Workshop - Model Calibration and Uncertainty Analysis Using PEST
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1 About PEST PEST (Parameter ESTimation) is a general-purpose, model-independent, parameter estimation and model predictive uncertainty analysis package developed by Dr. John Doherty. PEST is the most advanced software readily available for calibration and predictive uncertainty analysis of groundwater, reservoir, surface water, and other models. Using PEST you can: apply advanced and efficient regularization techniques in calibrating your models thereby extracting maximum information content from your data on the one hand and expert knowledge on the other hand undertake linear and nonlinear predictive error and uncertainty analysis of model outputs simultaneously parameterize and calibrate several models using multiple datasets accommodate heterogeneity using advanced spatial parameterization techniques combine PEST with stochastic field generation to efficiently explore pre- and post-calibration parameter and predictive uncertainty conduct parallel model optimization runs across PC or UNIX networks compare the worth of different proposed data acquisition strategies in reducing model predictive uncertainty, thereby optimizing resources allocated to such tasks quantify the contributions to model predictive uncertainty made by different parameter types establish the irreducible uncertainty of a model prior to calibrating that model quantify the reduction in predictive uncertainty accrued through model calibration use a model for quantitative hypothesis-testing test the contributions that model defects and simplifications make to potential pre- and post-calibration predictive error provide risk analysis input to the decision-support process Traditional methods of parameter estimation and uncertainty analysis based on a handful of zones of assumed piecewise parameter constancy do not provide the flexibility needed to extract vital information from expensive data, or to quantify the benefits and risks associated with different environmental management options. Some of the advances made over the last few years in PEST to overcome these problems include: Combining regularized inversion with the use of pilot points as a spatial parameterization device Use of the unique and extremely efficient SVD-assist regularized inversion methodology which combines subspace and Tikhonov methods. Inversion can be carried out with modelrun efficiencies comparable with traditional approaches even though the model may use hundreds of parameters Combining regularized inversion with stochastic field generation to produce many different calibration-constrained parameter fields with high levels of model run efficiency. All of these
2 can then be used in making any model prediction in order to explore the uncertainty of that prediction Use of Pareto methods to compare the merits of different environmental management strategies and implement model-based hypothesis testing Use of surrogate simple models or polynomial proxy models to increase the efficiency of the model calibration/uncertainty analysis processes, and/or accommodate difficult model numerical behaviour Deployment of linear methods to rapidly assess the relative worth of different strategies for future data acquisition PEST is accompanied by a large number of utility programs which support its use with commonly used models (such as MODFLOW-USG, FEFLOW, MODFLOW, MT3D, SEAWAT, TOUGH and others). This software automates PEST file set-up for complex parameter estimation and uncertainty analysis problems involving one or multiple models. Other members of the PEST suite implement the global SCE and CMA optimisation algorithms which can be employed where high levels of model nonlinearity and/or poor model numerical behaviour make use of gradient based inversion methods difficult. Detailed Workshop PROGRAM The course is taught over four days. The program for most days is a combination of lectures and practical sessions (hands on exercises). The preliminary program is found below. The content of practical sessions can be defined by individual students. A wide range of workshops is provided with the course. However students are welcome to bring their own models to use with PEST. If they do this, help in linking their models to PEST will be provided. Morning of day1: Overview of linear analysis and matrix algebra Description of matrices and vectors Matrix multiplication Subspaces Projection operators Orthogonality and orthogonal projections The null space Singular value decomposition Eigenvalues and eigenvectors Random vectors Covariance matrices
3 Principal component analysis Afternoon of day 1: Models and Decision Support: what models can and cannot achieve An overview of modelling Sources of predictive uncertainty - Bayes equation The role of risk in decision-making The role of uncertainty analysis in establishing risk What a simple model can achieve What a complex model can achieve The effects of model imperfections on model predictions The metrics for good modelling practice What calibration does for a model What calibration does not do for a model When bad models can make good predictions When good models make bad predictions Basics of uncertainty analysis Model-based hypothesis-testing Using models to encapsulate what we know Using models to quantify what we don t know Day 2: Basics of parameter estimation - theory and practice Nonlinear parameter estimation for well-posed inverse problems Application of nonlinear parameter estimation to model calibration Parameter correlation and non-uniqueness Formulation and minimization of an objective function Analysis of residuals The Jacobian matrix Parallelization of model runs Useful statistics arising from the parameter estimation process The nuts and bolts of using PEST
4 Building a PEST input dataset Analysis of PEST outputs Parameter non-uniqueness Parallel PEST and BeoPEST Morning of day 3: applied groundwater parameter estimation Multi-layered models Steady-state and transient calibration Utility support software supplied with PEST Avoiding structural noise caused by model inadequacies Temporal and spatial differencing in formulation of an objective function Problems associated with traditional approach to calibration of groundwater models Afternoon of day 3: highly parameterized inversion The benefits of highly parameterized inversion Tikhonov regularization Measurement and regularisation objective functions Pilot points as a parameterization device Singular value decomposition Solution subspace and null subspace Use of super parameters and SVD-assist for efficient inversion Difference between error and uncertainty Some case histories Morning of day 4: calibration-constrained uncertainty analysis Non-uniqueness and uncertainty Traditional uncertainty analysis Benefits of highly parameterized uncertainty analysis Linear error and uncertainty analysis
5 Nonlinear error and uncertainty analysis Null space Monte Carlo Pareto analysis and model-based hypothesis testing Assessment of the worth of new and existing data Paired simple and complex models Practical examples and demonstrations Afternoon of day 4: stochastic field generation The inherently stochastic nature of expert knowledge Brief overview of geostatistics Gaussian methods Multiple point geostatisics Other method of stochastic field generation Constraining parameter fields to respect calibration constraints What Participants will Receive Participants will receive a memory stick containing the following: Latest version of PEST Latest version of all PEST support utilities (over 200 programs) Copies of files and documentation for over 12 PEST workshops Literature (mainly published papers) on the use of PEST Copies of all slides used in the workshop Course Attendee Information Practitioners from a wide range of backgrounds will benefit from this course, whether new to PEST or with previous PEST experience. To get the most out of the course, attendees should have modelling experience, preferably in the groundwater or surface water disciplines. However the material presented on the afternoon of the first day will also benefit those who rely on models for decision-making purposes and need to have a better understanding of what models can and cannot achieve, but do not necessarily build them. This session will be open to the public for free. Hands-on labs are GUI-independent and cover a variety of modelling disciplines, so that anyone interested in model calibration, parameter estimation, or the analysis of numerical model
6 uncertainty can benefit from the course. Experience in working at the command line level is an advantage in doing the workshops. Make sure to bring your laptop so that we can install the software and workshops on it. Even if you are not a modeller you can still benefit from the course because the concepts explained in this course are vital to an understanding of the role of modelling in environmental management. They will also allow you to understand what models can and cannot do, and to separate fact from fiction in promises made by those who sell expensive models.
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