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Full Description
In most natural sciences, modeling is a widespread method of gaining new knowledge about natural and technical systems. This book analyses the concepts of 'model' and 'modeling' in different fields of research. The different methods of modeling as well as the potentials and limits of this concept are reflected and discussed. The book presents a variety of modeling techniques, from mathematical models in climatology, meteorology or oceanography to methods used in morphology, decision-making in ecology and physical modeling in oceanography. In this broad overview regarding modeling, the book is unique.
Contents
1 Models as Focusing Tools: Linking Nature and the Social World.- Abstract.- 1.1 Models as Focusing Tools: Linking Nature and the Social World.- 1.2 The Practice of Modeling.- 1.3 The Methodology of Modeling.- 1.4 Isomorphism.- 1.5 Quantification.- 1.6 Modeling Societal Sensitivity.- 1.7 Examples of Models.- 1.8 The Poverty of Economics.- 1.9 Hybrid Forms or the Linkage between Social and Physical Processes.- Appendix: Additional Comments of Modeling Climate and Societal Sensitivity.- 2 Models between Academia and Applications.- Abstract.- 2.1 Introduction.- 2.1.1 Laboratory Model.- 2.1.2 Miniaturisation:.- 2.1.3 Numerical Models.- 2.1.4 Specifics of Environmental Research.- 2.2 General Properties of Models.- 2.3 Purpose of Models.- 2.3.1 Quasi-realistic Models Surrogate Reality.- 2.3.2 Cognitive Models: Reduction of Complex Systems.- 2.4 Conclusions.- Acknowledgments.- 3 Basic Concepts in Dynamical Modeling.- Abstract.- 3.1 Introduction.- 3.2 Classical Mechanics.- 3.2.1 Equations of Motion.- 3.2.2 Hamiltonian Dynamics.- 3.2.3 Integrable Systems.- 3.2.4 Flow in Phase Space.- 3.3 Ideal Fluids.- 3.3.1 Lagrangian Description.- 3.3.2 Eulerian Description.- 3.4 Thermodynamics.- 3.4.1 The Second Law of Thermodynamics.- 3.4.2 Diffusion.- 3.5 Dynamical Systems.- 3.6 Statistical Mechanics.- 3.6.1 Combinatorics.- 3.6.2 H-theorem.- 3.7 Stochastic Processes.- 3.7.1 Random Walk.- 3.7.2 Autoregressive Process.- 3.7.3 Langevin Equation.- 3.7.4 Stochastic Differential Equations.- 3.8 Discussion.- Acknowledgments.- 4 Process-oriented Models in Physical Oceanography.- Abstract.- 4.1 Introduction.- 4.1.1 Philosophy of Process Models.- 4.1.2 Process Model Strategies.- 4.1.3 Parameter Space.- 4.2 Examples.- 4.2.1 Linear and Linearised Models.- 4.2.2 Nonlinear Models.- 4.2.3 Interdisciplinary Process Models.- 4.2.4 Sea Ice Models.- 4.3 Concluding Remarks.- 4.3.1 Outlook.- 4.3.2 Comments on Numerical Process Models.- Acknowledgments.- A HPE.- B QG.- C SWE.- D RG.- 5 Mathematical Models in Environmental Research.- 5.1 Introduction.- 5.2 Mathematical Models - an Overview.- 5.2.1 Box Models.- 5.2.2 Cellular Automata.- 5.2.3 Differential Equations.- 5.2.4 Other Techniques.- 5.3 From Nature to Navier-Stokes' Equations.- 5.3.1 The Ocean Currents.- 5.3.2 Wind and Sea Bottom.- 5.3.3 The Coriolis Force.- 5.3.4 River Runoff, Solar Heating, Surface Cooling.- 5.3.5 Sea Surface Elevation.- 5.3.6 Continuity.- 5.3.7 The Resulting Equations.- 5.3.8 Difficulties.- 5.3.9 Boundary Conditions.- 5.3.10 Simplifications.- 5.4 From Differential Equations to a Numerical Representation.- 5.4.1 Discretisation.- 5.4.2 Simulation.- 5.4.3 Simplifications.- 5.5 Summary.- Acknowledgments.- 6 Physical Modeling of Flow and Dispersion.- 6.1 Introduction.- 6.2 Properties of Wind-Tunnel Boundary Layers.- 6.3 Dimensional Analysis.- 6.4 Matching of Similarity Requirements.- 6.5 Experiments.- 6.6 Variation of Similarity Parameters.- 6.7 Parameterisation of Thermodynamic Processes.- 6.8 Small-Scale/Full-Scale Comparisons.- 6.9 Investigation of Obstacle Effects.- 6.10 Conclusions.- Acknowledgements.- 7 Conceptual Models for Ecology-Related Decisions.- Abstract.- 7.1 Introduction.- 7.2 The Wadden Sea - a Sensitive Environment.- 7.3 The Environmental Sensitivity Index (ESI) for Wadden Sea Areas.- 7.3.1 The Evaluation.- 7.3.2 Evaluation of Individual Categories.- 7.3.3 General Evaluation.- 7.4 Environmental (Ecological) Risk Assessment (ERA).- 7.4.1 Environmental (Ecological) Impact Assessment (EIA).- 7.4.2 The Construction Measures.- 7.4.3 The Integrated Ecological Monitoring-Investigations.- 7.5 Ecological Monitoring of the Benthos.- 7.6 Conclusions.- 8 Models in the Mechanics of Materials.- Abstract.- 8.1 Introduction.- 8.2 Modeling in the Mechanics of Materials.- 8.2.1 Testing.- 8.2.2 The Theory of Continuum Mechanics.- 8.2.3 Numerical Analysis.- 8.3 Examples.- 8.3.1 The Tensile Test.- 8.3.2 Micromechanical Modeling.- 8.4 Conclusions.- 9 Mathematical Morphology.- Abstract.- 9.1 Introduction.- 9.2 An Introductive Example.- 9.3 The Morphological Tool Box.- 9.3.1 The Four Operations.- 9.3.2 Characterisation of Openings and Filtering.- 9.3.3 Watersheds.- 9.3.4 The Construction Principle.- 9.3.5 Segmentation Programme.- 9.4 Quantification and Morphological Measurements.- 9.4.1 Granulomeres, Spectral Function and Curve by Erosion.- 9.5 Random Models.- 10 Statistical Interpolation Models.- Abstract.- 10.1 Introduction.- 10.2 The Random Function Model.- 10.2.1 TheVariogram.- 10.2.2 Kriging.- 10.3 Multivariate Geostatistics.- 10.3.1 Cokriging.- 10.3.2 Data Configurations.- 10.3.3 Isotopy: Intrinsic Correlation.- 10.3.4 Coregionalisation Models.- 10.3.5 Heterotopy: External Drift.- 10.3.6 Heterotopy: Collocated Cokriging.- 10.4 Non-Stationary Model.- 10.4.1 Intrinsic Random Functions of Order k.- 10.4.2 Kriging with Drift.- 10.4.3 Dual Kriging.- 10.4.4 Splines.- 10.5 Conclusion.- 11 Statistics - an Indispensable Tool in Dynamical Modeling.- Abstract.- 11.1 Environmental Research.- 11.2 State Space Models.- 11.3 Statistics and Quasi-realistic Models.- 11.3.1 Parameterisations.- 11.3.2 Analyzing Integrations of Quasi-Realistic Models.- 11.3.3 Merging Dynamical Knowledge and Observational Evidence.- 11.4 Reduced "Cognitive" Models.- 11.4.1 Principal Interaction Patterns.- 11.4.2 Principal Oscillation Pattern Analysis.- Acknowledgments.- References.
