Predictability and Nonlinear Modelling in Natural Sciences and Economics

661 Pages·1994·28.097 MB·English

by  J. Grasman, G. Van Straten (auth.), J. Grasman, G. van Straten (eds.)

Predictability and Nonlinear Modelling
in Natural Sciences and Economics
Support
The conference· has been financially supported by the following institutes and research
programmes:
Conunission of the European Communities, Directorate for Science, Research and
Development, Climatology Programme
Dutch Ministry of Housing, Physical Planning and Environment, National Research
Programme "Global Air Pollution and Climate Change" (NOP)
Netherlands Organization for Scientific Research, Priority Program "Nonlinear Systems"
Royal Netherlands Academy of Sciences
Wageningen Agricultural University, as part of its programme to commemorate its 75th
Anniversary.
Sponsors
Shell Nederland bv
Unilever
Predictability and
N onlinear Modelling
•
In
Natural Sciences and
Economics
edited by
J. Grasman
Department of Mathematics,
Agricultural University,
Wageningen, The Netherlands
and
G. van Straten
Department ofA gricultural Engineering and Physics,
Agricultural University,
Wageningen, The Netherlands
SPRINGER-SCIENCE+BUSINESS MEDIA, BV.
A C.I.P. Catalogue record for this book is available from the Library of Congress
ISBN 978-94-010-4416-5 ISBN 978-94-011-0962-8 (eBook)
DOI 10.1007/978-94-011-0962-8
Printed on acid-free paper
All Rights Reserved
© 1994 Springer Science+Business Media Dordrecht
Originally published by Kluwer Academic Publishers in 1994
No part of the material protected by this copyright notice may be reproduced or
utilized in any form or by any means, electronic or mechanical,
including photocopying, recording or by any information storage and
retrieval system, without written permission from the copyright owner.
CONTENTS
Introduction
1. Grasman and G. van Straten
1. Geophysics
Karl Popper and the accountability of scientific models 6
H. Tennekes
Evaluation of forecasts II
A.M. Murphy and M. Ehrendorfer
The Liouville equation and prediction of forecast skill 29
M. Ehrendorfer
An improved formula to describe error growth in meteorological models 45
1.-F Royer, R. Stroe, M. Deque and S. Vannitsem
Searching for periodic motions in long-time series 57
RA. Pasmanter
Comparison study of the response of the climate system to major volcanic eruptions
and el nino events 65
W. Bohme
Detection of a pertubed equator-pole temperature gradient in a spectral model of the
atmospheric circulation R6
SLJ. Mous
A simple two-dimensional climate model with ocean and atmosphere coupling 95
E.1.M. YeUng and ME. Wit
Climate modelling at different scales of space 113
G. Maracchi
2. Agriculture
Simulation of effects of climatic change on cauliflower production 127
1.E. Olesen and K. Grevsen
Validation of large scale process-oriented models for managing natural resource
populations: a case study 13R
R A. Fleming and C A. Shoemaker
Uncertainty of predictions in supervised pest control in winter wheat, its price
and its causes 149
W.AH. Rossing, RA. Daanen, E.M.T. Hendrix and MJ.W. Jansen
The implications and importance of non-linear responses in modelling the growth and
development of wheat 157
MA. Semenov and JR. Porter
Growth curve analysis of sedentary plant parasitic nematodes in relation to plant
resistance and tolerance 172
RJ.F. van Haren, E.M.L. Hendrikx and HI Atkinson
3. Population Biology
Using chaos to understand biological dynamics IR4
BE. Kendall, W.M. Schafler, L.F. Olsen, C.w. Tidd and B.L. Jorgensen
VI Contents
Qualitative analysis of unpredictability: a case study from childhood epidemics 204
R. Engbert and F.R. Drepper
Control and prediction in seasonally driven population models 216
lB. Schwartz and I. Triandaf
Simple theoretical models and population predictions 228
AA. Berryman and M. Munster-Swendsen
Individual based population modelling 232
SALM. Kooijman
Ecological systems are not dynamical systems: some consequenses of individual
variability 248
V. Grimm and J. Uchmafzski
Spatio-temporal organization mediated by hierarchy in time scales in ensembles of
predator-prey pairs 260
e.
Pahl-Wostl
Continental expansion of plant disease: a survey of some recent results 274
F. van den Bosch, J.e. Zadoks and JAJ. Metz
Modelling of fish behavior 282
J.G. Balchen
4. Systems sciences
Understanding uncertain environmental systems 294
MB. Beck
System identification by approximate realization 312
e.
Heij
Sensitivity analysis versus uncertainty analysis: when to use what? 322
l.P.C. Kleijnen
Monte Carlo estimation of uncertainty contributions from several independent
multivariate sources 334
MJ.W. Jansen, WA.H. Rossing and RA. DaaMn
Assessing sensitivities and uncertainties in models: a critical evaluation 344
P H.M. Janssen
UNCSAM: a software tool for sensitivity and uncertainty analysis of mathematical
models 362
P.S.e. Heuberger and P.H.M. Janssen
Set-membership identification of nonlinear conceptual models 377
KJ. Keesman
Parameter sensitivity and the quality of model predictions . 389
H.J. Poethke, D. Oertel and A. Seitz
Towards a metrics for simulation model validation 398
H. Scholten and M.W.M. van der Tol
Use of a Fourier decomposition technique in aquatic ecosystems modelling 411
I. Masliev
Multiobjective inverse problems with ecological and economical motivations 422
0.1. Nikonov
An expert-opinion approach to the prediction problem in complex systems 432
G.J. Komen
Contents vii
5. Environmental Sciences
Critical loads and a dynamic assessment of ecosystem recovery 439
J.-P. Hettelingh and M. Posch
Uncertainty analysis on critical loads for forest soils in Finland 447
M.P. Johansson and P.H.M. Janssen
Monte Carlo simulations in ecological risk assessment 460
U. Hommen, U. DiUmer and H.T. Ratte
Sensitivity analysis of a model for pesticide leaching and accumulation 471
A. Tiktak, FA. Swartjes, R. Sanders and P.H.M. Janssen
Bayesian uncertainty analysis in water quality modelling 485
P R.G. Kramer, A.C.M. de Nijs and T. Aldenberg
Modelling dynamics of air pollution dispersion in mesoscale 495
P. Holnicki
Uncertainty factors analysis in linear water quality models 505
A. Kraszewski and R. Soncini-Sessa
Uncertainty analysis and risk assessment combined: application to a bio-
accumulation model 516
T.P. Traas and T. Aldenberg
Diagnosis of model applicability by identification of incompatible data sets illustrated
on a pharmacokinetic model for dioxins in mamals 527
O. Klepper and W. Slob
Regional calibration of a steady state model to assess critical acid loads 541
H. Kros, P.S.c. Heuberger, PH.M. Janssen and W. de Vries
Uncertainty analysis for the computation of greenhouse gas concentrations in IMAGE 554
M.S. Krol
6. Economics
Forecast uncertainty in economics 568
FJ.H. Don
Some aspects of nonlinear discrete-time descriptor systems in economics 581
Th. Fliegner, H. Nijmeijer and 0. Kotta
Quasi-periodic and strange, chaotic attractors in Hick's nonlinear trade cycle model 591
CH. Hommes
Monte Carlo experimentation for large scale forward-looking economic models 599
R. Boucekkine
Erratic dynamics in a restricted tatonnement process with two and three goods 609
C. Weddepohl
Chaotic dynamics in a two-dimensional overlapping generation model: a numerical
investigation 621
CH. Hommes, SJ. van Strien and R.G. de Vilder
Nonlinearity and forecasting aspects of periodically integrated autoregressions 633
PH. Franses
Classical and modified rescaled range analysis: some evidence 638
B. Jacobsen
Subject index 648
Preface
These proceedings have been composed from selected papers presented at the International
Conference on 'Predictability and Non-Linear Modelling in Natural Sciences and Econo
mics', held at the occasion of the 75th anniversary of Wageningen Agricultural University,
The Netherlands. Some 160 participants from 18 countries gathered at Wageningen from
5-7 April 1993 for a most challenging and interesting meeting.
The organization of such a meeting is not possible without the help of many people.
The members of the National Programme Committee have been very instrumental in the
preliminary stages of the organization, in particular in the choice of outstanding plenary
speakers. Apart from us, members of the National Programme Committee were: H. Folmer
(Wageningen), J. Goudriaan (Wageningen), L. Hordijk (Wageningen), H.A.M. de Kruijf
(Bilthoven), J. Leentvaar (Lelystad), S. Parma (Nieuwersluis), C.J.E. Schuurmans (De
Bilt), H.N. Weddepohl (Amsterdam) and J.e. Willems (Groningen). We are also greatful
for advice of the International Scientific Advisory Committee, consisting of M.B. Beck
(London), J.D. Farmer (Sante Fe), J.-M. Grandmont (Paris), T.N. Palmer (Reading), M.L.
Parry (Oxford), W.M. Schaffer (Tucson) and L. Sornly6dy (Laxenburg). Several members
of both committees have been of great help in finding referees, and have played an active
role in the reviewing process.
The meeting itself, taking place at the International Agricultural Centre, was excellently
organized by the Wageningen University Congress Bureau, an accomplishment that should
largely be attributed to Mr. J. Meulenbroek and Mrs. A. van Wijk-van der Leeden.
Finally, the production of a book of this size is not an easy task. The cooperation of the
authors and numerous anonymous reviewers has been acknowledged. Special thanks have
to be awarded to Mrs. H. Evers-van Holland, Mrs. DJ. Massop-Schreuders and Mrs. M.
Slootman-Vermeer of the secretariat of the Department of Mathematics for their excellent
job in producing the camera ready text.
We are proud to present this book, and we hope that the reader will find the contents
interesting, stimulating and rewarding.
Johan Grasman Gerrit van Straten
Department of Mathematics Department of Agricultural Engineering and
Physics
Agricultural University
Wageningen, The Netherlands
INTRODUCTION
J. GRASMAN and G. VAN STRATEN
Agricultural University, Wageningen
Predicting the future behaviour of natural and economic processes is the subject of
research in various fields of science. After a period of considerable progress by refining
models in combination with large scale computer calculations, the scientific community is
presently confronted with problems that require a novel approach to further extend the
range of forecasts and to improve their quality. It is recognized that nonlinearity of a
system may significantly complicate the predictability of future states of the system. A
small variation of parameters can drastically change the dynamics, while sensitive
dependence on the initial state may severely limit the predictability horizon.
Predictability of dynamic systems has two sides. The notion that non-linear dynamic
systems may exhibit chaotic behaviour has contributed enormously to the understanding of
phenomena that could not be explained before. Although precise predictions of the state of
the system in the far or even nearby future is impossible in the chaotic regime, chaos
theory may have the key to open new pathways in predictability theory. Moreover, it
answers the question under which circumstances chaotic behaviour can be expected.
On the other hand, not every non-linear system shows chaotic behaviour in the
parameter range of interest, and therefore do not have a fundamental prediction problem.
Nevertheless, prediction capability is hampered also here, because of uncertainties. This is
the other side of the coin of predictability. Since models are abstractions of the real world,
they always are no more than approximations. Thus, errors made during model constructi
on and calibration will propagate when forecasts are made. The analysis of uncertainty is
therefore the second important issue when dealing with predictability.
The papers brought together in this book have been presented at a conference organized
at the occasion of the 75th anniversary of Wageningen Agricultural University in the
Netherlands. The conference aimed at bringing together scientists who are modelling the
dynamics of natural and economic processes on the one hand, with system analysts and
mathematicians who develop methods for quantifying the characteristic features of such
models on the other. Quite naturally, this has led to the meeting of the two main methodo
logical tools - the mathematical theory of nonlinear dynarnicalsystems and the analysis of
uncertainty in modelling - as is reflected in the various contributions.
Chaos
Non-linearity in the dynamic equations can give rise to irregular dynamics of a system.
This so-called chaotic behaviour is characterized by sensitive dependence on the initial
state. The degree of divergence of the trajectories in chaotic systems is determined by the
Lyaponov exponents. In contrast to stochastic systems, in chaotic systems the irregular
trajectories concentrate in state space on the (strange) attractor of the system. Such strange
attractors have a fractal structure and are said to have a non-integer dimension.
In the applied sciences chaos was first noticed from the properties of a simple model of
the atmospheric circulation (Lorenz, 1965) and in biology from the dynamics of an even
2 Introduction
more simple model of the changing size of a biological population (May, 1974). Not
amazingly, these two fields of applications are represented in this proceedings again, but
the questions that are addressed have evolved since then. Knowing that the error in the
meteorological forecast increases with time, one may wish to quantify the expected size of
the error, because this defines the forecast skill (Royer et al.). The analysis is based on the
behaviour of the system near the trajectory starting in the present state that is computed
from the observations. In the other field, that of population biology, presently a strong
interest exists in the data of childhood diseases, such as measles (Kendall et al., Engbert
and Drepper). Large time series of cities like New York are available. The first problem
concerning the irregular behaviour of such a time series was to find out whether the
dynamics of this epidemical process is really chaotic. Recently the answer could be given
and turned out to be confrrmative, see Olsen and Schaffer (1990). Presently other
properties of these processes, such as the nonuniform information content of data points
(Kendall et al.) and the possibility of controlled outbreaks, are being studied (Schwartz
and Triandat).
Chaos as an explanation for irregular behaviour and unpredictability was taken over by
other disciplines. At the conference it was, made explicit that economic processes can have
a nonlinear structure that may give rise to chaos. In these contributions the models are in
the form of nonlinear difference equations (Hommes, Weddepohl, Hommes et al.). Large
time series of prices at stock markets can be analyzed with the method of rescaled range
analysis introduced by Hurst, see Feder (1988). It turns out that this stochastic fractal
approach may help to quantify long term dependence in a time series (Jacobsen).
Uncertainty
Uncertainty arises from different sources. In the construction phase of the model,
observational noise and errors in input and output sequences lead to possibly erroneous
structures and biased parameters. Moreover, lack of fundamental knowledge, simplificati
ons, aggregations of variables, neglect of variables and processes, and approximations to
functional relationships all contribute to systems noise, and thus to uncertainty when the
model is used for predictions.
In the stage where calibrated and validated models are being used, prediction uncertain
ty may arise from three sources. First, there can be uncertainty in the expected future input
sequences. If the model responds to its inputs in a non-linear fashion, it is not justified to
use average values for future inputs (Semenov & Porter). But, if properly handled, input
uncertainty can be taken care off in scenario studies, and does not arise from the model
itself. Second, the uncertainties in model structure and parameters, as identified in the
construction stage, can be propagated into future projections, thus leading to distributions
or regions around future state trajectories. The third kind of uncertainty arises when
models are used outside their range of validity. This situation is met quite frequently in
the environmental field, where the purpose of the model is to forecast the future state of
the system under changed pollution load conditions. In all situations where the future is
different from the present, there is no absolute guarantee that the model structure will not
change. The dilemma here is to use complex, detailed models, which however cannot be
fully identified on the basis of present knowledge and data, or to accept smaller well
calibrated models, which however may give the wrong predictions under changed
conditions (Beck, 1991). A possible remedy to this situation has been indicated with the
term 'educated speculation', where relatively simple models are used as frame IIlf reference