Course ID: D86022VJ
Credits: 3
Objective: Numerical simulation of groundwater plays a crucial role in hydrogeology, and the theory of numerical inversion and parameter calibration in numerical simulations determines the success of the models. This course will cover the fundamental theories, mathematical derivations, and practical applications of numerical inversion. Students with a background in hydrogeology, groundwater hydrology, and numerical simulations will have the opportunity to learn about the latest international inversion theories and their applications in groundwater.
Course Prerequisites: Hydrogeology, Groundwater Numerical Simulation.
Outline:
I. Introduction to parameter estimation in hydrology
II. Inverse problems of parameter estimation in groundwater modeling
A. Parameter estimation using linear programming
B. Parameter estimation using quadratic programming
C. Ill-posedness and identifiability
D. Parameterization
III. Inverse problems of parameter estimation in groundwater modeling
A. Equation error criterion vs. output error criterion
B. Modeling error vs. parameter uncertainty error
C. Gauss-Newton minimization
IV. Inverse problems of parameter estimation in groundwater modeling
A. Sensitivity coefficient calculation
B. Covariance and correlation matrix of the estimated parameters
V. Inverse problems of parameter estimation in groundwater modeling
A. Model structure identification
B. Model structure error vs. least-squares error
VI. Groundwater management model
VII. Experiment design/Sampling strategies/Monitoring network design
A. Introduction
B. Classical criteria
C. Optimization of experimental design
Teaching Method:
Classroom instruction, oral presentations, practical exercises.
Reference:
Self-compiled course materials, journal articles.
Course Schedule (subject to change):
Week 1: Introduction to parameter estimation in hydrology
Week 2: Inverse problems of parameter estimation in groundwater modeling
Week 3: Parameter estimation using linear/quadratic programming
Week 4: Ill-posedness and identifiability/Parameterization
Week 5: Equation error criterion vs. output error criterion/Modeling error vs. parameter uncertainty error
Week 6: Gauss-Newton minimization/Sensitivity coefficient calculation
Week 7: Covariance and correlation matrix of the estimated parameters
Week 8: Bayesian estimation
Week 9: Oral presentation
Week 10: Model structure identification/ The generalized inverse problem
Week 11: Model structure error vs. least-squares error
Week 12: Model selection criteria
Week 13: Linking simulation with optimization/ Response matrix
Week 14: Classical criteria derived from linear statistical models
Week 15: Optimization of experimental design
Week 16: Tracer experiment
Week 17: Mixed integer programming formation
Week 18: Presentation
Evaluation:
Oral presentation: 50%
Project: 50%