 2.58
Row3rd 65-69 = 4yrs 32 160 15.91 2.03 5.93 1.01 1.83 1.64
65-76 = llyrs 39 157 21.86 4.09 1.37 1.47 3.75 1.92
65-82 = 17yrs 45 153 18.78 5.80 -5.12 3.22 -0.10 2.85
65-92 = 27yrs 55 163 28.68 15.58 -1.19 11.69 9.93 2.32
Row4_2 65-69 = 4yrs 32 163 17.58 3.03 7.59 2.28 3.70 1.53
65-76 = Ilyrs 39 144 24.27 1.25 4.92 2.75 4.98 4.51
65-82 = ”yrs 45 139 19.98 5.89 -1.23 6.59 -0.27 4.61
65-92 = 27yrs 55 151 30.73 9.90 1.55 12.46 10.00 4.03
Row4th 65-69 = 4yrs 32 171 19.18 2.32 6.90 2.55 3.60 1.47
65-76 = “yrs 39 155 24.73 3.79 1.46 6.08 3.88 4.25
65-82 = ”yrs 45 153 18.32 5.32 -8.47 6.46 -1.30 2.67
65-92 = 27yrs 55 154 20.64 3.44 -10.62 8.82 9.93 3.60
Control 65-69 = 4yrs 32 215 25.44 0.58 11.15 5.11 1.58 1.60
(1'1011111'1)65°76 = “yrs 39 246 57.49 1.85 23.65 9.55 -6.75 2.41
65-82 = I7yrs 45 270 69.89 2.38 30.33 12.50 -21.95 2.74
65-92 = 27yrs 55 275 89.13 9.46 65.13 18.05 -23.13 10.00

 

** BA: The plots actual basal area per acre at the end of the measurement cycle (start of the next cycle,
before thinning.)

24

Kellogg-Unlike the Hiawatha results, in most cases the FVS-LS NA simulations
predicted basal area more accurately than the AD simulations (Table 7). The AD
projections were more likely to under predict basal area, while the only NA projections
that under-predicted was the thin every 4th row treatment. The difference in the absolute
mean error between the two simulation types was not as large as that in the Hiawatha
simulations. RPAL mean basal area error was less than 10 ftZ/acre up to eight years in all
treatments. In stands with heavier thinning treatments, the mean error dramatically
increased in the 16 year cycle. In most cases the 27 year growth showed an over
prediction of 11 to 28 ftZ/acre, except in the control case where RPAL under-predicted

growth by 10 fiz/acre.

25

Table 7. Kellogg mean error (E) and standard deviation (3) of mean error for estimated
basal area by treatment and projection length for three types of simulation. (Error
expressed as predicted value minus observed value.)

 

 

 

”n-BA NA.---- ----- BA A1) ---------- BA RPAL-----
projection length BA" age it s c s E s
BAr70 64-67 = 3yrs 100 31 0.70 6.04 -5.45 9.29 -0.22 7.24
64-72 = 8y1‘S 1 15 36 4.49 6.04 -8.06 9.29 3.03 7.24
64-80 = 163/PS 106 44 7.47 6.00 -12.88 10.40 20.08 5.38
64-85 = 21yrs 115 49 6.73 6.91 -16.82 11.25 9.55 5.69
64-91 = 27yrs 128 55 14.85 11.35 -13.76 15.34 26.05 2.24
BAr90 64-67 = 3yrs 121 31 1.95 13.88 -5.11 13.95 -0.25 16.07
64-72 = 8yI‘S 112 36 10.29 13.88 -3.93 13.95 17.50 16.07
64-80 = 16yl‘S 119 44 18.24 21.85 —4.95 20.09 31.20 15.06
64-85 = 21yrs 128 49 16.37 22.02 -9.99 20.38 6.78 4.90
64-91 = 27yrs 146 55 21.76 20.77 -9.84 19.26 19.58 3.50
BAr110 64-67 = 3yrs 151 31 -1.64 9.32 -9.39 9.52 -5.87 5.22
64-72 = 8yrs 135 36 0.54 9.32 -14.59 9.52 4.58 5.22
64-80 = l6yrs 137 44 12.21 25.25 ~12.06 23.58 34.73 4.61
64-85 = 21yrs 140 49 13.94 30.61 -13.20 26.91 7.30 7.48
64-91 = 27yrs 155 55 22.03 35.32 -10.39 31.29 20.78 12.71
BAr130 64-67 = 3yrs 168 31 3.14 19.88 -5.20 15.85 -3.42 9.11
64-72 = 8yrs 156 36 11.13 19.88 -6.26 15.85 6.48 9.11
64-80 = l6yrs 150 44 27.11 38.89 -0.86 32.35 31.90 24.87
64-85 = 21yrs 163 49 25.00 42.41 -6.27 33.62 8.88 18.22
64-91 = 27yrs 186 55 71.86 122.48 35.42 1 16.64 28.03 47.26
Row2nd 64-67 = 3yrs 106 31 0.81 22.97 -6.81 24.12 -1.25 24.51
64-72 = 8yrs 116 36 9.47 22.97 -5.67 24.12 6.08 24.51
64-80 =16yrs 124 44 16.02 35.61 -13.83 31.92 15.05 3.64
64-85 = 21yrs 122 49 13.37 37.69 -16.82 31.93 15.70 19.09
64-91 = 27yrs 136 55 22.24 44.20 -14.57 38.96 20.13 6.61
Row3rd 64-67 = 3yrs 137 31 -0.57 5.28 -8.67 4.73 -5.75 4.97
64-72 = 8yrs 123 36 0.10 5.28 -15.17 4.73 7.05 4.97
64-80 = l6yrs 130 44 9.77 12.20 -15.83 13.21 21.60 19.15
64-85 = 21yrs 126 49 12.49 17.68 ~14.71 20.56 9.28 7.41
64-91 = 27yrs 146 55 15.41 18.63 ~17.87 23.59 18.78 8.88
Row4_2 64-67 = 3yrs 153 31 1.23 12.66 -9.57 11.35 -5.67 10.17
64-72 = 8yrs 128 36 10.00 12.66 -10.78 11.35 9.08 10.17
64-80 = 16yrs 138 44 10.91 18.50 -21.93 15.38 7.73 7.17
64-85 = 21yrs 150 49 8.45 18.75 ~28.76 15.73 5.40 8.04
64-91 = 27yrs 171 55 12.66 20.42 -32.41 17.42 11.63 8.25
Row4th 64-67 = 3yrs 153 31 -5. 12 19.59 -9.87 4.44 -6.02 4.42
64-72 = 8yrs 142 36 -7.49 19.59 -17.45 4.44 2.10 4.42
64—80 = l6yrs 149 44 -13.12 30.82 -28.77 6.74 7.33 3.61
64-85 = 21yrs 147 49 -19.19 33.07 -35.04 5.99 2.80 2.33
64-91 = 27yrs 164 55 -16.36 40.27 -35.04 8.06 14.63 6.71
Control 64-67 = 3yrs 179 31 6.79 3.73 -6.22 1.94 -0.37 1.00
(no thin) 64-72 = 8yTS 206 36 21.12 3.73 -11.68 1.94 0.33 1.00
64-80 = 16yrs 234 44 48.39 9.64 -7.80 5.51 -0.30 4.51
64-85 = 21yrs 246 49 60.88 16.26 -2.45 11.17 -2.85 12.09
64-91 = 27m 258 55 72.89 13.61 6.56 9.13 ~10.20 11.49

 

** BA: The plots actual basal area per acre at the end of the measurement cycle (start of the next cycle,
before thinning.)

26

Trees per acre Error

As with the basal area calculations of mean error, the trees per acre mean error
was based on a sample size of four for each treatment (Table 8 and Table 9). Error was
calculated for all three simulation types.

Hiawatha-The FVS simulations had a mean error of i 10 TPA except for the
high residual basal area treatments, BAr160, Row4_2, Row4th, and the Control. The
worst prediction accuracy for FVS was the control treatment (no thinning). The control
treatment, with a 27-year prediction interval, over-predicted by more than 175 trees per
acre. There was very little difference in the error between the NA and AD simulations.
RPAL also did a poor job at predicting treatments with higher residual basal area. In the
row thinning treatments and treatments with a residual basal over 100 ftz/acre RPAL
over-predicted by 21 to 95 TPA after the first cycle. In the control treatment, RPAL

under-predicted between 34 and 103 TPA over the 27 year period (Table 8).

27

Table 8. Hiawatha mean error (e) and standard deviation (5) of mean error for estimated
trees per acre by treatment and projection length for three types of simulation. (Error
expressed as predicted value minus observed value.)

 

 

 

----- TPA NA----- -----TPA AD---" -----TPA RPAL -----
trgatmcnt proiection length age TPA'" e s E s e s
BAr30 65~69 = 4yrs 32 148 —0. 18 0.02 0.18 0.02 0.00 0.00
65-76 = Ilyrs 39 75 -0.25 0.02 —0.25 0.02 1.75 3.77
65-82 = 17yrs 45 53 -0.27 0.03 -0.27 0.03 ~10.75 3.77
65-92 = 27yrs 55 53 -0.43 0.04 -0.43 0.04 -10.75 3.77
BAr45 65-69 = 4yrs 32 213 -0.26 0.04 -0.26 0.05 0.00 0.00
65-76 = Ilyrs 39 1 15 -0.38 0.06 -0.38 0.06 9.75 3.95
65-82 = 17yrs 45 73 -037 0.05 -0.37 0.05 -2.00 7.16
65-92 = 27yrs 55 70 1.91 4.96 1.91 4.96 0.50 6.56
BAr60 65-69 = 4yrs 32 300 2.14 4.97 2.14 4.97 2.50 5.00
65-76 = Ilyrs 39 175 1.91 4.93 1.91 4.93 11.50 4.20
65-82 = 17yrs 45 115 1.90 4.92 1.90 4.92 5.50 8.85
65—92 = 27yrs 55 115 1.55 4.88 1.55 4.88 5.50 8.85
BAr80 65-69 = 4yrs 32 433 -0.52 0.02 -0.52 0.02 0.00 0.00
65-76 = Ilyrs 39 275 -0.91 0.04 -0.91 0.04 13.00 13.61
65-82 = 17yrs 45 183 0.93 0.03 -0.93 0.03 7.00 12.75
65-92 = 27yrs 55 145 -1.17 0.05 -1.18 0.05 7.25 9.91
BAr100 65-69 = 4yrs 32 550 0.66 0.08 -1.10 0.85 0.00 0.00
65—76 = “yrs 39 365 -1.21 0.14 -1.22 0.16 24.50 6.95
65-82 = l7yrs 45 260 1.16 4.94 1.14 4.92 23.25 6.85
65-92 = 27yrs 55 205 3.30 5.68 3.28 5.66 21.25 10.59
BAr130 65—69 = 4yrs 32 755 -0.94 0.06 -| .05 0.12 0.00 0.00
65-76 = Ilyrs 39 543 0.66 4.98 0.53 4.95 30.75 14.86
65-82 = 17yrs 45 400 2.90 5.79 2.80 5.81 40.25 17.06
65-92 = 27yrs 55 328 2.33 5.82 2.22 5.83 46.75 21.03
BAr160 65-69 = 4yrs 32 978 8.66 19.89 7.86 19.74 10.00 20.00
65-76 = Ilyrs 39 753 7.28 19.84 6.26 19.70 50.75 20.19
65-82 = 17yIS 45 590 9.17 24.81 8.16 24.68 61.50 23.27
65-92 = 27yrs 55 485 10.62 23.40 9.63 23.05 69.50 27.33
ROW2nd 6569 = 4yrs 32 575 1.67 4.90 1.58 4.84 2.50 5.00
65-76 = Ilyrs 39 343 1.34 4.97 1.31 4.94 62.00 17.80
65-82 = l7yrs 45 238 1.23 4.93 1.20 4.89 45.00 22.91
65—92 = 27yrs 55 193 3.33 5.58 3.30 5.54 42.50 23.85
ROW3rd 65-69 = 4yrs 32 828 1.14 4.76 0.52 4.43 2.50 5.00
65-76 = Ilyrs 39 520 7.61 7.62 6.97 7.18 91.00 18.20
65-82 = 17yrs 45 385 6.92 7.27 6.15 6.72 80.00 16.43
65-92 = 27yrs 55 300 18.17 15.14 17.23 15.31 76.00 19.54
Row4_2 65-69 = 4yrs 32 818 8.66 19.84 7.99 19.55 10.00 20.00
65-76 = Ilyrs 39 540 17.65 17.88 16.68 17.60 -7.25 14.52
65-82 = 17yrs 45 363 28.08 34.29 31.14 30.62 20.25 20.12
65-92 = 27yrs 55 275 44.24 37.51 43.47 36.87 47.25 31.70
Row4th 65-69 = 4yrs 32 908 6.04 9.56 4.91 9.39 7.50 9.57
65-76 = Ilyrs 39 525 17.86 11.42 17.08 11.49 95.00 13.74
6582 = ”yrs 45 380 19.90 14.78 19.02 14.87 88.50 25.53
65-92 = 27yrs 55 318 24.25 16.49 23.26 16.39 89.25 26.81
Control 65-69 = 4yrs 32 1165 7.77 14.36 5.25 14.97 -10.75 15.22
(no thin)65—76 = Ilyrs 39 1158 10 16 22.68 2.75 25.55 -39.75 37.54
65—82 = ”yrs 45 1135 24.20 28.10 14.00 29.35 -103.25 30.19
65-92 = 27yrs 55 945 177.55 51.76 179.50 63.05 -34.00 64.47

 

*** TPA: The plots actual trees per acre at the end of the measurement cycle (start of the next cycle, before
thinning.)

28

Kellogg- Error was much larger for all three types of simulations on the Kellogg
site than for the Hiawatha. The F VS-LS, NA and AD simulations showed an increase in
error as the projection intervals increased, however this was not necessarily true for the
RPAL projections. The worst prediction accuracy for FVS-LS was the control treatment
(no thinning). The control treatment with a 27-year prediction interval was over-predicted
by more than 130 TPA (NA simulation) and 120 TPA (AD simulation). RPAL over-

predicted TPA afier the first cycle by 12 to 162 TPA (Table 9).

29

Table 9. Kellogg mean error (e) and standard deviation (3) of mean error for estimated
trees per acre by treatment and projection length for three types of simulation. (Error
expressed as predicted value minus observed value.)

 

 

 

----- TPA NA----- -----'I‘1’A AI)----- -----TPA RPAL-----
treatmem projection length age TPA". 6'; s E s E: s
BAr70 64-67 = 3yrs 31 360 14.59 22.38 14.31 22.93 15.00 22.17
64-72 = 8yrs 36 353 21.64 22.38 21.04 22.93 22.50 22.17
64-80 = I6yrs 44 168 21.49 18.90 21.33 18.99 55.00 31.80
64-85 = 21yrs 49 148 23.79 19.09 23.60 19.17 28.50 11.96
64-91 = 27yrs 55 145 25.92 23.58 25.68 23.68 31.00 12.83
BA190 64-67 = 3yrs 31 405 14.54 33.12 14.29 33.23 15.00 62.41
64-72 = 8yrs 36 250 36.64 33.12 36.39 33.23 93.75 62.41
64-80 = 16y13 44 180 46.03 44.37 45.64 44.58 98.75 60.64
64-85 = 2 1 yrs 49 160 45.67 44.44 45.22 44.67 42.25 20.11
64-91 = 27yrs 55 160 45.11 44.51 44.60 44.76 42.25 20.11
BAr110 64—67 = 3yrs 31 518 14.44 23.65 14.14 23.77 15.00 18.49
64-72 = 8yrs 36 320 16.51 23.65 16.09 23.77 89.00 18.49
64-80 = 16yrs 44 218 41.12 43.78 40.47 43.73 148.25 26.06
64-85 = 21yrs 49 180 45.59 48.59 44.98 48.25 78.25 15.00
64—91 = 27yrs 55 183 47.46 51.33 46.75 50.88 80.75 18.66
BArl30 64-67 = 3yrs 31 620 16.73 40.22 16.20 39.99 17.50 19.54
64-72 = 8)18 36 425 33.72 40.22 33.18 39.99 86.00 19.54
64-80 = 16yrs 44 300 65.65 62.44 65.21 62.25 162.25 91.47
64-85 = 2 1 yrs 49 258 67.79 64.00 67.28 63.72 102.00 20.61
64-91 = 27yrs 55 258 99.33 118.96 98.72 118.77 115.25 70.28
Row2nd 64-67 = 3yrs 31 383 14.63 62.45 14.53 62.58 15.00 62.38
64-72 = 8ytS 36 360 36.76 62.45 36.51 62.58 37.50 62.38
64-80 = l6yrs 44 223 41.22 71.95 41.05 71.88 49.00 22.21
64-85=21yrs 49 170 41.15 71.77 41.00 71.65 46.00 31.70
64—91 = 27yrs 55 168 43.25 76.55 43.06 76.39 32.25 13.33
Row3rd 64-67 = 3yrs 31 483 2.00 5.11 1.72 5.30 -1.00 9.59
64—72 = 8yrs 36 303 1.65 5.11 1.34 5.30 63.00 9.59
64-80 = I6yrs 44 223 21.06 32.54 20.62 32.09 76.00 51.22
64-85 = 21yrs 49 173 28.37 37.59 27.96 37.06 46.75 22.11
64-91 = 27yrs 55 173 27.87 37.33 27.41 36.73 46.75 22.11
Row4_2 64-67 = 3yrs 31 623 1.68 49.73 0.79 48.74 2.50 39.50
64-72 = 8yrs 36 393 33.36 49.73 31.88 48.74 59.50 39.50
64-80 = l6yrs 44 258 47.30 47.66 45.56 46.12 75.00 18.57
64-85 = 21yrs 49 220 49.20 51.86 47.47 50.47 74.75 35.07
64-91 = 27yrs 55 220 48.17 51.12 46.25 49.65 74.75 35.07
Row4th 64-67 = 3yrs 31 580 -2.39 4.43 -1.61 2.47 0.00 18.41
64-72 = 8yrs 36 395 -4.05 4.43 -2.92 2.47 53.50 18.41
64-80 = 16yrs 44 275 -2.72 2.70 -1.64 0.22 70.75 8.34
64-85 = 21yrs 49 215 -2.04 1.25 -1.51 0.20 61.75 6.65
64-91 = 27yrs 55 213 -0.01 5.73 0.58 5.11 64.25 8.81
Control 64—67 = 3yrs 31 723 9.14 9.09 7.43 8.36 10.00 11.81
(no thin) 64-72 = 8yrs 36 720 10.01 9.09 5.40 8.36 1 1.25 1 1.81
64-80 = 16ytS 44 673 54.26 24.50 45.45 22.54 22.50 25.51
64-85 = 21yrs 49 633 93.61 46.19 82.89 43.23 43.75 40.48
“-91 = 27yrs 55 585 133.44 15.76 121.49 14.45 46.00 10.36

 

**"‘ TPA: The plots actual trees per acre at the end of the measurement cycle (start of the next cycle, before
thinning.)

30

DISCUSSION

FVS predicted more accurate results than RPAL for trees per acre but not
necessarily for basal area per acre. FVS predict more accurately diameter at breast height
and basal area per acre with diameter growth calibration turned on, diameter grth

calibration had little to no effect on more accurately estimating mortality on either site.

FVS Options and Defaults

The F VS validation runs used version 6.2 of the FVS-LS variant with a revision
date of 12/01/1995. F VS variants are continuously being updated and improved. These
same data run through a current version of the model would yield different results. There
are many ways users can make adjustments in an FVS simulation to produce more
accurate results. One example of this involves using serial correlation of diameter growth.
This feature improves estimates from cycle to cycle by assuming the error terms from a
previous cycle are correlated with error terms of the next cycle. In other words, the error
term is not randomly distributed at each cycle. Trees that were growing well previously
continue to grow well and those that are not growing well continue to grow poorly
(Dixon 2002). This feature improves the overall distribution of diameter growth in a

stand. This feature was turned off by default in the version used for this validation

31

project. It could have been turned on by the use of a keyword, however the user did not
know of this feature at that time. This feature is now on by default in more current

version of FVS-LS.

RPAL Options and Defaults

The RPAL program had a date of 9/2/ 1999, with no known revisions to date.
RPAL is comprised of two basal area growth equations, one for stands less than 25 years
old and another for stands greater than or equal 25 years old. Stands that are less than 25
years old (at dbh) use an equation developed by Lundgren (1981). Stands greater than or
equal to 25 years old (at dbh) use an equation developed by Buckman (1962) that is based
on basal area per acre, age, and site index (base age 50 years). Therefore the only the
basal area grth equation for trees greater then 25 years in age was tested in this study.
Unlike F VS, there are no parameters that can be used to alter the growth equations in
RPAL except the site index set at the beginning of each run. The only changes that can be
made from cycle to cycle are the desired residual basal area after treatment and the cycle
length. These make the model easier to use and lead to more consistency among users,

yet also limits the capability of the user to make the model more site or location specific.

Model Performance

In both models as time increased error also tended to increase. This is in part due
to error propagation; over time the error builds upon its self. So that bias results are used
to predict into the future more bias results. “Outputs or estimates fiom the previous

period become inputs or initial values for the next. In this network of calculations,

32

uncertainty estimations can be a complex and tedious process at best” (Mowrer and Haas
1991). FVS-LS also did a better job at predicting the Hiawatha site compared to the
Kellogg site. This is probably in part due to the fact that the FVS-LS equations were not
created with data from southern lower Michigan (Miner et al. 1988).

Overall, the dbh mean errors were better predicted for F VS runs that used past
growth (AD) information to scale the equations than those that did not (NA). The
absolute dbh mean errors for the AD simulations were less than 1.0 inch. The scale
factors for Kellogg ranged from 0.42 to 0.75 with a mean of 0.56. The Hiawatha scale
factors ranged from 0.47 to 1.16 with a mean of 0.78. On, average, these were biased low.
This is due to how the diameter growth equations were applied. The first thinning
occurred (1962: Hiawatha, 1960: Kellogg) at the start of the growth measurement period.
The growth measurement period used to calibrate the dbh growth was three years long
(1962 to 1965) for the Hiawatha site and four years long (1960 to 1964) for the Kellogg
site. If the increase in growth was not immediate after the thin, in other words there was a
year or more delay before the trees took full advantage of the thin, then F VS would not
have captured the impact of the thinning in the short growth measurement period.
Therefore, the scale factor applied to the thinned stand may have scaled down growth too
much for the rest of the projection. A longer measurement period may have given more
accurate results. A second reason that the scale factors were biased low was because
mortality trees were recorded as “dead” trees in the input tree list instead of “recent
mortality” trees. If the trees had been recorded as recent mortality trees then FVS would

have included them in the stand density calculations which then would have affected how

33

the scale factors were calculated. It is important that users realize the impact that the scale
factor has on future tree simulated growth.

There were three main problems with how FVS calibrated the runs in this study.
First, the measurement periods in the simulations were too short and reflected the pre-
thinned growth, therefore scaling down (slowing) the original growth equations. Second,
trees were marked as “dead” instead of “recently dead,” making FVS incorrectly predict
past density. A third problem is that the growth measurements were not adjusted for bark
thickness. This could have been corrected by indicating the correct parameters on the
FVS GROWTH keyword. Since diameter increments included bark growth this added
another bias to the results.

For the FVS runs, mean error for trees per acre were very similar between the
scaled and non-scaled simulations for both sites. Typically denser red pine stands have
little mortality and will stagnate until released. Therefore, it would have been expected
that the models might over predict mortality (under-predict TPA). F VS and RPAL,
however, in most cases under-predicted mortality. The TWIGS mortality (Buchman
1983, Buchman et a1 1983, Buchman and Lentz 1984) equations imbedded in the FVS
framework actually calculate the survival probability for each tree. These survival rates
are annual rates and are converted to mortality rates and scaled to the number of years in
the run (Dixon 2002, Bush and Brand 1995). This estimate of mortality is then applied to
each tree record (or sampled tree). RPAL predicts stand level mortality in terms of basal
area mortality. This is then converted to TPA mortality, using the assumption that the
mean dbh of dead trees is equal to the stand’s QMD minus one standard deviation

(Lundgren, 1981). Both models may have under-predicted mortality because neither

34

assumed any type of stochastic mortality. The inventory history indicates that some trees
died by snow or ice storms, but no description was given for other trees. From the
previous inventory, however, most trees appeared to put on good growth prior to the
cycle in which death occurred. From this it is assumed that many of the trees died from
stochastic events such as wind, ice, snow, insect or disease. This suggests that when
running simulations, in order to get reasonable estimates of mortality, it is important to
include stochastic mortality events that are typical for the region and the species modeled.
In FVS a mortality multiplier could be included to model these events. RPAL does not
have this functionality and therefore stochastic mortality would have to be applied out-
side of the computer program.

For the typical user of FVS, who may not have a complete understanding of the
system, it is important to realize there are many adjustments that can be made to FVS in
order improve accuracy. FVS uses common stand exam data but is a complicated growth
and yield program. In order appropriately use the model a user must read the user’s
manual (Dixon 2002), variant guide (Bush and Brand 1995) and probably take an FVS
course. The more the user understands the capabilities of F VS, and the process it uses to
compute growth, the better estimates the user will obtain. At the beginning of this study
the author was a novice FVS user and found that even with out making many adjustments
to improve estimates of growth, F VS-LS did perform well in the prediction of individual
tree diameters, stand density, and mortality in most cases. RPAL on the other hand was
very easy to use. No user’s manual was needed to learn how to use the model and it
needed few input values (all stand level information). Over all it did a good job predicting

basal area growth, however it did not do a good job predicting trees per acre.

35

CONCLUSION

Land managers are under increasing pressure to meet their own objectives or
those set by the company which they work, or the public they serve. Whether it is short or
long term timber revenues, recreation areas, or wildlife habitat, RPAL and F VS can both
be used to estimate future red pine stand structure to help land managers make more
informed decisions. Land managers can apply knowledge from any number of red pine
management studies and test to see what management strategy will best meet the
objectives for their site. When comparing the two models FVS is more robust than
RPAL. That it is able to simulate almost any type of thinning, it allows for mixed species
stands and with past tree growth information (increment core data) the model will
calibrate growth to the specific site. However with the heterogeneity of red pine
plantations, managers may not need such a robust model, as red pine plantation thinning
regimes tend to be uncomplicated and growth is heterogeneous. One of the most common
quotes in modeling is, “All models are wrong, but some are useful” (George E. P. Box).
None the less, users of models want the predicted results to be truth. Model results are
used to make decisions. In forestry with 30 to 200 year timber rotations and uncountable
site variations, perfecting a model is virtually impossible. Both of these models, however,

perform well if the objective is to take standard forest inventory data to compare future

36

management options. For example, holding all things constant, will one thinning regime
versus another produce more red pine utility poles at final harvest. These models may not
predict exactly the number of poles produced in the future but they will estimate whether
one management plan will significantly provide more than another. FVS was a good
predictor of diameter grth and was even better when diameter calibration was used.
Absolute mean error at both sites when diameter calibration was included was less 1.0
inch and in many cases less then 0.5 inches. In many cases RPAL’s absolute mean error
for basal area was less then F VS. FVS and RPAL did poorly in predicting mortality past
the first cycle. At the Kellogg site (Lower Michigan) FVS frequently underestimated
mortality by 50 to 180 trees per acre. The large bias and variability that both models
showed in predicting trees per acre could certainly be a problem in estimating volume
production for the site. FVS and RPAL also lost accuracy and precision as cycle length
increased.

Foresters and natural resource professionals are under increasing pressure to make
the “right” forest management decision. A quality growth model can be one more tool in
their toolbox to help them make more informed decisions.

Future validation studies need to continue on growth and yield models in the Lake
States. This study only examined the red pine large tree growth and mortality equations
for RPAL and FVS-LS. Validation of the basal area growth equations for trees less than
25 years old should be done on RPAL and validation should be done on seedling/sapling
growth in FVS-LS for both hardwood and softwood species. This study covered a small
spatial distribution but was longitudinal in design. Follow-up studies should also consider

both longitudinal and spatial data to give a more complete understanding of the model’s

37

performance through out Michigan and over time. When consistent biases are discovered
old equations should be corrected or new equations should be developed. In modeling,
validation and revision should be an integral part of the model development and

maintenance process.

38

Figure 2. Hiawatha site mean error for estimated diameter at breast height by treatment
and prjection length for the F VS with out DBH growth calibration (NA). (Error
expressed as predicted value minus observed value.)

Image presented in color.

Mean Dbh Error-NA Simulation

 

 

 

 

 

2.53
3 0
1.5g .‘
; , . ‘
L I 0
0.51 7
g : I 9 I
u I V
g -o.s-j I : '
-1.5-§
I
—2.55 mm ......... , ......... . -. ......... . .........
O 5 10 15 20 25 30
Time (years)
n: 9 9 9 BAr100 9 9 9 BAr130 " 9 " BAr160 ' BArSO
9 9 9 BAr45 9 9 9 BArSO BAr80 9 9 9 Control
9 9 9 Row2nd 9 9 9 Row3rd 9 9 9 Row4th 9 9 9 Row4thdc2

Figure 3. Hiawatha site mean error for estimated diameter at breast height by treatment
and projection length for the FVS with growth calibration (AD). (Error expressed as
predicted value minus observed value.)

Image presented in color.

Mean Dbh Error-D6 Simulation

 

 

 

 

 

2.5‘:
1.5‘: e
e
‘g’ 0.5-g I :
u i 8 a 1 I
. - - ~ I
g a , a ' .
o ‘0.5‘:‘ v
: I
-1.5-j
45--. ......... . .........
0 5 10 15 20 25 30
Time (years)
1: 9 9 9 BAr100 "' 9 9 BAr130 '* "' " BAriSO ' BAr30
9 9 9 BAr45 9 9 9 BArSO ' ' BAr80 9 9 9 Control
9 9 9 Row2nd 9 9 9 Row3rd 9 9 9 Row4th 9 9 9 Row4thdc2

39

Figure 4. Kellogg site mean error for estimated diameter at breast height by treatment
and projection length for the FVS with out DBH growth calibration (NA). (Error
expressed as predicted value minus observed value.)

Image presented in color.

Mean Dbh Error—NA Simulation

 

 

 

 

 

2.591
1
i - ‘
1 55 i 9 .
3 8 e
E 0.5-3 5
u i E a
2 e
E -0.5-: ' e
E O
—1.5«j
—2.53 ......... . ......... , ......... . ......... . ......... . .........
0 5 10 15 20 25 30
Time (years)
1:: 9 9 9 BAr1 10 9 9 9 BArlSO 1.. BAr70
' BArQO 9 9 9 Control 9 9 9 Row2nd
Row3rd 9 9 9 Row4th 9 9 9 Row4thdc2

Figure 5. Kellogg site mean error for estimated diameter at breast height by treatment
and projection length for the FVS with growth calibration (AD). (Error expressed as
predicted value minus observed value.)

Image presented in color.

Mean Dbh Error—DG Simulation

 

 

 

 

 

2.53
1.5%
I . .
: a
I. I o e
0.51
E a - ' °
: I 3 I ‘ "
g .
1 e
3 .
-1.5-; 9
-2-5", ......... , ......... , ......... . ......... , ......... . ......... ,
O 5 10 15 20 25 30
Time (years)
1’): 9 9 9 BAr11O '9 9 9 BAr130 - ' BAr70
" BAr90 9 9 9 Control 9 9 9 Row2nd
- Row3rd 9 9 9 Row4th 9 9 9 Row4thac2

4o

Figure 6. Hiawatha site mean error for estimated basal area per acre by treatment and
projection length for the FVS with out DBH growth calibration (NA). (Error
expressed as predicted value minus observed value.)

Image presented in color.

BA Error

Mean BA Error—NA Simulation

 

90;
3°?
701
501
5°?
90‘}
30g
20;
10;

 

0?
-10€
—20«j
—30<;
-‘OJ

 

 

 

7x . . . BAI'IOO
9 9 9 BAr45
9 9 9 Row2nd

Time (years)

9 9 9 BAriSO
BAr80
9 9 9 Row4th

9 9 9 BAr130
9 9 9 BArBO
9 9 9 Row3rd

" BAr30
9 9 9 Control
9 9 9 Row4th8c2

Figure 7. Hiawatha site mean error for estimated basal area per acre by treatment and
projection length for the FVS with growth calibration (AD). (Error expressed as
predicted value minus observed value.)

Image presented in color.

BA Error

 

 

 

 

 

Mean BA Error-DG Simulation
90‘:
so;
701: .
60‘
5°:
40%
30f -
20g . °
10%
01 E :
-io~f ' 1 .
—2o-;
-30«;
40‘ .................. , ......... , ......... , ......... , .........
O 10 15 20 25 30
Time (years)
1': 9 9 9 BAr1OO 9 9 9 BAr130 9 ‘ 'BAr160 BAr30
9 9 9 BAr45 9 9 9 BArGO BAr80 9 9 9 Control

9 9 9 Row2nd

9 9 9 Row3rd 9 9 9 Row4th

41

9 9 9 Row4thdc2

Figure 8. Hiawatha site error for estimated basal area per acre by treatment and
projection length for RPAL . (Error expressed as predicted value minus Observed

value.)

Image presented in color.

BA Error

Mean BA Error—RPAL Simulation

 

 

 

 

 

90‘:
80-;
7o«;
wi
50‘:
40-3 0
30-3 ,
20‘:
10% ', g 3
of % 3 5
-1o§ °
_20‘; 9 e
-30~;
40“. ......... , ......... -. we-..” w...........
0 5 10 15 20 25 30
Time (years)
n: 9 9 9 BAr1OO 9 9 9 BAr130 9 9 9 BAr150 BArSO
9 9 9 BAr45 9 9 9 BArSO BAr80 9 9 9 Control
9 9 9 Row2nd 9 9 9 Row3rd 9 9 9 Row4th 9 9 9 Row4th6c2

Figure 9. Kellogg site mean error for estimated basal area per acre by treatment and
projection length for the FVS with out DBH growth calibration (NA). (Error
expressed as predicted value minus observed value.)

Image presented in color.

BA Error

 

 

 

 

 

Mean BA Error—NA Simulation

9°“:

80‘;

7o-; 9

601: 9

50‘; e

to;

30-1 . .

20% ° . ..

tog . s it .

o; ‘3' '
—lO~I ' .
-20.: e '
-30
40“ ......... , h-.. , ......... . ......... , ......... , ......... ,
0 5 IO 15 20 25 30
time (years)
n: 999BAr11O 999 BAr130 W BAr70
* ' BAr90 9 9 9 Control 9 9 9 Row2nd
Row3rd 9 9 9 Row4th 9 9 9 Row4thac2

42

Figure 10. Kellogg site mean error for estimated basal area per acre by treatment and
projection length for the FVS with growth calibration (AD). Error expressed as
predicted value minus observed value.

Image presented in color.

Mean BA Eror-DG Simulation

 

 

 

 

 

903
80-;
70‘;
w;
50:
L 40‘; .
g 30g
3 20?
‘0? e
O: ‘r 0
~10: '3 3 g z .
: ‘ e
—2o; ‘ .
_ig-g O : '
0 5 10 15 20 25 30
Time (years)
n 0°°BAr110 'OOBAHSO ... 4» BAr70
- . BAr90 0 0 0 Control 0 ‘ 0 Row2nd
Row3rd 0 ' 0 Row4th ' ’ '- Row4th8c2

Figure 11. Kellogg site mean error for estimated basal area per acre by treatment and
projection length for RPAL. (Error expressed as predicted value minus observed
value.) A

Image presented in color.

Mean BA Error-RPAL Simulation

 

9°:
80-;
7o-;
so;

50‘
mi
30.
20

D

BA Error

10‘:
0: ‘ e

-10-; I e
-20«;
-30
-w:

1.“
00 0
‘3

 

 

 

 

UUUUUUU I‘VVVUI'IIIIIII'TTTYIIITTTrTrVTrTTIIIVYTTl'VIIIIVI‘I

O 5 10 15 20 25 30
Time (years)

Tx '"BAr11O '0' BAr130 “' “ BAr70
- BAr90 0 ' 0 Control ‘ ‘ 0 Row2nd
Row3rd ' ' ' Row4th 0 ‘ ° Row4th8c2

43

Figure 12. Hiawatha site mean error for estimated trees per acre by treatment and
projection length for the FVS with out DBH growth calibration (NA). (Error
expressed as predicted value minus observed value.)

Image presented in color.

TPA Error

dd“““ “

\l

T:

UO‘NWGUMQQO
“0'0",“ momma
A‘AIJ‘AlAlAlAlAl‘l‘lAl

an
UIOI

lAlA

l dNOl (’0’
UIUIOIUIU UIUI
1 1.1.1.1 1

Mean TPA Error-NA Simulation

 

414 A

 

 

 

 

. l :
g 2 x .
O 5 10 15 20 25 30
Time (years)
O 0 0 BAr1OO ° ° " BAr130 ' ' ' BArlGO " BAr3O
' 0 0 BAr45 0 ° ‘ BArSO BAr80 0 0 0 Control
0 0 * Row2nd 0 r * Row3rd ‘ ' ° Row4th ' ' ° Row4thdc2

Figure 13. Hiawatha site mean error for estimated trees per acre by treatment and
projection length for the FVS with growth calibration (AD). (Error expressed as
predicted value minus observed value.)

Image presented in color.

TPA Error

 

 

 

 

 

Mean TPA Error-DG Simwation
1951
1851
175: °
1651
155:
1451
1351
1251
115:
105:
95:
851
75:
651
551
‘51 I
35:
2g: . i :
5i 1 2 g ..
-5‘ VVVVVVVVV rfTT r I VVVVVVVVV I IIIIIIIII I IIIIIIIII I VVVVVVVVV I
O 10 I5 20 25 30
Time (years)
n: ‘NBArlOO “'BAr130 ' " ‘8Ar160 ‘ " *BAr30
' ' 0 BAr45 ‘ ‘ ‘ BArSO ‘ ‘ BAr80 0 ' 0 Control
° ' ' Row2nd ° ' 0 Row3rd ' ' ' Row4th ' 0 0 Row4thac2

Figure 14. Hiawatha site mean error for estimated trees per acre by treatment and
projection length for RPAL. (Error expressed as predicted value minus observed

value.)

Image presented in color.

Mean TPA Error—RPAL Simulation

TPA Error

 

 

 

 

 

195‘
1851
1751
165:
155:
1‘5:
135:
125:
115:
'22
85a ' : '
751 ',
65': a ‘7
55: ,
‘5: 2 8
351 a
ggi ' I a
5i 2 ' . .2
-5‘ IIIIIIIII ITrTr Y I VVVVVVVVV 1'11? VVVVV I IIIIIIIII ‘V : rfr
O 5 10 15 20 25 30
Time (years)
1’): ' ' 0 BAriOO ‘ ' 0 BAr130 0 i * BArlSO -- " 4* BAr30
0 ' 0 BAr45 ° ‘ ‘ BArSO BAr80 0 0 0 Control

' 0 ' Row2nd

0 . ' Row3rd

o e o Row4th ' . . Row4th&2

Figure 15. Kellogg site mean error for estimated trees per acre by treatment and
projection length for the FV S with out DBH growth calibration (NA). (Error
expressed as predicted value minus observed value.)

Image presented in color.

TPA Error

Mean TPA Error—NA Simulation

 

m0
anon

MOON
UIUIU'I

‘fi‘fl“““

“GOO-"QM
UIUIUIQUUUI

8

L‘ALLIA‘AIAIA‘AIA‘A‘A A A A

825%
-

0|

0.. 9

 

 

1 _A
0| 0|
1 l
4 ID.-

. O.”

 

 

O
0..

Tx ' ° ' BAN 10
‘ BAr90
Row3rd

20
Time (years)

"' ‘ 4' BAr130
0 0 0 Control
0 0 0 Row4th

BAr70
° ° ' Row2nd
' ° * Row4th8c2

45

Figure 16. Kellogg site mean error for estimated trees per acre by treatment and
projection length for the FVS with growth calibration (AD). (Error expressed as
predicted value minus observed value.)

Image presented in color.

Mean TPA Enor—DG Simulation

 

 

 

 

 

1951
1851
175:
165:
155:
145:
ii? '
r 115%
g 105: .
1’ 32‘ '
.
75:
g: 65% ' ‘
33“ i t z
35% I ' ‘
25- .
Isl : :
-5: E a e r’ ’¢
rTTYrtvvvvlvrfirvvvvv] IIIIIIIII T ththththth 1 vvvvvvv [fitYfitht
O 5 10 15 20 25 30
Time (years)
Tx “'BAr110 '0'8Ar130 *“BAr7O
'* BAr90 ' ' 0 Control 0 ‘ 0 Row2nd
Row3rd ' ' ' Row4th ‘ ‘ ' Row4thdc2

Figure 17 . Kellogg site mean error for estimated trees per acre by treatment and
projection length for RPAL. (Error expressed as predicted value minus observed
value.)

Image presented in color.
Mean Tm Error— RPAL Simulation

 

 

 

 

 

1951

185:

175:

165‘ o

155:

145: '

l3?-
“ 115-j -
8 105: .
2 -
E: 75% 3 5 :

55: 5 o '

551 o .

‘5: 0

351 . e

25: a

a -

-5- ..... 'flfi ......... ,

0 5 10 15 20 25 30
Time (years)
Tx "'8Ar110 "H' 8Ar130 ' ' BAr70
BAr90 0 0 0 Control ° ° ° Row2nd
Row3rd ' 0 0 Row4th ' . ‘ Row4thac2

46

APPENDICES

Appendix A. Thinnings at the Kellogg and Hiawatha site. (Adapted from Rudolph et al.

1984)

 

Hiawatha site

 

 

 

 

Treatment name Initial thinning i969 1976 1982

BAr30: 3O ftZ/acre 30 fi2/acre 30 fi2/acre none

BAr45: 45 fi2/acre 45 ftZ/acre 45 fill/acre none

BAr60: 60 ft2/acre 60 fi2/acre 60 fiZ/acre none

BAr80: 80 fi2/acre 80 ftZ/acre 80 fi2/acre 85 fi2/acre

BArlOO: 100 11.2/acre 100 fiZ/acre 100 fi2/acre 105 fi2/acre

BArl30: 130 ftZ/acre 130 ftZ/acre 130 fi2/acre 135 fiZ/acre

BAr160: 160 fi2/acre 160 fi2/acre 160 fi2/acre 165 ftZ/acre

Row2nd: every other row 90 ftZ/acre 95 fi2/acre 100 fi2/acre

Row3rd: every third row 120 ftZ/acre 120 ftZ/acre 125 fiZ/acre

Row4_2: every fourth row every center row 110 ftZ/acre 115 fi2/acre

Row4th: every fourth row 22% height 22% height 22% height

Co_ntrol: non_e non_e non_e; none

Kellog site

Treatment name Initial thinning 1967 1970 1974 1980 1985

BAr70: 70 fiZ/acre none 70 fi2/acre none 95 ftZ/acre none
BAr90: 90 fi2/acre 9O fi2/acre none 95 ftZ/acre 105 ftZ/acre none
BM] 10: 110 ftZ/acre 110 fiZ/acre none 115fi2/acre 120 fi2/acre none
BAr130: 130 fi2/acre 130 ftZ/acre none 135 fi2/acre 140 fi2/acre none
Row2nd: every other row none 85 ftZ/acre none 100 ftZ/acre none
Row3rd: every third row 100 fiZ/acre none 105 11.2/acre 105 ftZ/acre none
Row4_2: every fourth row every center row none 110 ftZ/acre 125 ftZ/acre none
Row4th: every fourth row 115 ft2/acre none 120 fi2/acre 125 fi2/acre none
Control: none none none none none none

 

47

Appendix B. F VS-LS growth and mortality equations (Bush and Brand 1995)

FVS-LS Diameter Growth:

The LS-TWIGS diameter growth equation is comprised of two parts: a growth
equation which predicts grth as if there were no competition (Hahn and Leary
1979) and a modifier equation which reduces potential tree growth to reflect
stand competition based on stand basal area and the size of each tree in

relation to the tree of average stand diameter (Holdaway 1984) (Miner et al.

1988).

The diameter growth equation is:

where:

PG = A1 - A2*DA3 + A4*SI*CR*DA5

PG = potential annual diameter growth (inches/year)
D = current tree diameter at breast height

S1 = site index (base age 50)

CR = crown ratio code

A1 = 0.09446

A2 = 0.00012

A3 = 2.0596

A4 = 0.00035

A5 = 0.2423

The modifier equation is:

where:

CM = 1 - exp{-f(D/AD)*g(AD)*[(BAMAX - BA)/BA]1/2}

CM = competition modifier
BAMAX = maximum basal area expected for the species (RP=350)
BA = current basal area
AD = average stand diameter
f(R) = a function characterizing the individual tree's relative diameter
effect on the average stand diameter
= B1*[1 - exp(BZ*D/AD)]B3 + B4
g(AD) = a function characterizing the average stand diameter effect on the
modifier
= Cl *(AD + 1)C2

B1 = 2.310
B2 = -1.670
B3 = 3.94
B4 = 0.00
CI = 0.441
C2 = 0.173

48

A diameter adjustment factor is then added onto the product of the grth and
modifier equations. The equation, by Holdaway (1985), is as follows:

DAF = E1*D + E2*D2 + E3

where:
DAF = diameter adjustment factor
D = diameter breast height
E1 = 0.00
E2 = -0.00017
E3 = 0.018

LS-TWIGS calculates diameter growth on a yearly basis, FVS calculates diameter
growth on a 10 year interval. Therefore, the final diameter growth is

multiplied by 10. Since diameter, basal area, average stand diameter, and crown
ratio change on a yearly basis, diameter growth predicted by the LS-TWIGS
variant of FVS is slightly different than LS-TWIGS.

FVS- LS Mortality:
The individual-tree mortality model is that which is discussed in Buchman et al.
(1983) with additional species coefficients in Buchman (1983) and Buchman and
Lentz (1984). The equation is as follows:

M =1 - B0 - [1/(1 + exp(n))]

where:
n = B1 + B2*(DGR/10)B3 + B4*(D-1)B5 * exp[-B6*(D-1)]

and:
M = tree's annual probability of mortality
D = diameter at breast height
DGR = diameter growth
B0 = 0.9997
B1 = 1.9953
B2 = 57.97
B3 = 1.012
B4 = 0.26480
B5 = 1.6260
B6 = 0.1273

LS-TWIGS calculates mortality on a yearly basis, FVS calculates it every 10 years.
Hence, an interest rate approach is used for mortality periods longer than one year. Since
D and DGR change annually in LS-TWIGS, the LS-TWIGS variant of FVS results in
slightly different mortality estimates.

49

Appendix C. RPAL basal area growth equations for stands greater than 25 years in age.
RPAL Basal Area Growth (25 < age ):

For stands over 25 years old at dbh, the average annual basal area growth in square feet per
acre is estimated from Buckman (1962):

where:
ABAG = 1.6889 + 0.041066*B - 0.00016303"'B2 - 0.0769*A +.0002274"‘A2 +
0.064415‘8 '

All basal area increments are constrained by the maximum annual diameter growth
defined from Lundgren (1981):

DMAX = 0.007 * s * elf-““3”“

where:
DMAX = maximum annual diameter growth (inches)
S = site index
BHA = tree age at Dbh

This maximum constraint is applied to a tree of mean stand diameter.
RPAL Mortality:

If a stand has over 40 sq.ft./acre of basal area, mortality is estimated in terms of basal area
per acre:

BAM = B*exp(-20*S/B)
where:
BAM = annual basal area mortality (ft2 per acre)
S = site index at age 50
B = basal area in sq.ft. per acre

It is assumed that the mean dbh of the dead trees will be equal to the stands quadratic
mean dbh minus one standard deviation (Lundgren 1981), or MDBH - SD, where:

SD = 0.37628 * MDBH * exp(-0.093346*MDBH)

Mortality is then estimated in number of trees per acre (MN OT):
MNOT = BAM/((MDBH - so)2 * n/576)

50

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55