Cnpt nd hn n Mdrn Grph Cl nd Sltn Mdlln Un St n r. In Mfftt Snr rh ll rth Atrl rh Unt O x 42, Crn 08 Atrl ISS 006642 1991 IS I 82464 0 x 0 I. Mfftt Listing of Catmogs in print CATMOGS (Concepts and Techniques in Modem Geography) are edited by the Quantitative Methods Study Group of the Institute of British Geographers. These guides are both for the teacher, yet cheap enough for students as the basis of classwork. Each CATMOG is written by an author currently working with the technique or concept he describes. For details of membership of the Study Group, write to the Institute of British Geographers 1: Collins, Introduction to Markov chain analysis. 3.00 2: Taylor, Distance decay in spatial interactions. 3.00 3: Clark, Understanding canonical correlation analysis. 3.00 4: Openshaw, Some theoretical and applied aspects of spatial interaction shopping models. (fiche only) 3.00 CAUSAL AND SIMULATION 5: Unwin, An introduction to trend surface analysis. 3.00 6: Johnston, Classification in geography. 3.00 MODELLING USING 7: Goddard & Kirby, An introduction to factor analysis. 3.00 8: Daultrey, Principal components analysis. 3.50 9: Davidson, Causal inferences from dichotomous variables. 3.00 SYSTEM DYNAMICS 10: Wrigley, Introduction to the use of logit models in geography. 3.00 11: Hay, Linear programming: elementary geographical applications of the transportation problem. 3.00 12: Thomas, An introduction to quadrat analysis (2nd ed.). 3.00 13: Thrift, An introduction to time geography. 3.00 14: Tinkler, An introduction to graph theoretical methods in geography. 3.50 15: Ferguson, Linear regression in geography. 3.00 16: Wrigley, Probability surface mapping. An introduction with examples and FORTRAN programs. (fiche only) 3.00 17: Dixon & Leach, Sampling methods for geographical research. 3.00 18: Dixon & Leach, Questionnaires and interviews in geographical research. 3.50 Dr Ian Moffatt 19: Gardiner & Gardiner, Analysis of frequency distribution .(fiche only) 3.00 20: Silk, Analysis of covarience and comparison of regression lines. 3.00 Senior Research Fellow 21: Todd, An introduction to the use of simultaneous-equation regression North Australia Research Unit analysis in geography. 3.00 PO Box 41321, Casuarina NT 0811 Australia 22: Pong-wai Lai, Transfer function modelling: relationship between time series variables. 3.00 23: Richards, Stochastic processes in one dimensional series: an introduction. 3.50 24: Killen, Linear programming: the Simplex method with geo-graphical applications. 3.00 25: Gaile & Burt, Directional statistics. 3.00 26: Rich, Potential models in human geography 3.00 27: Pringle, Causal modelling: the Simon-Blalock approach. 3.00 28: Bennett, Statistical forecasting. 3.00 29: Dewdney, The British census. 3.50 (continued inside back cover) LIST OF FIGURES CONTENTS 1 A river basin water system 8 LIST OF FIGURES 3 2 Seven phases in system dynamics model building 10 LIST OF TABLES 4 3 Types of causality 13 ACKNOWLEDGEMENTS 6 4 The trajectory of a state variable to a 14 state o dynamic equilibrium CHAPTER I DYNAMIC MODELS AND 7 5 Causal diagrams illustrating positive and 16 ENVIRONMENTAL SYSTEMS negative feedback loops 6a A population dynamics model 17 CHAPTER II CAUSAL MODELS AND 9 QUALITATIVE SYSTEM DYNAMICS 6b A four age cohort demographic model 17 i The use of a systems approach in environmental science 9 7 Two trajectories of population growth 18 ( Causality and causal models 12 iiiFeedback loops 14 8 A simple demographic digraph 19 9 A DYNAMO flowchart of population dynamics 19 CHAPTER III COMPUTER SIMULATION AND QUANTITATIVE 18 SYSTEM DYNAMICS 10 Time subscripts J, JK, KL in DYNAMO 21 From digraphs to DYNAMO flowcharts 18 11 A digraph of a new model of population dynamics 24 (ii Writing a DYNAMO program 20 iii Logistic growth model 23 12 A DYNAMO flowchart of the new model of 24 (iv Difference equations and system dynamics 26 population dynamics (v The mathematical basis of all system dynamics models 29 13 Graphing the population increase, A POP, 27 during a time interval, A t CHAPTER IV MODEL EVALUATION AND SYSTEM DYNAMICS 30 14 Actual and predicted temperature change 33 Model evaluation 30 for a hypothetical system The use of statistical methods 34 Eutrophication: an example of basic 35 15a A digraph for simulating algal growth 36 scientific research (iv) World dynamics: an example of 39 15b A DYNAMO model of algal growth 37 policy orientated research 16 Hypothesised reference modes of the 'limits to growth' 39 global models CHAPTER V CONCLUSION: 43 THE LIMITS TO SYSTEM DYNAMICS 17 The basic mechanisms that underlie the reference 40 mode of Figure 16b REFERENCES 47 18a World 3 reference run 41 18b World 3: equilibrium through adaptive policies 42 LIST OF TABLES 1 An elementary DYNAMO program 23 2 Results of the exponential and logistic population 28 growth model for England and Wales, 1901-2001 3 Tests for evaluating system dynamics models 30 4 A DYNAMO program for Nitrogen Algal Model 38 5 Results of the Nitrogen Algal Model 39 4 5 I DYNAMIC MODELS AND ACKNOWLEDGMENTS ENVIRONMENTAL SYSTEMS Geographers and environmental scientists have a common philosophical goal namely to understand 'the vast interacting system comprising all humanity with its natural environment on the surface of the earth' (Ackerman, 1963, 453). In an attempt to understand such a complex I would like to thank the following people for helping to produce this system or set a subsystems it is essential that we develop appropriate manuscript. Ken Docherty for drawing the figures; Elizabeth Urqhart and techniques to aid our substantive investigations. There are, of course, a whole host of techniques available to geographers and environmental scientists but only a few pedagogic studies have examined the role of Janet Sincock for wordprocessing my early drafts of the text; Martyn Senior dynamic model building (Wilson, 1981a, 1981b; Thomas and Huggett, 1980). The system dynamics approach offers another approach to building for his helpful editorial comments. Richard Huggett and Dennis Meadows dynamic simulation models of environmental systems. and their publishers, Oxford University Press and Wright Allen for giving Any dynamic model may be defined as a simplification of a real world system which changes through time and space. This apparently their permission to reproduce figures from their books. Finally, I would like straightforward definition of dynamic models hides a bewildering array of dynamic behaviour found in such models (May, 1976). This dynamic to thank my former students at the University of Stirling for their constructive behaviour has been uncovered by using various techniques such as dynamic comments on several courses on modelling environmental systems from entropy maximizing models (Wilson, 1981a, 1981b), dynamic systems theory (Clarice and Wilson, 1981), statistical forecasting (Bennett, 1980) and system dynamics (Forrester, 1961). It is important to stress, however, that these which this book emerged. various forms of dynamic behaviour are observed in the real world rather than being an artefact of the methods used to investigate the 'real' world. Furthermore, it is important to note that system dynamics modelling is not a statistical technique per se but one approach to causal and simulation modelling which geographers and environmental scientists may find useful in their substantive work. There are numerous texts which describe examples of environmental systems (Bennett and Chorley, 1978; Wilson, 1981b; Jorgensen, 1986; Jeffers, 1978, 1987). Fundamentally, any environmental system can be conceptualized as a series of inputs, outputs and most important a series of inter-dependencies between the elements which make up the system. These interactions can be illustrated by the flows of water in a catchment forming a river basin water system (Figure 1). This system consists of stores of water which are interconnected by a series of causal processes. Generally, precipitation is the major exogenous input to the system. The water from this source enters the soil directly by infiltration, is temporarily stored on the soil surface as surface storage such as lochs, or is intercepted by and temporarily stored on vegetated- surfaces. Water stored in or on the soil may flow down the valley side slopes by overland flow, throughflow or pipe-flow to feed the rivers in the catchment. Alternatively, the sub-surface water may percolate downwards to recharge the ground water storage. The latter may be influenced by deep-storage or the water may rise by capillary action and pass in to the soil storage. Often in environmental systems human activity is responsible for extractmg resources such as water for agricultural, industrial and domestic uses. Furthermore, water used by us is often returned to the system in a polluted form. In most stores evaporation or evapotranspiration feeds moisture back to the surrounding atmosphere. 7 6 Several general points emerge from this simple illustration of an environmental system. First, any description of a real system attempts to bring together various aspects of knowledge from systemic disciplines. As Wilson (1981b, 19) notes, "an important advantage of a systems approach is the natural tendency to avoid disciplinary myopia '. Next, as a corollary, in any systems approach it is almost inevitable to omit some apparently less important aspect of the real system under investigation so that the model of the system is a simplified and intelligible version of complex real phenomena. Third, the major feature of the flows between these various stores are controlled by processes. These processes may be natural, man- made or a combination oT both. Yet, it is the correct specification of these processes which gives a causal model of a system its dynamic behaviour. Failure to specify these causal processes exacthr can result in a misleading simulation of the system under investigation. Fourth, it is obvious from the above informal stages of the argument that causal processes underlying an environmental system are complex and much basic scientific research is required to comprehend the ways in which these individual processes interact to give a system its dynamism.