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```1.1 What if there was life on Mars?                                                  1
1.2  What is a model?                                                                2
1.3  Why use models?                                                                 4
1.4  Which model should I use?                                                       8
1.41 Determining what type of model to use                                      9
1.4.2 Determining what type of mathematics to use in the mode                  15
1.5  Choosing an existing model                                                     20
1.6  How is a model made?                                                           21
Summary                                                                        23
Problems                                                                       24
2      How to develop a model                                                              26
2.1  Choose the type of model                                                       27
2.1.1 Why am I doing this?                                                     27
2.12 How should I do this?                                                     27
2.1.3 The principle of parsimony                                               29
2.1.4 What do I do now?                                                        30
2.2  Draw up a conceptual model                                                     31
2.2.1 Draw a pictue                                                            32
2.2.2  List all hypotheses                                                     33
2.2.3  List all assumptions                                                    33
2.2.4 Set the boundary conditions                                              33
2.3  Attach a mathematical model                                                    35
2.3.1 The parts of a mathematical model                                        36
2.3.2 Linking together fixed parameters and input variables                    36
23.3 Choosing the mathematical approach to derive the model                    38
2.3.4 Example                                                                  40
2.4  Construct a computer model                                                     45
2.4.2 Specialist modelling software                                            52
2.4.3 High-level programming languages                                         55
2.5  And then..?                                                                    61
Summary                                                                        62
Problems                                                                       63
References                                                                          67
How to evaluate a model                                                                   69
3.1  Decide what type of evaluation is needed                                             70
3.2  Plot the results (graphical analysis)                                                71
3.2.1 Plots to reveal the accuracy of the simulation                                 72
3.2.2 Plots to illustrate the behaviour of the model components                      76
3.23 Plots to establish the important model components                               78
3.3  Calculate the accuracy of the simulation (quantitative analysis)                     81
"33.1 Analysis of ccincidence                                                        84
3.3.2 Analysis of association                                                        94
3.3.3 An example of the use of statistics to assess the accuracy of a model: the model of soil
carbon change on Mars                                                          98
3.4  Examine the behaviour of the model (sensitivity analysis)                           106
3.4.1 What is sensitivity analysis and why is it important?                         106
3.4.2 Methods used in sensitivity analysis                                          107
3.43 Expressing sensitivity                                                         107
3.5  Determine the importance of the model components (uncertainty analysis)             109
3.5.1 What is uncertainty analysis and why is it important?                         109
3.5.2 Methods used in uncertainty analysis                                          110
3.5.3 Representing variation in the input parameters and model outputs              110
3.54 Expressing uncertainty                                                         111
3.6  Andthen.. ?                                                                         113
Summary                                                                             114
Problems                                                                            115
References                                                                          117
S    How to apply a model                                                                     119
4.1  Scientific representation                                                           122
4.11 Who is the end-user?                                                           123
41.2 How is the model used?                                                         124
4.1.3 Guard against input error                                                     126
4.1.4 Guard against misinterpretation of the results                                126
4.1.5 Documentation                                                                 127
4.2  Expert and decision support systems                                                 128
4.2.1 Who is the end-user?                                                          129
4.2.2 How is the model used?                                                        130
4.2.3 Guard against input error                                                     130
4.2.4 Guard against misinterpretation of the resuts                                 132
4.2.5 Documentation                                                                 132
4.3   Risk assessment                                                                    134
4.3.1 Who is the end-user?                                                          135
4.3.2 How is the model used?                                                        136
43 Gua rd aga ins nut error                                                    137
4 .34  Guard against  isinterpreation of ithe r ts                              37
43.5 Documentation                                                              38
.4   Spatially-explicit applications                                                139
4.4.1 Who is the end-usr ?                                                     139
4.4.2 How io the model used?                                                    40
4.3 Guard againstnput err                                                       143
4.44 Guard against misinterpretaion oi the O reuls                              44
4.4,5 Documentation                                                            144
45   Epilogue                                                                         6
4.51 How has life on Mars been improved?                                        46
4.5.2 The real-Earth application of the models ed in this book                  47
4.6  So is this the end?                                                             10
Summary                                                                        152
Problems                                                                       156