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JOURNAL OF GEOPHYSICAL RESEARCH,
VOL. 100, NO. C10,
PAGES 20,763–20,778,
1995
Upwind-weighted advection schemes for ocean tracer transport: An evaluation in a passive tracer context
Matthew W. Hecht
National Center for Atmospheric Research, Boulder, Colorado
William R. Holland
National Center for Atmospheric Research, Boulder, Colorado
Philip J. Rasch
National Center for Atmospheric Research, Boulder, Colorado
Abstract
Centered-in-space, centered-in-time integration has generally been used for the advection of scalars in ocean models. An assessment
is made of the implications of centered leapfrog integration in the context of two-dimensional passive tracer advection within
a Stommel (1948) gyre. Nonphysical ripples in the tracer field grow to alarming levels in purely advective integrations. Diffusive
parameterizations of eddy mixing moderate these ripples, but it is found that Laplacian diffusion greatly reduces the peak
amplitude of the tracer field, while biharmonic or weaker Laplacian diffusion allows ripples of large amplitude. Several forward-in-time,
upwind-weighted schemes are found to provide better solutions. Smolarkiewicz's (1984) Multi-Dimensional Positive-Definite
Advection and Transport Algorithm (MPDATA) scheme is slightly superior for an integration at moderate resolution within which
the western boundary current is poorly resolved in typical fashion. Third-order, upwind-based schemes exhibit little sensitivity
to the details of multidimensional treatment for this problem of passive tracer advection, with results nearly as good as
for MPDATA.
Received 28
December
1994;
accepted 13
June
1995.
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Citation: Hecht, M. W., W. R. Holland, and P. J. Rasch
(1995),
Upwind-weighted advection schemes for ocean tracer transport: An evaluation in a passive tracer context,
J. Geophys. Res.,
100(C10),
20,763–20,778.
Copyright 1995 by the American Geophysical Union.
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