Chapter 4
ON THE USE OF HYBRID VERTICAL
COORDINATES IN OCEAN
CIRCULATION MODELING
Rainer Bleck
Los Alamos National Laboratory, Los Alamos, New Mexico, USA
Abstract
The rationale for building hybrid-coordinate ocean circulation models
is discussed in the context of various approaches presently taken to
improve mathematical and physical aspects of ocean models. Design
choices made in formulating the vertical grid generator, the core component of hybrid models, are laid out. A new experimental approach
toward minimizing numerical errors and inconsistencies during simultaneous advection of temperature, salinity and density is presented.
Keywords: Ocean models, vertical coordinate, hybrid coordinate.
1.
Introduction
Motion systems interacting in the ocean range in size from centimeters to planetary, a spread of 9 orders of magnitude. Ocean circulation
modeling therefore is a textbook example of a multiscale problem. Since
even our fastest computers cannot spatially resolve the earth’s surface
by more than a few thousand grid points in each direction, only about
one-third of those 9 orders of magnitude can be explicitly resolved in
state-of-the-art ocean models, meaning that the other two-thirds are
relegated to the “subgrid” scale. Hence, a perpetual challenge to ocean
modeling is the need to parameterize the interaction of physical processes
across the threshold between resolved and unresolved scales of motion.
This need will be with us until computers become (10 6 ) 3 = 10 18 times
faster than they are today – i.e., practically forever.
The ability of today’s ocean models to correctly simulate essential
aspects of the global circulation has led to a proliferation of applications
109
E. P. Chassignet and J. Verron (eds.), Ocean Weather Forecasting, 109-126.
© 2006 Springer. Printed in the Netherlands.
ON THE USE OF HYBRID VERTICAL
COORDINATES IN OCEAN
CIRCULATION MODELING
Rainer Bleck
Los Alamos National Laboratory, Los Alamos, New Mexico, USA
Abstract
The rationale for building hybrid-coordinate ocean circulation models
is discussed in the context of various approaches presently taken to
improve mathematical and physical aspects of ocean models. Design
choices made in formulating the vertical grid generator, the core component of hybrid models, are laid out. A new experimental approach
toward minimizing numerical errors and inconsistencies during simultaneous advection of temperature, salinity and density is presented.
Keywords: Ocean models, vertical coordinate, hybrid coordinate.
1.
Introduction
Motion systems interacting in the ocean range in size from centimeters to planetary, a spread of 9 orders of magnitude. Ocean circulation
modeling therefore is a textbook example of a multiscale problem. Since
even our fastest computers cannot spatially resolve the earth’s surface
by more than a few thousand grid points in each direction, only about
one-third of those 9 orders of magnitude can be explicitly resolved in
state-of-the-art ocean models, meaning that the other two-thirds are
relegated to the “subgrid” scale. Hence, a perpetual challenge to ocean
modeling is the need to parameterize the interaction of physical processes
across the threshold between resolved and unresolved scales of motion.
This need will be with us until computers become (10 6 ) 3 = 10 18 times
faster than they are today – i.e., practically forever.
The ability of today’s ocean models to correctly simulate essential
aspects of the global circulation has led to a proliferation of applications
109
E. P. Chassignet and J. Verron (eds.), Ocean Weather Forecasting, 109-126.
© 2006 Springer. Printed in the Netherlands.