1 Springer Series in Physical Environment Managing Editor D. Barsch, Heidelberg Editors I. Douglas, Manchester· F. Joly, Paris M. Marcus, Tempe· B. Messerli, Bern Advisory Board F. Ahnert, Aachen· R. Co que, Paris· Y. Dewolf, Paris W Eriksen, Hannover· O. Franzle, Kiel A. Godard, Meudon . A. Guilcher, Brest H. Leser, Basel· J. Nicod, Aix-En-Provence H. Rohdenburg, Braunschweig· A. Semmel, Frankfurt G. Stablein, Berlin· H. Svensson, K0benhavn H. Bremer, Koln . J. R. Mather, Newark A. R. Orme, Los Angeles Richard J. Huggett Earth Surface Systems With 162 Figures Springer-Verlag Berlin Heidelberg New York Tokyo Dr. RICHARD J. HUGGETT University of Manchester School of Geography Manchester, M13 9PL England ISBN-13:978-3-642-82498-2 e-ISBN-13:978·3-642-82496-8 DOl: 10.1007/978-3-642-82496-8 This work is subject to copyright All rights are reserved, whether the whole or part of the material is concerned, specifically those of translation, reprinting, re-use of illustra tions, broadcasting, reproduction by photocopying machine or similar means, and stor age in data banks. Under § 54 of the German Copyright Law where copies are made for other than private use a fee is payable to 'Verwertungsgesellschaft Wort', Munich. © by Springer-Verlag Berlin Heidelberg 1985 Softcoverreprintof the hardcover lst edition 1985 The use of registered names, trademarks etc: in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant pro tective laws and regulations and therefore free for general use. Typesetting: K + V Fotosatz GmbH, Beerfelden. 2132/3130.543210 For my parents Preface 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". However, the reviewer thought that the term notion sumqled it up and proceeded to list synonyms from the Oxford English Dictionary - general, fancy, invention, small, cheap, speculative,' abstract. Regardless of the merits or demerits of the paper in question, the dismissal of the systems approach in such an at~abilious and uncompromising a fashion is unjustified. Not all members of the anti-systems lobby are so unreasonable and unconstructive. Nonetheless, they do see in the systems ap proach a number of contradictions and difficulties. An aim of this book is to show that these contradictions and difficulties are more apparent than real and arise from misinterpretations and mis undeIstandings of systems concepts and terms. Two main sources of misunderstanding can be identified. The first is the erroneous belief that the systems approach is new-fangled: taken in wide per spective, the systems approach has a long pedigree dating back at least to the sixteenth-century scientific revolution. A second source of misunderstanding is the erroneous belief that systems are invariably complex: systems can be viewed and defined as VIII Preface either simple or complex structures. Bearing in mind these sources of misunderstanding, and in an attempt to show that the systems approach is inextricably linked with the traditional scientific ap proach, the systems and systems methods dealt with in this book are, when first met with, placed in an historical setting. The scope of a book on Earth surface systems is broad indeed. Only a small sample from the rich literature in the field can be of fered here. In taking the sample, I have tried to pick case studies from the full range of systems research carried out by scientists with an interest in the surface of the Earth. Inevitably, however, I shall have left myself open to the charge of partiality in giving the lion's share of attention to topics with which I am most familiar and in which my main interests lie. I trust that any bias in the selection of topics does not detract from the development of the general theme of the book. I should like to thank a number of people without whose as sistance the boek would never have appeared: for asking me to write the book and for help and encouragement at all stages in writing it, Ian Douglas; for producing the typescript, the sec retaries in the Geography Department at Manchester University; for drawing most of the diagrams, Nick Scarle and Graham Bowden; and lastly, for never succeeding in stopping me from writing for more than a few hours at a time, my family. Macclesfield, June 1985 RICHARD HUGGETT Contents Part I Introduction Chapter 1 Systems and Models . . . . . . . . . . . . . . . . . . . . . . . 3 1.1 Defining Systems ............................... 3 1.1.1 Systems as Form and Process Structures ..... 4 1.1.2 Systems as Simple and Complex Structures ... 4 1.1.3 Systems and'Their Surroundings.... . .. .... . 5 1.1.4 A Problem of Scale. . . . . . . . . . . . . . . . . . . . . . . 7 1 .. 2 Models of Systems .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 1.2.1 Conceptual Models ... . . . . . . . . . . . . . . . . . . . . 9 1.2.2 Scale Models ............................ 10 1.2.3 Mathematical Models ... . . . . . . . . . . . . . . . . . . 11 Part II Conceptual Models Cha)lter 2 Simple and Complex Systems ............... 17 2.1 Simple Systems. . ... ... .... . ... . . . ... . .. . ... .... 17 2.2 .Systems of Complex Disorder .......... ,......... 20 2.2.1 Irreversible Processes ..................... 20 2.2.2 Accounting Models: the Laws of Thermodynamics ........................ 22 2.3 Systems of Complex Order .... . . . . . . . . . . . . . . . . . . . 25 2.3.1 Nonequilibrium Systems .................. 25 2.3.2 Systems Far from Equilibrium ............. 26 2.3.3 Open Systems attheEarth's Surface ........ 27 Chapter 3 Form and Process Systems ................. 30 3.1 Models of System Form ......................... 30 3.1.1 Models of System Constitution ............. 30 3.1.2 Models of System Geometry ............... 30 3.2 Models of System Process . . . . . . . . . . . . . . . . . . . . . . . . 32 3.2.1 Land-Surface Cascades ................... 33 3.2.2 Solid-Phase and Liquid-Phase Cascades ..... 35 x Contents 3.3 Models of System Form and Process. . . . . . . . . . . . . . . 37 3.3.1 Concepts of Landscape Development . . . . . . . . 39 3.3.2 Concepts of Soil Development ............. 41 3.3.3 Concepts of Soil-Landscape Development. . . . 43 Part m Mathematical Models Chapter 4 Deductive Stochastic Models 47 4.1 Introduction to Probability ...................... 47 4.1.1 The Classical View of Probability ... . . . . . . . . 48 4.1.2 The Relative Frequency View of Probability .. 48 4.1.3 Axioms of Probability Theory . . . . . . . . . . . . . . 49 4.2 Independent Events in Time . . . . . . . . . . . . . . . . . . . . . . 51 4.2.1 Binomial Processes.... . ... . ... . ...... . ... 51 4.2.2 Poisson Processes ........................ 53 4.3 Independent Events in Space ..................... 55 4.3.1 Point Patterns.... . ..... .... .... . ..... . .. 55 4.3.2 Line Patterns. . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 4.3.3 Area Patterns.. .... . . ... . .... . ... . . .... . . 60 4.4 Random-Walk Models .......................... 60 4.4.1 Stream Networks. . . . . . . . . . . . . . . . . . . . . . . . . 61 4.4.2 Alluvial Fans ............................ 65 4.5 Markov Chains ................................ 70 4.5.1 Transition Probabilities ................... 70 4.5.2 Sedimentary Sequences ................... 72 4.5.3 Volcanic Activity .. ..... . ... . ... . . . ... . . .. 73 4.6 Entropy Models ................................ 74 4.6.1 EntropyMaximization.................... 74 4.6.2 Entropy Minimization .................... 75 4.6.3 Developments of the Thermodynamic Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76 Chapter 5 Inductive Stochastic Models ................ 78 5.1 B'ox and Jenkins's Models: an Introduction. . . . . . . . . 78 5.1.1 System Definition ........................ 81 5.1.2 Stages in Systems Analysis. . . . . . . . . . . . . . . . . 82 5.2 Autoregressive Moving-Average Models of Time Series. ............ ... . ..... . ....... ..... .... .. 83 5.2.1 Model Formulation. .. ... ... . ..... .... . . .. 83 5.2.2 Modelling Procedures . . . . . . . . . . . . . . . . . . . . . 85 5.2.3 The Lagan Rainfall Series ................. 87 5.3 Autoregressive Moving-Average Models of Distance Series..... ... .......... . . .... ....... . ..... ... . 88 5.3.1 Model Formulation.. . .... ... . ..... . .... .. 88 5.3.2 River Meanders. . . . . . . . . . . . . . . . . . . . . . . . . . 89 Contents XI 5.3.3 Landforms.............................. 92 5.4 Transfer Function Models ....................... 95 5.4.1 Model Formulation... ...... . .... ... .... .. 95 5.4.2 Rainfall and Runoff in the Lagan Drainage Basin................................... 97 5.4.3 Channel Form in the Afon Elan, Wales ...... 97 5.5 Problems ofInductive Stochastic Modelling ........ 100 Chapter 6 Statistical Models . . . . . . . . . . . . . . . . . . . . . . . . . 102 6.1 Simple Regression and Correlation ................ 103 6.1.1 The Regression Line ...................... 103 6.1.2 The Correlation Coefficient. . . . . . . . . . . . . . . . 104 6.1.3 Problems of Correlation .................. 106 6.1.4 Linear Relations ......................... 107 6.1.5 Linear Versus Nonlinear Relations. . . . . . . . . . 108 6.2' Multiple Regression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112 6.2.1 "Simple" Multiple Regression. . . . . . . . . . . . . . 113 6.2.2 Trend Surface Analysis ................... 114 6.2.3 Stepwise Regression ...................... 117 6.2.4 Problems of Multiple Regression ........... 121 6.3 Correlation Systems ............................ 122 6.3.1 Principal Component Analysis ............. 123 6.3.2 Principal Coordinate Analysis. . . . . . . . . . . . . . 125 6.3.3 Factor Analysis .......................... 125 6.3.4 Canonical Correlation .............•...... 129 6.3.5 Problems with Correlation Systems ......... 134 Chapter 7 Deterministic Models of Water and Solutes ... 135 7.1 Ice........................................... 137 7.1.1 Glaciers ................................ 137 7.1.2 IceSheets............................... 138 7.2 Water ........................................ 142 7.2.1 Overland Flow ........................... 142 7.2.2 Open Channel Flow ...................... 144 7.2.3 Flow in Porous Media .................... 145 7.2.4 Unsaturated Flow ........................ 148 7.3 Solutes........................................ 151 7.3.1 SeasandLakes .......................... 151 7.3.2 Solutes in Groundwater ................... 154 1.3.3 SolutesinSoils ........................... 157 Chapter 8 Deterministic Models of Slopes and Sediments 161 8.1 Discrete Component Models ..................... 161 8.2 Analytical Models .............................. 162 8.2.1 Heuristic Models. . . . . . . . . . . . . . . . . . . . . . . . . 162 XII Contents 8.2.2 Models Based on the Continuity Equation. . . . 173 8.3 Simulation Models. . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 180 8.3.1 Landscape Simulation .................... 181 8.3.2 Drainage Basin Simulation ................ 185 8.3.3 Nearshore Bar Formation ................. 192 8.3.4 Sand Dune Formation .................... 193 Chapter 9 Dynamical Systems Models. . . . . . . . . . . . . . . . . 198 9.1 Model Building ................................ 198 9.1.1 State and State Change . . . . . . . . . . . .. . . . . . . . 198 9.1.2 Transfer Equations . . . . . . . . . . . . . . . . . . . . . . . 201 9.2 System Stability ................................ 202 9.2.1 State Space. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202 9.2.2 Sensitivity Analysis. . . . . . . . . . . . . . . . . . . . . .. 204 9.3 Biogeochemical Cycles .......................... 206 9.3.1 Tl).e Global Cycle of Phosphorus ........... 206 9.3.2 The Global Cycle of Carbon Dioxide and Oxygen ............. , . . . . . . . . . . . . . . . . . . . 206 9.3.3 Strontium and Manganese in a Tropical Rain Forest.................................. 214 9.3.4 Water in Soils ........................... 216 9.3.5 Nutrients in Lake Erie .................... 218 9.4 Dissipative Structures ........................... 222 9.4.1 Bifurcations and Catastrophes ...... ;...... 222 9.4.2 Thresholds.............................. 226 9.4.3 Dominance Domains ..................... 231 Cltapter 10 Conclusion and Prospect. . . . . . . . . . . . . . . . . . 233 10.1 Models as a Complement to Field Studies. . . . . . . . . . . 234 10.2 Models as a Testing Ground for Long-Term Change. 238 10.3 Models as Good Predictors of Complex Situations ... 239 References ......................................... 243 Subject Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 263