Inverse problem in groundwater modeling

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.