A new approach to bathymetry smoothing in sigma-coordinate ocean models

σ -coordinate ocean models are currently used in large basin and coastal seas simulations. When there is a strongly varying bathymetry, σ -coordinate system solutions exhibit an intrinsic error in the horizontal pressure gradient (HPG) term. In this paper, a new, linear programming (LP) procedure has been proposed to deal with this problem. The success of the procedure in alleviating HPG error is gauged in comparison with two implementations of the Shapiro filter, the Mellor–Ezer–Oey (1994) algorithm (MEO), and the recently (2006) proposed procedure of Martinho and Batteen (MB). All are applied to three idealised cases and then to the Adriatic Sea, as modelled with the Rutgers version of ROMS. The comparisons reveal that even the improved Shapiro filter creates very large modifications to the bathymetry and should be avoided. The MB procedure performance is comparable to that of LP when the slope factor is larger than approximately 0.2, and inferior to it at smaller slope factor values. In cases where volume conservation is required, the MB method is inferior to both MEO and LP. The difference between the above-mentioned solutions is more pronounced for coarser grids.