Modeling Uncertainty in the Earth Sciences highlights the various issues, techniques and practical modeling tools available for modeling the uncertainty ofcomplex Earth systems and the impact that it has on practical situations. Theaim of the book is to provide an introductory overview which covers a broad range of tried-and-tested tools. Descriptions of concepts, philosophies, challenges, methodologies and workflows give the reader an understanding of the bestway to make decisions under uncertainty for Earth Science problems. The book covers key issues such as: Spatial and time aspect; large complexity and dimensionality; computation power; costs of 'engineering' the Earth; uncertainty inthe modeling and decision process. Focusing on reliable and practical methodsthis book provides an invaluable primer for the complex area of decision making with uncertainty in the Earth Sciences. INDICE: Preface. Acknowledgements. 1 Introduction. 1.1 Example Application. 1.1.1 Description. 1.1.2 3D Modeling. 1.2 Modeling Uncertainty. 2 Review on Statistical Analysis and Probability Theory. 2.1 Introduction. 2.2 Displaying Data with Graphs. 2.2.1 Histograms. 2.3 Describing Data with Numbers. 2.3.1 Measuring the Center. 2.3.2 Measuring the Spread. 2.3.3 Standard Deviation and Variance. 2.3.4 Properties of the Standard Deviation. 2.3.5 Quantiles and the QQ Plot. 2.4 Probability. 2.4.1 Introduction. 2.4.2 Sample Space, Event, Outcomes. 2.4.3 Conditional Probability. 2.4.4 Bayes' Rule. 2.5 Random Variables. 2.5.1 Discrete Random Variables. 2.5.2 Continuous Random Variables. 2.5.2.1 Probability Density Function (pdf). 2.5.2.2 Cumulative Distribution Function. 2.5.3 Expectation and Variance. 2.5.3.1 Expectation. 2.5.3.2 Population Variance. 2.5.4 Examples of Distribution Functions. 2.5.4.1 The Gaussian (Normal) RandomVariable and Distribution. 2.5.4.2 Bernoulli Random Variable. 2.5.4.3 UniformRandom Variable. 2.5.4.4 A Poisson Random Variable. 2.5.4.5 The Lognormal Distribution. 2.5.5 The Empirical Distribution Function versus the Distribution Model. 2.5.6 Constructing a Distribution Function from Data. 2.5.7 Monte Carlo Simulation. 2.5.8 Data Transformations. 2.6 Bivariate Data Analysis. 2.6.1 Introduction. 2.6.2 Graphical Methods: Scatter plots. 2.6.3 Data Summary: Correlation (Coefficient). 2.6.3.1 Definition. 2.6.3.2 Properties of r. 3 Modeling Uncertainty: Concepts and Philosophies. 3.1 What is Uncertainty? 3.2 Sources of Uncertainty. 3.3 Deterministic Modeling. 3.4 Models of Uncertainty. 3.5 Model and Data Relationship. 3.6 Bayesian View on Uncertainty. 3.7 Model Verification and Falsification. 3.8 Model Complexity. 3.9 Talking about Uncertainty. 3.10Examples. 3.10.1 Climate Modeling. 3.10.1.1 Description. 3.10.1.2 Creating Data Sets Using Models. 3.10.1.3 Parameterization of Subgrid Variability. 3.10.1.4 Model Complexity. 3.10.2 Reservoir Modeling. 3.10.2.1 Description. 3.10.2.2Creating Data Sets Using Models. 3.10.2.3 Parameterization of Subgrid Variability. 3.10.2.4 Model Complexity. 4 Engineering the Earth: Making Decisions Under Uncertainty. 4.1 Introduction. 4.2 Making Decisions. 4.2.1 Example Problem.4.2.2 The Language of Decision Making. 4.2.3 Structuring the Decision. 4.2.4 Modeling the Decision. 4.2.4.1 Payoffs and Value Functions. 4.2.4.2 Weighting.4.2.4.3 Trade-Offs. 4.2.4.4 Sensitivity Analysis. 4.3 Tools for Structuring Decision Problems. 4.3.1 Decision Trees. 4.3.2 Building Decision Trees. 4.3.3 Solving Decision Trees. 4.3.4 Sensitivity Analysis. 5 Modeling Spatial Continuity. 5.1 Introduction. 5.2 The Variogram. 5.2.1 Autocorrelation in 1D. 5.2.2 Autocorrelation in 2D and 3D. 5.2.3 The Variogram and Covariance Function. 5.2.4Variogram Analysis. 5.2.4.1 Anisotropy. 5.2.4.2 What is the Practical Meaningof a Variogram? 5.2.5 A Word on Variogram Modeling. 5.3 The Boolean or ObjectModel. 5.3.1 Motivation. 5.3.2 Object Models
- ISBN: 978-1-119-99262-2
- Editorial: John Wiley & Sons
- Encuadernacion: Rústica
- Páginas: 248
- Fecha Publicación: 24/06/2011
- Nº Volúmenes: 1
- Idioma: Inglés