Deleersnijder, E. and P.F.J. Lermusiaux, (Guest Eds.), 2008. *Multi-Scale Modelling: Nested Grid and Unstructured Mesh Approaches, Editorial.* Ocean Dynamics, 58, 335-336, Springer. doi: 10.1007/s10236-008-0170-5.

In 1969, the Journal of Computational Physics published a
seminal article by K. Bryan presenting the first ocean
general circulation model. Since then, many numerical
studies of the World Ocean, as well as regional or coastal
flows, used models directly or indirectly inspired by the
work of Bryan and his colleagues. A number of these
models have evolved into highly modular and versatile
computational systems, including multiple physical modules
and options as well as varied biogeochemical,
ecosystem and acoustics modeling capabilities. Several
modeling systems are now well-documented tools, which
are widely used in research institutions and various
organizations around the world. The list of such modeling
systems is large and too long to be summarized in this
editorial.
Over the last three decades, significant progress has been
made in the parameterization of subgrid-scale processes, in
data assimilation methodologies and in boundary condition
schemes, as well as in the efficient implementation of
algorithms on fast vector and subsequently parallel computers,
allowing higher and higher resolution in space and
time. However, many of today’s popular modeling systems
can still be regarded as members of the first generation of
ocean models: at their core, rather similar geophysical fluid
dynamics equations are solved numerically using a conservative
finite-difference method on a structured grid.
Today, several aspects of structured-grid models could
benefit from significant upgrades, learning from major
advances in computational fluid dynamics. In particular, the
use of a structured grid limits the flexibility in the spatial
resolution and does not allow one to take full advantage of
numerical algorithms such as finite volumes and finite
elements, which can achieve their best performance when
implemented on unstructured meshes.
Even though many of today’s complex marine modeling
and data assimilation systems have evolved significantly
since Bryan’s prototype, it would be challenging to modify
them step-by-step from a structured-grid approach to an
unstructured-grid one. Therefore, novel marine model
design research is underway, paving the way for the second
generation of ocean modeling systems. It is difficult to
predict today if this new generation of ocean models will
achieve its chief objective: widening the range of resolved
scales of motion with increased efficiencies and accuracies,
possibly allowing multi-resolution, multi-scale, and multidynamics
numerical simulations of marine flows, all
occurring seamlessly within distributed computing environments.
In fact, hybrid approaches merging the advantages
of structured and unstructured-grid modeling may be the
way forward.
Whether or not unstructured mesh approaches will
prevail is all the more difficult to predict now that
structured mesh modelers have developed powerful solutions
for increasing the resolution when and where
needed. For instance, grid embedding is still a popular
and useful method for enhancing model resolution. It can
involve multiply nested domains and allows the relatively straightforward use of different dynamics or models in each
domain. Research is also underway for developing multigrid,
wavelet, and other multi-scale decompositions for the
numerical solution of dynamical equations but also for the
study of results, model evaluation or data assimilation.
This special issue presents a number of examples of the
abovementioned developments. Ringler et al. examine the
potential of spherical centroidal Voronoi tessellations for
performing multi-resolution simulations; they apply this
method to the Greenland ice sheet and the North Atlantic
Ocean. Lambrechts et al. present a triangular mesh
generation system and its applications to the World Ocean
and various shelf seas, including the Great Barrier Reef,
Australia. Finite element models on unstructured grids are
described and utilized in several manuscripts. Bellafiore et
al. study the Adriatic Sea and the Lagoon of Venice, while
Jones and Davies simulate tides and storm surges along the
western coast of Britain. Danilov et al. assess two finite
element discretizations, i.e., a continuous element and a
non-conforming one, and compare the results of these
discretizations with those of a finite-difference model. In
Harig et al., the tsunami generated by the great Sumatra-Andaman earthquake of 26 December 2004 is simulated by
means of a finite element model. Comparisons are carried
out with various types of data as well as with the results of
a structured mesh model using a nested structured-grid
system. A nested-grid ocean circulation model is also
employed by Yang and Sheng to carry out a process study
on the Inner Scotian Shelf, Canada, focusing on the
circulation induced by a tropical storm. Debreu and Blayo
present a detailed review of two-way embedding algorithms
for structured-grid models. Finally, Logutov develops a
multi-scale assimilation scheme for tidal data within the
framework of a multiply nested structured-grid barotropic
tidal modeling approach.
As illustrated by these manuscripts, the next generation
of ocean modelers is motivated by a wide range of research
opportunities over a rich spectrum of needs. Future progress
will involve fundamental and applied numerical and
computational research as well as new multi-scale geophysical
fluid modeling. Domains of ongoing interest range
from estuaries to the global ocean, including coastal regions
and shelf seas. New multi-scale modeling of physical as
well as biological, chemical or interdisciplinary processes
will flourish in the coming decades.
We are grateful to the authors for their contributions and
to the chief-editor for his support in this endeavor. We are
thankful to the reviewers for their time and help in assessing
the manuscripts submitted to this special issue. Eric
Deleersnijder is a Research associate with the Belgian
National Fund for Scientific Research (FNRS); he is
indebted to the Communaut Francaise de Belgique for its
support through contract ARC 04/09-316. Pierre Lermusiaux
is grateful to the Office of Naval Research for support under
grant N00014-08-1-1097 to the Massachusetts Institute of
Technology.