Earth Surface Systems: (1 Springer Series in Physical Environment)

Discussions of "systems" and the "systems approach" tend to fall into one of two categories: the panegyrical and the disparaging. Scholars who praise the systems approach do so in the belief that it is a powerful and precise method of study. Scholars who try to shoot it down fail to see any advantage in it; indeed, many deem it periIicious. Van Dyne (1980, p. 889) records a facetious comment he once heard, the gist of which ran: "In instances where there are from one to two variables in a study you have a science, where there are from four to seven variables you have an art, and where there are more than seven variables you have a system". This tilt at the systems approach is mild indeed compared with the com- ments of an anonymous reviewer of a paper by myself concerned with the systems approach as applied to the soil. The reviewer stated bluntly that he or she had no time for an approach which falsifies and belittles work that has been done and is of no use for future work. My summary of the paper opened with the seemingly innocuous sentence "The notion of the soil as a system is placed on a . formal footing by couching it in terms of dynamical systems theory".

Table of Contents:
I Introduction.- 1 Systems and Models.- 1.1 Defining Systems.- 1.1.1 Systems as Form and Process Structures.- 1.1.2 Systems as Simple and Complex Structures.- 1.1.3 Systems and Their Surroundings.- 1.1.4 A Problem of Scale.- 1.2 Models of Systems.- 1.2.1 Conceptual Models.- 1.2.2 Scale Models.- 1.2.3 Mathematical Models.- II Conceptual Models.- 2 Simple and Complex Systems.- 2.1 Simple Systems.- 2.2 Systems of Complex Disorder.- 2.2.1 Irreversible Processes.- 2.2.2 Accounting Models: the Laws of Thermodynamics.- 2.3 Systems of Complex Order.- 2.3.1 Nonequilibrium Systems.- 2.3.2 Systems Far from Equilibrium.- 2.3.3 Open Systems at the Earth's Surface.- 3 Form and Process Systems.- 3.1 Models of System Form.- 3.1.1 Models of System Constitution.- 3.1.2 Models of System Geometry.- 3.2 Models of System Process.- 3.2.1 Land-Surface Cascades.- 3.2.2 Solid-Phase and Liquid-Phase Cascades.- 3.3 Models of System Form and Process.- 3.3.1 Concepts of Landscape Development.- 3.3.2 Concepts of Soil Development.- 3.3.3 Concepts of Soil-Landscape Development.- III Mathematical Models.- 4 Deductive Stochastic Models.- 4.1 Introduction to Probability.- 4.1.1 The Classical View of Probability.- 4.1.2 The Relative Frequency View of Probability.- 4.1.3 Axioms of Probability Theory.- 4.2 Independent Events in Time.- 4.2.1 Binomial Processes.- 4.2.2 Poisson Processes.- 4.3 Independent Events in Space.- 4.3.1 Point Patterns.- 4.3.2 Line Patterns.- 4.3.3 Area Patterns.- 4.4 Random-Walk Models.- 4.4.1 Stream Networks.- 4.4.2 Alluvial Fans.- 4.5 Markov Chains.- 4.5.1 Transition Probabilities.- 4.5.2 Sedimentary Sequences.- 4.5.3 Volcanic Activity.- 4.6 Entropy Models.- 4.6.1 Entropy Maximization.- 4.6.2 Entropy Minimization.- 4.6.3 Developments of the Thermodynamic Approach.- 5 Inductive Stochastic Models.- 5.1 Box and Jenkins's Models: an Introduction.- 5.1.1 System Definition.- 5.1.2 Stages in Systems Analysis.- 5.2 Autoregressive Moving-Average Models of Time Series.- 5.2.1 Model Formulation.- 5.2.2 Modelling Procedures.- 5.2.3 The Lagan Rainfall Series.- 5.3 Autoregressive Moving-Average Models of Distance Series.- 5.3.1 Model Formulation.- 5.3.2 River Meanders.- 5.3.3 Landforms.- 5.4 Transfer Function Models.- 5.4.1 Model Formulation.- 5.4.2 Rainfall and Runoff in the Lagan Drainage Basin.- 5.4.3 Channel Form in the Afon Elan, Wales.- 5.5 Problems of Inductive Stochastic Modelling.- 6 Statistical Models.- 6.1 Simple Regression and Correlation.- 6.1.1 The Regression Line.- 6.1.2 The Correlation Coefficient.- 6.1.3 Problems of Correlation.- 6.1.4 Linear Relations.- 6.1.5 Linear Versus Nonlinear Relations.- 6.2 Multiple Regression.- 6.2.1 "Simple" Multiple Regression.- 6.2.2 Trend Surface Analysis.- 6.2.3 Stepwise Regression.- 6.2.4 Problems of Multiple Regression.- 6.3 Correlation Systems.- 6.3.1 Principal Component Analysis.- 6.3.2 Principal Coordinate Analysis.- 6.3.3 Factor Analysis.- 6.3.4 Canonical Correlation.- 6.3.5 Problems with Correlation Systems.- 7 Deterministic Models of Water and Solutes.- 7.1 Ice.- 7.1.1 Glaciers.- 7.1.2 Ice Sheets.- 7.2 Water.- 7.2.1 Overland Flow.- 7.2.2 Open Channel Flow.- 7.2.3 Flow in Porous Media.- 7.2.4 Unsaturated Flow.- 7.3 Solutes.- 7.3.1 Seas and Lakes.- 7.3.2 Solutes in Groundwater.- 7.3.3 Solutes in Soils.- 8 Deterministic Models of Slopes and Sediments.- 8.1 Discrete Component Models.- 8.2 Analytical Models.- 8.2.1 Heuristic Models.- 8.2.2 Models Based on the Continuity Equation.- 8.3 Simulation Models.- 8.3.1 Landscape Simulation.- 8.3.2 Drainage Basin Simulation.- 8.3.3 Nearshore Bar Formation.- 8.3.4 Sand Dune Formation.- 9 Dynamical Systems Models.- 9.1 Model Building.- 9.1.1 State and State Change.- 9.1.2 Transfer Equations.- 9.2 System Stability.- 9.2.1 State Space.- 9.2.2 Sensitivity Analysis.- 9.3 Biogeochemical Cycles.- 9.3.1 The Global Cycle of Phosphorus.- 9.3.2 The Global Cycle of Carbon Dioxide and Oxygen.- 9.3.3 Strontium and Manganese in a Tropical Rain Forest.- 9.3.4 Water in Soils.- 9.3.5 Nutrients in Lake Erie.- 9.4 Dissipative Structures.- 9.4.1 Bifurcations and Catastrophes.- 9.4.2 Thresholds.- 9.4.3 Dominance Domains.- 10 Conclusion and Prospect.- 10.1 Models as a Complement to Field Studies.- 10.2 Models as a Testing Ground for Long-Term Change.- 10.3 Models as Good Predictors of Complex Situations.- References.