  The advent of digital computing in the 1950s sparked a revolution in the
science of weather and climate. Meteorology, long based on extrapolating
patterns in space and time, gave way to computational methods in a decade of
advances in numerical weather forecasting. Those same methods also gave rise to
computational climate science, studying the behaviour of those same numerical
equations over intervals much longer than weather events, and changes in
external boundary conditions. Several subsequent decades of exponential growth
in computational power have brought us to the present day, where models ever
grow in resolution and complexity, capable of mastery of many small-scale
phenomena with global repercussions, and ever more intricate feedbacks in the
Earth system.
  The current juncture in computing, seven decades later, heralds an end to
what is called Dennard scaling, the physics behind ever smaller computational
units and ever faster arithmetic. This is prompting a fundamental change in our
approach to the simulation of weather and climate, potentially as revolutionary
as that wrought by John von Neumann in the 1950s. One approach could return us
to an earlier era of pattern recognition and extrapolation, this time aided by
computational power. Another approach could lead us to insights that continue
to be expressed in mathematical equations. In either approach, or any synthesis
of those, it is clearly no longer the steady march of the last few decades,
continuing to add detail to ever more elaborate models. In this prospectus, we
attempt to show the outlines of how this may unfold in the coming decades, a
new harnessing of physical knowledge, computation, and data.
