Environmental Modelling

Finding Simplicity in Complexity

John Wainwright, Mark Mulligan

• Publisher: Wiley
• Year: 2013
• ISBN:
  9781118351482
• Edition: 2
• Topic: Technology & Engineering
• Subtopic: Civil Engineering
• Index: Technology & Engineering

Simulation models are an established method used to investigate processes and solve practical problems in a wide variety of disciplines. Central to the concept of this second edition is the idea that environmental systems are complex, open systems. The authors present the diversity of approaches to dealing with environmental complexity and then encourage readers to make comparisons between these approaches and between different disciplines.

Environmental Modelling: Finding Simplicity in Complexity 2 nd edition is divided into four main sections:

• An overview of methods and approaches to modelling.
• State of the art for modelling environmental processes
• Tools used and models for management
• Current and future developments.

The second edition evolves from the first by providing additional emphasis and material for those students wishing to specialize in environmental modelling. This edition:

• Focuses on simplifying complex environmental systems.
• Reviews current software, tools and techniques for modelling.
• Gives practical examples from a wide variety of disciplines, e.g. climatology, ecology, hydrology, geomorphology and engineering.
• Has an associated website containing colour images, links to WWW resources and chapter support pages, including data sets relating to case studies, exercises and model animations.

This book is suitable for final year undergraduates and postgraduates in environmental modelling, environmental science, civil engineering and biology who will already be familiar with the subject and are moving on to specialize in the field. It is also designed to appeal to professionals interested in the environmental sciences, including environmental consultants, government employees, civil engineers, geographers, ecologists, meteorologists, and geochemists.

Part I

Model Building

Chapter 1

Introduction

John Wainwright¹ and Mark Mulligan²

¹Department of Geography, Durham University, UK

²Department of Geography, King's College London, UK

1.1 Introduction

There seems to be a tradition for books on complex systems to start from chapter zero (after Bar-Yam, 1997).

In one sense, everything in this book arises from the invention of the zero. Without this Hindu-Arabic invention, none of the mathematical manipulations required to formulate the relationships inherent within environmental processes would be possible. This point illustrates the need to develop abstract ideas and apply them. Abstraction is a fundamental part of the modelling process.

In another sense, we are never starting our investigations from zero. By the very definition of the environment as that which surrounds us, we always approach it with a number (non-zero!) of preconceptions. It is important not to let them get in the way of what we are trying to achieve. Our aim is to demonstrate how these preconceptions can be changed and applied to provide a fuller understanding of the processes that mould the world around us. From this basis, we provide a brief general rationale for the contents and approach taken within the book.

1.2 Why Model The Environment?

The context for much environmental modelling at present is the concern relating to human-induced climate change. Similarly, work is frequently carried out to evaluate the impacts of land degradation due to human impact. Such application-driven investigations provide an important means by which scientists can interact with and influence policy at local, regional, national and international levels. Models can be a means of ensuring environmental protection, as long as we are careful about how the results are used (Oreskes et al., 1994; Rayner and Malone, 1998; Sarewitz and Pielke, 1999; Bair, 2001).

On the other hand, we may use models to develop our understanding of the processes that form the environment around us. As noted by Richards (1990), processes are not observable features but their effects and outcomes are. In geomorphology, this is essentially the debate that attempts to link process to form (Richards et al., 1997). Models can thus be used to evaluate whether the effects and outcomes are reproducible from the current knowledge of the processes. This approach is not straightforward, as it is often difficult to evaluate whether process or parameter estimates are incorrect, but it does at least provide a basis for investigation.

Of course, understanding-driven and applications-driven approaches are not mutually exclusive. It is not possible (at least consistently) to be successful in the latter without being successful in the former. We follow up these themes in much more detail in Chapter 2.

1.3 Why Simplicity and Complexity?

In his short story ‘The Library of Babel’, Borges (1970) describes a library made up of a potentially infinite number of hexagonal rooms containing books that contain every permissible combination of letters and thus information about everything (or alternatively, a single book of infinitely thin pages, each one opening out into further pages of text). The library is a model of the universe—but is it a useful one? Borges describes the endless searches for the book that might be the ‘catalogue of catalogues’! Are our attempts to model the environment a similarly fruitless endeavour?

Compare the definition by Grand (2000: 140): ‘Something is complex if it contains a great deal of information that has a high utility, while something that contains a lot of useless or meaningless information is simply complicated.’ The environment, by this definition, is something that may initially appear complicated. Our aim is to render it merely complex! Any explanation, whether it be a qualitative description or a numerical simulation, is an attempt to use a model to achieve this aim. Although we will focus almost exclusively on numerical models, these models are themselves based on conceptual models that may be more-or-less complex (see discussions in Chapters 2 and 17). One of the main issues underlying this book is whether simple models are adequate explanations of complex phenomena. Can (or should) we include Ockham's razor as one of the principal elements in our modeller's toolkit?

Bar-Yam (1997) points out that a dictionary definition of complex suggests that it means ‘consisting of interconnected or interwoven parts’. ‘Loosely speaking, the complexity of a system is the amount of information needed in order to describe it’ (p. 12). The most complex systems are totally random, in that they cannot be described in shorter terms than by representing the system itself (Casti, 1994)—for this reason, Borges' ‘Library of Babel’ is not a good model of the universe, unless it is assumed that the universe is totally random (or alternatively that the library is the universe). Complex systems will also exhibit emergent behaviour (Bar-Yam, 1997), in that characteristics of the whole are developed (emerge) from interactions of their components in a non-apparent way. For example, the properties of water are not obvious from those of its constituent components, hydrogen and oxygen molecules. Rivers emerge from the interaction of discrete quantities of water (ultimately from raindrops) and oceans from the interaction of rivers, so emergent phenomena may operate on a number of scales.

A number of types of model complexity can be defined:

a. Process complexity (complication)—the sophistication and detail of the description of processes (see Section 2.2.4).

b. Spatial complexity—the spatial extent and grain of variation (and lateral flows) represented.

c. Temporal complexity—the temporal horizon and resolution and the extent of representation of system dynamics.

d. Inclusivity—the number of processes included.

e. Integration—the extent to which the important feedback loops are closed.

Researchers have tended to concentrate on (a) whereas (b)–(e) are probably more important in natural systems.

The optimal model is one that contains sufficient complexity to explain phenomena, but no more. This statement can be thought of as an information-theory rewording of Ockham's razor. Because there is a definite cost to obtaining information about a system, for example by collecting field data (see discussion in Chapter 2 and elsewhere), there is a cost benefit to developing such an optimal model. In research terms there is a clear benefit because the simplest model will not require the clutter of complications that make it difficult to work with, and often difficult to evaluate (see the discussion of the Davisian cycle by Bishop 1975 for a geomorphological example).

Opinions differ, however, on how to achieve this optimal model. The traditional view is essentially a reductionist one. The elements of the system are analysed and only those that are thought to be important in explaining the observed phenomena are retained within the model. Often this approach leads to increasingly complex (or possibly even complicated) models where additional process descriptions and corresponding parameters and variables are added. Generally the law of diminishing returns applies to the extra benefit of additional variables in explaining observed variance. The modelling approach in this case is one of deciding what level of simplicity in model structure is required relative to the overall costs and the explanation or understanding achieved.

By contrast, a more holistic viewpoint is emerging. Its proponents suggest that the repetition of simple sets of rules or local interactions can produce the features of complex systems. Bak (1997), for example, demonstrates how simple models of sand piles can explain the size of occurrence of avalanches on the pile, and how this approach relates to a series of other phenomena (see Chapter 16). Bar-Yam (1997) provides a thorough overview of techniques that can be used in this way to investigate complex systems. The limits of these approaches have tended to be related to computing power, as applications to real-world systems require the repetition of very large numbers of calculations. A possible advantage of this sort of approach is that it depends less on the interaction and interpretations of the modeller, in that emergence occurs through the interactions at a local scale. In most systems, these local interactions are more realistic representations of the process than the reductionist approach that tends to be conceptualized so that distant, disconnected features act together. The reductionist approach therefore tends to constrain the sorts of behaviour that can be produced by the model because of the constraints imposed by the conceptual structure of the model.

In our opinion, both approaches offer valuable means of approaching understanding of environmental systems. The implementation and application of both are described through this book. The two different approaches may be best suited for different types of application in environmental models given the current state of the art. Thus the presentations in this book will contribute to the debate and ultimately provide the basis for stronger environmental models.

1.4 How to Use This Book

We do not propose here to teach you how to suck eggs (or give scope for endless POMO discussion), but would like to offer some guidance based on the way we have structured the chapters. This book is divided into four parts. We do not anticipate that many readers will want (or need) to read it from cover to cover in one go. Instead, the different elements can be largely understood and followed separately, in almost any order. Part I provides an introduction to modelling approaches in general, with a specific focus on issues that commonly arise in dealing with the environment. Following from background detail, which in turn follows the more basic material covered in Mulligan and Wainwright (2012), we have concentrated on providing details of a number of more advanced approaches here. The chapters have been written by leading modellers in the different areas, and give perspectives from a wide range of disciplines, applications and philosophical standpoints.

The 11 chapters of Part II present a ‘state of the art’ of environmental models in a number of fields. The authors of these chapters were invited to contribute their viewpoints on current progress in thei...

Table of contents

• Cover
• Companion Website
• Title Page
• Copyright
• Dedication
• Preface to the Second Edition
• Preface to the First Edition
• List of Contributors
• Part I: Model Building
• Part II: The State of the Art in Environmental Modelling
• Part III: Models for Management
• Part IV: Current and Future Developments
• Index