Hydrostatic Consistency in Sigma Coordinate Ocean Models
Chu, Peter C.
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Truncation error and hydrostatic inconsistency at steep topography are two concerns in sigma coordinate ocean models due to the horizontal pressure gradient being difference of two large terms. A consensus is reached in the ocean modeling community on the first concern (truncation error), but not on the second concern (hydrostatic inconsistency). Since the integration of the pressure gradient over a finite volume equals the integration of the pressure over the surface of that volume (always dynamically consistent), dynamical analysis on finite volumes is used to determine the hydrostatic consistency of a sigma coordinate ocean model. A discrete, hydrostatically consistent scheme is obtained for the sigma coordinate ocean models. Comparison between finite-volume and finite-difference approaches leads to the conclusion that a Boussinesq, hydrostatic, sigma coordinate ocean model with second-order staggered scheme is always hydrostatically consistent. Guidance for improving numerical accuracy is also provided.
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