Teaching Advanced Soil Physics as a Dialogue Between Discrete and Continuum Perspectives.

We (Horton and Ewing) have co-taught the Advanced Soil Physics course at Iowa State University for at least the last 10 years.  Horton’s original course was largely focused on analytical and numerical solutions of soil physics problems expressed as partial differential equations.  Ewing’s research, which views soil as an ensemble of discrete pores undergoing discrete pore-scale events, has focused on pore-scale network modeling and percolation theory.  The combination has turned the class into a dialogue between two (or sometimes more) different ways of looking at the same phenomena.  The soil physics topics are reinforced by numerical homework exercises in a MATLAB-like environment; the procedural thinking that is required is new and difficult (but important!) to many students.  We explore the utility of analytical solutions in developing numerical models, and the utility of numerical models in gaps not covered by analytical solutions.  By the end, the students see multiple approaches to a given problem, with strengths and weaknesses to each.  An underlying message of the class, that all models are inherently incorrect, reinforces the flexibility and skepticism with which one should use models.