This textbook introduces step by step the basic numerical methods to
solve the equations governing the motion of the atmosphere and ocean,
and describes how to develop a set of corresponding instructions for the
computer as part of a code. Today's computers are powerful enough to
allow 7-day forecasts within hours, and modern teaching of the subject
requires a combination of theoretical and computational approaches.
The presentation is aimed at beginning graduate students intending to
become forecasters or researchers, that is, users of existing models or
model developers. However, model developers must be well versed in the
underlying physics as well as in numerical methods. Thus, while some of
the topics discussed in the modeling of the atmosphere and ocean are
more advanced, the book ensures that the gap between those scientists
who analyze results from model simulations and observations and those
who work with the inner works of the model does not widen further.
In this spirit, the course presents methods whereby important balance
equations in oceanography and meteorology, namely the
advection-diffusion equation and the shallow water equations on a
rotating Earth, can be solved by numerical means with little prior
knowledge. The numerical focus is on the finite-difference (FD) methods,
and although more powerful methods exist, the simplicity of FD makes it
ideal as a pedagogical introduction to the subject. The book also
includes suitable exercises and computer problems.