Courseware - Terrestrial Systems Ecology
Contents
1. Baltensweiler amp M Ulrich 1991 Systems Ecology Report No 1 Erh ltlich bei Download from www sysecol ethz ch publications reports Diese Berichte k nnen in gedruckter Form auch bei folgender Adresse zum Selbstkostenpreis bezogen werden Order any of the listed reports against printing costs and minimal handling charge from the following address SYSTEMS ECOLOGY ETH ZURICH IBZ DEPARTMENT OF ENVIRONMENTAL SCIENCES UNIVERSIT TSTR 16 CH 8092 ZURICH SWITZERLAND2. e g to study tabulated results or change parameters Fig 10 shows the different program states with the associated menu and window commands and also the commands which permit a state change grayed out menu or window commands are inactive and can not be invoked by the user menu and window commands shown in black are active and can be freely invoked in any order at any time by the user Page setup Set Tile windows Start run Print graph Global simulation parameters Stack windows Halt run Pause or Preferences Project description Models Pe aume Kink _ Stop Kill run Quit Select stash file State variables Reset Model parameters Execute Experiment Global simulation parameters Monitorable variables Project description Table Stash File Name Clear table Windows Graph All model s integration methods Clear Graph All model s initial values All model s parameters All model s stash filing All model s tabulation All model s graphing All model s scaling All model s curve attributes Initialize session All above a Menubar and menu commands b Program states and transition commands of menu Simulation No simulation Menu status O window status gt _ I U Model SS u D State variables Stop kill run or Stop time reached or Termination condition true Parameters Fig 10 Interactive user interface of ModelWorks The simulation environment can only be in one of the fol
3. rich Institut of Integrative Biology IBZ Universit tsstrasse 16 CHN E21 1 CH 8092 Z rich Switzerland SWITZERLAND e mail andreas fischlin env ethz ch Dr M M Fischlin Kissling Systems Ecology ETH Zurich Institut of Integrative Biology IBZ Universitatsstrasse 16 CHN E21 2 CH 8092 Zurich Switzerland SWITZERLAND e mail margrit fischlin env ethz ch Recommended citation FISCHLIN A amp M M FISCHLIN KISSLING 2011 Courseware World Model 2 Update and translation of Unterrichtsprogramm Weltmodell 2 by Fischlin A T Blanke D Gyalistras M Baltensweiler amp M Ulrich 1991 Systems Ecology Report No 1 Systems Ecology Report No 34 Institute of Integrative Biology IBZ ETH Zurich Zurich Switzerland 41 pp http www sysecol ethz ch publications reports 34 Limits to Growth and Courseware World Model 2 Updated and Translated by A Fischlin and M M Fischlin Kissling Based on Unterrichtsprogramm Weltmodell 2 originally written by A Fischlin T Blanke D Gyalistras M Baltensweiler T Nemecek O Roth and M Ulrich Systems Ecology ETH Z rich IBZ Department of Environmental Sciences ETH Z rich Universit tsstrasse 16 CH 8092 Z rich Switzerland Table of Content 1 Introduction ae 1 1 1 Theme and purpose of the courseware unn nn en 1 1E2 Educauonale east eier Nessie 3 1 3 System requirements of the courseware program hard and software 3 Ze V
4. THONY J NEMECEK T BUGMANN H amp THOMMEN F 1994 ModelWorks 2 2 An Interactive Simulation Environment for Personal Computers and Workstations 15 FISCHLIN A BUGMANN H amp GYALISTRAS D 1992 Sensitivity of a Forest Ecosystem Model to Climate Parametrization Schemes 16 FISCHLIN A amp BUGMANN H 1993 Comparing the Behaviour of Mountainous Forest Succession Models in a Changing Climate 17 GYALISTRAS D STORCH H v FISCHLIN A BENISTON M 1994 Linking GCM Simulated Climatic Changes to Ecosystem Models Case Studies of Statistical Downscaling in the Alps 18 NEMECEK T FISCHLIN A DERRON J amp ROTH O 1993 Distance and Direction of Trivial Flights of Aphids in a Potato Field 19 PERRUCHOUD D amp FISCHLIN A 1994 The Response of the Carbon Cycle in Undisturbed Forest Ecosystems to Climate Change A Review of Plant Soil Models Out of print 20 THONY J 1994 Practical considerations on portable Modula 2 code 21 THONY J FISCHLIN A amp GYALISTRAS D 1994 Introducing RASS The RAMSES Simulation Server 22 GYALISTRAS D amp FISCHLIN A 1996 Derivation of climate change scenarios for mountainous ecosystems A GCM based method and the case study of Valais Switzerland 23 LOFFLER T J 1996 How To Write Fast Programs 24 LOFFLER T J FISCHLIN A LISCHKE H amp ULRICH M 1996 Benchmark Experiments on Workstations 25 FISCHLIN A LISCHKE H am
5. The other two windows will be used to display simulation results An World Model 2 app 5 File Edit Settings Windows Solve TabFuncs Model parameters Parameter names Ident Unit Value World model 2 by J W Forrester Birth rate normal No 1 ERNI fraction year 0 04 Capital investment discard norma CIDN1 fraction year 0 025 Capital investment generation nor CIGN1 capital units pers 0 05 Death rate normal No 1 DRNI fraction year 0 028 Food coefficient No 1 FC1 dimensionless 1 0 KKP wa Monitorable variable names Ident Unit Monitoring am World model 2 by J Y Forrester S Population Pi people Y Mma R Birth rate BR Z people year T Birth rate from material mul BRMM 3 dimensionless EHRM CA Material standard of living MSL 4 dimensionless A Effective capital investment ECIR S capital units pers KI lt P gt gt m 0 0 1900 0 1920 0 1940 0 1960 0 1980 0 2000 0 2020 0 2040 0 2060 0 2080 0 Minimum Max imum Unit 0 00 8 000E 09 people 1 000E 12 natural resource units 2 000E 10 capital units 40 000 dimensionless 2 000 satisfaction units Fig 11 Startup screen of the courseware program World Model 2 Mac OS X variant Best start by executing the standard simulation run Choose in menu Simulation the command Start Run If not already open the window Graph will be opened where you can track the fate of humans and other monitored variables The curves are named with the very same abbreviated identi
6. a similar manner World Model 2 uses table functions extensively for the many complicated non linear relationships it contains Look e g at how the birth rate is varied by other influences at any given moment The model contains seven different modifying factors that affect it Fig 13 table functions influencing birth rate BR Remember any missing values e g if such a factor reaches a value that falls between two values tabulated in the table function then the missing value is calculated by linear interpolation between the nearest coordinates cf chapter 2 2 especially Fig 8 Table Function Editor m7 a T un HI wd Co n a cn J DI cd bo on E E 00 j on 1 z 3 4 5 6 T o J bd 2d eed 5 TESES on 5 olola BA ba ha cn Fr H Be 1 44 2 Ei 3 8 4 48 2 GE CR Fig 12 Editor for table functions shown here for the table function QLCT The graph shows QLC quality of life from crowding vs crowding ratio CR population density Similar to the editable model parameters these table functions can also be modified Choose command Edit from menu TabFuncs A window appears where you can select the table function you wish to edit Confirm your choice by clicking button OK Now another window opens Fig 12 To the left you see a graphical representation of the table function to the right the value table of the coordin
7. called Forrester signal flow diagram see e g Fig 4 5 6 and Fig 13 in the Annex System elements are represented by specific symbols Fig 3 named in a manner unique to the approach For example instead of the widely used term state variable Forrester uses the term Level The time derivative of a state variable is typically split into an additive and a subtractive term the so called rates The sum of those two terms then forming an ordinary first order differential equation If we take population size x t and its time derivative x t dx t dt as the difference between births rate B and death rate D we get the following differential equation x t dx t dt B x t D x t 2 The corresponding Forrester signal flow diagram is shown in Fig 4 10 Massachusetts Institute of Technology Courseware World Model 2 Fig fp ne signal flow diagram used for a graphical representation of the differential equation x B The birth rate B determines the amount of inflow from the source to the level variable x and enters the differential equation as a positive additive term The death rate rate D determines the outflow from the level variable x to the sink and enters the differential equation as a negative additive term This Forrester signal flow diagram assumes there is some material flow going from the source into the level and then out from the level to the sink The inflow into the level being regulated by the rate B the outflow
8. complex that the human mind is not capable to relate properly the multitude of causes with the multitude of possible consequences Oltmans 1974 p 12 Courseware World Model 2 1 2 Educational goal Getting to know a dynamic nonlinear and complex system and first exposure to systems analytical approaches Experiencing that the behaviour of a complex system is often difficult to predict and may contrast with the expectations Experiencing the difficulty to steer the behaviour of a complex system in a desired direction and learning to accomplish a control only through considering and respecting the system s internal dynamics 1 3 System requirements of the courseware program hard and software The learning program here called courseware program was written in Modula 2 MacMETH with the modelling and simulation software ModelWorks version 2 0 or later based on the DialogMachine gt version 2 0 or later and runs on any Apple Macintosh or Windows machine The program is designed as an independent application double clickable and requires only standard system Software details in Annex III It may be useful to record certain simulations on paper but the educational goal does not require students to have access to a printer 2 Theory 2 1 General Models especially mathematical models are central to understanding complex systems They are important because they enable us to learn about inaccessible or to improve our un
9. first the window Model Parameters click on it or choose menu command Model Parameters in menu Windows Then activate NRUN1 and click on the button with the downward facing triangle in the top left corner A dialog window appears where the new value can be entered As a general rule it is important to document your changes The Annex I contains a form that helps you to keep track of your changes That form illustrates its use by describing the standard run in the top row Now write down the change you just made e g by documenting it with NRUNI 0 25 in the second row fo the form Then most importantly sketch your expectations before you launch a new run Only once you formed an opinion of the possible outcome run the simulation with the new value for NRUN1 Surprise the crisis becomes still larger Did you expect this Are you interested in what happens beyond 2100 Note that Forrester and his team Forrester 1971 seem not to have performed such an experiment but World Model 2 lets you easily explore this Choose from menu Settings the command Set global simulation parameters A dialog window appears in which you can increase the Stop time for simulation say from 2100 to 2300 You may also wish to increase the monitoring interval to speed up the simulation say to 10 0 years Note merely changing the monitoring interval does not affect the results Note some curves such as QL 37 material standard of living or POLR 29 pollut
10. gold suddenly jumped upwards and a wave of consternation and concern seized the mass media throughout the industrialized world All caused merely by the publication of the book The limits to growth a report for the Club of Rome s Project on the Predicament of Mankind Meadows et al 1972 Meadows amp Meadows 1976 The book written in a popular language described the findings of Dennis Meadows a former student of J W Forrester team including the simulation results of the aforementioned model The book became a bestseller across the world and was translated into innumerable languages The projections for this century were perceived as a dark future for mankind namely a catastrophic population collapse in the 2 half of the 21 century Several simulations indicated that this collapse would be inevitable if no fundamental change in policies should take place and human kind would maintain its current course This courseware comes with the learning or courseware program World model 2 It permits to intervene by changing policies and thereby to steer the course of humankind towards a better future Selected model parameters can e g boost the economy the efficiency of resource use enhance environmental protection or introduce birth control The program then calculates the fate of mankind under the conditions as changed by the user by calculating population size and other variables such as material standard of living food supply or the qua
11. latter bottle enclosed in aluminum foil allows for respiration only under otherwise identical conditions Courseware World Model 2 focuses on the human population and attempts to consider well the major factors influencing this population Note that one distinguishes different model categories There are physical models such as the toy train or the wind tunnel There are conceptual models such as the Rutherford or the Bohr Sommerfeld atomic model and there are mathematical models such as a system of coupled non linear differential equations as this is the case with the World model 2 Systems consist of system elements and relationships between these elements System elements can be grouped according to their particular mathematical properties into following types input variables state variables auxiliary variables output variables and model parameters For example the World model 2 knows following five state variables Fig 2 Population P Natural Resources NR Capital Investment Cl Pollution POL Capital Investment in Agriculture Fraction CIAF i QL Fig 2 Relational graph of World model 2 by Forrester 1971 1972 P Human population world Pol Pollution CIAF Capital Investment in Agriculture Fraction NR Natural Resources non renewable resources CI Capital Investment QL Quality of Life Influences between system elements The output variable Quality of Life QL Fig 2 is of particula
12. open for a table function 4 3 Print or store current screen screen dump Macintosh only Command Shift 3 all pressed simultaneously Creates a file named Screen means a unique digit This file can be printed with a drawing program e g GraphicsConverter or later inserted into a documention of your simulation experiments 4 4 Cited references Fischlin A Gyalistras D Roth O Ulrich M Thoeny J Nemecek T Bugmann H K amp Thommen F 1994 ModelWorks 2 2 An interactive simulation environment for personal computers and workstations Systems Ecology Report No 14 Institute of Terrestrial Ecology Swiss Federal Institute of Technology ETH Zurich Switzerland 324 pp http www sysecol ethz ch publications 14 Forrester J W 1971 World dynamics Wright Allen Press Inc Cambridge Massachusetts 142 pp 19 This option is only available on black and white screens or on color screens set to black and white mode Set the number of screen colors in the control device Monitors in the desk accessory Control panel 20 BERICHTE DER FACHGRUPPE SYSTEM KOLOGIE SYSTEMS ECOLOGY REPORTS ETH Z RICH Nr No 1 FISCHLIN A BLANKE T GYALISTRAS D BALTENSWEILER M NEMECEK T ROTH O amp ULRICH M 1991 erw und korr Aufl 1993 Unterrichtsprogramm Weltmodell2 2 FISCHLIN A amp ULRICH M 1990 Unterrichtsprogramm Stabilit t 3 FISCHLIN A amp ULRICH M 1990 Unterr
13. use Any program that can read text files can read the stash file Graphical output can only be interpreted correctly by programs which can fully read the RTF format e g Microsoft Word Select stash file Specify the name and location of the so called stash file a file holding your monitored output Note stash files are written in the rtf format and can document your simulation runs fully A stash file will not only store the results but also contain sufficient information to precisely repeat a simulation experiment for details see ModelWorks 2 2 Fischlin et al 1994 Reset Reset all configurations values window objects etc of the World Model 2 back to their initial condition at program start WINDOWS Tile Windows Arranges the windows on the screen so that they do not overlap and are positioned side by side Depending on the screen size the windows may become rather small Stack Windows Stacks the windows in an overlapping manner Windows become larger but content is partly obscured Model Parameters Opens the window to inspect or edit the model parameters Monitorable variables Opens the window to inspect or edit all monitoring variables i e all system elements that can be plotted tabulated or written to the stash file Table Opens the window Table showing values of system elements set for tabulation T Clear Table Deletes the contents of the window Table Graph Opens the window Graph showing curves for the
14. variable to be plotted on the ordinate of the graph window shows a Y any to be tabulated in the table window a T in the column Monitoring To get the wanted graph we need first to get rid of all superfluous curves e g NR 8 would only distract us Click its row and make sure it is inverted From now on we call this an activated monitoring variable You find in the upper left corner of the window a panel of thirteen quadratic buttons Generally a facing down triangle __ means Change the activated item and a left facing triangle oi means reset the activated item to the value of the standard run Click on the button Ba Confirm that the Y the column Monitoring for NR 8 has now disappeared The effect will be that in the next simulation run NR 8 will no longer be monitored graphically i e no such curve will appear in the graph anymore Note the button actually toggles the graphing Click it once more and the Y should appear again Click it a last time to really remove it from the graph and repeat this procedure for CI 24 POLR 29 and QL 37 Now only the population P shows still a Y Proceed similarly by activating the birth and death rates BR 2 and DR 10 Activate the corresponding rows and click on button bal Start another simulation run You can see that population growth is slowed down by a rising death rate not a declining birth rate Return to the original state by first clicking on the all gray button select al which will activate all
15. 980 417 429 Clark W C ed 1982 Carbon dioxide review 1982 Oxford University Press New York a o 469pp Diamond J 2009 Maya Khmer and Inca Nature 461 7263 479 480 http dx doi org 10 1038 461479a Dickinson R E amp Cicerone R J 1986 Future global warming from atmospheric trace gases Nature 319 109 115 http dx do1 org 10 1038 319109a0 Dorner D 1997 65 69 Tsd 1997 ed Die Logik des Misslingens strategisches Denken in komplexen Situationen Rowohlt Reinbek bei Hamburg 320 pp Forrester J W 1968 Principles of systems Wright Allen Press Cambridge Massachusetts 1 1 W 10 20pp Forrester J W 1971 World dynamics Wright Allen Press Cambridge Massachusetts 142pp Forrester J W 1972 Der teuflische Regelkreis Deutsche Verlagsanstalt Stuttgart 115pp IPCC 2007 Synthesis Report of the IPCC Fourth Assessment Report Cambridge University Press Cambridge UK 52 pp _ http www ipcc ch 13 Forrester hat obviously no difficulties to imagine that the results of his studies would immediately alter world policy what indeed was the case for a limited period of time Whatever importance one may assign to the following historical events it is a fact that the price of gold did rise immediately after the publication of the study Limits to growth Meadows er al 1972 and that an era of a new awareness of environmental problems was launched The latter is manifested in the founding of
16. E ae ee 38 Program Par UCU AE NCGS aaa ches case a 39 Program CLUE CV meag cs ee ee ee ee 39 Use m teachin isani ea nes ee 39 boscone Are Chases ie E She EA ee 39 Ced references need 40 il Daddy Daddy it was just like you said now that the living outnumber the dead by Laurie Anderson from song Speak my language from album Bright Red l This statement is actually only true if one counts the dead only since A D 1500 The latter are roughly a bit more than 6 billions and as of this writing there are more than 6 971 billion 10 humans alive today Rough estimates of accumulated dead humans in billions 10 are 10 since A D 1000 16 since A D 0 and 95 assuming modern man exists since about 60 000 years il 1V Courseware World Model 2 1 Introduction This courseware serves as an introductory example to familiarise oneself with the basic concepts of modelling analysis and simulation of complex dynamic systems by dealing with fundamental problems associated with the growth of the human population known by the phrase Limits to Growth or with the words of the Club of Rome the probl amp matique 1 1 Theme and purpose of the courseware Many of us have limited experience in dealing with complex systems such as nonlinear dynamic systems and often consider this to be a bewildering and baffling experience Such difficulties are inextricably linked with the characteristics of complex dynamic systems a
17. NC ONY JPPREERENRFEE PERS PER A a ENEEEBEEREERERE 3 2 1 Generalsin Base seele 3 2 2 OPEC Dacke Lo Und ee ae 5 23 Cited relerencesand Turtner Tead ns u a ee 11 3 Progr mdesceripuon nee ak 14 4 Using the courseware program User manual ssernsenensnonnennnnennnenunnennnnnnnnenunnnnnnnns 15 4 1 TVo alte ee ee a ee esse 15 4 2 Reference by meni commands anne aa engen 18 Fiese en nee al ee a erm Tee eee 18 Eli ven ee een Nee 18 SELLINSS ee a ee en ae 18 WINA OWS een ee 19 SIMUlAU ON ae a a nee 19 TabFuncs Table Funetlons un essen 20 4 3 Print or store current screen screen CUM sccscsssssssescessecscesecersscocsestscessneseesesescosacensndecnssesestenseonsaieees 20 4 4 CACO Ce ORCL CIN COS czas ea 20 5 Problems Exercise 2n naar 21 ANNEX I or the Studenis 2 22 ei aa 22 List of model variables state auxiliary variables table functions ssssnnsrnenneeeennnnnnnnnnennnnnnnn 24 List of the unmodifiable model parameters unusnsnnsenennneenennnenennnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnennnnnnnnnnnnnnnnnann 25 Listof modifiable modelparameters 2es he einen 26 Listo the model equUations etre meet sneer rer orm essen den 26 ANNEX TI sS0lutionS 2 52 28 SOIULION Aus ae ee ee ae ee 28 ANNEX III for teachers and programmers 0244020n0n000nnenonennnnenunnennnenunnennnnennnnnannenann 37 Program descriptio Misissieossa i liessen a E ESA 37 Reguired Source tiles and tools aA AA 37 PFOSTaM SEFUCL T
18. SYSTEM KOLOGIE ETHZ SYSTEMS ECOLOGY ETHZ BERICHT REPORT Nr 34 March 2011 Courseware World Model 2 A Fischlin and M M Fischlin Kissling Update and translation of Unterrichtsprogramm Weltmodell 2 by Fischlin A T Blanke D Gyalistras M Baltensweiler amp M Ulrich 1991 Systems Ecology Report No 1 Eidgenossische Technische Hochschule Zurich ETHZ Swiss Federal Institute of Technology Zurich Departement fur Umweltnaturwissenschaften Department of Environmental Sciences Institut fur Integrative Biologie Institute of Integrative Biology The System Ecology Reports consist of preprints and technical reports Preprints are art cles which have been submitted to scientific journals and are hereby made available to interested readers before actual publication The technical reports allow for an exhaustive documentation of important research and development results Die Berichte der System kologie sind entweder Vorabdrucke oder technische Berichte Die Vorabdrucke sind Artikel welche bei einer wissenschaftlichen Zeitschrift zur Publikation eingereicht worden sind zu einem m glichst fr hen Zeitpunkt sollen damit diese Arbeiten interessierten LeserInnen besser zug nglich gemacht werden Die technischen Berichte dokumentieren ersch pfend Forschungs und Entwicklungsresultate von allgemeinem Interesse Adresse der Autoren Address of the authors Prof Dr A Fischlin Systems Ecology ETH Z
19. See in particular the signal flow diagram of the entire World model2 in the Annex I Fig 13 Courseware World Model 2 linearities Nonlinearities are functions f x which do not satisfy following condition fla V b V d f b fV Definition of linearity v variable vector E g in the World model 2 we find a non linear function that represents the dependence of the usage of natural resources from the material standard of living Fig 7 4 3 5 3 2 5 Natural Resource Usage 0 5 Material Standard of Living Fig 7 Usage of natural resources as a function of material standard of living as used in World model 2 Sometimes such a function can be described analytically or can be derived from analytical considerations For example physics tells us that we can describe in an electrical system a diode by an exponential function while in the Lotka Volterra predator prey model X ax b x x x Number of prey animals i C Xt X d X x Number of predator animals the nonlinear term b X X in the first equation can be justified with the argument that the number of prey will decrease the faster the more predators are present e g as long as many prey animals are present the likelihood remains high that a predator encounters its victim leading to a faster depletion of the prey population etc While modelling complex systems it often occurs that a non linearity cannot be formulated analytically For exa
20. UNEP United Nations Environmental Program the formation of the Club of Rome the emergence of widely recognized mottos such as Limits to Growth or qualitative growth and the founding of the International Institute for Applied Systems Analysis IIASA in Luxenburg near Vienna etc 14 A complete list of all editable model parameters can be found in the Annex 11 Courseware World Model 2 Jacobi C 1987 Uns bleiben 100 Jahre Ursachen und Auwirkungen der Bev lkerungsexplosion Ullstein Berlin 156pp Lane H U et al 1986 The world almanac and book of facts 1986 Newspaper Enterprise Association New York 928pp Lucero L J 2002 The collapse of the classic Maya a case for the role of water control Am Anthropol 104 3 814 826 http www jstor org stable 3567259 Meadows D H J Randers D L Meadows amp W W Behrens 1972 The limits to growth a report for the Club of Rome s Project on the Predicament of Mankind Universe Books New York 205 pp Meadows D L amp Meadows D H 1976 Das globale Gleichgewicht Modellstudien zur Wachstumskrise Rowohlt Taschenbuch Verlag Reinbek bei Hamburg 331pp Schneider S H 1989 The greenhouse effect science and policy Science 243 771 81 http dx doi org 10 1126 science 243 4892 771 Southwick C H ed 1985 Global ecology Sinauer Associates Thunderland Mass 323pp United Nations 2011 The World at Six Billion lpp Table 1 http www
21. an influence the temporal behaviour of an autonomous deterministic model system in general only by modifying the values of its model parameters or initial values The latter is not possible in case of the World model 2 The reasons are firstly that the initial values have to use the values of the year 1900 and secondly the model has to reproduce as accurately as possible the past temporal evolution of the human population from 1900 up to the present The only possibility to affect the behaviour of the model is to alter values of model parameters note that the coordinates defining a table function may also be considered model parameters NRUN1 NRUN NRUNSY t Fig 9 A policy intervention in the World model 2 is done by a discrete step i e the value of the model parameter NRUN Natural Resource Usage Normal switches from value NRUN to value NRUNI in the switching year NRUNSY In the original model the switching year is 1970 In the simulation model offered with this courseware the user can freely change both NRUNI as well as NRUNSY World model 2 offers means to influence the future not the past by so called switches see Fig 9 This switch allows a human user to intervene in the world affairs starting with the switching year SY This gives the user means to formulate better policies that would eventually lead to a desirable future development of humankind according to the users values This is accomplished by changing values of a few s
22. ates The left column of this table contains the independent x values here CR crowding ratio CR 15 the right column the dependent y values here QLC quality of life from crowding QLC 39 Use the tabulator key or click directly into a field holding a value to edit it Update the graphical representation by clicking the button Draw You may stumble over following restriction The x values must be in ascending order and the y values must not exceed or fall below internally defined limits or you would risk a simulation model that could no longer be solved Alternatively you can grab a point in the graph on the left side and drag it to another value Clicking on button Use saves all edits and assures the new table function will be used in all subsequent simulations Click button Initial any time to forget most recent edits and return to the original values 16 Identifiers of the table functions are formed from the identifier from the dependent auxiliary variable to be interpolated suffixed by the letter T e g the table function for auxiliary variable QLC is named QLCT Fig 12 17 Courseware World Model 2 Button Close closes the window In case you should have forgotten to first click button Use don t worry you will be asked whether you wish to retain or discard your edits press buttons Yes or No accordingly Choose menu command Reset from menu TabFuncs to reset an entire table function and return all its values to those initially con
23. can easily implement deviations from the business as usual policies by adjusting model parameters 4 For example a new policy of birth control can be implemented by setting the birth rate BRN1 to a lower value than the one valid for the past i e BRN Consequently with the switching year BRNSY fewer children would be born while other policies remain the same Is this sufficient to improve the fate of humankind Forrester 1971 1972 has followed a similar approach and has postulated a possible remedy towards a global equilibrium that avoids the population collapse Please go ahead dear reader Well begun is half done The simulation of the computer model will give you answers swiftly and perhaps you can design at least in the model world a small earthly paradise Fortunately in contrast to the bitter reality no real human lives are at stake in the computer simulations 2 3 Cited references and further reading Seminal works or publications central to the topic of this courseware are listed in bold CITED REFERENCES Barney G O et al 1980 The Global 2000 report to the president United States Department of State Washington USA Global 2000 der Bericht an den Pr sidenten Verlag Zweitausendundeins Frankfurt am Main 8 Auflage 1438pp Cellier F E amp Fischlin A 1980 Computer assisted modelling of ill defined systems In Proc of the 5th Europ Meeting on Cybernetics and Systems Research Vienna Austria April 8 11 1
24. che Buchhandlung Weiss H amp R Bradley 2001 Archaeology What drives societal collapse Science 291 5504 609 610 http dx doi org 10 1126 science 1058775 13 Courseware World Model 2 3 Program description The courseware provides an interactive simulation program It allows to execute simulation experiments with the simulation model World model 2 in any time domain and changing interactively parameter values freely Simulation results are shown in form of graphs and tables The courseware was realized using the simulation environment ModelWorks Fischlin amp Ulrich 1988 Fischlin et al 1994 Some options of ModelWorks normally available have been omitted intentionally E g neither the integration method nor the initial values of the state variables may be changed On the other hand all functions that are crucial to reach the learning goal are readily available Among those are the interactive simulation the ability to modify parameter values or to control a graphical or tabular representation of the simulation results monitoring For details the user refers to the ModelWorks description Fischlin et al 1994 Like any ModelWorks model definition program the World model 2 program remains in one of following three states always No simulation Model and program variables can be changed interactively Simulation The user can only abort or pause the current simulation and Pause The simulation is temporarily halted
25. derstanding of hardly accessible characteristics of the real system they are modelled after This is particularly relevant for the investigation of environmental systems E g a forecast can of course never be carried out experimentally Or to estimate the impact of a new agrochemical on human health and the environment the substance is first tested on a small model system before it is applied at larger scales let alone worldwide Which test pilot would board the plane unless he or she is assured that a model of this plane has proven to be able to fly Or a certain variable cannot be measured directly but can be computed from other measurements under the assumption a particular model is valid E g a limnologist cannot measure directly the primary production of a lake However through the increase of oxygen or the respective decrease of carbon dioxide from the lake water kept for some time in a pair of bottles one exposed to light the other not makes it possible to measure primary productivity assuming the stoichiometry of photosynthesis holds Vollenweider 1974 For these and similar reasons scientists and engineers build often first a model and investigate it in place of the real system they built the model after With digital computers it became possible to solve very complex models by executing so called simulation experiments Consequently in recent decades modelling and simulation has become popular in almost all scientific fields in particula
26. differential equations which is also the case for World model 2 State variables and model parameters are particularly important For example in the Worldmodel the actual human birth rate Bp varies as an auxiliary variable measured in number of births per capita per year in function of other variables such as the auxiliary variable material standard of living m t This variable influence results from following calculation Br t Brn m t t continuous time or tTEN 1 Brn Birth Rate Normal is a model parameter which typically is a constant as long as certain assumptions remain valid which may be the case for the duration of a finite period e g from 1900 till 2100 Many modifying factors influence then this birth rate as follows E g the material standard of living is assumed to have normally the value 1 However system influences may cause this value to become larger i e a value higher than 1 Otherwise they may cause the value to become smaller i e a value smaller than 1 If multiplied with the standard birth rate normal equation 1 the deviation within the material standard of living influences thus the number of births The normal value e g the value of the model parameter Bgy is determined by relatively fixed biological properties of the human species and cultural values and behaviours Therefore model parameters are not necessary constant for all times but they may change their values as assumptions are relaxed or s
27. elected parameters such as the 12 We were first not able to reproduce the published simulation results since there was an error in the simulation language DYNAMO which Forrester and his team originally used Only by reproducing the very same error could we reproduce the original results i e we had to use another extrapolation method than the one described in the original code 10 Courseware World Model 2 efficiency by which one uses natural resources or implements birth control These changes are assumed to occur abruptly in a specific switching year by default 197013 An example is shown in Figure 9 for the parameter NRUN rate of usage of natural non renewable resources Before the switching year NRUNSY the simulation model uses the default value NRUN after year NRUNSY the user altered value NRUNI The standard behaviour of the World model 2 standard run whereby the spectacular collapse of the world s human population in the 21 century occurs Forrester 1971 was simulated using unchanging parameter values This means that for each model parameter that can switch the same value is used before and after the switch year 1970 In other words World politics stay the same and are continued till the end of this century a business as usual scenario Exactly as this was the case with the original model Forrester 1971 those normal circumstances are specified by default in the simulation model coming with this courseware Moreover you
28. eltmodelle auf dem Priifstand Interdisciplinary Systems Research 2 Birkhauser Verlag Basel 178pp Lutz W W Sanderson amp S Scherbov 2001 The end of world population growth Nature 412 2 Aug 543 545 http dx doi org 10 1038 35087589 Meadows D H D L Meadows amp J Randers 1992 Beyond the limits confronting global collapse envisioning a sustainable future Chelsea Green Publishing Company Post Mills VT 300pp Meadows D H J Randers amp D L Meadows 2004 The limits to growth the 30 year update Chelsea Green White River Junction USA 338pp Meadows D H J Randers amp D L Meadows 2009 3 Aufl ed Grenzen des Wachstums das 30 Jahre Update Signal zum Kurswechsel Hirzel Stuttgart 323pp Mesarovic M amp Pestel E 1974 Menschheit am Wendepunkt 2 Bericht an den Club of Rome zur Weltlage Deutsche Verlags Anstalt Stuttgart pp Oltmans W L 1974 Die Grenzen des Wachstums Pro und Contra Reinbek bei Hamburg Rowohlt Taschenbuch Verlag Pimentel D amp M Pimentel 2006 Global environmental resources versus world population growth Ecological Economics 59 2 195 198 http dx doi org 10 1016 j ecolecon 2005 1 1 034 Rosnay J de 1977 Das Makroskop neues Weltverst ndnis durch Biologie Oekologie und Kybernetik Stuttgart Deutsche Verlags Anstalt Vester F 1978 Unsere Welt ein vernetztes System Stuttgart Verlagsgemeinschaft Ernst Klett J G Cotta s
29. eties due to drought has probably resulted from just a small quantitative change in climatic conditions causing e g precipitation decreases that rippled through society till an entire civilization collapsed e g Weiss amp Bradley 2001 Lucero 2002 Diamond 2009 To be able to study such phenomena e g for the purpose of forecasting prevention or mitigation we need a suitable approach overcoming the limitations of the human mind in understanding the dynamics of a complex system e g D rner 1997 An important goal of systems analysis is to provide techniques and methods in particular modelling and simulation which enable us humans to better understand complex systems The courseware program World Model 2 is such a tool It tries to capture world affairs especially the fate of the human population in terms of the processes economic growth consumption agriculture and pollution Forrester 1971 1972 The model is grossly simplistic but it is a noteworthy attempt and by the way also the first one of its kind to address such relationships at the global scale Beginning in the year 1900 the model first simulates the past and then calculates the future development of the world population the economy agriculture the consumed non renewable resources plus environmental pollution till the end of the 21st century A more refined successor of this model World model3 has garnered worldwide fame At the New York Stock Exchange the price of
30. fiers Forrester originally used Forrester 1971 In the annex you find a list of all these system elements their names identifiers meaning and unit For the actual values see the program First notice that all curves reach or are at a maximum followed by a decline towards the year 2100 Limited growth Watch in particular what happens to the world population P It reaches its peak around 2020 and then collapses What causes this drastic collapse in which billions of human beings die To explore this we will try to plot the world population together with the birth and death rates Activate the window Monitorable variables This can be accomplished by either clicking into the window title or by choosing in menu Windows the command Monitorable variables You see now the first part of the list of all the variables which can be monitored Scroll to make the rest of the window content visible by clicking on 15 Courseware World Model 2 the scrolling icons at the top right corner Listed are the five state variables S cf Fig 2 their rates R and all the auxiliary variables A cf Fig 13 The system elements are numbered as originally published Forrester 1971 and according to the order in which they are listed in the Annex I All elements have a unique abbreviated name identifier which prefixes its number from which it is separated by a slash e g NR 8 The window also shows by default the unit as well as its monitoring settings Any
31. from the level being regulated by the rate D note the valve like symbol used for rates b d Fig 5 Forrester signal flow diagram of the differential equation X bx dx to describe the increases and decreases in human population x or x t the level variable or state variable Shown are two feedback loops in addition to the material flow through the level compare Fig 4 The rates B t bx and D t dx are the birth and death rates determining inflow and outflow of the level variable x Both rates are time dependent just as x whereas the constants b and d are time independent model parameters The process is time continuous i e the time t NR The next step is to find those elements that determine the number of births and deaths 1 e the birth and death rate respectively It is certainly safe to assume that both the births and deaths increase with the number of people and vice versa Therefore as a first approximation we can assume that both the birth and the death rate are directly proportional to the current population size x x t dx t dt b x t d x t 3 The birth rate B becomes b x and the death rate d x The coefficients b and d are model parameters and are in contrast to the population size x time independent They are called relative birth and death rates to distinguish them from the absolute number of births B and deaths D In the Forrester diagram this dependence of the birth rate B respectively t
32. he death rate D on the level variable x and the respective model parameters b and d is represented by information flows Fig 5 These information flows form two feedback loops In reality of course the situation is far more complicated and neither the relative birth nor the relative death rates remain constant over long periods This can be taken into account by replacing the constants by auxiliary variables which in turn depend on other system components Fig 6 This couples the differential equation for Courseware World Model 2 the human population with other differential equations hereby constituting a complex system 11 The resulting complex system in its entirety can exhibit completely different behaviour than any of its individual parts does in isolation The World model 2 is in fact a system of 5th order e formed by five complicated coupled ordinary differential equations containing many non linearities Fig 13 in the Annex remaining system death F Z N Lu mortality rate normal birth rate normal death rate gt remaining remaining system system Fig 6 Excerpt from the Forrester signal flow diagram of the World model 2 modelling growth and decline of the human population by Forrester 1971 1972 see also entire diagram in the Annex I System dynamics emphasizes the importance of feedback loops and recommends to analyze signal flow diagrams for their presence closed signal flows see e g Fig 5 p
33. he urban population is forced to spend on average approximately one third of their income for the purchase of wood Southwick 1985 An example from developed countries The combustion of fossil fuels for industrial production transport and habitation has Courseware World Model 2 significantly contributed to an increase in atmospheric carbon dioxide of roughly 40 compared to preindustrial conditions According to many projections using climate models this will lead to global climate change with likely undesirable impacts Clark 1982 Dickinson amp Cicerone 1986 Schneider 1989 IPCC 2007 However this is not the place to really look into all these problems in detail Rather we intend to show that there exist important linkages between diverse aspects i e between population size agriculture industrial activities and the environment that form a complex net of interdependencies which can hardly be understood without special means Yet the effect of these interdependencies onto the fate of the human population may be not only crucial but may also bring surprises such as a population collapse see below Surprises often arise when changes within a certain period can only be detected by precise quantitative measurements yet the accumulated effect of those causes in the end a drastic qualitative change The latter is then only too often perceived as a complete surprise For example a complete crop failure or the extinction of entire soci
34. ichtsprogramm Drosophila 4 ROTH O 1990 Maisreife das Konzept der physiologischen Zeit 5 FISCHLIN A ROTH O BLANKE T BUGMANN H GYALISTRAS D amp THOMMEN F 1990 Fallstudie interdisziplin re Modellierung eines terrestrischen Okosystems unter Einfluss des Treibhauseffektes 6 FISCHLIN A 1990 On Daisyworlds The Reconstruction of a Model on the Gaia Hypothesis 7 i GYALISTRAS D 1990 Implementing a One Dimensional Energy Balance Climatic Model on a Microcomputer out of print 8 FISCHLIN A amp ROTH O GYALISTRAS D ULRICH M UND NEMECEK T 1990 ModelWorks An Interactive Simulation Environment for Personal Computers and Workstations for new edition see title 14 9 FISCHLIN A 1990 Interactive Modeling and Simulation of Environmental Systems on Workstations 10 ROTH O DERRON J FISCHLIN A NEMECEK T amp ULRICH M 1992 Implementation and Parameter Adaptation of a Potato Crop Simulation Model Combined with a Soil Water Subsystem 11 NEMECEK T FISCHLIN A ROTH O amp DERRON J 1993 Quantifying Behaviour Sequences of Winged Aphids on Potato Plants for Virus Epidemic Models 12 FISCHLIN A 1991 Modellierung und Computersimulationen in den Umweltnaturwissenschaften 13 FISCHLIN A amp BUGMANN H 1992 Think Globally Act Locally A Small Country Case Study in Reducing Net CO Emissions by Carbon Fixation Policies 14 FISCHLIN A GYALISTRAS D ROTH O ULRICH M
35. into window Graph successful only if the clipboard actually contains graphical content can be used e g to represent the same graphic with different aspect ratios Clear Clears the current graph SETTINGS Set global simulation parameters Retrieves an inputs form in which the following values can be changed Simulation start Start time for simulation Simulation end Stop time for simulation Length of the integration step Integration step Step length of the output on the graphics and in the table Monitoring interval Set project description Opens a dialog window in which you can enter a header footer and or remark strings to be shown in graphs when printing Use the check boxes Use in Graph to specify whether the header and the comment should also be shown on screen in the window Graph 17 Research Aids for Modeling and Simulation of Environmental Systems 18 Courseware World Model 2 The following data and information can be written onto the stash file check the corresponding check boxes Models Names of all models and Global simulation parameters currently in use State variables Initial values of all state variables Model parameters values of all model parameters currently in use Monitorable variables Information on all monitorable variables Graph Current aD as resulting at the end of a simulation run Table functions Information on all table functions incl their value tables currently in
36. ion but that may also influence each other Together they represent the current world situation as it determines the fate of humanity Neither the inter dependence of direct and indirect influences nor the derivation of the model equations can be meaningfully summarized here for this they are simply too complex Know that the team of Professor Jay W 9 All elements used in the model their meaning units and equations are tabulated in the Annex Courseware World Model 2 Forrester who built the model at MIT consisted of scientists from various disciplines Despite its relative simplicity does the model consider cleverly and quite elegantly many more aspects of the real world than one might think at first glance To fully appreciate the model the interested reader is referred to the original literature Forrester 1971 1972 Meadows et al 1973 Meadows amp Meadows 1976 Rate dL dt m 14 Material flow Information flow A k Source u A j YY _ nl Sink NALA L 7 Auxiliary variable Table function T C O Constant IN Me Fig 3 Symbols used in a Forrester signal flow diagram Forrester 1968 During the 2 half of the 1950s Forrester has developed a methodology to model and simulate any kind of dynamic system an approach especially targeted at economic and social phenomena This approach is called System Dynamics and is characterized by the fact that the modeller starts modelling by drawing a graph a so
37. ion reaches values outside the ones shown in the graph Let us change the scaling Activate window Monitorable variables and activate QL 37 Click on the button with a downward facing triangle over a double arrow the Set Scaling button BA A dialog window appears in which you can enter new scaling values Set the new maximum Max for QL 37 to 15 0 Rerun the simulation and confirm that you can now see all of the curve for QL 37 The world s population 15 Model parameters you can modify to implement a change in policy are the birth and death rates BRNI DRN1 natural resources usage NRUN1 food coefficient FC1 pollution POLN1 and the economic growth determining capital investment generation and discard CIGN1 and CIDN1 For more details see the list in the Annex I 16 Courseware World Model 2 fluctuates enormously not pleasant times to live Merely reducing the usage of natural resources is obviously not a real solution although this might be an important step in the right direction This run is worth documenting and calls for some interpretation Did it match your expectations If not be not irritated and embrace the opportunity for learning by searching for an explanation Write down your thoughts in the last column of the form no matter how vague or hypothetical they are You are likely to profit later from these notes when you can compare several runs It is therefore highly recommended to document all further simulation runs in
38. lity of life The user should try to influence the model in such a manner that the devastating population collapse in the 21st century is avoided Although the model represents a coarse simplification of the world the attempts to steer the world towards a more desirable course is far from trivial Here system theory may help It deals among other things not only with the necessary mathematical methods to represent complex systems in form of models and to simulate their behaviour but also to search systematically for possibilities to control such complex systems In particular solutions are of special interest that optimize certain aspects of the system Important properties of complex model systems such as their sensitivity to built in assumptions or to changes in parameters that can be estimated only with limited accuracy sensitivity analysis can only be studied using sound analytical methods This includes the identification of equilibria and their stability properties stability analysis 2 JW Forrester the father of system dynamics said in this context Thus we have an enormeous wealth of exquisite information available on the parts of the system yet no useful approach to predict reliably the system s behavior so that different people draw different conclusions from the same input factors Often accepted conclusions are in conflict with accepted assumptions and such discrepancies go a long time unnoticed since the systems are so
39. lowing three states In the state No simulation where most editing is done e g setting of initial values parameter values or choice of graphical representations The state Simulation is entered during a simple simulation run or a simulation experiment consisting of several runs In this state user actions are restricted to abort the simulation or pause it temporarily In state Pause the values of RTC Run Time Changeable model parameters can be changed Moreover the simulation can be continued or aborted From each state it is possible to quit the simulation environment 14 Courseware World Model 2 4 Using the courseware program User manual 4 1 Tutorial This section contains step by step instructions on how to work with the courseware program as needed to solve the problems cf section 5 It is recommended to instantly perform the described steps on the computer while reading this tutorial Assuming you are familiar with operating your computer and that you have successfully installed the courseware program as described in the distribution you need first to launch the program World Model 2 typically by double clicking its icon A screen similar to the one shown in Fig 11 becomes visible The window Model parameters lists all editable model parameters and the window Monitorable variables lists all system elements that can be displayed graphically or tabulated regardless whether that element is a state auxiliary or output variable
40. monitoring variables note even the ones not visible If you now click the button with the left facing triangle reset button you reset all monitoring exactly to what you had initially when you performed first the standard run If you have made further changes say in other windows too it may be handy to use even a more comprehensive resetting technique Choose menu command Reset all above from menu Settings To reset really everything including table functions you need in addition to choose also menu command Reset all from menu TabFuncs Forrester believed as mentioned earlier that world politics can be altered and that Earth s fate can effectively be changed To deviate from the business as usual course change the values of the editable model parameters Fig 9 Lets say we wish to strengthen birth control then the relevant model parameter is BRN1 All editable model parameters have the suffix l at the end of their names e g BRN1 compared to the default value used before the switching year i e BRN Remember in the standard run all values are the same e g BRNI BRN Thus to intervene and implement birth control simply decrease the value of BRN1 BRNI lt BRN How to change an editable model parameter Suppose we believe that recycling and efficient resource usage would make a difference To implement the corresponding policy we need to reduce the parameter NRUNI from 1 0 to 0 25 To accomplish this in our program activate
41. mple the World Model 2 contains a quantity capital investment which is expressed as a function of the material standard of living i e capital investment f material standard of living How can we formulate such a relationship For complicated relationships we may end up having to combine several analytical non linear functions which would lead to expensive computations during simulation or otherwise considerable numerical difficulties or even numerical error accumulation One remedy is to describe the nonlinear function using simply a dense table of values with coordinates defining the wanted function called a table function This approach is particularly handy in cases where one has only discrete measurements available that define the relationship During simulation one is likely to need values for which there is no corresponding entry in the table of values Interpolation or extrapolation is then a means to find values that are missing in the simplest case using straight lines While linear interpolation is well defined and results only in the difficulty of a discontinuous derivative of the wanted function extrapolation may be less well defined The simulation language of System Dynamics DYNAMO offers two approaches One is to retain the last function value beyond the range of the tabulated values for the independent variable see the example below A second is to extrapolate along the last interpolation line using the first or last respec
42. nd particularly large when we try to correctly predict the behaviour of such systems or to steer them in a desired direction This courseware is dedicated to such a system 1 e the worldwide interdependencies that regulate the fate of the human population At least for the last 1000 years the human population of the Earth has increased without constraints following a hyperexponential growth Fig 1 see also Varfolomeyev amp Gurevich 2001 Earth s Human Population N Ko LO oO lt oO N S a9 O a N 0 500 1000 1500 2000 Years Fig 1 Development of the world population United Nations 2011 This led on our globe to special conditions in particular in the last decades which are unique in mankind s history A tiny disturbance or impact on the environment typically resulting from ordinary daily activities seemingly minor and negligible from the perspective of an individual human being can grow to enormous implications first at the regional later at the global scale see also Jacobi 1987 An example from developing countries The demand for firewood needed for cooking resulted in some regions of the Sahel Africa in a total clearance of all trees and shrubs within a radius of up to 100 km from human settlements Barney et al 1980 Global 2000 Southwick 1985 This affects the local climate with concomitant adverse impacts on agriculture Even economical consequences result so that for example t
43. oom a critique of the limits to growth Universe Books New York 244 pp Commoner B 1972 The closing circle Bantam Books Inc New York 340pp Diamond J 2005 Collapse how societies choose to fail or succeed Viking New York 575 pp Diamond J 2009 Maya Khmer and Inca Nature 461 7263 479 480 http dx do1 org 10 1038 461479a Dorn H 1962 World population growth international dilemma Science 135 3500 283 290 http dx doi org 10 1126 science 135 3500 283 12 Courseware World Model 2 Dorner D 1990 The logic of failure Philosophical Transactions of the Royal Society of London B Biological Sciences 327 1241 463 473 http www jstor org stable 55318 D rner D 1997 Die Logik des Misslingens strategisches Denken in komplexen Situationen Rowohlt Reinbek bei Hamburg 320 pp Foerster H P Mora amp L Amiot 1960 Doomsday Friday 13 November A D 2026 Science 132 3436 1291 1295 http dx doi org 10 1126 science 132 3436 1291 Gabor D Colombo U King A Galli R 1976 Das Ende der Verschwendung Deutsche Verlags Anstalt Stuttgart 251 pp Garrels R M Mackenzie F T amp Hunt C 1975 Chemical cycles and the global environment William Kaufmann Inc Los Altos Cal 206pp Holdren J P amp Ehrlich P R eds 1971 Global ecology Readings toward a rational strategy for man Harcourt Brace Jovanovich Inc New York a o 295pp Hugger W 1974 W
44. ositive feedback from x to B and back to x However such an analysis is only of limited value since in meshed feedback loops Fig 13 allow no longer for a clear classification into negative stabilizing or positive destabilizing feedback loops as this is possible for simple feedback loops Fig 6 13 In meshed feedback loops some system element can be simultaneously part of a positive as well as a negative feedback loop and the overall effect may then be positive or negative depending on the actual relative strength of the counteracting influences Forrester signal flow diagrams cannot be mapped to mathematical equations in a unique manner For example the differential equation dx dt x b x d would be also equivalent to the graph of Fig 5 Therefore system dynamics despite advantages such as its lucidity comes with a considerable number of drawbacks and deficiencies and cannot be generally recommended for modelling see also Cellier amp Fischlin 1980 In particular it is also limited to the continuous time formalism i e modelling is constrained to systems of ordinary differential equations Moreover system dynamics was always strongly linked to a particular simulation language i e DYNAMO and more recently STELLA which invite unfortunately the skipping of the step of the explicit formulation of the mathematical equations While modelling a complex system such as the World model 2 arises often the need to introduce so called non 11
45. p BUGMANN H 1995 The Fate of Forests In a Changing Climate Model Validation and Simulation Results From the Alps 26 LISCHKE H L FFLER T J FISCHLIN A 1996 Calculating temperature dependence over long time periods Derivation of methods 27 LISCHKE H L FFLER T J FISCHLIN A 1996 Calculating temperature dependence over long time periods A comparison of methods 28 LISCHKE H L FFLER T J FISCHLIN A 1996 Aggregation of Individual Trees and Patches in Forest Succession Models Capturing Variability with Height Structured Random Dispersions 29 FISCHLIN A BUCHTER B MATILE L AMMON K HEPPERLE E LEIFELD J amp FUHRER J 2003 Bestandesaufnahme zum Thema Senken in der Schweiz Verfasst im Auftrag des BUWAL 30 KELLER D 2003 Introduction to the Dialog Machine 2 ed Price B editor of 2 ed 31 FISCHLIN A 2008 IPCC estimates for emissions from land use change notably deforestation 32 FISCHLIN A 2007 Leben im und mit dem Klimawandel Lebensgrundlagen in Gefahr 33 FISCHLIN A 2010 Andreas Fischlin nimmt Stellung zu Fragen rund um die Klimaproblematik unter Mitwirkung von Markus Hofmann Christian Speicher Betty Zucker Martin L ubli und Jiirg Fuhrer 34 FISCHLIN A amp FISCHLIN KISSLING M M 2011 Limits to Growth and Courseware World Model 2 Update and translation of Unterrichtsprogramm Weltmodell 2 by Fischlin A T Blanke D Gyalistras M
46. r interest among the many outputs of the World model 2 There are no input variables such as temperature which would influence the world dynamics This means that the model system is autonomous and e g climate change effects are by definition excluded However there is a large number of auxiliary variables e g the material standard of living or food ratio and a many model parameters The relationships between the system elements determine the system structure which can be very complex For example natural resources affect the human birth rate indirectly through influencing the capital investment the food production the pollution and the existing land surface in an extremely complicated manner Fig 2 see also Forrester 1971 1972 The arrows symbolize influences of particular system elements on other system Courseware World Model 2 elements Such relationships typically represent the dependency of the temporal derivation of a state variable from other system elements whether that may be other state variables inputs or model parameters The World model 2 is therefore a dynamic model and describes phenomena such as population increase or decrease economic growth or decrease the consumption of natural resources or increase and the decrease of environmental pollution All relationships together form the so called system structure and are described in form of mathematical equations Many models are formulated as systems of coupled ordinary
47. r to many it has been previously absent To the basic methodology of science Le theory and experiment has been added a third pillar simulation Models always differ from the systems they are modelled after otherwise we would not build them Typically models are simpler than their original real system Given a specific problem at hand the model is built to exhibit only those properties that are of interest in that given context Others system characteristics can and should be neglected as much as possible parsimony Occam s razor This means however that any results derived by means of only the model must not be transferred back to the original without caution In principle model results apply only to those aspects of the original which have been represented adequately in the model E g the World model 2 is a gross simplification compared to its original the real world On the other hand it 1987 Swiss Federal Institute of Technology Ziirich ETHZ 1988 M Ulrich A Fischlin amp Swiss Federal Institute of Technology Z rich ETHZ 1987 1988 A Fischlin amp Swiss Federal Institute of Technology Ziirich ETHZ With at least 1 Kbyte RAM random access memory and 128 Kbytes ROM read only memory starting with Finder version 5 3 or Windows 95 oO Ny AMARA W A pair of samples of lake water is kept in a so called light and dark bottle of glass The former bottle allows for photosynthesis by the entrapped algae the
48. system elements set for plotting Clear Graph Deletes the curves in the graphics window SIMULATION Start run Starts a simulation run Halt run Pause Temporarily halts pauses a simulation run In the resulting state windows can be viewed repositioned and model parameters can be changed see Fig 10 Resume run Resume the previously halted paused simulation run This command is only available active if the program is in state Pause see Fig 10 Stop Kill run Stops aborts the currently executing run This command is only available active when the simulation program is in state Simulation or Pause see Fig 10 18 Optionally available when at least one model uses a table function which is the case for World Model 2 19 Courseware World Model 2 TABFUNCS TABLE FUNCTIONS Edit Opens first a window to select an individual table function and once the selection has been confirmed by pressing button OK the actual editing window is opened It can be used to make changes to the selected table function cf 4 1 Tutorial Reset Opens a window to select a table function compare command Edit Once the selection has been confirmed by pressing button OK the selected table function will be reset in its entirety to the initial values Reset all Reset all table functions to their initial values Show window Brings the editor window for table functions into the foreground This command is inactive if no editor window is
49. tained in the value table as used in the standard run Again when you use this menu command a window appears where you need first to select the table function you wish to reset Be warned once you confirm your choice with OK the selected table function will be reset completely not revocable You can even reset all table functions by choosing menu command Reset all from menu TabFuncs By now you should have familiarized yourself sufficiently with the most important features of this courseware program having made you fit to answer the problems from section 5 Note the simulation environment ModelWorks on which the courseware program World model 2 is based offers many more features and means than introduced here can tackle considerably more complex systems Visit the home of RAMSES http www sysecol ethz ch ramses for further information Have fun and lively discussions 4 2 Reference by menu commands FILE Page Setup Sets the paper size the magnification and other settings needed for printing Print Graph Prints the graphics window on the connected printer s Preferences Specify modes of the simulation environment Quit Quit the program EDIT Undo This command is generally not available The following commands are relevant only for the window Graph Cut Copies first the current graph into the clipboard before clearing it Copy Copies the current graph into the clipboard Paste Pastes the content of the clipboard
50. tively two entries from the value table Thus the aforementioned non linear dependence of natural resource usage f material standard of living cf Fig 7 is substituted for a value table together with means of interpolation for value pairs missing in between and possibly extrapolation for values beyond the domain of the value table Fig 8 Courseware World Model 2 Two tabulated data 4 pairs points f Sect x here 2 5 extrapolation Natural 9 L Resource Usage lin interpolation between 1 5 ra the two values 1 ja 0 5 gf Domain of table function 0 oO N N a to co N co o gt oO Te N Material Standard of Living Fig 8 The non linear table function used by the World model 2 representing the relationship between natural resource usage and material standard of living Note that the simulation model needs only the coordinates defining the red square points that were derived from statistical data Remaining function values are then calculated by the simulation software using linear interpolation and possibly linear extrapolation The BANNER by which non linearities are taken into account in a model may critically affect the simulation results 2 In particular note that greatest errors may result in case of frequent but undetected extrapolations due to a mismatch between the domain for which the table function is defined and the actual domain into which the model values typically fall You c
51. trengthened For example some culture may rate having a large number of children a blessing Spreading such value systems worldwide would of course require to increase the parameter Bgy accordingly Since the temporal behaviour of a system is not only determined by the form of the equations but also by the parameter values a surprisingly large spectrum of model behaviours may result alone from changes in its parameter values To explain or predict such effects is a typical task of systems theory Under certain circumstances it may be possible to turn the behaviour of a system completely around by a mere modification of parameter values so that the new behaviour meets some human expectations or needs much better 2 2 Specific background The focus of the World model 2 is on the world population which has been growing hyper exponentially Fig 1 Tab 1 a phenomenon often termed population explosion Millions 10 300 510 625 Millions 710 910 1 130 1 600 Millions 2 070 2 510 3 020 3 575 Tab 1 World population in million humans from 10 000 BC to 1987 Lane et al 1986 United Nations 2011 The purpose of the model is to project the development of mankind in the near future till the end of this century It considers a set of critical variables which may change during the course of these years Thus the model contains state and auxiliary variables that influence not only the human populat
52. un org esa population accessed 12 Mar 2011 Varfolomeyev S amp K Gurevich 2001 The hyperexponential growth of the human population on a macrohistorical scale Journal of Theoretical Biology 212 3 367 372 http dx do1 org 10 1006 jtb1 2001 2384 Vollenweider R A 1974 A manual on methods for measuring primary production in aquatic environments IBP Handbook No 12 Blackwell Oxford 213pp Weiss H amp R Bradley 2001 Archaeology What drives societal collapse Science 291 5504 609 610 http dx doi org 10 1126 science 1058775 FURTHER READING Austin A amp J Brewer 1970 World population growth and related technical problems IEEE Spectrum 7 12 43 54 http dx doi org 10 1109 mspec 1970 5213084 Brown L 1981 World population growth soil erosion and food security Science 214 4524 995 1002 http dx doi org 10 1126 science 7302578 Brundtland G H et al 1987 Our common future World Commission on Environment and Development Oxford University Press Oxford a o 383pp Clark W C amp Munn R E eds 1987 Sustainable development of the biosphere Cambridge University Press Cambridge a o 491 pp Cohen J E 1995 Population growth and Earth s human carrying capacity Science 269 341 346 http dx do1 org 10 1126 science 7618100 Cohen J E 1995 How many people can the Earth support Norton New York a o X 532 pp Cole H S D 1973 Models of d
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