A Neural Network Approach to an Individual Tree Model for Nova Scotia

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1

A Neural Network Approach

to an Individual Tree Model for
Nova Scotia




Eldon A. Gunn

Professor, Department of Industrial Engineering

Matthew Nelson

Undergraduate Student, Department of Industrial Engineering




Working Paper Abstract


This working pape
r summarizes the results of a project carried out during May
-
August, 2005.
The project was aimed at demonstrating that it was possible to use neural networks to model
individual tree growth and survival. The NS Department of Natural Resources provided a
ccess
to their Inventory Permanent Sample Plot and their Research Permanent Sample Plot data. This
was processed and amalgamated into a working data base using the 4
-
D database software
package. Several macros were written to manipulate this data base a
nd create the data in the
form suitable for training the neural networks. The MATLAB neural network toolbox was used
to carry out the training. Several sets of results are presented showing the neural network
approach to be promising.


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2



A Neural Network Approach to an Individual Tree Model for Nova Scotia
...............................
1


Introduction
................................
................................
................................
............................
3

Background

Stand and Single Tree Models
................................
................................
..........
3

Artificial Neural Networks
................................
................................
................................
.....
5

Developing a Neural Network Approach to Individual Tree Growth Models
..........................
7

The Data “Information” Tables
................................
................................
...........................
8

The Training Tables
................................
................................
................................
............
9

Training the Neural
Networks
................................
................................
...............................
10

Analysis of the Models
................................
................................
................................
.........
12

Confidence Intervals for the Tree Survival
................................
................................
........
12

Assessing the Performance of the Diameter Growth Networks
................................
.........
14

Concluding Remarks
................................
................................
................................
............
14

References:
................................
................................
................................
...........................
22

Appendix A
-
Elements of Single Tree Models
................................
................................
...
23

NE Twigs model (FVS)
................................
................................
................................
....
24

LS TWIGS Growth Functio
ns:
................................
................................
..........................
26

Prognosis (Original Inland Empire Version)
................................
................................
........
28

Appendix B. Data Base To Support the Neural Network Analysis
................................
.......
32

Appendix B.1 Data Base Description
................................
................................
................
33

Appendix B.2 Data Base Tables and Relational Structure
................................
.....................
38

Appendix B.3
-
4D Database Structure
................................
................................
.............
39

Appendix B
-
4 4
-
D Data Base Methods (Macros)
................................
.............................
40

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3

Int
roduction


This paper describes the basis for the development of a individual tree growth model suitable for
the Acadian forest. Instead of traditional regression based models, it proposes an artificial
neural network framework that would appear to have
significant benefits. The work reported
here is the result of a joint project between the Department of Industrial Engineering at
Dalhousie University and the N.S. Department of Natural Resources
1
.


After giving a short background on single tree models,
we describe briefly a neural network
based modeling approach. We describe briefly the database that has been constructed
amalgamating the inventory permanent sample plots and the research plots. This has resulted in
a data set of more than 700,000 tree
measurements, taken 5 years apart. We have developed two
different types of neural network models, one describing tree survival and the other describing
diameter growth. We used approximately 400,000 of the tree measurements as a training set to
develop
the neural networks and tested the resulting networks on the remaining tree
measurements. Some results of this testing are reported. The results appear to be quite
encouraging.



Background

Stand and Single Tree Models


The growth modeling techniques cu
rrently used in Nova Scotia and much of the rest of Eastern
Canada are stand
-
based models. As such, they operate on a stand described by (DBH
t
, AHT
t
,
BA
t
) where DBH
t
is stand total breast height diameter, AHT
t
is stand average height and BA
t
is
stand
basal area. Taking into account aspects of site capability, some type of species
characterization of the stand (for example classification by cover type or ecosystem class) as well
as regional issues ( such as climate zones), growth models transform the
stand into a new stand a
certain period of time later. Using five year periods the growth model G transforms the stand
from (DBH
t
, AHT
t
, BA
t
) => (DBH
t+5
, AHT
t+5
, BA
t+5
). In Nova Scotia, extensive data is
available based on the randomly located inventory
permanent sample plots (Inventory PSP’s)
established in the period 1965
-
1969 and remeasured every five years since then. This Inventory
PSP data set has recently been expanded to approximately 3500 plots. In addition to the
Inventory PSP s, Nova Scotia
also has an extensive set or research permanent sample plots
(Research PSP) established in managed stands (plantations, precommercially thinned stands,
commercially thinned stands). Based on this stand data, the NS Department of Natural
Resources (NS DNR)
has developed a series of regression based models that enable the



1

The participants have included Eldon Gunn and
Matthew Nelson
in the Industrial Engineering
Department at Dalhousie and Tim McGrath and Peter Townsend at NS. Department of Natural Resources.
Eldon Gunn developed the neural network framework and Matt Nels
on did the database and neural
network calculations. Tim McGrath has managed the process of data collection, analysis and growth
modeling for the research data sets and Peter Townsend supplied the inventory data sets


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4

prediction of average stand growth. Some of these results can be found in the NS Growth and
Yield models
2
.


Stand based models have a significant advantages for prediction of forest growth
at the forest
level. Because they are based on overall provincial data, their calculations provide a good basis
for predicting overall provincial average results. However, they also suffer from a significant
disadvantage. They are based on the assumpt
ion that the past evolution of the stand is a good
predictor of future performance. The past evolution of the stand is based on past management
practices. Of the so
-
called unmanaged forest, this includes the harvest decisions that often
resulted in the h
igh
-
grading of the forest. For managed stands, the stand data is based on only a
limited number of cases specifying spacing at planting and PCT as well as basal area percentage
removal for commercial thinning. The response of the forest to different manag
ement policies
than have been used in the past is not readily calculated.


Single tree models attempt to model the average development of each tree within the stand,
based on the attributes of that tree and the attributes of the stand within which it is g
rowing. The
models account for two effects. The first is the survival or mortality of the tree to the next
measurement period. The second is the change in diameter and height for those trees that do
survive. In implementation, the model starts with a
list of trees that make up the stand, each
tree with its own individual attributes. The model then produces a tree list five years later by
first calculating for each tree the probability of survival and then, using these probabilities,
simulating the s
urvival of the trees on the list. For each surviving tree, its DBH and height
attributes are then calculated five years later, using the growth part of the model.


A broad variety of individual tree models exist. The US Forest Service Forest Vegetation
S
imulator (FVS) (
http://www.fs.fed.us/fmsc/fvs/
) is based on two groups of models, the
Prognosis model developed by Stage and the STEMS/TWIGS model. At first sight all of the
models are Prognosis models.
However, this is deceptive. For a number of regions, Prognosis
was fit to the pre
-
existing TWIGS model outputs, not to the original data sets. Outlines of these
models are given in Appendix A. Both are taken from the website mentioned above.


In these m
odels , the mortality probability is a function of, among other variables, DBH , the
diameter at Breast Height and the BAL, the basal area of trees on the stand larger than the given
DBH as well as SI, the site index. Similarly the diameter growth in the
period is also a function
of DBH, BAL, and SI. In Prognosis, the site index has often been represented in terms of a
variety of biophysical variables such as slope, aspect and elevation (see appendix A.)


The major disadvantage we see with these individu
al tree models is that they are the result of
independent data fitting procedures for each species. It is true that even the single species model
fitting process is not particularly easy. This approach might thus be acceptable if substantial data
sets were
available for each species. This is seldom the case. In the particular data sets available
in Nova Scotia, there are a very large number of measurements available for the most common
species, red spruce, on the most common site capabilities. There are
a very small number of



2
These can be found at
http://www.gov.ns.ca/natr/forestry/gny2004/growthandyield.htm


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5

measurements for less common species such as Eastern Hemlock or Red Oak over the required
range of site capabilities and age classes. In addition to the data problems, there is nothing to
guarantee that combining the estimates from
the individual tree species into stand and forest
level estimates will give an unbiased estimate of the aggregate response.


Artificial Neural Networks


There are many different perspectives on artificial neural networks. The perspective taken here
is th
at a way of modeling an input
-
output process. Any of the individual tree models uses this
type of framework (figure 1). The input are the attributes of a given tree and the attributes of the
stand within which that tree is located. The outputs are the
probability that this tree will survive
the current 5 year period, and, if it survives, the tree attributes at the end of the period. The
process of growing a stand is to run every tree in the stand through this model, thus creating a
new stand 5 years
later.



Figure 1. Input
-
output concept of an Individual Tree Model



Neural networks represent a particular way of representing input output processes. A neural
network has a number of input nodes and a number of output nodes.
The network achieves its
nonlinear modeling capabilities by using one (or more hidden layers) of artificial “neurons”;
nodes with a nonlinear activation function that takes on values between 0, 1. Typical activation
functions include functions as the l
ogistic function:
, plotted in figure 2.


Figure 2. Logistic Function

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6


The network is of the form indicated in figure 3. There are a number of input nodes, and a
number of output nodes characteristic of the real system. The neural
network fitting process is to
first create a number of hidden layer nodes. In the simple case we will put forward here, there
will be a single set of hidden layer but more complex models exist with multiple hidden layers.
Each of the hidden layer node
s transform an input to an output via the neural activation function.
The inputs to each of the hidden layer nodes are made up of a weighted sum of the values at the
input nodes. The outputs from the hidden layer nodes are also combined via a set of weig
hts in
to the overall network outputs.




Figure 3. Schematic of Neural network


If we let x
i
denote the input value at input node i and y
j
denote the output from output node j, and
let I
k
and O
k
denote the input and output fro
m the k
th
node in the hidden layer. The weights
connecting input I and hidden layer node k are w
ik
and the weights connecting hidden layer
output k with output node j are v
kj
. Then the overall neural network is given by

where the
network
is defined by the following sets of equations:




Thus if we have the weights
w
and
v
, the neural network is a well defined and easily computed
function
. The second part of the neural network fitting process is to “train the network” by
finding appropriate weights. There are many methodologies to do this but most amount to an
attempt to solve a least squares problem over a large set of observations of in
put and output
denoted
. The training problem is to choose w
and v to:

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7


There are a large number of programs available to carry out the construction of the networks and
the optimization
of the weights. In the neural network community, this optimization process is
often referred to as
training.



Developing a Neural Network Approach to Individual Tree Growth
Models


In this section we describe the steps that we have taken in order to d
evelop an initial neural

network based model. We began with two databases
3
, one from the Inventory Permanent
Sample Plots (PSPs), the other from the Research PSPs. We processed these data bases into a
single database which we refer to as the LiveDieGrow
database. Although there are 77 tree
species recognized in Nova Scotia, we have used only the species categories shown in table 1.


Table 1. Tree species used in the database

Tree Species and Types

Code

Species

Type

Code

Species

Type

BF

Balsam Fir

Sof
twood

PO

Poplar

Hardwood

RS

Red Spruce

Softwood

RM

Red Maple

Hardwood

BS

Black Spruce

Softwood

SM

Sugar Maple

Hardwood

WS

White Spruce

Softwood

YB

Yellow Birch

Hardwood

WP

White Pine

Softwood

WB

White Birch

Hardwood

RP

Red Pine

Softwood

WA

White Ash

Hardwood

EH

Eastern Hemlock

Softwood

RO

Red Oak

Hardwood

OS

Other Softwood

Softwood

OH

Other Hardwood

Hardwood




UK

unknown

unknown



The LiveDieGrow database has been organized into three main data input tables, the
Plot
Information
, the
Sample Inf
ormation
and the
Tree Information
and two sets of data output tables
Mortality Training
(Check) and
Growth Training
(Check). The three “information” tables



3
The Inventory and Research PSP’s are maintained by Peter Townsend and Tim McGrath,
respectively, NS DNR, Truro.

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8

contain the base information on the measurements, the “Training” tables are the inputs to the
neu
ral network model and the “Check” tables are for testing purposes.


The Data “Information” Tables



These data in the three “Information” tables are discussed briefly below. More information on
the overall database structure can be found in appendix B




Plot Information

plot, subplot, plot type, plot status, inactive reason, county, map sheet, plot size, GIS land
capability


This table contains the information regarding each plot that does not change when a
sample is taken on that plot. Plot number a
nd subplot numbers were provided with the
data for the research plots, while only plot numbers exist for the inventory plots. To solve
this problem, subplot numbers of 0 were added to the inventory plots. Map sheet data
and land capability information is
not available for the research plots. Plot type and plot
status are foreign keys to the plot type table and plot status table respectively. Several
fields have been omitted for clarity since they are not used in the processing of the data.


Sample Inform
ation

plot, subplot, sample year, sample date, owner, treatment, treatment year, cut type, average
stump age, cover type, age of cut, plot age code, plotBAS, plotBAH, plot BAU, sidentifier


This table contains summary information for each plot, subplot and
year that a sample
was taken. Any changes in ownership can be recorded as well as the state of the plot at
each sampling instance. The type of cutting, age of cutting, average stump age and cover
type are recorded. The plot basal area softwood hardwood
and unknown are calculated
by a method. The “sidentifier” number is a tracking number that is unique to each plot,
subplot and year combination and was used to eliminate several numerical comparisons
when sorting data. Three plot basal areas are compute
d. These are the basal area of
softwood trees (plotBAS), hardwood trees (plotBAH) and unknown trees (plotBAU).
The total plot basal area is the sum of these three. The plot basal areas for the sample year
are computed by running macros on the tree records
. In the 4
-
D data base we use,
macros are called “methods”. The 4
-
D methods we use are all listed in appendix D.
Listings of the code behind these methods are all available in the database.


Tree Information

plot, subplot, tree, sample year, species,
status, health, diameter at breast height, height, basal
area, BAS below, BAH below, BAU below, identifier


This table contains the basic information regarding each tree at each measurement period.
The primary key is a combination of the plot number, subp
lot number and tree number.
The plot and subplot numbers are foreign keys to the plot information table. The basal
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9

area was calculated with a method based on the diameter at breast height. Basal area
softwood, hardwood and unknown were also calculated
with a method. The sidentifier
number is a foreign key to the sample table. The BAS below,

BAH below, BAU below
refer to the total basal area of all softwood, hardwood and unknown, respectively, trees
with diameter less than or equal to the current tree.
This is again computed with a method
described in appendix B.


The Training Tables


There are two tables for neural network training these are the
Mortality Training
and
Growth
Training
tables. There are two tables of identical format which are the che
ck tables used to test
the neural networks post
-
training.


Mortality Training

diameter, height, plotBAS, plotBAH, plotBAU, BAS larger, BAH larger, BAU larger, dominant
height, BF, RS, BS, WS, WP, RP, EH, OS, PO, RM, SM, YB, WB, WA, RO, OH, UK, live or
d
ie


Mortality
Check

diameter, height, plotBAS, plotBAH, plotBAU, BAS larger, BAH larger, BAU larger, dominant
height, BF, RS, BS, WS, WP, RP, EH, OS, PO, RM, SM, YB, WB, WA, RO, OH, UK, live or
die


The mortality tables contain all trees that have been sam
pled at least two times over a five
year period. Mortality Training is 75% of the trees and Mortality Check is the remaining
25%. The BAS larger, BAH larger, BAU larger are computed as the difference between
the plot basal areas (plotBAS, plotBAH, plotBA
U respectively) and the basal areas below
(BAS below, BAH below, BAU below respectively) from the Tree Information table.
The dominant height is the average height of the three tallest trees on the plot. The
species codes are 0
-
1 variables. All of these
are 0 except for the species of the particular
tree for the record. The “live or die” is another indicator variable which is 1 of the tree is
alive at the end of the five year period, 0 if it is dead. From these tables, two files are
exported for use in M
ATLAB. One file contains all the information about the tree in the
record except the live or die indicator. This file is the set of input records for training
(checking) the neural network. The other file is the live or die indicator by itself. This is

the set of output records for training (checking) the neural network.

Method that creates table: Mortality 1



Growth
Training

diameter, height, plotBAS, plotBAH, plotBAU, BAS larger, BAH larger, BAU larger, dominant
height, seasons, BF, RS, BS, WS, WP
, RP, EH, OS, PO, RM, SM, YB, WB, WA, RO, OH, UK,
diameter change


Growth
Training

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diameter, height, plotBAS, plotBAH, plotBAU, BAS larger, BAH larger, BAU larger, dominant
height, seasons, BF, RS, BS, WS, WP, RP, EH, OS, PO, RM, SM, YB, WB, WA, RO, OH, U
K,
diameter change


The growth tables contain only the trees that have survived for at least one five year
period. The seasons field is the number of growing seasons between measurements of
diameter. Normally this should be five but some changes in proced
ure in the Department
in recent years have meant that we cannot count on this. The method “output8”
calculates this quantity. The growing season is treated as June 1 to August 15. Sample
dates between these dates ate treated as partial seasons. Growth T
raining is 75% of the
trees and Growth Check is the remaining 25%. For the results reported hear, we have
only used trees with exactly five growing seasons between measurement. The meaning of
the other fields is the same as in the case of the mortality ch
eck with the exception of the
diameter change. This is the change in diameters over the five year period. From these
tables, two tables are exported for use in MATLAB. One file contains all the information
about the tree (excluding diameter change infor
mation) and the other contains the
diameter change information.

Method that creates table: Mortality 2



Training the Neural Networks


Following the organization into the mortality training, mortality check, growth training, and
growth check, the data was
exported as text files. Each table was output into two data sets. The
mortality tables were output into the tree information and the survival data. The growth tables
were output into the tree information and the diameter change data. These data sets we
re input
into the neural network toolbox of MATLAB.


The neural network toolbox in MATLAB recommends that the data be normalized prior to
training. Pre
-
analysis and post
-
analysis of the data was performed to normalize the data to the
range of
-
1 to 1. T
his was done based on the minimum and maximum value in each range of
data using the following formulas:

Let:

input values be in p.


minp = minimum p value for each data field


maxp = maximum p value

for each data field


The normalization formula is:


newp
= (p
-
shift)/scale



where: shift = 1/2 (minp + maxp)



scale = 1/2 (maxp
-
minp)


To un
-
normalize the output to an actual value, the minimum and maximum target values
are needed:




mint = minimum target value




maxt = maximum target value

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11


Then the f
ormula is:


actual output = (nnout * scale) + shift



where: nnout = output from the network










shift = 1/2 (mint + maxt)










scale = 1/2 (maxt
-
mint)


This pre
-
analysis ensures that the data is all of a common magnitude and prevents errors due
to
round
-
off during training.



After pre
-
analysis, the networks were trained using the
scaled conjugate gradient
method.
MATLAB has several training methods, including Levenberg
-
Marquardt and scaled conjugate
gradient. The Levenberg
-
Marquardt is usuall
y recommended as a reliable and efficient method.
However it requires the computation of an approximate Hessian matrix. We originally attempted
to sue Levenberg
-
Marquardt as a training method but since the data set is so large, the Hessian
could not be ca
lculated with the available memory of the computer; therefore a move to scaled
conjugate gradient was made.

Both the growth and mortality models were modeled as feed
-
forward networks with twelve
hidden nodes and one output node. The Mortality data set h
ad 26 input nodes. These are the
diameter, height, plotBAS, plotBAH, plotBAU, BAS larger, BAH larger , BAU larger and
dominant height plus the 17 0
-
1 species indicators. The Growth data set has 27 input nodes.
These are diameter, height, plotBAS, plotBA
H, plotBAU, BAS larger, BAH larger , BAU
larger, dominant height and seasons plus the 17 0
-
1 species indicators. The choice of twelve
hidden nodes is arbitrary and justified only by the fact that it seems to work reasonably well.


Both models were train
ed over 500 epochs to a MSE target of 1E
-
5; however neither reached this
level of precision.


For the mortality model, a tansigmoidal and a logsigmoidal transfer function were used in the
hidden and output node respectively. The tansigmoidal transforms
the input based on:


tansig(
s
)
= 2/(1+exp(
-
2*s))
-
1


And the logsigmoidal transforms the input based on:


logsig(s) = 1 / (1 + exp(
-
s))


This allowed for any value to come out of the hidden nodes but only values of between 0 and 1
to exit the output node.
The output from the mortality model is a value between 0 and 1 that is
the probability that the tree will survive until the next sampling instance.


For the growth model, a tansigmoidal transfer function was used for both the hidden nodes and
the output
node. A purelinear transformation was considered for the output node, but since the
data is to be post
-
analyzed, the tansigmoidal not only can predict all growth levels, it also
prevents any predictions from being negative (since negative growth cannot oc
cur).


Page
12

Analysis of the Models


A problem with using neural networks is that most of the statistical tests that one would use in
regression analysis are not readily available. Complicating this is the high levels of variability
normally found in most fores
try problems.


There are two quite separate analysis problems, i) the tree survival model and ii) the diameter
growth model. The two are qualitatively different. The output of the tree survival neural
network is a probability p
i
that the i
th
tree sur
vives for the measurement period. However the
actual data is a 0 or 1 outcome of mortality or survival. The diameter growth, on the other hand
is a continuous numerical quantity which is the measured diameter growth.

Tree Survival


Confidence Intervals f
or the Tree Survival


If we have n random variables, each with a given probability of survival p
i
, i=1,n, then we can
treat the number of trees that survive as the sum of n Bernoulli random variables, each with mean
p
i
and variance
p
i
(1
-

p
i
). If n is lar
ge enough, then the total number of surviving trees can be
approximated as normal with a mean of
and variance of
. Thus we
can compute approximate confidence on the total number of survivals. We have used th
e neural
network estimates of the
p
i
for each tree and compared the computed confidence intervals to the
actuals observed

Following training, confidence intervals for several segments of the data as well as the
verification data were
calculated.
The data
was broken into the following categories: all the
training trees, all the check trees, small trees (diameter of up to 150mm), medium trees (diameter
of between 150mm and 300mm), large trees (diameter of greater than 300mm), hardwood trees,
and softwood t
rees. Three species that represent a large portion of the data (Red Spruce), a small
portion of the data (Eastern Hemlock) and an average portion of the data (Sugar Maple) were
also tested. It would appear from the results that the outcome from the morta
lity model is
fundamentally flawed since only a few of the confidence intervals actually contain the real
number of living trees, but in reality the intervals are so small because the neural ]network model
is fit to the data in a pretty good way. The resu
lts of the confidence interval are presented in
Table 2.


In most cases the actual number of surviving trees does not fall within even the 99% confidence
interval. For example, there were 100410 hardwood trees observed to actually survive while the
99% co
nfidence limits are (100631, 101069). Although the actual survival is not within this
limit it misses the lower bound by only 0.22%. Because of the large sample sizes, all of the
confidence intervals are very narrow. In every case the actual survivals
either lie within the
99% confidence interval or come very close.


Page
13

Table 2 Results of Confidence Interval Calculations

Small Trees (<150mm)




Medium Trees (150
-
300mm)


E(x) =

197490




E(x) =

105770



V(x) =

19984




V(x) =

10431



99% CI:

197126

≤µ≤

197854


99% CI:

105507

≤µ≤

106033

95% CI:

197213

≤µ≤

197767


95% CI:

105570

≤µ≤

105970

80% CI:

197309

≤µ≤

197671


80% CI:

105639

≤µ≤

105901

actual live =

197240




actual live =

105260












Large Trees (>300mm)




Red Spruce Trees



E(x) =

9802




E(x) =

67047



V(x) =

913




V(x) =

6159



99% CI:

9724

≤µ≤

9880


99% CI:

66845

≤µ≤

67249

95% CI:

9743

≤µ≤

9861


95% CI:

66893

≤µ≤

67201

80% CI:

9763

≤µ≤

9841


80% CI:

66946

≤µ≤

67148

actual live =

9669




actual live =

66853












East
ern Hemlock Trees




Sugar Maple Trees



E(x) =

3036




E(x) =

23071



V(x) =

180




V(x) =

969



99% CI:

3002

≤µ≤

3071


99% CI:

22991

≤µ≤

23151

95% CI:

3010

≤µ≤

3062


95% CI:

23010

≤µ≤

23132

80% CI:

3019

≤µ≤

3053


80% CI:

23031

≤µ≤

23111

actual live
=

3007




actual live =

22846












Hardwood Trees




Softwood Trees



E(x) =

100850




E(x) =

208960



V(x) =

7223




V(x) =

23757



99% CI:

100631

≤µ≤

101069


99% CI:

208563

≤µ≤

209357

95% CI:

100683

≤µ≤

101017


95% CI:

208658

≤µ≤

209262

80%
CI:

100741

≤µ≤

100959


80% CI:

208762

≤µ≤

209158

actual live =

100410




actual live =

208520












Training Trees





Check Trees




E(x) =

313050




E(x) =

103120



V(x) =

31328




V(x) =

10324



99% CI:

312594

≤µ≤

313506


99% CI:

102858

≤µ≤

103382

95% CI:

312703

≤µ≤

313397


95% CI:

102921

≤µ≤

103319

80% CI:

312823

≤µ≤

313277


80% CI:

102990

≤µ≤

103250

actual live =

312260




actual live =

102960



Page
14

Assessing the Performance of the Diameter Growth Networks



In order to assess the diamet
er growth networks, we developed a different approach. Again we
looked at various tree categories. What we did here is assess the neural network outputs for each
tree in the category. We then ordered the trees in order of increasing diameter growth as
calculated by the network. When the actual data is plotted with the sorted predicted values, there
is a slight trend following observed but the sheer volume of data to be analyzed makes this trend
difficult to see, mainly because there is a very large nois
e signal in the actual growths.


We applied simple exponential smoothing to the actual growth values using a small smoothing
coefficient. The formula is:



y
n
=
α
g
n
+ (1
-
α
) y
n
-
1

where
y
n
is the smoothed value and
g
n

is the actual diameter growth observ
ed for the n
th
tree.
The ordering n= 1,2,3, … is in terms of increasing values of the neural network diameter growth
estimates.
We used a smoothing coefficient of
α
= .05 which is relatively large given this
amount of data. Even with this large value of
α
, the smoothed data and the predicted value are
within 2mm of each other for all trees on the training and check data sets.


The data was broken into several segments to check if the model works for most situations. The
data was broken into hard and so
ftwood trees, hard and softwood stands, stands with less total
basal area per hectare of 0
-
10m
2
, 10
-
20m
2
, 20
-
30m
2
, 30
-
40m
2
, 40
-
50m
2
, 50
-
60m
2
, 60
-
70m
2
, and
70+m
2
. As can be seen from the following graphs, the model appears to work well for all
situations, t
he predicted growth falls in the middle of the exponentially smoothed growth data.
As the number of trees in the sample decreases (the case with stands of more than 60 m
2
basal
area) the accuracy of the becomes less, but this is to be expected.


Concludi
ng Remarks


The work reported here is very preliminary. Site index was not included in the neural network
fits except indirectly via the dominant height and stand diameters and basal areas. There was no
attempt to include more information such as ecosys
tem location. We have also not yet attempted
to fit height growth neural networks. However the results are encouraging and we intend to
continue to pursue this approach.
Page
15

Figure 4 a) Training and Check Trees



Page
16

Figure 4 b) Hardwood and Softwood Trees



Page
17

Figure 4 c) Softwood Stands and Hardwood Stands



Page
18

Figure 4 d) Trees in Stands of Varying Basal Areas




Page
19

Figure 4 d) Trees in Stands of Varying Basal Areas (continued)



Page
20

Figure 4 d) Trees in Stands of Varying Basal Areas (continued)




















Page
21











































Page
22

References:

Crookston, Nicholas L. 1990.
User's Guide to the Event Monitor: Part of Prognosis Model
Version 6.
Gen. Tech. Rep. INT
-
275. U.S. Department of Agriculture. Forest Service.
Intermountain R
esearch Station. Ogden, UT. October 1990. 21 pp.


Stage, A.R. 1973.
Prognosis Model for stand development.
Research Paper INT
-
137. Ogden,
UT: USDA Forest Service, Intermountain Forest and Range Experiment Station.


MINER, CYNTHIA L.; NANCY R. WALTERS; MONI
QUE L. BELLI. 1988.
A Guide to the
TWIGS Program for the North Central United States.
Gen. Tech. Rep. NC
-
125.U.S. Department
of Agriculture, Forest Service, North Central Forest Experimental Station.




Page
23






Appendix A
-
Elements of Single Tree Models



a)

North East

Twigs

b)

Lake States TWIGS

c)

Prognosis (Inland Empire)





Page
24

NE Twigs model (FVS)


I. The Large
-
tree Model.


Growth Functions:


A. Large
-
tree Diameter Growth Model.


The basic function is similar to that described in Teck and Hilt (1991). In
the

national model, the dependent variable is the logarithm of change in diameter

growth (inside bark) squared. The equation for NE
-
TWIGS is for basal area

growth (outside bark). To maintain consistency within FVS, basal area growth

(outside
bark) is translated into logarithm of diameter growth (inside bark)

squared as follows:


Ln(dds) = Ln(10.0 * POTBAG * BAGMOD * BARK**2 / .0054542) (1)


where:


BARK

= species specific bark ratio

POTBAG

= B1 * SI * (1.0
-

exp(
-
B2 * DBH))

BAGMOD

= exp(
-
B3 * BAL)

SI


= species specific site index

DBH

= diameter at breast height

BAL

= basal area per acre in trees with diameters larger than or equal to




subject tree

B1
-
B3

= species depend
ent regression coefficients (see Table 1.)


NE
-
TWIGS calculates diameter growth on a yearly basis, FVS calculates diameter

growth on a 10 year interval. The factor of 10 in equation (1) approximates

this difference. Since BAL and DBH change on a y
early basis, diameter growth

predicted by the NE
-
TWIGS variant is slightly different than NE
-
TWIGS.



B. Site Index Conversion Equation.


This equation takes a site index value (base age 50) for the predominant species

of the stand and converts it to a
site index for each species that comprises the

stand. This equation is presented by Teck and Fuller (1987). A user may

override the site index conversion and enter their own site index for a species

using the SITECODE keyword. If no site index i
s given, a default of sugar maple

with site index of 56 is used. The equation is:


SI(FGS) = B1 + 1.104 * SI(SGS) (2)


Page
25

where:




FGS = faster
-
growing species

SGS = slower
-
growing species



B1 = species sp
ecific coefficient (see Table 2. and 3.)


Species are grouped according to similar growth rates and then ranked from

fastest to slowest growing (see Table 5.), B1 is then looked up in table 6.

Note: If the site index of the faster
-
growing species is
known, equation (2) can

be rearranged to estimate the site index of the slower
-
growing species.



E. Mortality Model


The individual
-
tree mortality model is that which is discussed in Teck and Hilt

(1990). The equation is as follows:



M = 1/[1 + exp(n)] (4)


where:




n = B1 + B2*(DBH + 1)**B3 * exp[
-
B4 * DBH
-
B5 * BAL
-
B6 * SI]



M = tree's annual probability of mortality

DBH = Diameter at breast height

BAL = basal area per acre in trees wit
h diameters larger than or equal to

subject tree



SI = species specific site index



B1
-
B6 = species specific coefficients (Table 5.)



Page
26

LS TWIGS Growth Functions:


A. Large
-
tree Diameter Growth Model.


The LS
-
TWIGS diameter growth eq
uation is comprised of two parts: a growth

equation which predicts growth 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:


PG = A1
-
A2*D
A3
+ A4*SI*CR*D
A5
(1)


where:


PG = potential annual diameter gro
wth (inches/year)

D = current tree diameter at breast height

SI = site index (base age 50)

CR = crown ratio code

A1
-
A5 = species dependent regression coefficients (see Table 1.)


The modifier equation is:


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


where:




CM


= competition modifier



BAMAX

= maximum basal area expected for the species (Table 2.)



BA


= current basal area



AD


= average stand diameter



f(R)


= a function characterizing the individ
ual tree's relative diameter




effect on the average stand diameter

= B1*[1
-
exp(B2*D/AD)]B3 + B4

g(AD)


= a function characterizing the average stand diameter effect on the




modifier = C1*(AD + 1)C2

B1
-
B4,C1,C2

= species speci
fic coefficients (Table 2.)


A diameter adjustment factor is then added onto the product of the growth and

modifier equations. The equation, by Holdaway (1985), is as follows:



DAF = E1*D + E2*D2 + E3 (3)

Page
27


where:




DAF


= diameter adjustment factor



D


= diameter breast height

E1
-
E3


= species specific coefficients (Table 3.)




LS
-
TWIGS calculates diameter growth on a yearly basis, FVS calculates diameter

growth on a 10 year interval. Therefor
e, 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.



Page
28

Prognosis (Or
iginal Inland Empire Version)



LARGE TREE DIAMETER GROWTH MODEL



--
Based on log
-
linear model form (pages 53
-
65 INT
-
133, pages 5
-
8 INT
-
208)


--
Actually estimates the natural logarithm of the change in diameter

growth squared


--
Equa
tion form:



LN(DDS) = HABITAT CONSTANT

+ LOCATION CONSTANT

+ B1 * COS(ASPECT) * SLOPE

+ B2 * SIN(ASPECT) * SLOPE

+ B
3 * SLOPE

+ B4 * SLOPE SQUARED

+ B5 * ELEVATION

+ B6 * ELEVATION SQUARED

+ B7 * LN(DBH)

+ B8 * CROWN RATI
O

+ B9 * CROWN RATIO SQUARED

+ B10 * (BAL / 100)

+ B11 * BAL / LN(DBH+1)

+ B12 * DBH SQUARED

+ B13 * (CCF / 100
)

+ USER SUPPLIED SPECIES CORRECTION

+ CALIBRATION ADJUSTMENT



LARGE TREE HEIGHT GROWTH (pages 65
-
66 INT
-
133)



Equation form:


LN(HTG) = HABITAT CONSTANT


+ SPECIES CONSTANT

+ B1 * LN(HEIGHT)

+ B2 * LN(DBH)

+ B3 * LN(DG)

+ B4 * HEIGHT SQUARED


+ USER SUPPLIED SPECIES CORRECTION




Page
29

LARGE TREE CROWN CHANGE (pages 77
-
80 INT
-
133)



--
Predicts crown ratio as a function of species, habitat type, basal

area, crown competition factor, dbh, height, and soci
al position



--
Very static; does not respond well to changing stand conditions



--
Equation form:



LN(CR) = HABITAT
-
SPECIES CONSTANT

+ B1 * BASAL AREA

+ B2 * BAS
AL AREA SQUARED

+ B3 * LN(BASAL AREA)

+ B4 * STAND CCF

+ B5 * STAND CCF SQUARED

+ B6 * LN(STAND CCF

+ B7 *
DBH

+ B8 * DBH SQUARED

+ B9 * LN(DBH)

+ B10 * HEIGHT

+ B11 * HEIGHT SQUARED

+ B12 * LN(HEIGHT)


+ B13 * TREE'S BASAL AREA PERCENTILE

+ B14 * LN(TREE'S BASAL AREA PERCENTILE)




SMALL TREE HEIGHT GROWTH (pages 66
-
69 INT
-
133)



--
Small tree height growth estimates are combined with large tree


height growth estimates over the diameter range 2.0"
-
10.0"

(1.0"
-
5.0" for lodgepole pine)



--
Equation form:


LN(HTG) = LOCATION CONSTANT

+ HABITAT CONSTANT


+ SPECIES CONSTANT

+ B1 * LN(HEIGHT)

+ B2 * STAND CCF

+ B3 * SLOPE * COS(ASPECT)

+ B4 * SLOPE * SIN(ASPECT)



+ B5 * SLOPE

Page
30

+ USER SUPPLIED SPECIES CORRECTION

+ CALIBRATION ADJUSTMENT



SMALL TREE DIAMETER GROWTH



--
Uses the height dubbing function solved for diameter



SMAL
L TREE CROWN CHANGE



--
No change; crown ratios are assumed to remain constant


REGENERATION / ESTABLISHMENT (reference INT
-
161)



--
Height growth

Height growth is estimated using the same function as for small

tree he
ight growth, EXCEPT estimates are NOT combined with large

tree height growth estimates



--
Diameter growth

Diameters are assigned using the height dubbing function solved

for diameter

Minimum assigned diameter i
s 0.1 inch



MORTALITY (pages 70
-
76 INT
-
133; pages 9
-
11 INT
-
108)



--
Hamilton's logistic rate (R1)

R1 = F(HABITAT TYPE, SPECIES, DBH, DIAMETER GROWTH,

ESTIMATED POTENTIAL DIAMETER GROWTH, BASAL AREA,


AND RELATIVE DIAMETER (dbh/mean stand dbh) )



--
Hamilton's logistic rate is adjusted by a factor based on Reineke's

SDI to account for expected differences in mortality rates on different

habitat types and National Forests



R1 = R1 * (SDI ADJUSTMENT FACTOR)



--
BA maximum rate (R2)

Based on proximity of stand BA to max BA and estimated rate

of basal area increment




Rate applied to a tree is a weighted combination of R1 and R


R = (1
-
W)*R1 + W*R2

Page
31


where W = BA / BAMAX

Page
32

Appendix B. Data Base To Support the Neural Network Analysis




B. 1

Description of Data Base


B.2

Data Base Tables


B.3

Organization of 4D Data Base Implementation


B.4

4D Data Base Methods (Mac
ros)
































Page
33

Appendix B.1 Data Base Description


For the purposes of this project, the database was used primarily to
organize and collate the data
that was received from the Nova Scotia department of natural resources. Two types
of data were
received, one set consisting of the PSP inventory plots and one set containing the PSP research
plots. While these two data sets contain the same fundamental information major differences
exist in the format of the data, extraneous informatio
n and in some cases the units of
measurement. Significant time was spent to reduce the data to a common point with
standardized formatting, information and units. Following this standardization, the data was put
into the base tables of the database. App
endix B
-
2 and B
-
3 give a visual organization of the
database. The base tables consist of the following:


Tree Information

plot, subplot, tree, sample year, species, status, health, diameter at breast height, height, basal
area, BAS below, BAH below, BAU be
low, identifier


This table contains the basic information regarding each tree at each measurement period.
The primary key is a combination of the plot number, subplot number and tree number.
The plot and subplot numbers are foreign keys to the plot in
formation table. The basal
area was calculated with a method based on the diameter at breast height. Basal area
softwood, hardwood and unknown were also calculated with a method. The identifier
number is a foreign key to the sample table.


Plot Informat
ion

plot, subplot, plot type, plot status, inactive reason, county, map sheet, plot size, GIS land
capability


This table contains the information regarding each plot that does not change when a
sample is taken on that plot. Plot number and subplot numbe
rs were provided with the
data for the research plots, while only plot numbers exist for the inventory plots. To solve
this problem, subplot numbers of 0 were added to the inventory plots. Map sheet data
and land capability information is not available fo
r the research plots. Plot type and plot
status are foreign keys to the plot type table and plot status table respectively. Several
fields have been omitted for clarity since they are not used in the processing of the data.


Sample Information

plot, subp
lot, sample year, sample date, owner, treatment, treatment year, cut type, average
stump age, cover type, age of cut, plot age code, plotBAS, plotBAH, plot BAU, identifier


This table contains summary information for each plot, subplot and year that a samp
le
was taken. Any changes in ownership can be recorded as well as the state of the plot at
each sampling instance. The type of cutting, age of cutting, average stump age and cover
type are recorded. The plot basal area softwood hardwood and unknown are
calculated
by a method. The identifier number is a tracking number that is unique to each plot,
Page
34

subplot and year combination and was used to eliminate several numerical comparisons
when sorting data.



Plot Type

type, description


This table contains th
e types of plot. Currently there is only research and inventory plots.


Plot
Status

status, description


This table contains the status of the plot. Choices are active, inactive and spare.


Inactive Plot Reasons

reasonID, description


For any plots t
hat are inactive there is a reason recorded. This table contains the possible
reasons for the plot to be inactive.


County Information

countyID, description


This table is a list of the counties in Nova Scotia and the code for each county. Future
develo
pment should alter this table to contain the ecoregion of the plot instead of the
county.


Species

speciesID, description, wood type


This table contains the species that have been recorded on plots in the province of Nova
Scotia. There are currently 77
possible species but for the neural network inputs this is
reduced to 16.


Tree

Status

status, description


This table contains the possible status choices available for each tree. Live, dead
(standing), ingrowths, cut and dead (downed) are the current c
hoices.


Tree Health

healthID, description


This table contains the possible health status for each tree. Good, fair, poor, cut and dead
are the current choices.


Page
35

Owner Information

ownerID, description


This table is a list of the owners of forests in t
he province of Nova Scotia.


Treatments

treatmentID, description


This table is a listing of the possible treatments that can be performed to a stand of wood.
The list included is pared down version of the total possible treatments. Currently
included
are: natural, artificial regeneration, cleaning/thinning, harvest, pre
-
merchantable
thinning and commercial thinning.


Cut Type

type, description


This table is a list of the possible cut types. No cut, partial cut and clear cut are the
current choices
.


Plot Age

Plot age code, description


This table is a list of plot ages. Ages are broken down into 20 year time segments.



From these base tables the functional tables of the database are created by using the methods that
will be discussed in the nex
t section. The functional tables are:


Live or Die

plot, subplot, tree, year, year plus5, live or die, identifier


Live or Die contains a list of all trees that have data recorded more than one time.
Included here is the years in which information is rec
orded about a tree and if the tree
survived from one sample to the next.

Methods that create table: Live or Die 1, Live or Die 2


Diameter

plot, subplot, tree, year, year plus 5, seasons, initial diameter, diameter change, identifier


Diameter is a listin
g of all the trees that survived from one sample to the next in Live or
Die. Included is the number of growing seasons between samples (calculated by
method), the initial diameter and diameter change (calculated by method).

Methods that create table: Live
or Die 3, Live or Die 4


Output1

Page
36

plot, subplot, tree, year, year plus 5, seasons, initial diameter, diameter change, plotBAS,
plotBAH, plotBAU, BAS larger, BAH larger, BAU larger, height, dominant height, BF, RS, BS,
WS, WP, RP, EH, OS, PO, RM, SM, YB, WB
, WA, RO, OH, UK, identifier


Output1 is the final functional table that combines the information in Live or Die and
Diameter into a form that can be used to create the output tables. A set of nine methods
is used to create this table. The dominant heigh
t is the average of the three tallest trees on
the plot. The 17 two letter codes are binary operators that indicate the species of the tree.
Only one of these variables will ever be one since a tree can only ever be one species.

Methods that create table
: Output 1, Output 2,

Output 2a,

Output 3,

Output 4,



Output 5,

Output 6,

Output 7,

Output 8


From the functional tables, specifically Output1, the final output tables are created. These tables
contain the data that is exported for use in training and te
sting the neural network. The output
tables are:


Mortality Training

diameter, height, plotBAS, plotBAH, plotBAU, BAS larger, BAH larger, BAU larger, dominant
height, BF, RS, BS, WS, WP, RP, EH, OS, PO, RM, SM, YB, WB, WA, RO, OH, UK, live or
die


Mortal
ity
Check

diameter, height, plotBAS, plotBAH, plotBAU, BAS larger, BAH larger, BAU larger, dominant
height, BF, RS, BS, WS, WP, RP, EH, OS, PO, RM, SM, YB, WB, WA, RO, OH, UK, live or
die


The mortality tables contain the trees that have been sampled at le
ast two times over a
five year period. Mortality Training is 75% of the trees and Mortality Check is the
remaining 25%. From these tables, two tables are output for use in MATLAB. One file
contains all the information about the tree (excluding mortalit
y information) and the other
contains the mortality information.

Method that creates table: Mortality 1



Growth
Training

diameter, height, plotBAS, plotBAH, plotBAU, BAS larger, BAH larger, BAU larger, dominant
height, seasons, BF, RS, BS, WS, WP, RP, EH
, OS, PO, RM, SM, YB, WB, WA, RO, OH, UK,
diameter change


Growth
Training

diameter, height, plotBAS, plotBAH, plotBAU, BAS larger, BAH larger, BAU larger, dominant
height, seasons, BF, RS, BS, WS, WP, RP, EH, OS, PO, RM, SM, YB, WB, WA, RO, OH, UK,
diame
ter change


The growth tables contain only the trees that have survived for at least one five year
period. Growth Training is 75% of the trees and Growth Check is the remaining 25%.
From these tables, two tables are output for use in MATLAB. One file c
ontains all the
Page
37

information about the tree (excluding diameter change information) and the other
contains the diameter change information.

Method that creates table: Mortality 2





Page
38

Appendix B.2 Data Base Tables and Relational Structure


Page
39

Appendix B.3
-
4D Database Structure


The databases were implemented using the 4
-
D database software. The 4
-
D structure diagram is shown
below.






Page
40

Appendix B
-
4 4
-
D Data Base Methods (Macros)


The 4
-
D data base system allows the users to
write “methods” using the 4
-
D language. In other
systems, methods are often referred to as macros. These methods allow the user to process the
data base in quite sophisticated ways and to create a variety of output tables.

Some 24 methods have been crea
ted to process the tables of the 4
-
D data base. Since there is a
relatively large amount of data to be dealt with, the methods were broken down into small parts
that each performs one operation. The following methods were used in processing the data. The

method code can be found with the database itself.


Identifier 1

This method assigns a unique number to each plot, subplot and year combination in the
sample information table by first ordering the data by ascending plot number, ascending
subplot number a
nd ascending sample year and then sequentially numbering the
combinations. This makes future methods much simpler since comparisons can be done
on one number to determine if three values are also equal.



Identifier 2

Transcribes the unique number from t
he sample information table to each tree that is
involved in the plot, subplot and year in the tree information table. This is done by first
ordering the data in both tables by ascending plot, ascending subplot and ascending
sample year and then comparing
these values. If all three are equal, the identifier number
is copied onto the tree.


Wood Type

Records the type of wood (hard or soft) for each tree in the tree information table based
on the species of the tree. This method searches the list of speci
es types, finds the species
of the tree and copies the type of wood from the species table to each tree.


Basal Area

Calculates the basal area of each tree in the tree information table by cycling through
each tree and doing the calculation based on the di
ameter at breast height.


Basal Area Below

Calculates the total basal area of softwood, hardwood and unknown that is lower than the
current tree for each plot and sampling year. The tree information is ordered by
ascending identifier number and ascending
breast height and sample information is
ordered on identifier. While the diameter is equal, the basal area is summed. Once a
different diameter is encountered, the area is recorded. This process leaves the trees that
were passed without a recorded basal
area.



Basal Area Below2

As mentioned in basal area below, there are gaps in the records that need to be filled.
This method fills in the basal areas that are excluded by Basal Area Below. The tree
information is ordered by ascending identifier and de
scending diameter at breast height.
Page
41

This places the recorded basal area below at the top of the list for each diameter. The
basal area is copied down until a new diameter is reached.


Total Basal Area

Calculates the total basal area of each plot for ea
ch sampling year. The sample
information table and tree information table are sorted ascending on the identifier number
(plot, subplot and sample year) and while the identifier numbers are equal the basal area
from each tree is added to the total. When t
he tree information identifier no longer equals
the sample information identifier, the total basal area for softwood, hardwood and
unknown are recorded in the sample information table.



Date Repair

Several trees had the year of sampling improperly recorde
d. This method replaces
incorrect years with correct years obtained from the sample information table.


Live or Die 1

Transcribes the information for all trees that have at least two samples from the tree
information table to the live or die table. The t
ree information table is sorted by
ascending plot, ascending subplot, ascending tree, and ascending sample year. A check is
made for living trees (status 1 or 3); this prevents excessive copying of dead tree
information. Samples starting after 2000 are e
xcluded since the data for 2005 and
beyond is not available yet. A record is created and the tree information is copied into it,
then the date information for the tree next in line (possibly the next sample or a different
tree). A check is made to ensure
that the second tree was the next sample not a different
tree, if this checks out the routine continues through the remaining trees, if not the record
is deleted.


Live or Die 2

Assigns the alive or dead field for each tree in the live or die table by co
mparing the tree
health for each tree. Living trees get assigned a 1 and dead trees a 0.


Live or Die 3

Based on the alive or dead field, this method transcribes the information for the living
trees into the diameter table. If the tree has a 1 assigned b
y Live or Die 2, then a record is
created in Diameter, and the information is copied from Live or Die into the Diameter
table.


Live or Die 4

For the records in the diameter table, the initial diameter and diameter change over the
sampling period is calcul
ated. The information in Diameter and tree information is
ordered by ascending plot, ascending subplot, ascending tree, and ascending sample year.
Several comparisons are made to ensure that the correct information is copied and then
the initial diameter
of the tree is transcribed and the diameter change over the sampling
period is calculated.



Output 1

Page
42

Transcribes the information from live or die into output 1. All the information in live or
die is copied into created records in output 1.




Output 2

Attaches the information from diameter to the information in output1. After ordering
output1 and diameter on ascending plot, ascending subplot, ascending tree and ascending
sample year some checks are made to ensure that the information is copied to the c
orrect
location and the diameter change and initial diameter are transcribed into output1.


Output 2a

Transcribes the diameter at breast height from the tree information table in to output1 for
trees not included in diameter. Method output2 only copies th
e diameter for living trees,
so this method transcribes the diameter for dead trees from tree information to output1 in
much the same manner as output2.



Output 3

Transcribes the plot basal area softwood, hardwood and unknown from the sample
information t
able into output1. Sample information and Output1 are ordered by
ascending plot, ascending subplot and ascending sample year and the values are
compared to ensure that the area information is copied to the correct location. The plot
basal area for softwo
od, hardwood and unknown are transcribed into the Output1 table.



Output 4

Calculates the basal area softwood larger, basal area hardwood larger and basal area
unknown larger based on the plot basal area and basal area below. Tree information and
Output1
are ordered by ascending plot, ascending subplot, ascending tree and ascending
sample year and the appropriate comparisons are done to confirm correct location. Using
the plot basal areas from method output 3, and the basal area below the basal area larg
er
than the tree in question is calculated for each plot.



Output 5

Converts the species number into the binary values of the 17 species fields. Using the
wood type information from Wood Type the tree is categorized as either hard or
softwood and based o
n this categorization the “other” column if filled with a 1. If the
species of tree is one of the tracked species then the “other” category is changed back to a
0 and the proper column changed to 1.



Output 6

Transcribes the height of each tree at the st
art of the five year period form the tree
information table. Tree information and Output1 are ordered by ascending plot,
ascending subplot, ascending tree and ascending sample year, after the appropriate
checks the height of each tree at the beginning of
the sampling period is transcribed to
Output1.




Output 7

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43

Calculates the dominant height of each plot and year based on the average height of the
three largest trees on each plot. The records in Output1 are ordered ascending by the
identifier number and
descending by the height. The top three heights are averaged and
this value is recorded as the dominant height, if less than three trees were recorded on a
plot the average of the number of trees recorded is used as the dominant height.


Output 8

Calculat
es the number of growing seasons between sampling dates. The growing season
was assumed to extend from June 1 to August 15. For samples taken during the growing
season, the number of days into the season is calculated and the fraction of a growing
season
is also calculated. Thus samples taken in May of one year and September five
years later have 6 growing seasons. Samples taken initially in September of a particular
year and May five years later have four growing seasons. A sample taken initially in
Sep
tember and subsequently on June 30, five years later will have 4 and 30/76 seasons of
growth.


Mortality 1

Separates the trees from Output1 into Mortality Training and Mortality Check, placing
75% in the former and 25% in the latter. Currently, this meth
od is set to filter any
seasons that are longer or shorter than 5. The split into the two tables is done by a
random number between 1 and 100, if the number if less than or equal to 25 the records
are copied to Mortality Check and if the random number is
larger than 25 the records are
copied into the Mortality Training table.


Mortality 2

Separates the trees from Output1 into Growth Training and Growth Check, placing 75%
in the former and 25% in the latter.

Currently, this method is set to filter any se
asons that
are longer or shorter than 5. The split into the two tables is done by a random number
between 1 and 100, if the number if less than or equal to 25 the records are copied to
Growth Check and if the random number is larger than 25 the records ar
e copied into the
Growth Training table.


Mortality
3

This method is the same as Mortality 2, except is fills Grow Training2 and Grow Check2,
which are aggregated tables that remove the distinction between softwood, hardwood and
unknown wood and carry on
ly the percentage of wood that is softwood. These tables
were used during the initial testing periods to determine if a lower number of fields
would allow the use of Levenberg
-
Marrquardt in the training of the neural network. This
is discussed later.