Computational Oceanography is the study of ocean phenomena by numerical
simulation, especially dynamical and physical phenomena. Progress in
information technology has driven exponential growth in the number of
global ocean observations and the fidelity of numerical simulations of
the ocean in the past few decades. The growth has been exponentially
faster for ocean simulations, however. We argue that this faster growth
is shifting the importance of field measurements and numerical
simulations for oceanographic research. It is leading to the maturation
of Computational Oceanography as a branch of marine science on par with
observational oceanography. One implication is that ultra-resolved ocean
simulations are only loosely constrained by observations. Another
implication is that barriers to analyzing the output of such simulations
should be removed. Although some specific limits and challenges exist,
many opportunities are identified for the future of Computational
Oceanography. Most important is the prospect of hybrid computational and
observational approaches to advance understanding of the ocean.