A neural network approach to identify forest standssusceptible to wind damage

Marc Hanewinkela,*, Wenchao Zhoub, Christian Schilla

aInstitute of Forestry Economics (IFE), University of Freiburg, Tennenbacherstr. 4, D-79106 Freiburg, GermanybInstitute of Forest Economics, Swedish Agricultural University, 90183 Umea, Sweden

Received 23 September 2002; received in revised form 18 November 2003; accepted 20 February 2004

Abstract

The artificial neural network technique to model wind damage to forests was examined. The network used in the investigation

was a three-layered feed-forward neural network with a backpropagation training-algorithm using a momentum term and flat

spot elimination. To yield insights into the performance of the network, a logistic regression model was fitted as a baseline. Two

different types of models were set up and analyzed for both approaches. A dichotomous model that predicted the categories

‘‘damaged’’ versus ‘‘undamaged’’ for two different damage thresholds and a multinomial model that predicted the damage in

four damage classes. The performance of the network and the logistic regression model was measured using the mean squared

sensitivity error. The results of the dichotomous model demonstrate that a feed-forward network is able to better classify forests

susceptible to wind damage than a logistic regression model, especially when the frequency of the undamaged and damaged

forest stands differs significantly. This study also shows that the network has a higher capacity to identify damaged forest stands,

compared to the logistic regression model applied in this investigation. With the specific dataset used in the present study, the

proportion of damaged forest stands predicted by the network was between the observed proportion and the proportion predicted

by the logistic regression model. The results of the multinomial models showed that both, the statistical model and the neural

network were unable to classify all four damage classes but showed a dichotomous behavior in predicting the damage only in the

two extreme damage classes. Possibilities to optimize the network performance by using different training algorithms or

topologies and principal differences between the two models referring to their specific properties are discussed.

# 2004 Elsevier B.V. All rights reserved.

Keywords: Logistic regression model; Backpropagation; Dichotomous model; Multinomial model; Risk management

1. Introduction

Climatic hazards, causing damages to forests

mainly in the form of storms or snowbreakage have

reached a level that is constantly threatening regular

forest management. The storm of February 1990

caused more than 100 million m3 of damage to the

forests of Europe. After the catastrophic gale of 26

December 1999 in France and Germany, where

more than 30 million m3 of timber were blown down

only in Southwest Germany (Baden-Wurttemberg), a

necessity of proper risk management is obvious.

Beside these catastrophic events we have to consider

a constant high level of so-called ‘‘incidental exploi-

tations’’. An investigation of Hanewinkel (2001)

Forest Ecology and Management 196 (2004) 227–243

* Corresponding author. Tel.: þ49-761-203-3686;

fax: þ49-761-203-3690.

E-mail address: m.hanewinkel@ife.uni-freiburg.de

(M. Hanewinkel).

0378-1127/$ – see front matter # 2004 Elsevier B.V. All rights reserved.

doi:10.1016/j.foreco.2004.02.056

showed that the percentage of exploitations that were

not the result of planned silvicultural interventions

but were due to the impact mainly of storm and

snow reached 44% for the period of 1980–1994 in

the state-forest of the northern Black Forest.

Several distinctly different ways for risk assessment

have been developed. The first one is sometimes only

partly a scientific approach. Based on an extensive

literature review or even only on local experience, an

expert system assigns forest stands and/or site units to

risk classes using more ore less simple expert rules. An

example for such an expert system is a scheme to

estimate the risk for storm damage in forest stands in

South Germany by Rottmann (1986, p. 96), or a

similar approach for snow damage by the same author

(Rottmann, 1985, p. 111). Mitchell (1998) has devel-

oped a diagnostic framework for windthrow risk esti-

mation in Canada that is very similar to an expert

system.

In addition to expert systems mechanistic models or

empirical mechanistic models such as HWIND (Pel-

tola et al., 1999) or GALES (Gardiner and Quine,

2000) have been developed as generic tools for risk

assessment and tested against each other (Gardiner

et al., 2000). Both of these tools require a very high

quality of input data and are primarily meant to be

used to evaluate the risk linked to a particular regime

of management. Component models integrate the risk

assessment on different levels, from single trees to

stands and whole regions (Talkkari et al., 2000).

Meteorological components of the models such as

windspeed or airflow modeling (Konig, 1995; Lekes

and Dandul, 2000) seek to improve the performance of

the risk assessment. An overview of different model

approaches for risk assessment that is accessible via

the World Wide Web is given by Miller et al. (2000).

However, the most common way to assess risk on a

scientific base is still the use of statistical models.

These models use data of historical damage occur-

rences to predict future risk events or to classify forests

according to their vulnerability towards risks. A clas-

sic deterministic approach is thereby to derive transi-

tion probabilities for age classes of stand types on

defined site units. The theory behind these models has

mainly been developed by Suzuki (1971) based on

Markov-chains. This approach has been widely

applied in eastern Germany for forests dominated

by Norway spruce (Kurth et al., 1987). The standard

tool to predict risk for forests or forest stands is usually

a variant of a regression model. Thereby, the logistic

regression model has been utilized as the most com-

mon statistical approach to examine wind damage to

forests (Hinrichs, 1994; Konig, 1995; Fridman and

Valinger, 1998; Valinger and Fridman, 1997, 1999;

Jalkanen and Mattila, 2000; Mitchell et al., 2001).

This technique was mainly successful when it was

applied for numerically analyzing influential factors

causing wind damages. The different factors that were

analyzed in the different studies vary widely. Hinrichs

(1994) uses the same variables to model wind damage

as in the present study (see Section 3). Konig (1995)

basically adds wind speed as an explaining variable.

Fridman and Valinger (1998) use stem volume, dbh, h/

dbh, taper, mean diameter, mean height, N/ha, basal

area, volume index and site index as independent

variables. According to the basic logistic regression

model developed by Jalkanen and Mattila (2000), the

susceptibility of a stand to wind damage was increased

by large mean diameter, high stand age, seed-tree

cutting (felling), special cutting (tree felling for

ditches, roads or power lines, or sanitation cutting

after damage), and decreasing temperature sum. Key

variables in the models built by Mitchell et al. (2001)

included site quality, stocking boundary orientation,

time since harvest and topographic exposure. As a

classifier for wind damage to forests, however, the

logistic regression model did not always perform as

well as one might hope. Its ability to predict damages

to forest stands decreases, especially when the number

of undamaged and damaged stands in the sample

dataset to which the logistic regression model is fitted,

differs significantly. The study of Fridman and Valin-

ger (1998), for example, showed that with the specific

dataset used in that investigation, the predicted pro-

portion of damaged plots was highly over-estimated.

The low performance of the logistic regression models

necessitates efforts to find new approaches to classify

wind damage to forests.

2. Goal of the investigation

Goal of the present study was to predict the prob-

ability and intensity of wind damage for a given stand

and its vulnerability towards this kind of damage using

rather simple and easy to assess inventory and booking

228 M. Hanewinkel et al. / Forest Ecology and Management 196 (2004) 227–243

data. In order to improve the weak performance of the

commonly used logistic regression models that is

reported in the literature in these cases, a new meth-

odology for damage prediction was tested.

In this study, the possibility of using an artificial

neural network as an alternative approach to identify

forest stands susceptible to wind damage was there-

fore investigated. A second goal of the investigation

was to compare the performance of the classical

statistical approach with that of the neural network.

3. Materials and methods

3.1. Neural networks—a brief introduction

An artificial neural network (ANN) is a technology

in the field of artificial intelligence that is especially

designed to deal with complex and ill defined problems,

for example, pattern recognition (Patterson, 1996).

ANNs are able to learn from incomplete, disturbed

and ‘‘noisy’’ datasets. Therefore, they should be espe-

cially suited to deal with data concerning risk like in the

present investigation. Applications of ANNs in forestry

mainly deal with mortality estimation (Guan and Gert-

ner, 1991a,b, 1995), uncertainty assessment of forest

growth models (Guan et al., 1997) or multi resource

forest land use planning (Nogami, 1991).

The first step to start a risk analysis using artificial

neural networks is to define the decisive input vari-

ables that will be used for the input layers of the

network. In our case this input is defined by the

parameters of the inventory (stand description,

Fig. 1). In a next step the topology (the architecture)

of the neural network to be used has to be defined. As

there is no general rule or recipe how to design the

network (Nauck et al., 1994) this is a very complex

trial and error process.

The different nodes (perceptrons) of the neural

network are connected to each other with weights.

Each perceptron evaluates the sum of the weighted

inputs by a special activation function and ‘‘fires’’ this

result to each perceptron to which its output is con-

nected. In the present investigation the processing

units in the networks used a logistic activation func-

tion of the form:

f ðxÞ ¼ ½1 þ expð�xÞ��1(1)

where x is the activation of the processing unit exclud-

ing all the units in the input layer.

The final output value that leaves the output layer of

the neural network is compared to a target value. The

difference between these two values which represents

the error of the network is minimized by backpropa-

gating this error through the net and adjusting the

weights between the different perceptrons. The target

values (the output for the different damage types) were

standardized using a linear standardization method to

force them into the range of the activation function.

The error function that calculates the mean quad-

ratic error for each input pattern has the following

form:

Ep ¼ 1

2

Xm

k¼1

ðtpk � z

pkÞ

2(2)

with: 1; . . . ; p the number of training patterns; tpk the

known output of kth variable of training pattern p; zpk

the calculated value for variable k in training pattern p;

k ¼ 1; . . . ;m number of variables describing one input

pattern.

This type of ‘‘supervised learning’’ uses the back-

propagation algorithm and the generalized delta rule

(Rumelhart and McClelland, 1986) to adjust the

weights of the different connections between the

nodes. The magnitude of the weight adjustment is

determined by the learning coefficient Z. The conver-

gence rate of the network can be improved by adding a

momentum term a to the gradient expression, that

means by adding a fraction of the previous to the

actual weight change (formula (3); Patterson, 1996,

p. 187 f):

Dwjðt þ 1Þ ¼ �Z@E

@wjðtÞþ aDwjðtÞ (3)

where DwjðtÞ is the previous weight change,

Dwjðt þ 1Þ the actual weight change, E the error, Zthe learning coefficient, and a the momentum term.

To adjust the weights within the described learning

process it is necessary to confront the network with a

training set. The performance of the net must then be

evaluated using a dataset that has not been part of the

training set. The type of architecture for an artificial

neural network and the learning procedure briefly

described here is only one possibility to design and

train an artificial neural network (Nauck et al., 1994).

M. Hanewinkel et al. / Forest Ecology and Management 196 (2004) 227–243 229

3.2. The topology of the neural network

The network used in this study was a general three-

layered feed-forward neural network trained with a

backpropagation algorithm with momentum term and

flat spot elimination called BackpropMomentum,

implemented in the neural network simulator SNNS

that was used in the present investigation (Zell et al.,

2000). Beside the usual learning parameter Z of the

standard backpropagation that specifies the step width

of the gradient descent, this enhanced backpropaga-

tion learning algorithm uses a momentum term m

0

200

400

600

800

1000

4 8 12 16 20 Age index

0%

20%

40%

60%

80%

100%

Perc

en

tag

e o

f d

am

ag

e

Frequency

(a)

0

200

400

600

800

1000

3 4 5 6 7 Height index

0%

20%

40%

60%

80%

100%

Perc

en

tag

e o

f d

am

ag

e

Frequency

(b)

0

200

400

600

800

1000

Other Spruce Species

0%

20%

40%

60%

80%

100%

Perc

en

tag

e o

f d

am

ag

e

Frequency

(c)

0

200

400

600

800

1000

N NE E SE S SW W NW Aspect

0%

20%

40%

60%

80%

100%

Perc

en

tag

e o

f d

am

ag

e

Frequency

(d)

0

200

400

600

800

1000

1 2 3 4 Site stability

0%

20%

40%

60%

80%

100%

Perc

en

tag

e o

f d

am

ag

e

Frequency

(e)

0

200

400

600

800

1000

400 450 500 550Elevation, m

0%

20%

40%

60%

80%

100%

Perc

en

tag

e o

f d

am

ag

e

Frequency

(f)

0

200

400

600

800

1000

0 5 10 15 20 25 Slope

0%

20%

40%

60%

80%

100%

Perc

en

tag

e o

f d

am

ag

e

Frequency

(g)

0

200

400

600

800

1000

0 50 100 150 Topex

0%

20%

40%

60%

80%

100%P

erc

en

tag

e o

f d

am

ag

eFrequency

(h)

Damaged Undamaged + Damaged Percentage of damage

Fig. 1. The relationships between the occurrence of damage and the variables.

230 M. Hanewinkel et al. / Forest Ecology and Management 196 (2004) 227–243

which defines a relative amount of the old weight

change that is added to the current change of the

weights and a flat spot elimination value c, a constant

value which is added to the derivative of the activation

function to enable the network to pass flat spots of the

error surface. To prevent over-training of the network

an additional parameter, dmax, defined as the max-

imum difference dj ¼ tj � oj between a teaching value

tj and an output oj of an output unit which was

tolerated and propagated back as dj ¼ 0 was also used

(Zell et al., 2000, 67ff).

Two different approaches to model damage to forest

stands due to storms were applied:

(i) A dichotomous model, which predicted damage

due to storm for forest stands as two categories

‘‘damaged’’ and ‘‘undamaged’’ according to a

predefined damage threshold. For this model the

network was composed of one input layer, one

hidden layer and one output layer. Dependent

upon the features of the variables in the dataset

used, the resulting size of the network was as

follows: 16 units (nodes) in the input layer

receiving inputs describing the stand state and

the site; 1 unit (node) in the output layer,

representing the damage due to storm of the

stand. For the hidden layer, five processing units

(nodes) were considered. Other training algo-

rithms and network topologies and different

settings of the above-mentioned parameters of

the network were examined in a sensitivity

analysis.

Thus, the output from the proposed network can

be explained as the estimated conditional prob-

ability of a forest stand being damaged given the

input vector, since the response from the output

unit is always between 0 and 1 (Hinton, 1989;

Guan and Gertner, 1991b). When the trained net-

work is applied to an unknown case, the output

unit receives activation, corresponding to each

vector of inputs. Based on the achieved activation

level the forest stand was classified as ‘‘unda-

maged’’ or ‘‘damaged’’. Damaged stands

exceeded the threshold of 0.5 for the activation

level. All other forests were classified as ‘‘unda-

maged’’.

(ii) A multinomial model that tried to predict damage

to forest stands due to storms in four different

damage classes. The same network type (three-

layered, feed-forward), learning algorithm and

activation function was applied in this model, but

the network topology was changed into a 16–5–4

structure with 16 nodes in the input, 5 in the

hidden and 4 units in the output layer. The four

output units encoded the four damage classes

using a 0/1-encoding scheme. Thus, damage

class 0 (very low damage) was represented as 0 0

0 1 in the output units, whilst damage class 3

(high damage) was encoded by 1 0 0 0, with the

damages classes 1 (0 0 1 0) and 2 (0 1 0 0) in

between. The output unit with the highest

activation level in the learned output was looked

upon as the ‘‘winning’’ unit that decided on the

resulting damage class (for example, see Table 8).

3.3. The logistic regression model

In order to obtain insights into the performance of

the different neural network models the following two

different statistical models were also fitted to the

dataset using a logistic regression (formula (2)):

lnp

1 � p

� �¼ b0 þ b1x1 þ b2x2 þ � � � þ bnxn (4)

where p is the probability of an arbitrary stand being

damaged, x1; x2; . . . ; xn the independent variables, and

b1; b2; . . . ; bn the parameters.

(i) For the dichotomous model wind damage to a

forest stand was treated as a binary event,

‘‘undamaged’’ (encoded as 0) or ‘‘damaged’’

(encoded as 1).

With the estimated parameters from (2) by

using logistic regression, the probability of

damage (p) for a forest stand was calculated as

p ¼ expðb0 þ b1x1 þ b2x2 þ � � � þ bnxnÞ1 þ expðb0 þ b1x1 þ b2x2 þ � � � þ bnxnÞ

(5)

The threshold between the undamaged and

damaged stand was set at 0.5. If the estimated

probability was higher than 0.5, then the stand

was classified as ‘‘damaged’’, or ‘‘undamaged’’

otherwise.

(ii) For the multinomial model a multinomial logistic

regression model (MLR) was fitted using the

M. Hanewinkel et al. / Forest Ecology and Management 196 (2004) 227–243 231

identical damage classes as for the multinomial

neural network model. The MLR model can be

described as

pj ¼expðb0;j þ x1b1;j þ x2b2;j þ � � � þ xnbn;jÞ

1 þP2

j¼0expðb0;j þ x1b1;j þ x2b2;j þ � � � þ xnbn;jÞ;

j ¼ 0; 1; 2 (6)

where pj is the probability of class j at an arbitrary

stand (the last class 3 is assumed to be the reference

class); xi the observed value of independent vari-

able i, i ¼ 1; . . . ; n; bi;j the parameter associated

with variable i for class j.

3.4. Performance measures

The performance of both the neural network and the

logistic regression model can be measured by the

sensitivity, which is defined as the proportion of events

labeled as a given class that are correctly identified

(Lawrence et al., 1998, 303). Table 1 shows a 2 2-

classification table illustrated for our classification

problem.

From Table 1, the sensitivity for each class can be

calculated. Specifically, the sensitivity of the class

‘‘Undamaged Stand’’, S0, which measures the propor-

tion of the correctly classified undamaged stands, can

be calculated as

S0 ¼ n00

n00 þ n01

(7)

The sensitivity of the class ‘‘Damaged Stand’’, S1,

which measures the proportion of the correctly clas-

sified damaged stands, is calculated as

S1 ¼ n11

n10 þ n11

(8)

The overall sensitivity, denoted by SS, can be calcu-

lated as

SS ¼ n00 þ n11

n00 þ n01 þ n10 þ n11

(9)

with n00 being a correctly classified undamaged stand,

n11 a correctly classified damaged stand, n01 an unda-

maged stand classified as damaged and n10 a damaged

stand classified as undamaged.

In the present study we used the mean squared

sensitivity error (MSSE), a performance measure

introduced by Lawrence et al. (1998), to evaluate

the performance of the neural network and the logistic

regression model. The MSSE was calculated by

MSSE ¼ 12½ð1 � S0Þ2 þ ð1 � S1Þ2� (10)

Since the sensitivities take values between 0 and 1, a

lower MSSE indicates a higher performance. Com-

pared to SS, MSSE as an overall performance measure

has the advantage of giving equal importance to each

class, instead of depending mostly on the most com-

mon class.

For the multinomial model the sensitivity and

MSSE were calculated, respectively, but instead of

using only two classes S0 and S1, four classes (S0, S1,

S2, S3) were included in the calculation.

By directly comparing the MSSE for the neural

network and the MSSE for the logistic regression

model, it was decided which of the two models

performed better for our classification problem. In

this paper, the sensitivity was expressed as a percen-

tage, while the MSSE was represented as a decimal

value.

3.5. Database of the investigation

The database of the present investigation was book-

ing records from the 4000 ha state forest unit ‘‘Beben-

hausen’’ in south-west Germany (Hinrichs, 1994). The

original dataset contained historical records of wind

damage to more than 2800 forest stands in the years

1967–1991. The complete investigated period was

divided into three sub-periods. Damage was expressed

as the average of the sub-period. In addition, regular

inventory data of the periodical forest management

that were assessed every 10 years (1967, 1977, 1987)

and a site classification characterized the forest stands

in terms of species composition, growing stock, age,

height and site unit. The input described the status of

the stand at the beginning of the sub-period for which

the damage was assessed. A GIS was used to deter-

mine the position of each stand and assign the site

units to the forest stands. Filtering out all stands

Table 1

Classification table for undamaged (0) and damaged stands (1)

Observed Predicted

Undamaged (0) Damaged (1)

Undamaged (0) n00 n01

Damaged (1) n10 n11

Rows are the observed values and columns are the predicted values.

232 M. Hanewinkel et al. / Forest Ecology and Management 196 (2004) 227–243

younger than 30 years reduced this dataset. Stands

with no recorded growing stock were also removed.

As a result, a total of 1600 stand records were

obtained. The reduced dataset was then used to gen-

erate the training and test sets for the neural network.

A test set (TTS) was generated by randomly selecting

400 stands (25%) from the reduced dataset. The rest of

the 1200 stands were used as a training set (TGS). Five

pairs of training- and test sets were obtained by

repeating this procedure. In the following they will

be referred to as: TGS-1/TTS-1; TGS-2/TTS-2; TGS-

3/TTS-3; TGS-4/TTS-4; TGS-5/TTS-5, respectively.

Defining whether a forest stand is damaged or not is

always somewhat arbitrary. In this study, the degree of

damage (damage rate) was calculated as a percentage

by dividing the recorded damage due to wind by the

standing volume of the forest stand. For the dichot-

omous model a predefined value of damage rate was

set as the cut line between ‘‘undamaged’’ and

‘‘damaged’’. Specifically, a forest stand was classified

as ‘‘undamaged’’ (encoded as 0) if the observed

damage rate was below 2%, otherwise as ‘‘damaged’’

(encoded as 1). Different values of the cut line will

result in different distributions of the frequency of the

undamaged and damaged stands; consequently, the

performance of the model may change more or less. In

order to determine the effectiveness of the cut value, a

damage rate of 5% was also used. For the multinomial

model the four damage classes were fixed at 0–2 (class

0), 2–5 (class 1), 5–10 (class 2) and >10% (class 3).

This classification follows a scheme proposed by

Hinrichs (1994), where a 2%-damage is considered

to be a low damage that already leads to higher costs

for salvage cuttings. A damage of 10% is considered to

be a ‘‘high damage’’ that severely influences the

stability of a stand and leads to larger gaps or open

areas. A 5%-damage is already visible in aerial photo-

graphs (Hinrichs, 1994, 51).

For each of the generated datasets, the frequency of

the undamaged and damaged stands for the dichot-

omous model is depicted in Table 2. It is obvious that

the frequency of the undamaged and damaged stands

was significantly unbalanced. The proportion of

damaged stands amounted to around 30% in all the

sets when 2% of damage rate was used as the cut value,

and to around 20% when 5% was used. Table 3 shows

how the percentage of the damaged stands in the test

sets is reduced when four different damage classes are

formed in the multinomial model. Risk class 2 (5–

10%) reaches a level of less then 9% of damaged

stands in all the test sets, while classes 1 and 3 are

within 9 and 13%. For the training sets the shares of

the different risk classes were within the same range as

for the test sets.

Table 2

Frequency distribution of undamaged and damaged stands in training sets (TGS) and test sets (TTS) for the dichotomous model

Damage rate 2% as cut value Damage rate 5% as cut value

Undamaged 0 Damaged 1 Percentagea Undamaged 0 Damaged 1 Percentage

TGS-1 858 342 28.5 972 228 19.0

TTS-1 274 126 31.5 323 77 19.2

TGS-2 854 346 28.8 969 231 19.3

TTS-2 277 123 30.8 326 74 18.5

TGS-3 855 345 28.8 974 226 18.8

TTS-3 277 123 30.8 321 79 19.8

TGS-4 854 346 28.8 976 224 18.7

TTS-4 278 122 30.5 319 81 20.3

TGS-5 844 356 29.7 969 231 19.3

TTS-5 288 112 28.0 329 71 17.75

Of a total of 1600 stands, 400 are randomly selected, forming a test set. The rest, 1200 stands, are used for training. Five pairs of training and

test sets are generated. They are referred to as TGS-1/TTS-1, TGS-2/TTS-2, TGS-3/TTS-3, TGS-4/TTS-4, and TGS-5/TTS-5, respectively.a The percentage of the observed damaged stands.

M. Hanewinkel et al. / Forest Ecology and Management 196 (2004) 227–243 233

The stand age, the dominant height of the stand, the

tree species, the site stability for Norway spruce, the

aspect, elevation, slope, and Topex1 of the site were

selected as preliminary input variables. Fig. 1 shows

the relationships between the occurrence of damage

and these variables using the reduced dataset, where a

damage rate of 2% is used as the cut line between

‘‘undamaged’’ and ‘‘damaged’’. The proportion of

damaged stands changes significantly as the stand

age index increases (Fig. 1a), and when the site aspect

varies (Fig. 1d). It increases as the height index

increases (Fig. 1b), and when the stand changes from

non-spruced to spruced-dominated stands (Fig. 1c).

On the other hand, no clear tendencies are observed

between the occurrence of damage and the variables

site stability, elevation, slope or Topex. Fig. 1 reveals

that the database implies some difficulties for a mod-

eling approach.

In the reduced dataset, ‘‘site stability’’ as fixed by

the site classification was formulated as an ordinal

variable with four values between 1 (stable) and 4

(unstable). For the logistic regression model, the

stability was directly presented to the model as a

categorical variable. For the neural network, it was

encoded as an ordinal variable and presented to the net

as a so-called thermometer (Master 1993, 260–262),

thus requiring only three input units. The variable

‘‘tree species’’ was presented as a categorical variable

to both the logistic regression model and the network.

It was encoded by giving a value of 0 for spruce

while all other species (Not spruce) were given the

number 1.

The variable ‘‘aspect’’ was measured by degree in

the interval of 0–360 using a digital terrain model

within the GIS as the source of information. For the

logistic regression model, aspect was classified into

eight directions (north, northeast, east, southeast,

south, southwest, west, and northwest) and presented

as a categorical variable. The same classification

system was applied to the neural network, for which

the eight directions of aspect were encoded into seven

8-tupels using the n � 1 encoding scheme recom-

mended for the type of learning algorithm that was

used in the present investigation.

For the logistic regression model, the variables

elevation, slope, and Topex were directly presented

to the model as continuous variables in the measured

values. For the network model, they were scaled to be

in the interval of [0, 1] using formula zi ¼ ðyi � yminÞ/ðymax � yminÞ in order to make training faster and

reduce the chances of getting stuck in local optima.

3.6. Training procedure

After trying several levels and combinations of the

learning parameters for the BackpropMomentum

algorithm the learning rate Z was set at 0.02 with a

momentum m of 0.02, a flat spot elimination value c of

0.1 and dmax of 0.1. This configuration of the net was

used for all the training- and test runs with the datasets

TGS1/TTS1–TGS5/TTS5. Alterations of these para-

meter settings were subject to a sensitivity analysis

that was applied only to selected training- and test-

sets. The training procedure was run iteratively to

minimize the mean squared error (MSE) that was

Table 3

Percentage of the different risk classes (observed damaged stands) in the test sets for the multinomial model

Class 0 (0–2%)a Class 1 (2–5%)a Class 2 (5–10%)a Class 3 (>10%)a

TTS-1 68.5 12.3 7.3 12.0

TTS-2 69.5 12.0 5.8 12.8

TTS-3 69.3 11.0 8.8 11.0

TTS-4 69.5 10.3 8.3 12.0

TTS-5 72.0 10.3 8.5 9.3

a Damage rate.

1 The Topex score is assessed by measuring the angle of

elevation in degrees from a fixed point to the horizon for a

predetermined number of compass directions (Pyatt, 1969). The

sum of all the angles taken at each sample point is the Topex score.

In the present investigation, the Topex was calculated based on the

GIS and the digital terrain model, where eight directions (north,

northeast, east, southeast, south, southwest, west, and southwest)

are considered.

234 M. Hanewinkel et al. / Forest Ecology and Management 196 (2004) 227–243

controlled on a logfile-panel and an error-graph of the

network simulator. To avoid over-fitting (over-train-

ing) of the network the training process was stopped

after 2000 epochs. The epoch size was set to the

number of samples of the whole training set. Specific

to our dataset, the epoch size was 1200. The obtained

network was then applied to the test set, and the

performance measures were calculated. In order to

alleviate the influence of the initial value of the

weights and the danger of dropping into a local

minimum, 10 trials were performed for each training

and test set, the median of which were considered as

the final performance measure.

We fitted the logistic regression model for the

dichotomous approach by using the binary logistic

regression procedure implemented in SPSS for win-

dows (SPSS for Windows 10.0, 2000), which derives

the parameters through maximum likelihood estima-

tion. For the multinomial model the multinomial

logistic regression procedure was applied that uses

the same estimation method (SPSS for Windows 10.0,

2000). We started with a model including all the eight

variables as stated in the previous section. Then, a

backward stepwise procedure using the Bayesian

Information Criterion (BIC) (Schwarz, 1978) as vari-

able removal criterion was used to eliminate the non-

significant variables and to select the most appropriate

models. The BIC can be calculated by

BIC ¼ �2 lnðLÞ þ ð1 þ kÞ lnðnÞ (11)

where L is the model’s likelihood, k the number of

explanatory variables, and n the total number of

samples.

The fitted model was then applied to the test data.

The probability of the occurrence of a stand being

damaged (dichotomous model) or belonging to one of

the four damage classes (multinomial model) was

predicted for each stand contained in the set. The

performance measures were finally calculated for the

logistic regression model.

4. Results

4.1. Comparison of the dichotomous models

The parameter estimates for variables included in

the fitted logistic regression model are listed in Table 4

with a damage rate of 2% and in Table 5 with a damage

rate of 5% as cut value between undamaged and

damaged. Tables 4 and 5 show that four variables

enter all the fitted models, including stand age, tree

species, dominant height and aspect. In contrast, the

variables ‘‘site-stability for Norway spruce’’, eleva-

tion, slope and Topex are not selected for all the cases.

No effort to explain this phenomenon is taken here

since the purpose of this study is to investigate the

performance of the trained neural network compared

to the fitted logistic regression model when they are

applied to test sets identical for both models.

Fig. 2 shows the performances of the trained net-

work and the fitted logistic regression model measured

by MSSE when they are applied to the test sets. Fig. 2a

demonstrates for each of the five test sets that the

median of the MSSE for the neural net is lower than

the MSSE for the logistic regression model when the

cut value between the undamaged and damaged stand

is set at a damage rate of 2%. This indicates that the

neural network might perform better than the logistic

regression model. However, the differences between

the two models for the lower damage rate especially

for the test sets TTS1 and TTS4 are rather small (see

also the sensitivity in Fig. 3.a.2). Further, Fig. 2b

shows that the performance of the network can be

more promising compared to the logistic regression

model if 5% is used as cut value. In addition, it can be

observed that both models tend to perform worse when

the cut value changes from 2 to 5%. As shown in

Table 1, an increase of the cut value from 2 to 5%

actually changes the distribution of the frequency of

both the undamaged and damaged stands in the train-

ing and test set. More specifically, a change of the cut

value from 2 to 5% results in a reduction of the

proportion of the damaged stands from around 30

to 20%. Consequently, both the trained network and

the fitted logistic regression model show a lower

performance, since the number of the damaged stands

is further reduced in favor of the undamaged stands.

Thus, the results of the present study indicate that the

neural network may be preferable as a classifier for a

dichotomous approach compared to a logistic regres-

sion model, when the frequencies of the classes vary

significantly.

Fig. 3 shows the sensitivity of the models when they

are applied to the test sets under different cut values

between undamaged and damaged. Both Fig. 3.a.1 and

M. Hanewinkel et al. / Forest Ecology and Management 196 (2004) 227–243 235

3.b.1, demonstrate that the sensitivity for the argument

‘‘undamaged stand’’ is in most cases somewhat lower

for the neural network than for the logistic regression

model. This means that the ability of the neural net-

work to correctly classify undamaged stands may

sometimes be lower than the logistic regression

model. However, looking at Fig. 3.a.2 and 3.b.2 it

should be noted that the neural network performs

much better than the logistic regression model in

identifying damaged stands, especially when the cut

value between undamaged and damaged is set at 5%.

Fig. 3.a.3 and 3.b.3 give the overall sensitivity for both

Table 4

Parameter estimates for variables included in the fitted logistic regression model

Code TGS-1 TGS-2 TGS-3 TGS-4 TGS-5

Constant �5.565 �5.863 �5.794 �8.896 �5.625

Age �0.278 �0.302 �0.283 �0.276 �0.303

(55.082)a (65.916) (52.157) (52.345) (60.808)

Species 0 Not spruce �0.602 �0.486 �0.668 �0.702 �0.663

(7.277) (2.035) (10.422) (12.484) (10.437)

Height 1.063 1.151 1.136 1.096 1.123

(107.836) (127.125) (119.023) (114.233) (116.635)

Aspectb (14.327) (10.728) (10.559) (14.932) (15.654)

1 N 1.561 1.263 1.348 4.392 1.475

2 NE 1.996 1.967 1.897 5.251 1.894

3 E 2.136 2.167 2.087 5.370 2.372

4 SE 2.175 2.088 1.925 5.179 1.882

5 S 1.556 1.652 1.496 4.835 1.695

6 SW 1.394 1.545 1.365 4.733 1.532

7 W 1.971 1.918 1.652 5.189 2.088

BICa 1254.542 1248.796 1238.025 1238.463 1256.142

Percentage of correct

classification

Undamaged 90.2 89.2 89.2 88.6 89.7

Damaged 35.7 37.9 39.1 43.6 40.2

Total 74.7 74.4 74.8 75.7 75.0

MSSEc 0.2115 0.1987 0.1913 0.1655 0.1841

Damage rate (defined as the rate of recorded storm damage of a stand in percent of its standing volume) 2% as the cut value between the

undamaged (encoded as 0) and damaged stand (encoded as 1).a The Bayesian Information Criterion (Schwarz, 1978). The values in the parenthesis are the changes in BIC if the term were removed from

the fitted model.b North west (code: 8) was used as reference.c Mean squared sensitivity error.

0,0

0,2

0,4

0,6

0,8

1,0

TTS-1 TTS-2 TTS-3 TTS-4 TTS-5

MS

SE

Logistic Model

Neural Network

0,0

0,2

0,4

0,6

0,8

1,0

TTS-1 TTS-2 TTS-3 TTS-4 TTS-5

MS

SE

Logistic Model

Neural Network

(a) (b)

Fig. 2. Performance of the fitted logistic regression model and the trained neural network when they are applied to test sets, including: TTS-1,

TTS-2, TTS-3, TTS-4 and TTS-5. The performance is measured by mean squared sensitivity error. The MSSEs for the neural network are the

median value of the MSSE of 10 trials. (a) Damage rate 2% as cut line between undamaged and damaged stand, (b) damage rate 5% as cut line

between undamaged and damaged stand.

236 M. Hanewinkel et al. / Forest Ecology and Management 196 (2004) 227–243

models. Under this overall evaluation criterion, the

performance of the neural network is only slightly

different from the logistic regression model. As a

general observation it can be noted that for the dichot-

omous model the network has a distinctly stronger

ability to identify damaged stands, compared to the

logistic regression model. This significant advantage

may be accompanied by a slight loss in precision on

the side of the undamaged stands.

Table 6 lists the proportion of the observed and the

predicted number of damaged stands by the logistic

regression model and the neural network for the test

sets. In general, it can be noted that both the logistic

regression model and the network tend to under-pre-

dict the proportion of damaged stands. However, using

a neural network instead of a logistic regression model

can increase the number of correctly predicted

damaged stands. Specific to the database used in this

investigation is that, with a damage rate of 2% as the

cut value between undamaged and damaged, the

observed proportion of damaged stands is about

30%. The predicted proportion of damaged stands

is about 20% when the logistic regression model is

applied. This proportion increases to an average of

23% when the neural network model is used. When a

damage rate of 5% is used as the cut value, the

observed proportion of damaged stands amounts to

about 20%. The predicted proportion of damaged

stands is then only about 6% for the logistic regression

model, but 14% for the network.

4.2. Comparison of the multinomial models

Table 7 shows the parameter estimates for the

variables that were included in the fitted multinomial

logistic regression using the Bayesian Information

Table 5

Parameter estimates for variables included in the fitted logistic regression model

Code TGS-1 TGS-2 TGS-3 TGS-4 TGS-5

Constant �5.104 �5.616 �5.196 �9.651 �5.424

Age �0.215 �0.285 �0.250 �0.293 �0.258

(18.592)a (34.623) (21.744) (31.473) (25.463)

Species 0 Not spruce �0.903 �0.782 �0.994 �0.942 �0.934

(17.585) (11.119) (22.384) (19.305) (19.298)

Height 0.908 1.104 1.005 1.099 1.040

(55.852) (82.002) (62.989) (75.762) (70.210)

Aspectb (12.400) (9.638) (5.512) (13.660) (9.182)

1 N 1.332 1.243 1.123 5.206 1.295

2 NE 1.301 1.389 1.276 5.652 1.299

3 E 1.517 1.472 1.313 5.600 1.639

4 SE 1.495 1.495 0.228 5.582 1.148

5 S 0.669 0.526 0.567 4.734 0.772

6 SW 0.669 1.065 0.749 4.994 0.839

7 W 1.138 1.289 0.883 5.551 1.383

BICa 1035.946 1012.733 1008.362 981.617 1025.719

Percentage of correct

classification

Undamaged 96.5 95.8 95.8 95.7 95.5

Damaged 12.7 21.6 16.8 20.1 17.5

Total 80.6 81.5 80.9 81.6 80.3

MSSEc 0.3817 0.3082 0.3470 0.3201 0.3413

Damage rate (defined as the rate of recorded storm damage of a stand in percent of its standing volume) 5% as the cut value between the

undamaged (encoded as 0) and damaged stand (encoded as 1).a The Bayesian Information Criterion (Schwarz, 1978). The values in the parenthesis are the changes in BIC if the term were removed from

the fitted model.b North west (encoded as 8) was used as reference.c Mean squared sensitivity error.

M. Hanewinkel et al. / Forest Ecology and Management 196 (2004) 227–243 237

Criterion. The fitted models for all training sets only

use four variables: age, species, height and slope. The

variable aspect that entered the binary models

(Tables 4 and 5) was not selected. Secondly it can

be observed that the model is not able to predict the

damage classes 1 and 2, but shows instead a dichot-

omous behavior in assigning the stands in the training-

(and test-) sets either to damage class 0 or 3. The

sensitivity for damaged stands in the training sets is

distinctly lower than for the 2% binary model (Table 4)

and lower than for the 5% damage rate (Table 5)

especially for the training sets 1, 2 and 4, while the

training sets 3 and 5 show a slightly higher sensitivity

than the 5% binary model. Overall sensitivity

decreases by 10% compared to the dichotomous

model with 5% damage rate due to 0-sensitivity in

damage classes 1 and 2.

Table 8, in which the performance of both multi-

nomial models when applied to the test sets is

depicted, reveals that the neural network shows the

same behavior as the logistic multinomial regression.

Damage classes 1 and 2 are not identified by the

network with multiple outputs, a damaged stand is

either assigned to damage class 0 or 3. Except training

set 1, the sensitivity for damage class 3 of the neural

network with multiple outputs is higher and the MSSE

is lower than the multinomial regression model which

may again indicate a higher performance of the neural

network to detect damaged stands. The sensitivity for

undamaged stands is again slightly lower for the

a.1 Sensitivity for Undamaged Stand

0

20

40

60

80

100

TTS-1 TTS-2 TTS-3 TTS-4 TTS-5

Sen

siti

vit

y [

%]

b.1 Sensitivity for Undamaged Stand

0

20

40

60

80

100

TTS-1 TTS-2 TTS-3 TTS-4 TTS-5

Sen

siti

vit

y [

%]

a.2 Sensitivity for Damaged Stand

0

20

40

60

80

100

TTS-1 TTS-2 TTS-3 TTS-4 TTS-5

Sen

siti

vty

[%

]

b.2 Sensitivity for Damaged Stand

0

20

40

60

80

100

TTS-1 TTS-2 TTS-3 TTS-4 TTS-5S

en

siti

vit

y [

%]

a.3 Overall Sensitivity

0

20

40

60

80

100

TTS-1 TTS-2 TTS-3 TTS-4 TTS-5

Sen

siti

vty

[%

]

b.3 Overall Sensitivity

0

20

40

60

80

100

TTS-1 TTS-2 TTS-3 TTS-4 TTS-5

Sen

siti

vit

y [

%]

Logistic Model Neural Network

(a) (b)

Fig. 3. Sensitivities of the fitted logistic regression model and the trained neural network when they are applied to test sets, including: TTS-1,

TTS-2, TTS-3, TTS-4 and TTS-5. The sensitivities for the neural network are the median value of the sensitivity of 10 trials. (a) Damage rate

2% as cut line between undamaged and damaged stand, (b) damage rate 5% as cut line between undamaged and damaged stand.

238 M. Hanewinkel et al. / Forest Ecology and Management 196 (2004) 227–243

Table 6

Proportion (%) of observed damaged and predicted damaged stands for test sets (dichotomous model)

Undamaged stands Damaged stands

Observed Network Logistic model Observed Network Logistic model

Damage rate 2% as cut line between undamaged and damaged stand

TTS-1 68.5 76.2 80.8 31.5 23.8 19.3

TTS-2 69.5 78.5 83.5 30.5 21.6 16.5

TTS-3 69.3 74.7 83.8 30.8 25.3 16.3

TTS-4 69.5 77.1 78.8 30.5 22.9 21.3

TTS-5 72.0 77.9 80.8 28.0 22.1 19.2

Damage rate 5% as cut line between undamaged and damaged stand

TTS-1 80.75 87.6 95.0 19.25 12.5 5.0

TTS-2 81.50 85.4 94.0 18.50 14.7 6.0

TTS-3 80.25 83.8 94.0 19.75 16.3 6.0

TTS-4 79.75 84.8 93.0 20.25 15.2 7.0

TTS-5 82.25 89.5 93.0 17.75 10.5 7.0

Table 7

Parameter estimates for variables included in the fitted multinomial logistical regression model

Category Constant Age Species, 0 (not spruce) Height Slope Sensitivity S (%) MSSEa

TGS-1 0 4.200 0.301 1.173 �1.142 0.091 97.4

1 �0.248 0.002 1.117 �0.129 0.074 0 0.6988

2 �0.333 0.106 0.689 �0.241 0.045 0

3b 10.9

Overall 70.8

TGS-2 0 4.816 0.360 1.280 �1.318 0.060 97.1

1 0.273 0.099 1.356 �0.373 0.056 0 0.6805

2 �0.310 0.078 1.091 �0.162 �0.001 0

3 15.1

Overall 70.7

TGS-3 0 4.434 0.330 1.305 �1.255 0.108 96.4 0.6682

1 �0.317 0.069 1.267 �0.223 0.074 0

2 �0.446 0.086 0.752 �0.233 0.076 0

3 18.0

Overall 70.7

TGS-4 0 4.503 0.379 1.232 �1.307 0.072 97.3

1 0.254 0.164 1.015 �0.454 0.068 0 0.6820

2 �0.785 0.102 0.622 �0.144 0.037 0

3 14.7

Overall 70.8

TGS-5 0 4.595 0.332 1.173 �1.260 0.072 96.4

1 0.454 0.047 1.026 �0.327 0.074 0 0.6632

2 �0.243 0.077 0.638 �0.229 0.045 0

3 19.3

Overall 70.1

Damage rate is classified into four categories: 0–2% (encoded as 0); 2–5% (encoded as 1); 5–10% (encoded as 2); 10–100% (encoded as 3).

The Bayesian Information Criterion (Schwarz, 1978) was used to determine which variable enters the model.a Mean squared sensitivity error.b Reference category.

M. Hanewinkel et al. / Forest Ecology and Management 196 (2004) 227–243 239

neural network with an almost identical overall-sen-

sitivity for both models. However it is obvious that

both of the models do not qualify as a classifier to four

classes of storm damage with the present database.

5. Discussion

5.1. Overall analysis of the performance of the two

models

This study indicates that the artificial neural net-

work technology may be a promising approach to

classify forests susceptible to wind damage in a dichot-

omous classification mode. A feed-forward network

tends to have a stronger ability to identify damaged

stands than a classic logistic regression model. Its

ability will be reduced with a decrease in the frequency

of damaged stands. Nevertheless, the network per-

forms better than the logistic regression model, espe-

cially when the cut value between ‘‘undamaged’’ and

‘‘damaged’’ is increased. A slight loss in precision

when predicting undamaged stands compared to the

logistic regression model, as observed in some of the

datasets of this investigation, seems to be acceptable

since a significant gain in precision on the side of

predicting damaged stands is available. Hasenauer

et al. (2000) found that neural networks were suitable

for the prediction of the number of juvenile trees/unit

area. Prediction results were more accurate than results

from the conventional statistical approach based on

regression analyses. In a study from a completely

different field, Arana et al. (1999) compared the

performance of a neural network and a logistic regres-

sion as a predictive radiological model. They found

that the neural network had a higher performance as a

classifier than the logistic regression when the models

were built with 3-fold cross-validation (similar to the

approach that was chosen in the present paper that can

be looked upon as a 5-fold cross-validation), while two

other validation methods (leave-one-out and bootstrap

algorithm) did not detect this difference (Arana et al.,

1999, 636). Both of these studies seem to support the

results of the present paper, but they can not be directly

applied to the problem of our study. Furthermore, both

of the models reveal fundamental differences in the

processing of the input and their application that will

be discussed in the following.

5.2. Differences of the models in processing

input information

In order to keep both of the models comparable

we started with the same set of input (independent)

Table 8

Performance measures for the fitted multinomial logistic regression models and the trained neural network when they are applied to the test

datasets

Model Performance measure

Sensitivity (%) for damage classesa MSSE

0 1 2 3 All

TTS-1 Logistic model 98.5 0 0 20.8 70.0 0.6567

Neural Network 95.6 0 0 19.8 67.9 0.6613

TTS-2 Logistic model 96.8 0 0 15.7 69.2 0.6780

Neural Network 95.7 0 0 21.6 69.3 0.6542

TTS-3 Logistic model 96.8 0 0 15.9 68.8 0.6770

Neural Network 93.7 0 0 40.9 69.4 0.5882

TTS-4 Logistic model 97.1 0 0 16.7 69.5 0.6738

Neural Network 93.7 0 0 24.0 68.0 0.6455

TTS-5 Logistic model 96.9 0 0 18.9 71.5 0.6646

Neural Network 93.9 0 0 28.4 70.3 0.6291

MSSE: mean squared sensitivity error.a Damage classes: 0 ¼ 0�2% damage; 1 ¼ 2�5% damage; 2 ¼ 5�10% damage; 3 10% damage.

240 M. Hanewinkel et al. / Forest Ecology and Management 196 (2004) 227–243

variables. However the logistic regression model

using Schwarz’ Bayesian Information Criterion

eliminated for both model types some of the inde-

pendent variables as non-significant which led to a

different final model-layout of the logistic regression

compared to the neural network. In order to analyze

whether a neural network would produce similar

results to a logistic regression if the input nodes

where reduced to the significant independent vari-

ables detected by the logistic regression, a neural

network with four nodes in the input layer, represent-

ing the variables age, species, height and slope was

set up and was tested for the multinomial approach

with a randomly selected pair of training- and test

sets. The result was that this 4–5–4 network (4 nodes

in the input, 5 in the hidden and 4 in the output layer)

was not able at all to correctly assign damaged stands

to a damage class. All the stands were classified into

damage class 0. The same happened with a 4–3–4

network. The network obviously needed additional

information to be able to divide between damaged

and undamaged stands.

In an attempt to optimize the topology of the

neural network the number of input units for the

variable ‘‘aspect’’ was reduced applying an encod-

ing scheme proposed by Master (1993, 270ff).

Therefore, a pair of new variables: sin(aspect) and

cos(aspect) that have the feature of changing

smoothly were introduced. Consequently, two units

were required in the network to represent one value

of aspect. For example, a forest stand with aspect of

908 was represented as (1, 0) in the training and test

sets. The result of that 11–5–1 network was almost

the same as for the 16–5–1 network in the dichot-

omous model for the 2%-damage threshold,

although a less efficient training algorithm without

flatspot-elimination was used. This indicates that

such a modification that enhances the speed of the

learning process and normally reduces the danger of

over-training does not negatively affect the perfor-

mance of the network. However, applying this sin–

cos coding scheme for the variable ‘‘aspect’’ when

fitting the logistic regression models led to an exclu-

sion of the variable ‘‘aspect’’ in all the fitted logistic

regression models and reduced the performance of

these regression models, which again is an indication

of a different processing of input information of the

two approaches.

5.3. Further optimization of the neural network—a

sensitivity analysis

It is well known that the design of a neural network

is a ‘‘trial-and-error’’-process. Taking into account

that in the present study the final measures for the

networks’ performance are the median of only 10

trials, and that the training procedure is stopped after

2000 epochs, one may argue that the topology of the

present network in comparison to the logistic regres-

sion model is not optimized, and furthermore, that it

may be over-trained. It is indeed most likely that it is

not optimized. Therefore different trials to optimize

the network and reduce the effect of over-training

were tested. As already stated, a change in the network

structure of the multinomial model did not lead to

positive results. Early stopping of the learning process

with less than 100 epochs or a general decrease of the

number of epochs below 2000 did not improve the

performance, neither did the change of the learning

parameters (Z, m, c or dmax). Changing the network

topology for the dichotomous model from a 16–5–1

into a 16–7–1 structure by increasing the number of

nodes in the hidden layer lead to a slightly higher

performance of around 5% for damaged stands with

the damage threshold 2% only for the training/test set

1. Using a different learning algorithm called Quick-

prop (Zell et al., 2000, 148), a method to speed up the

learning process by using information about the cur-

vature of the error surface (Fahlman, 1988) improved

the performance of the dichotomous model with the

2%-damage rate for the training- and test set 4, but did

not show a stable behavior and led in one case to the

network getting trapped in a local minimum. Pruning

the network, using a magnitude based pruning algo-

rithm (Zell et al., 2000:127f) did not lead to an

improvement of the performance of the net but

revealed at least some similarities between the proces-

sing of input information of the neural network and the

logistic regression model. Pruning, a way to make

networks smaller by excluding unnecessary units or

links, e.g. by removing the links with the smallest

weights, showed that mainly the links to the units that

were also removed in the logistic regression (such as

aspect or stability) were subject to pruning, while the

input variables that were identified as significant by

the logistic model (age, species, height,) remained

untouched.

M. Hanewinkel et al. / Forest Ecology and Management 196 (2004) 227–243 241

6. Conclusions

The results of the present study indicate that a

neural network may perform better than a classical

logistic regression as a predictive dichotomous model

for storm damage. Yet, we have to accept that using an

artificial neural network instead of a statistical model

like the logistic regression may also limit our analy-

tical capacities. Due to the ‘‘black-box character’’ of

the network we are not able to identify the significance

level of the different input variables as we are with a

statistical approach. This might, however, be useful

information, as a decision maker might not only be

interested in the result of a risk-classification but also

in knowing which of the relevant factors are the most

influential. Comparing both the approaches exclu-

sively by calculating a performance measure like

the MSSE might therefore be not completely satisfac-

tory as the different character of both of the models is

not adequately taken into account. In our case, a forest

manager who is mainly interested in the output of a

risk-classification system may choose a neural net-

work whilst a decision maker who wants to know more

about the reasons behind the classification might

prefer a logistic regression despite a possibly lower

performance. Using the pruning technique for neural

networks or training algorithms including weight

decay to detect unnecessary units and links may go

in this direction but does not deliver the same quality

of information. Numerical results further demonstrate

that, specific to the dataset used in this study, both the

network and the logistic regression model under-pre-

dict the proportion of damaged stands, but the esti-

mated proportion of damaged stands by the network

lies between the observed proportion and the propor-

tion estimated by logistic regression model.

In this study, the training procedure for the neural

network iteratively minimizes the MSE until a pre-

defined number of epochs are reached, and the per-

formance measures are then calculated for the trained

net. We recommend that the network be directly

trained through minimizing the MSSE of the model.

Thus, a further improvement of the performance of the

neural network can be expected.

The experiences in the present investigation clearly

showed the limits of both technologies for risk classi-

fication when applied to the present database, although

it might be one of the most detailed assessments of risk

due to storm available for the southern part of Ger-

many, as this parameter is usually not recorded at the

stand level. Relying on a similar database, we would

therefore not recommend applying a neural network or

a logistic regression as a risk-classifier in a multi-

nomial or even a continuous variable approach. Pre-

vious investigations in which a neural network was

used to predict the risk of storm damage as a con-

tinuous variable (Hanewinkel and Zhou, 2000)

resulted in a non-satisfactory performance of the net-

work, especially for higher damage rates. We would

instead stick to a dichotomous approach and try to find

the most useful damage threshold that matches the

information needs of forest managers. To go beyond

this, meaning to try to predict risk in several risk

classes or to directly estimate the actual damage rate,

obviously needs additional parameters that better

characterize the stands and their vulnerability towards

storm damage.

Acknowledgements

We want to thank Alex Hinrichs for the initial

preparation of the data in 1994. Furthermore we would

like to thank Kai Fischer (M.Sc.) of IFE for calcula-

tions done within our Geographic Information System

(GIS). The research has been supported by the German

Ministry of Formation, Research and Technology

(BMBF) under the grant number 0339732/5. The

authors would also like to thank Greg Biging,

University of California in Berkeley for his useful

comments on the text.

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