Stochastic Subsurface Hydrology
Semester Taught - Fall
Stochastic modeling of subsurface flow and transport modeling including geostatisitcs, time series analysis, Kalman filtering, and physically based stochastic models.
Prerequisites for the course include calculus (through ordinary differential equations), undergraduate probability and statistics, and previous coursework in subsurface hydrology. Familiarity with computer operating systems and computer programming will be assumed.
Dr. Wendy Graham
UF Water Institute
570 Weil Hall
Phone: 352-392-5893 x2113
Class Materials Required
Course notes will be provided at http://abe.ufl.edu/Faculty/graham/cwr6536_lecture_notes.html
The following texts are useful as references but not required
- Papoulis, A., Probability, Random Variables, and Stochastic Processes, 3rd edition, Published by McGraw Hill, 1991
- Goovaerts, P., Geostatistics for Natural Resources Evaluation , Published by Oxford University Press, 1997.
- Gelhar, L. Stochastic Subsurface Hydrology, Published by Prentice-Hall, 1993.
Recommended Journal Article Reading List: Stochastic Subsurface Hydrology Reading List 2012.docx
Two lectures/discussions each week.
- Review of Probability and Random Field Theory: Lectures 1-8
- Properties of Random Variables and Random Fields
- Distributional assumptions
- Spatial and temporal correlation
- Stationarity & ergodicity
- Estimation of Properties from field data
- Estimating the mean and variance
- Estimating the covariance and variogram
- Estimating the cross-covariance and cross-variogram
- Estimating the pdf and cdf
- Mean, covariance and variogram models
- stationary & nonstationary mean models
- hole and non‑hole covariance & variogram models
- isotropic & anisotropic covariances & variograms
Case Study: Estimation of pdfs, sample means, covariances, cross covarainces, variograms and cross variograms from mystery random fields.
- Physically-Based Stochastic Modeling Methods: Lectures 9-19 (Weeks 6-12)
- Why Stochastic Modeling?
- Effective "macro‑scale" model parameters
- Model prediction uncertainty analysis
- Data assimilation/conditioning with model-derived covariances and cross-covariances
- Monitoring network design
- Theoretical Approaches to Stochastic Modeling
- Exact Analytic Solutions
- Monte Carlo Methods
- Approximate Analytic Solutions
- Approximate Numerical Soltuions
- Applications of Stochastic Modeling to Multidimensional Groundwater Flow and Transport Problems
- Monte Carlo Methods (Freeze 1975; Delhomme, 1979; Smith & Freeze 1979; Graham & McLauglin, 1989a)
- First-order Spectral methods (Mizell et al 1982, Bakr et al 1978, Gelhar 1993; Vomvoris, 1990)
- First-order state space techniques (Hoeksema & Kitanidis1985, McLaughlin & Wood 1988; James and Graham, 1998; Graham and McLaughlin 1989a,b, 1991
- First‑order Lagrangian techniques (Dagan, Neuman, Destouni, Cvetkovic&Dagan)
Case Study: Stochastic Model Development using 1-D Environmental Fate and Transport Model
- Optimal Estimation of Hydrogeochemical Parameters: Lectures 20-23 (Weeks 13-14)
- Theory of Kriging
- Simple Kriging (known mean)
- Ordinary Kriging (constant but unknown mean)
- Non-stationary Kriging
- Log–Kriging, Block-Kriging, Indicator-Kriging
- Theory of Co-Kriging
- Development of Equations
- Simple Co-Kriging (known mean)
- Ordinary Co-Kriging (constant but unknown mean)
- Kalman Filtering
- Generalized Likelihood Uncertainty Estimation
- Particle Filtering
Case Study: Geostatistical Analysis of Upper Floridan Aquifer Data
- Student Presentations of Current Literature in Data Assimilation (e.g. Kalman Filtering, Particle Filtering, Generalized Likelihood Uncertainty Estimation, Variational Methods (Weeks 13-17 )
Select paper and submit for approval by instructor deadline. All students responsible for reading all papers and participating in discussions.
|Term projects (3 @25% each)||75%|
|Written and Oral presentation
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Resources are available on-campus for students having personal problems or lacking clear career and academic goals which interfere with their academic performance. These resources include:
- University Counseling Center, 301 Peabody Hall, 392-1575, personal and career counseling;
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