1. How much complexity is too much? “you should try to make things as simple as possible, but not too simple” A. Einstein “All modeling is a gross simplification of the real system.” G. Whelan “Don’t work any harder than you have to.” K. Castleton

2. Talking Points Who is Karl Castleton and “What does he do?” The ADVECTIVE, DISPERSIVE, and DECAY equation. Intuition about the system Intuition about the equation Semi-Analytical techniques Numerical techniques Conclusions

3. Who is Karl Castleton Mesa State Graduate: A.A.S. 1987, B.S. 1992 Computer Science and Mathematics Washington State University: M.S. Computer Science 1997 Works at Pacific Northwest National Laboratory Master Project solved the advective, dispersive, decay equation by three different methods

4. The “Equation” Used in Civil Engineering, Environmental, Pharmaceutical, System Biological modeling Is a partial differential equation A number of analytical solutions for simplified cases Flow, spreading, and degrading

5. Intuition about the system C Dz Dx Ux Uy

6. Intuition about the equation Plug flow Spreading in three dimensions Degradation, decay within the cell Simplification can yield analytical results

7. Semi-Analytical Techniques Take the mathematics as far as it can go and then use a computer to put you over the top. Reduce the model to a system that has an analytical result for instantaneous release. Convolute the instantaneous release with input forcing function.

8. Numerical Techniques Just implement the equation “Easy” to implement Code can be very close to equation Can consume a lot of computer resources Does allow for a variety of values

9. Conclusion There are many ways to solve a modeling question Use no more or less than you need Do not always use the same tool/technique Do not work any harder than you have to.