Amaro A., Reed D., Soares P. (editors) Modelling Forest Systems

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Amaro Forests Prelims 25/7/03 11:03 am Page viii

viii Contents

30. Landscape Visualization with Three Different Forest Growth 347

Simulators

F.-J. Knauft

31. How Good is Good Enough? Information Quality Needs for 359

Management Decision Making

D.D. Reed and E.A. Jones

Part 5: Model Archives and Metadata 367

32. Forest Modelling: Conserving the Past and Building the 369

Future

K. Rennolls

33. A Logic Approach to Design Speciﬁcations for Integrated 379

Application of Diverse Models in Forest Ecosystem Analysis

K.M. Reynolds

Part 6: Conclusions 387

34. Emerging Trends and Future Directions: a Workshop 389

Synthesis

D.D. Reed, A. Amaro, R. Amateis, S. Huang and M. Tomé

Index 395

Amaro Forests Prelims 25/7/03 11:03 am Page ix

Principal Contributors

V. Alenius, Finnish Forest Research Institute, Rovaniemi Research Station, PO Box 16,

FIN – 96300 Rovaniemi, Finland

A.C. Almeida, Aracruz Celulose, S.A., Rodovia Aracruz/B. Riacho, PO Box 33101

291-9500 Aracruz – ES, Brazil

A. Amaro, Instituto Superior de Gestão, Departamento de Matematica, Rua V

itorino

Nemesio, N° 5, 1750-306 Lisbon, Portugal

R. Amateis, V

irginia Tech, Department of Forestry, College of Natural Resources,

Blacksburg, VA 24061-0324, USA

H. Burkhart, Department of Forestry, College of Natural Resources, Blacksburg, VA,

24061-0324, USA

H. Carino, Auburn University, School of Forestry & Wildlife Sciences, Auburn, AL 36849,

USA

G. Chirici, Università di Firenze, DISTAF – Dipart. Scienze Tecnologie Ambientali

For

estali, Via San Bonaventura 13, 50145 Florence, Italy

J. Colbert, USDA – Forest Service, Disturbance Ecology & Management of Oak-Dominated

For

ests, 180 Canﬁeld Street, Morgantown, WV 26505-3101, USA

F. de Coligny, INRA, UMR botAnique et bioinforMatique de l’Ar

chitecture des Plantes

(AMAP), TA 40/PS2 Boulevard de la Lironde, 34398 Montpellier Cedex 5, France

C. Dean, CRC for Greenhouse Accounting, GPO Box 475, Canberra ACT 2601, Australia

G. Deckmyn, University of Antwerp UIA, Research Group Plant and Vegetation Ecology,

Universiteitsplein 1, 2620 W

ilrijk, Belgium

T. Eid, Agricultural University of Norway, Department of Forest Sciences, PO Box 5044,

NO-1432 Ås, Norway

R. Fleming, Canadian Forest Service, Great Lakes Forest Research Centre, 1219 Queen St

East, Sault Ste Marie, Ontario P6A

2E5, Canada

J.H. Gove, USDA Forest Service, Northeastern Research Station, PO Box 640, 271 Mast

Road, Dur

ham, NH 03824, USA

M. Hauhs, University of Bayreuth, Bitoek, Dr – Hans – Frisch – Str. 1–3, D-95448

Bayr

euth, Germany

S. Huang, Forest Management Branch, Land and Forest Service, Alberta Sustainable

Resour

ce Development, 8th Floor – 9920 – 108 Street Edmonton, Alberta T5K 2M4,

Canada

Amaro Forests Prelims 25/7/03 11:03 am Page x

x Principal contributors

A. Kiviste, Estonian Agricultural University, Kreutzwaldi 5, 51014 Tartu, Estonia

F.-J. Knauft, University of Bayreuth, Bayreuth Institute for Terrestrial Ecosystem Research,

D-95440 Bayr

euth, Germany

H. Kotze, Komatiland Forests, Research Division, PO Box 574, 1260 Sabie, South Africa

S. Magnussen, Canadian Forest Services, Natural Resources of Canada, 506 West Burnside

Road, V

ictoria, BC V8Z 1M5, Canada

C. Meredieu, INRA, Unité de Recher

ches Forestières, 69 Route d’Arcachon, 33612 Cestas

Cedex, France

R.A. Monserud, USDA Forest Service, PNW Research Station, 620 SW Main St, Suite

400, Portland, OR 97205, USA

N. Nanos, Unidad de Anatomia, Fisiologia y Genética Forestal, ETS de Ingenieros de

Montes, Ciudad Universitária, 28080 Madrid, Spain

N. Picard, CIRAD – Forêt, Bamako, BP 1813, Mali

F. Rodriguez, Universitat de Lleida, ETSEA-Udl, Dept. Pr

oducción Vegetal y Ciencia

Forestal, Av. Rovira Roure 177, 25198 Lleida, Spain

P. Radonja, SE Serbiaforest – Institute of Forestry, Kneza Viseslava 3, 11030 Belgrade,

ugoslavia

D. Reed, Michigan Technological University, School of Forest Resources and

Envir

onmental Science, 1400 Townsend Drive, Houghton, MI 49931-1295, USA

K. Rennolls, University of Greenwich, School of Computing and Mathematical Sciences, 30

Park Row

, London SE10 9LS, UK

K. Reynolds, USDA Forest Service, Paciﬁc Northwest Research Station, 3200 SW Jefferson

ay, Corvallis, OR 97331, USA

N.A. Ribeiro, Universidade de Évora, Departamento de Fitotecnia, Apartado 94, 7002-554

Evora, Portugal

P. Soares, Instituto Superior de Agronomia, Departamento de Engenharia Florestal, Tapada

de Ajuda, 1349 017 Lisbon, Portugal

N. Tchebakova, Institute of For

est Siberian Branch, Russian Academy of Sciences,

Akademgorodok, 660036 Krasnoyarsk, Russia

P. van Gardingen, University of Edinbur

gh, CECS John Muir Building, Mayﬁeld Road,

Edinburgh EH9 3JK, UK

Amaro Forests Prelims 25/7/03 11:03 am Page xi

Preface

The real world – the forest ecosystem – can be analysed in multiple dimensions (e.g.

from the cellular to the landscape level). The ‘thinking’, in order to understand and

simplify the forest’s complex reality so that it can be modelled, can begin from the

simple univariate scenario and proceed to multivariate and complex scenarios.

Different mathematical and philosophical approaches can thus be adopted in order

to design and obtain a model. The mathematical tools selected to quantify the rates,

coefﬁcients and constants that are used in the models can range from the simple use

of the sample mean, to complex numerical algorithms that may violate every possi-

ble statistical assumption. Once the model has been built, the process of validating it

and understanding its limits or ranges of applicability must be deﬁned, particularly

if it will be used for management decision support.

A workshop on the interface between reality, modelling and the parameter esti-

mation pr

ocesses, jointly sponsored by IUFRO (4.01 and 4.11), Instituto Superior de

Gestão and Instituto Superior de Agronomia (Portugal), was held in Sesimbra,

Portugal (2–5 June 2002). The contents of this book are based on this workshop and

both reﬂect the state of the art and identify the key issues that should be considered

as priorities for further research in this area.

We would like to acknowledge and thank all the involved institutions,

all the

scientists involved as authors and the following referees:

Alexander Fedorec, Bob Monserud, Chris Dean, Fréderic Raulier, Glen W.

Armstr

ong, Harold Burkhart, Isabel Cañellas, Jeff Gove, Jim Colbert, J.P.

Skovsgaard, Keith Rennolls, Keith Reynolds, Kevin O’Hara, Lianjun Zhang,

Margarida Tomé, Marion Reynolds, Mark J. Ducey, Michael Rauscher, Mike R.

Strub, Mingliang Wang, Nadarajah Ramesh, Paul Doruska, Paul van

Gardingen, Quang V. Cao, Quao Cao, Ralph Amateis, Rod Keenan, Shongming

Fundação para a Ciência e Tecnologia (Apoio do Programa Operacional Ciência, Tecnologia e Inovação

do Quadro Comunitário de Apoio III); Fundação Calouste Gulbenkian; British Council; Fundação Luso-

Americana; Embaixada do Canadá; Ministério da Agricultura, do Desenvolvimento Rural e das Pescas;

Raiz, Instituto de Investigação da Floresta e do Papel; Aliança Florestal; Soporcel, SA; Grupo Amorim;

Costa Azul; Câmara Municipal de Sesimbra.

Amaro Forests Prelims 25/7/03 11:03 am Page xii

xii Preface

Huang, Steen Magnussen, Stephen Roxburgh, Susan S. Hummel, Thomas J.

Seablom, Timo Pukkala, Tony Ackroyd, Valerie Le May, Victor Lieffers, William

B. Leak, Yue Wang,

and Luisa Santos for her invaluable editorial assistance. All together they made the

development of this volume possible.

Modelling forest systems is a powerful discipline that promotes knowledge and

understanding of for

est functioning. This is by no means a simple or small task. The

purpose of this book is to promote and advance the systematic understanding of

these complex, but critical, systems.

Ana Amaro, David Reed, Paula Soares

The Editors

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Part 1

Forest Reality and Modelling Strategies

Modelling objectives is one of the most important considerations when determining mod-

elling strategies. The importance of user interaction and the deﬁnition of the modelling

objectives allow the identiﬁcation of the three main types of users with whom the mod-

ellers interact: scientists, forestry practitioners and managers, and ‘Administration’ and

society. It is essential to expand the scope of modelling to address the needs of these vari-

ous users.

Until now, modelling has mainly focused on wood production. New approaches are

needed: for instance, modelling natural for

ests, modelling the evolution of the sustainability

of the systems, modelling deadwood, modelling wildlife habitats and modelling unusual

events (e.g. catastrophes, diseases).

It is also important to interact with other professions and disciplines, to get in touch with

specialists in other ar

eas and to communicate with them to a greater extent than has hap-

pened in the past. The enhancement of forest structure modelling, e.g. connecting with habi-

tat modelling and deadwood and taking into consideration boundary effects, will be critical

as demands for information increase.

It is essential to communicate the theory and reporting of the modelling process.

Modellers work with models – when these models fail, as would be expected on occasion,

these failur

es may promote understanding of the faulty model functioning. However, this

phase is almost never reported. An absence of published ‘negative results’ is a consequence

of the reporting system; no-one is prepared to publish reports on modelling exercises that did

not go well. However, it is important to discuss the reasons why a model did not evolve well,

as this is a source of understanding for the entire modelling community.

It is important to think ahead about possible uses and to collect data that will be useful

and ﬂexible in application. Data at the extr

emes – very low and very high stand densities and

site qualities, and young and old ages – are essential for broad-scale inferences and precise

parameter estimates.

It is very difﬁcult to decide which criteria should be followed in order to plan data

acquisition. The balance between data quality and quantity is always dif

ﬁcult to deﬁne:

there is always a need for quantity in order to have representative samples but, at each

sampling point, quality is needed. From a practical standpoint, quantity and quality push

in opposite directions, creating the difﬁcult task of deﬁning the balance between both

objectives.

01Amaro Forests Part 1 25/7/03 11:04 am Page 2

2 Part 1

There are contrasts between the data used for modelling and the data available for using

the model, especially when the models are included in decision-support systems. It is very

important to deﬁne the data characteristics. Often the models are good, as are the decision

tools, but the decisions may still not be as good as they should be due to a lack of speciﬁc

quality in the data.

When publishing the results, documentation about the data is often reduced to simple

tables, making it dif

ﬁcult to evaluate the importance of the results, due to the lack of informa-

tion on the data sets that were used to build the models. It is important to deﬁne minimum

standards for data description, which should be presented along with the report of the

research. In order to complement this and to make sure that data characterization is self-

explanatory, a Web-based tool could be built in order to allow data publication or at least fur-

ther details that could help the users to understand the possibilities of the application.

For some applications, there are links that modellers should or could have with national

for

est inventories (NFIs), both on using data from national inventories to calibrate models, as

well as using data from the NFI for model evaluation and scenario development. However,

this can result in extensive assumptions and serious extrapolations being made, the repercus-

sions of which must be considered.

On the other hand, when planning a forest inventory, it is important to be aware that there

e a lot of data that can be collected, much of which are not directly usable by the growth

models. Such data may be very interesting for other modelling objectives. It is therefore

important to plan to acquire data that may be useful for many objectives.

It is also important to work on different scales, e.g. time scale, spatial resolution, diversity,

but especially on the linkage between the dif

ferent scales (i.e. how the links between the dif-

ferent scales are going to be established).

The following chapters address these and other issues concerning modelling strategies

and r

elationships between models and actual system behaviour. The editors wish to

acknowledge the efforts of Harold Burkhart (USA) and Margarida Tomé (Portugal) for coor-

dinating this section, and thank them for their contributions to this volume.

02Amaro Forests - Chap 01 25/7/03 11:04 am Page 3

1 Suggestions for Choosing an

Appropriate Level for Modelling

Forest Stands

Harold E. Burkhart

Abstract

Models are abstractions of reality. In order to be useful, models must include essential ele-

ments of the real world system that are to be mimicked to meet some speciﬁed modelling

objective. The pattern in a data set can often be described with a relatively simple model.

Models of forests have been constructed for numerous management and research objectives.

To determine an appropriate modelling unit (e.g. cell, organ, tree, stand, landscape), one must

deﬁne the modelling objective and the forecasting time frame. Often the level of modelling

detail possible is dictated by the data available. However, there are guiding principles that can

aid in selecting an appropriate level for modelling. These principles include: (i) developing as

parsimonious a model as possible, and (ii) adjusting the number of state variables for the fore-

casting period involved. The application of these principles is discussed within the framework

of forest growth and yield models.

Introduction

Scientiﬁc inquiry often consists of describing reality through models. No natural

system is so simple that it can be grasped and controlled without abstraction.

Abstraction involves replacing the natural system under consideration by a model

of similar but simpler structure. In order to be useful, models must include essential

elements of the real world system that are to be mimicked in order to meet some

speciﬁc modelling objective.

Prediction, Parsimony and Noise

To have high utility, models must be accurate. Model accuracy can be improved by

increasing the size of a data set, improving the quality of the data obtained, or by

applying more sophisticated modelling techniques to existing data. Collecting data

Department of Forestry, Virginia Polytechnic Institute and State University, USA

Correspondence to: burkhart@vt.edu

02Amaro Forests - Chap 01 25/7/03 11:04 am Page 4

4 H.E. Burkhart

is expensive relative to performing analyses, so it behoves us to make the best possi-

ble use of the data available. When planning data collection efforts, it is important

that a wide range of site and stand conditions be included in the sample. Vanclay et

al. (1995) recommend that permanent plot systems for developing growth models

include experimental observations that are manipulated to provide data on a wide

range of stand densities and thinning treatments, and data from stands which have

been allowed to develop beyond normal rotation ages.

Model accuracy

It is commonly believed that a model can be no more accurate than the data on

which it is based. However, because models can amplify patterns and discard

unwanted noise, they can be more accurate than the data used to build them. Gauch

(1993) emphasized that models being more accurate than the data available is

dependent on: (i) the precise question being asked of the model, (ii) the design of the

experiment, and (iii) the quantity and accuracy of the available data.

Typical modelling efforts attempt to enhance prediction by amplifying a pattern

and discar

ding noise. Ordinarily, most of the pattern in a data set is recovered

quickly with relatively simple models. Patterns usually depend on a few main

causal factors that can be summarized readily. Noise, on the other hand, is recov-

ered slowly as a model’s complexity increases. The accuracy of prediction, therefore,

increases quickly as parameters are added to relatively simple models. Predictive

ability tends to peak rather quickly (this point is sometimes referred to as ‘Ockham’s

Hill’) and then decrease with increasingly complex models (Gauch, 1993). Figure 1.1

illustrates how model accuracy (in terms of predictive ability) is affected by the

recovery of pattern and noise through increasing model complexity. Modelling thus

offers its greatest beneﬁts when a parsimonious, simple model captures the essence

of the data’s pattern in a large, noisy data set.

An Example

As an illustration of the relationship between model accuracy and complexity, data

from a loblolly pine spacing trial (Amateis et al., 1988) were used to predict stand

volume. This spacing trial consists of three replicates at four locations. Each repli-

cate contains 16 plots of varying spacing with number of trees per hectare ranging

from 747 to 6725. Two locations were randomly selected for model ﬁtting and the

Prediction

Noise

Pattern

Model complexity

Fig. 1.1. P

attern is generally determined by a few main factors, meaning that relatively simple models

recover much of it in a data set; noise is more idiosyncratic and complex and is thus recovered more slowly

as model complexity increases; predictive ability arises from pattern recovery minus noise recovery so it is

expected to increase quickly in simple models but to peak on ‘Ockham’s Hill’ and then decrease in

increasingly complex models. (Adapted from Gauch, 1993.)

observations from the other two locations were used to evaluate model accuracy.

For this example, accuracy was deﬁned as the reciprocal of the square root of mean

squared error (MSE), a combination of bias and precision. As shown in Fig. 1.2, the

pattern of increasing mean volume per hectare over time (stand age) is clearly dis-

cernible, but there is large variability at each age; this variability is assumed to stem

from differences in numbers of trees and site index levels of the individual plots.

Stand volume was, accordingly, to be predicted over time using the variables age,

trees per hectare and site index. The models ﬁtted, in sequence, were:

ln(Y) =

(1/A) (1)

ln(Y) =

(1/A) +

(N) (2)

ln(Y) =

(1/A) +

(N) +

(S) (3)

where Y is stand volume (m

/ha), A is stand age (years), N is trees/ha and S is site

index (m at base age 25 years). Data from the individual spacing plot measurements

from ages 6 to 16 years were utilized in ﬁtting Equations 1–3 and the ﬁtted equa-

tions were applied to the plot observations from the two locations not used in ﬁtting

to compute the MSE for the differences between observed and predicted volume per

hectare. The resulting values at stand age 16 years (trends in results were the same

at other ages) were:

Choosing Appropriate Level for Modelling 5

100

150

200

250

300

350

57911131517

Age (years)

Volume/ha

Fig. 1.2. Plotting of data from a loblolly pine spacing trial shows a readily identiﬁable pattern of increasing

mean volume per hectare with increasing age, but with fairly large variability at each age.

Model R

√ MSE Accuracy

1 0.84 15.89 0.0629

2 0.90 6.44 0.1553

3 0.93 30.02 0.0333

Although the R

value increased for models 1–3 from 0.84 to 0.90 to 0.93, respec-

tively, and all parameter estimates were signiﬁcantly different from zero (P < 0.001)

using the t-test, the accuracy of the models, as measured by the reciprocal of the

square root of MSE, reached a peak (Ockham’s Hill) with two predictor variables,

age and trees per hectare, but declined when site index was added. Following the

dictum of parsimony and relying on the results from the MSE computations, the

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