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contributor authorSong, Y. Tony
date accessioned2017-06-09T16:12:12Z
date available2017-06-09T16:12:12Z
date copyright1998/12/01
date issued1998
identifier issn0027-0644
identifier otherams-63219.pdf
identifier urihttp://onlinelibrary.yabesh.ir/handle/yetl/4204198
description abstractA Jacobian formulation of the pressure gradient force for use in models with topography-following coordinates is proposed. It can be used in conjunction with any vertical coordinate system and is easily implemented. Vertical variations in the pressure gradient are expressed in terms of a vertical integral of the Jacobian of density and depth with respect to the vertical computational coordinate. Finite difference approximations are made on the density field, consistent with piecewise linear and continuous fields, and accurate pressure gradients are obtained by vertically integrating the discrete Jacobian from sea surface. Two discrete schemes are derived and examined in detail: the first using standard centered differencing in the generalized vertical coordinate and the second using a vertical weighting such that the finite differences are centered with respect to the Cartesian z coordinate. Both schemes achieve second-order accuracy for any vertical coordinate system and are significantly more accurate than conventional schemes based on estimating the pressure gradients by finite differencing a previously determined pressure field. The standard Jacobian formulation is constructed to give exact pressure gradient results, independent of the bottom topography, if the buoyancy field varies bilinearly with horizontal position, x, and the generalized vertical coordinate, s, over each grid cell. Similarly, the weighted Jacobian scheme is designed to achieve exact results, when the buoyancy field varies linearly with z and arbitrarily with x, that is, b(x,z) = b0(x) + b1(x)z. When horizontal resolution cannot be made fine enough to avoid hydrostatic inconsistency, errors can be substantially reduced by the choice of an appropriate vertical coordinate. Tests with horizontally uniform, vertically varying, and with horizontally and vertically varying buoyancy fields show that the standard Jacobian formulation achieves superior results when the condition for hydrostatic consistency is satisfied, but when coarse horizontal resolution causes this condition to be strongly violated, the weighted Jacobian may give superior results.
publisherAmerican Meteorological Society
titleA General Pressure Gradient Formulation for Ocean Models. Part I: Scheme Design and Diagnostic Analysis
typeJournal Paper
journal volume126
journal issue12
journal titleMonthly Weather Review
identifier doi10.1175/1520-0493(1998)126<3213:AGPGFF>2.0.CO;2
journal fristpage3213
journal lastpage3230
treeMonthly Weather Review:;1998:;volume( 126 ):;issue: 012
contenttypeFulltext


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