Introduction to the Modelling of Marine Ecosystems (eBook)

W. Fennel, T. Neumann (Autoren)

eBook Download: PDF | EPUB

2014 | 2. Auflage
372 Seiten
Elsevier Science (Verlag)
978-0-444-63415-3 (ISBN)

Infos

Introduction to the Modelling of Marine Ecosystems, Second Edition provides foundational information on the construction of chemical and biological models - from simple cases to more complex biogeochemical models and life cycle resolving model components. This step-by-step approach to increasing the complexity of the models allows readers to explore the theoretical framework and become familiar with the models even when they have limited experience in mathematical modeling. Introduction to the Modelling of Marine Ecosystems shows how biological model components can be integrated into three dimensional circulation models and how such models can be used for numerical experiments. - Covers the marine food web from nutrients, phytoplankton to higher trophic levels - Presents information on the response of marine systems to external pressures as seen in physical biological models - Provides an extended discussion of unifying theoretical concepts and of physical biological interaction - Covers higher trophic levels, in particular multi-species fish models and their interaction with the biogeochemical models - Offers MATLAB scripts on a companion website for many of the described example models to facilitate reproduction of the findings in the book and guide reader to writing own code

Dr. Wolfgang Fennel is professor emeritus of physical oceanography at the University of Rostock and he was head of the section of physical oceanography of the Baltic Sea Research Institute, (IOW). His background is theoretical oceanography and he is a specialist in oceanic circulation and wave processes. He is also working on the coupling of physics and marine biology. Wolfgang Fennel was President of SCOR (2008-2012) and is now Past SCOR President until 2016. He promoted interdisciplinary co-operation.

Inhalt

Front Cover 1
Introduction to the Modelling of Marine Ecosystems 4
Copyright 5
Contents 6
Preface 9
Chapter 1: Introduction 12
1.1 Models of Marine Ecosystems 12
1.2 Models from Nutrients to Fish 15
1.2.1 Models of Individuals, Populations and Biomass 15
1.2.2 Fisheries Models 17
1.2.3 Unifying Theoretical Concept 19
1.2.4 The Plan of the Book 22
Chapter 2: Chemical-Biological Models 24
2.1 Chemical-Biological Processes 24
2.1.1 Biomass Models 25
2.1.2 Nutrient Limitation 29
2.1.3 Recycling 31
2.1.4 Zooplankton Grazing 35
2.2 Simple Models 36
2.2.1 Construction of a Simple NPZD Model 36
2.2.2 First Model Runs 43
2.2.3 A Simple NPZD Model with Variable Rates 45
2.2.4 Eutrophication Experiments 49
2.2.5 Discussion 55
2.3 Simple Plankton Models for the Ocean 56
2.3.1 A Simple NPZ Model for the Ocean Mixed Layer 57
2.3.2 NPZ and NPZD Models for the Annual Cycle of the Oceanic Mixed Layer 59
Chapter 3: More Complex Models 64
3.1 Competition 64
3.2 Several Functional Groups 66
3.2.1 Succession of Phytoplankton 74
3.3 N2 Fixation 79
3.4 Denitrification 85
3.4.1 Numerical Experiments 91
3.4.1.1 Experiment 1 91
3.4.1.2 Experiment 2 95
3.4.1.3 Experiment 3 100
3.4.2 Processes in Sediments 102
Chapter 4: Modelling Life Cycles of Copepods and Fish 108
4.1 Growth and Stage Duration 109
4.2 Stage-Resolving Models of Copepods 111
4.2.1 Population Density 112
4.2.2 Stage-Resolving Population Models 115
4.2.3 Population Model and Individual Growth 116
4.2.4 Stage-Resolving Biomass Model 122
4.3 Experimental Simulations 125
4.3.1 Choice of Parameters 125
4.3.1.1 Grazing Rates 125
4.3.1.2 Loss Rates 126
4.3.1.3 Reproduction 127
4.3.1.4 Mortality and Overwintering 127
4.3.2 Rearing Tanks 128
4.3.3 Inclusion of Lower Trophic Levels 130
4.3.4 Simulation of Biennial Cycles 133
4.4 A Fish Model 138
4.4.1 Formulation of the Theory 138
4.4.2 Structure of the Fish Model Equations 1
4.4.3 Predator–Prey Interaction and Effective Growth 145
4.4.4 Modelling Reproduction and Mortality 148
4.4.5 Coupling Fish and Lower Trophic Levels 150
4.4.6 Example Scenarios 1
4.4.7 Discussion 162
Chapter 5: Physical–Biological Interaction 164
5.1 Irradiance 164
5.1.1 Daily, Seasonal and Annual Variation 164
5.1.2 Production–Irradiance Relationship 166
5.1.3 Light Limitation and Mixing Depth 169
5.2 Coastal Ocean Dynamics 173
5.2.1 Basic Equations 174
5.2.2 Large-Scale Winds and Coastal Jets 179
5.2.3 Kelvin Waves and Undercurrents 183
5.2.4 The Role of Wind-Stress Curls 189
5.2.5 Discussion 200
5.3 Advection–Diffusion Equation 201
5.3.1 Reynolds Rules 201
5.3.2 Analytical Examples 203
5.3.3 Turbulent Diffusion in Collinear Flows 205
5.3.3.1 Turbulent Diffusion in a Shear Flow 208
5.3.3.2 Turbulent Diffusion in Eddies 210
5.3.3.3 Turbulent Diffusion in Deformation Fields 211
5.3.3.4 Aggregation at Convergence Lines 212
5.3.4 Patchiness and Critical Scales 213
5.4 Upscaling and Downscaling 216
5.5 Resolution of Processes 219
5.5.1 State Densities and Their Dynamics 220
5.5.2 Primary Production Operator 222
5.5.3 Predator–Prey Interaction 223
5.5.4 Mortality Operators 226
5.5.5 Model Classes 226
Chapter 6: Coupled Models 228
6.1 Introduction 228
6.2 Regional to Global Models 229
6.3 Circulation Models 231
6.4 Baltic Sea 233
6.5 Description of the Model System 241
6.5.1 Baltic Sea Circulation Model 241
6.5.2 The Biogeochemical Model ERGOM 242
6.6 Simulation of the Annual Cycle 250
6.7 Simulation of the Decade 1980–1990 260
6.8 A Load Reduction Experiment 270
6.9 Projection of Future Changes 274
6.10 Tracking of Elements 276
6.11 Discussion 276
Chapter 7: Circulation Model, Copepods and Fish 278
7.1 Recruitment (Match–Mismatch) 279
7.2 Copepods in the Baltic Sea Model 279
7.3 Three-Dimensional Simulations 280
7.3.1 Time Series of Basin Averages 281
7.3.2 Spatial Distribution 284
7.4 Modelling of Behavioural Aspects 288
7.4.1 Vertical Motion 289
7.4.2 Visibility and Predation 291
7.4.3 Individual-Based Versus Population Models 292
7.4.4 Water-Column Models 293
7.5 Fish in a Three-Dimensional Model 297
7.5.1 Coupling Upper and Lower Food Webs 298
7.5.2 Horizontally Moving Fish 299
7.5.3 Initialization and First Simulation 301
7.5.4 Results and Discussion 302
7.5.5 Fish and Biogeochemistry 304
7.6 ERGOM: A Biogeochemical Model for Regional Seas 309
Chapter 8: A Brief Introduction to MATLAB 310
8.1 Fundamentals 310
8.1.1 Matrix and Array Operations 312
8.1.2 Figures 313
8.1.3 Script Files and Functions 317
8.2 Ordinary Differential Equations 319
8.3 Miscellaneous 323
Appendix: Content of the Booksite 326
Bibliography 330
Index 340
Color Plates 343

Textauszug

Chapter 1

Introduction

1.1 Models of marine ecosystems

Understanding and quantitatively describing of marine ecosystems requires an integration of physics, chemistry and biology. Coupling biology and physical oceanography in models has many attractive features: We can do experiments with models of marine systems while the real system can only be observed in the state at the time of the observation. We can also employ the predictive potential of models for applications such as environmental management or, on a larger scale, we can study past and future developments with the aid of experimental simulations. Moreover, a global synthesis of sparse observations can be achieved by using coupled three-dimensional models to extrapolate data in a coherent manner.

However, running complex coupled models requires substantial knowledge and skill. To approach the level of skill needed to work with coupled models, it is reasonable to proceed step-by-step from simple to complex problems.

What are biological models? We use the term ‘model’ synonymously for theoretical descriptions in terms of sets of differential equations that describe the food web dynamics of marine systems. The food webs are relatively complex systems, which can sketched simply as a flux of material from nutrients to phytoplankton to zooplankton to fish and recycling paths back to nutrients. Phytoplankton communities consist of a spectrum of microscopic single-cell plants, microalgae. Many microalgae in marine or freshwater systems are primary producers, which build up organic compounds directly from carbon dioxide and various nutrients dissolved in the water. The captured energy is passed along to components of the aquatic food chain through the consumption of microalgae by secondary producers, the zooplankton. The zooplankton in turn is eaten by fish, which is caught by man. Moreover, there are pathways from the different trophic levels to nutrients through respiration, excretion and dead organic material, detritus, which is mineralized by microbial activity. The regenerated nutrients can then again fuel primary production.

It is obvious that the complex network of the full marine food web cannot practically be covered by one generic model. There are many models that were developed for selected, isolated parts of the food web. For these models the links to the upper or lower trophic levels must be prescribed or parameterized effectively in an appropriate manner. In order to construct such models, we may consider a number of individuals or we can introduce aggregated state variables to characterize a system. State variables must be well defined and measurable quantities, such as concentration of nutrients and biomass or abundance (i.e. number of animals per unit of volume). The dynamics of the state variables (i.e. their change in time and space), is driven by processes, such as nutrient uptake, respiration or grazing, as well as physical processes such as light variations, turbulence and advection.

Ecosystem models can be characterized roughly by their complexity, i.e. by the number of state variables and the degree of process resolution. The resolution of processes can be scaled up or down by aggregation of variables into a few integrated ones or by increasing the number of variables, respectively. For example, zooplankton can be considered as a bulk biomass or can be described in a stage resolving manner. Models with very many state variables are not automatically better than those with only a few variables. The higher the number of variables, the larger the requirements of process understanding and quantification. If the process rates are more or less guesswork, there is no advantage to increase the number of poorly known rates and parameters. Moreover, not every problem requires a high process resolution, and the usage of a subset of aggregated state variables may be sufficient to answer specific questions. Models should be only as complex as required and justified by the problem at hand. Model development needs to be focused, with clear objectives and a methodological concept that ensures that the goals can be reached.

Alternatively, models can be characterized also by their spatial dimension, ranging from zero-dimensional box models to advanced three-dimensional models. In box models, the physical processes are largely simplified while the resolution of chemical biological processes can be very complex. Such models are easy to run and may serve as workbenches for model development. The next step is one-dimensional water column models, which allow a detailed description of important physical controls of biological processes by, for example, vertical mixing and light profiles. Such models may be useful for systems with weak horizontal advection. In order to couple the biological models to full circulation models, it is advisable to reduce the complexity of the biological representations as far as reasonable. If, for example, advection plays an important part for the life cycles of a species, the biological aspects may be largely ignored. Extreme cases of reduced biology coupled to circulation models are simulations of trajectories of individuals, cells or animals, which are treated as passively drifting particles.

The process of constructing the equations, i.e. building a model, will be described in the following chapters, starting with simple cases followed by increasingly complex models. Ecologists often are uncomfortable with the numerous simplifying assumptions that underlie most models. However, modelling marine ecosystems can benefit from looking at theoretical physics, which demonstrates how deliberately simplified formulations of cause–effect relationships help to reproduce predominant characteristics of some distinctly identifiable, observable phenomena. It is illuminating to read the viewpoint of G.S. Riley, one of the pioneers in modelling marine plankton, to this problem, as mentioned in his famous paper (Riley, 1946). He wrote: ‘…physical oceanography, one of the youngest branches in the actual years, is more mature than the much older study of marine biology. This is perhaps partly due to the complexities of the material. More important, however, is the fact that physical oceanography has aroused the interest of a number of men of considerable mathematical ability, while on the other hand marine biologists have been largely unaware of the growing field of bio-mathematics, or at least they have felt that the synthetic approach will be unprofitable until it is more firmly backed by experimental data’.

There is another important issue that deserves some consideration. The biological model equations are basically nonlinear and, in general, not analytically solvable. Thus, early attempts to model marine ecosystems were retarded or even stopped by mathematical problems. These difficulties could only be resolved by numerical methods that require computers, which were not available in an easy-to-use way until the 1980s. This frustrating situation may be one of the reasons that many marine biologists or biological oceanographers were not very much interested in mathematical models in the early years.

With the advent of easily accessible computers, the technical problems were removed. However, it seems the interdisciplinary discussion on modelling develops slowly. Some biologist are doubtful whether anything can be learned from models, but a growing community sees a beneficial potential in modelling. Why do we need models? The reasons include,

• to develop and enhance understanding,

• to quantify descriptions of processes,

• to synthesize and consolidate our knowledge,

• to establish interaction of theory and observation,

• to develop predictive potential,

• to simulate scenarios of past and future developments.

Models are mathematical tools by which we analyse, synthesize and test our understanding of the dynamics of the system through retrospective and predictive calculations. Comparison with data provides the process of model validation. Owing to problems of observational undersampling of marine systems, data are often insufficient when used for model validation. Validation of models often amounts to fitting the data by adjusting parameters, i.e. calibrating the model. It is important to limit the number of adjustable parameters, because a tuned model with too many fitted parameters can lose any predictive potential. It might work well for one situation but could break down when applied to another case. Riley stated this more than 50 years ago, when he wrote ‘…(analysis based on a model, expressed by a differential equation,)… is a useful tool in putting ecological theories to a quantitative test. The disadvantage is that it requires detailed quantitative information about many processes, some of which are only poorly understood. Therefore, until more adequate knowledge is obtained, any application of the method must contain some arbitrary assumptions and many errors due to over-simplification’ (Riley, 1947).

Because many modelers have backgrounds in physics and mathematics, ecosystem modelling is an interdisciplinary task that requires a well-balanced dialogue of biologists and modelers to address the right questions and to develop theoretical descriptions of the processes to be modelled. The development of the interdisciplinary dialogue is a process which should start at the universities where students of marine biology should...

Produkt-Details

• Erscheint lt. Verlag: 18.9.2014
• Sprache: englisch
• Themenwelt: Naturwissenschaften ► Biologie ► Limnologie / Meeresbiologie
• Themenwelt: Naturwissenschaften ► Biologie ► Ökologie / Naturschutz
• Themenwelt: Technik
• ISBN-10: 0-444-63415-0 / 0444634150
• ISBN-13: 978-0-444-63415-3 / 9780444634153