This text grew out of notes for a course taught to graduate students in physical oceanography at the College of Oceanic and Atmospheric Sciences at Oregon State University. The students are typically in their second year of graduate school, having passed introductory courses in theoretical physical oceanography. This is the background assumed for the course. Most of the students at this point have seen some numerical analysis.

The course, and hence this text, is intended for all students of physical oceanography. Major emphasis is on those features that distinguish models of the ocean from other models in computational fluid mechanics. The intent is to examine ocean models critically, and determine what they do well and what they do poorly. We will ask when we can be confident that the model reflects nature, and when we can say that it is likely that we are looking at a feature of the model itself.

This is not a mathematics text as such, but it has a high mathematical content. Numerical analysis is introduced as needed. The reader may wish to consult supplementary references for basic numerical analysis of partial differential equations such as Sod (1985) (many typos, but reasonably current on fundamentals) or Richtmyer and Morton (1967), which is useful and commonly cited, though outdated. The reader might also find Isaacson and Keller (1966) or Allen et al. (1988) useful as general references. We will take examples from the two-volume work by Fletcher (1991) and the monograph by Leveque (1992). Durran (1999) contains useful and closely related material, from a slightly different viewpoint.