Introduction to Environmental Modeling

This textbook presents an understanding of how basic physical descriptions can be translated into mathematical analogues that provide an opportunity to investigate environmental processes. Examples come from a range of hydrologic, atmospheric, and geophysical problems. The emphasis is on simple examples and calculations that add to understanding. The book provides a sense for the meaning of mathematical expressions, a physical feel for their relations to processes, and confidence in working with mathematical solutions. The goal of this book, in essence, is to present the timeless basic physical and mathematical principles and philosophy of environmental modeling, often to students who need to be taught how to think in a different way than they would for more narrowly-defined engineering or physics problems. Minimum prerequisites for the student reader include a knowledge of calculus through differential equations, but the book provides the mathematical and physical tools needed as the occasion arises.

1. Philosophy and approach; 2. Thoughts on use of data; 3. Models as a framework for study of data; 4. Length and time scales; 5. Mechanisms of change; 6. Dimensional analysis; 7. Mathematical instruments of change; 8. Derivatives and scales; 9. Integral theorems and volume kinematics; 10. Mass conservation; 11. Species mass conservation; 12. Statement of conservation of momentum; 13. Conservation of total energy; 14. Mixed scale modeling; 15. Porous media and groundwater systems; 16. Advection-dispersion equation solution; 17. Stability revisited.