The problem of predicting the future state of the weather and and climate of
the earth has a long history in applied mathematics. Both problems were
identified by John von Neumann as prime areas of study for the earliest
electronic computers. Over the past 50 years, many mathematical challenges
have been inspired by the problems associated with predicting weather and
simulating the past present and future climate. Amongst these are stable
integration of geophysical fluid equations for indefinite periods of time,
the development of a theory of chaos and predictability and successful
fusion of models and observational data in systems with extremely large
dimensionality.
New challenges are arising in the 21st century which will require new
computational and applied math techniques to resolve. I will present as
survey of both the past successes and the future problems in my talk.
