Chapter 1

1.1  The purpose of this book

1.2 The aims of environmental modelling

1.3 Seven reasons not to use uncertainty analysis

1.4 The nature of the modelling process

1.4.1  From perceptual to procedural models

1.4.2  Parameters, variables and boundary conditions

1.5 The scale problem and the concept of incommensurabilty

1.6 The Model Space

1.7 Ensembles of models

1.8 Modelling for formulating understanding

1.9 Modelling for practical applications

1.9.1  Simulation with no historical data available

1.9.2  Simulation with historical data available

1.9.3  Forecasting the near future

1.10 Guidelines for Effective Modelling

1.11 The Meanings of Uncertainty

1.12 Deciding on an uncertainty estimation method

1.13 Uncertaint y in model predictions and decision making

1.14 A Review of Chapter 1.

Chapter 2:  A Philosophical Diversion

2.1 Why worry about philosophy?

2.2 Pragmatic realism

2.3 Other philosophical concepts of realism

2.4 Models as instrumentalist tools

2.5 The model validation issue

2.6 The model falsification issue

2.7 The model confirmation issue: Bayesian approaches

2.8 The information content of observations as evidence for the confirmation of models.

2.9 Explanatory depth and expecting the unexpected

2.10 Uncertainty, Ignorance, and Factors of Safety

2.11 Review of Chapter 2

Chapter 3:  Simulation with No Historical Data Available

3.1 Sensitivity, Scenarios and Forward Uncertainty Analysis

3.2 Making decisions about prior information

3.2.1  Prior distributions of parameters

3.2.2  Belief Networks

3.3 Sampling the Model Space

3.3.1  Analytical propagation of probabilistic uncertainty

3.3.2  Discrete samples or Random Monte Carlo Search?

3.3.3  Pseudo-random numbers and the realisation effect

3.3.4  Guided Monte Carlo Search

3.3.5  Copula Sampling

3.3.6  Case Study: Copula Sampling in mapping groundwater quality

3.4 Fuzzy representations of uncertainty

3.4.1  Case Study: Forward Uncertainty Analysis using fuzzy variables

3.5 Sensitivity Analysis

3.5.1  Point sensitivity analysis

3.5.2  Global sensitivity analysis: Sobol’ Generalised Sensitivity Analysis

3.5.3  Case Study:  Application of Sobol’ GSA to a hydrologic models

3.5.4  Global sensitivity analysis:  HSY Generalised Sensitivity Analysis

3.6 Model emulation techniques

3.7 Uncertain Scenarios

3.8 Summary of Chapter 3

Box 3.1  Simple operations with probability distributed variables

Box 3.2  Monte Carlo Sampling of a Model Space

Box 3.3  Choosing a random number generator

Box 3.4  Fuzzy representations of uncertainty

Chapter 4:   Simulation with historical data available

4.1 Model calibration and model conditioning

4.2 Weighted nonlinear regression approaches to model calibration.

4.2.1  Choosing the cost (objective) function

4.2.2  Evaluating Parameter and Prediction Uncertainties

4.2.3  Assessing the value of additional data

4.3  Formal Bayesian approaches to model conditioning

4.3.1  Formal likelihood measures

4.3.2  Markov Chain Monte Carlo Search (MC2)

4.3.3  Case Study:  Assessing Uncertainties in a conceptual water balance model (Engeland et al., 2005)

4.4  Pareto Optimal Sets

4.5  Generalised Likelihood Uncertainty Estimation

4.5.1  The basis of the GLUE methodology

4.5.2  Deciding on whether a model is behavioural or not

4.5.3  Equifinality, confidence limits, tolerance limits and prediction limits

4.5.4  Equifinality and model validation

4.5.5  Equifinality and model spaces: sampling efficiency issues

4.5.6  Fuzzy Measures in Model Evaluation

4.5.7  Case Study: Hypothesis Testing Models of Stream Runoff Generation using GLUE

4.5.8  Variants on the GLUE methodology

4.5.9 What to do if you find that all your models can be rejected?

4.6  Fuzzy Systems:  Conditioning Fuzzy Rules using Data

4.7  Comparing Methods for Model Conditioning: Coherence and the Information Content of Data

4.8  Summary of Chapter 4

Box 4.1  Weighted nonlinear regression

Box 4.2  Formal Bayes Methods

Box 4.3  Markov Chain and Population Monte Carlo Methods

Box 4.4  Generalised Likelihood Uncertainty Estimation (GLUE)

Chapter 5:  Forecasting the near future

5.1 Real-time data assimilation

5.2 Least squares error correction models

5.3 The Kalman Filter

5.3.1  Updating a model of the residual errors

5.3.2  Updating the gain on a forecasting model

5.3.3  Case study: flood forecasting on the River Severn

5.3.4  The Extended Kalman Filter

5.4 Ensemble Kalman Filter

5.4.1  Case Study:  Application of the The Ensemble Kalman Filter to the Leaf River Basin

5.4.2  The Ensemble Kalman Smoother

5.5 The Particle Filter

5.5.1  Case Study:  Comparison of EnKF and PF methods on the River Rhine

5.6 Variational methods

5.7 Ensemble Methods in Weather Forecasting

5.8 Review of Chapter 5

Box 5.1  Kalman Filter Methods for Data Assimilation

Box 5.2  Variational Methodsfor Data Assimilation

Chapter 6:  Decision making when faced with uncertainty

6.1  Uncertainty and Risk in Decision Making

6.2  Uncertainty in Framing the Decision Context

6.3  Decision Trees, Influence Diagrams, and Belief Networks

6.4  Methods of Risk Assessment in Decision Making

6.5  Risk-Based Decision Making Methodologies

6.5.1  Assessing the preferences of the decision maker

6.5.2  Indifference between actions

6.5.3  Adding uncertainty and more information

6.5.4  Case Studies:  Decisions for Flood Warning and Control in Lake Como, Italy and the Red River, N. Dakota

6.6 The use of expert opinion in decision making

6.7 Combining the opinions of experts: Bayesian Belief Networks

6.7.1  Adding empirical evidence to a Belief Network

6.7.2  A Case Study

6.8 Evidential Reasoning Methods

6.8.1  Case Study: Use of Evidential Reasoning in assessing management options for Rupa Tal Lake Nepal.

6.9 Decision Support Systems.

6.10 Info-Gap decision theory

6.10.1 Case Study:  Info-Gap Decision Making in Designing Flood Defences

6.11 The Issue of Ownership of Uncertainty in Decision Making

6.12  The NUSAP methodology

6.13  Robust Adaptive Management in the Face of Uncertainty

6.14  Uncertainty and the Precautionary Principle in Decision Making

6.15  Summary of Chapter 6

Box 6.1  Basic Risk-based Decision Theory

Box 6.2  Info-Gap decision theory

Chapter 7:  An uncertain future?

7.1  So what should the practitioner do in the face of so many uncertainty estimation methods?

7.2  The problem of future histories – unknowability and uncertainty

7.3  But is the uncertainty problem simply a result of using poor models?

7.4  Accepting an uncertain future

7.4.1  Modelling as a learning process about places

7.4.2  Learning about Model Structures

7.5  Future proofing modelling systems: adaptive modelling, adaptive management

7.6  Summary of Chapter 7


Appendix:  A (Brief) Guide to Matrix Algebra


Appendix:  A (Brief) Guide to Software