Effects of stencil width on surface ocean geostrophic velocity and vorticity estimation from gridded satellite altimeter data

Abstract

This paper examines the effect of “stencil width” on surface ocean geostrophic velocity and vorticity estimated from differentiating gridded satellite altimeter sea surface height products. In oceanographic applications, the value of the first derivative at a central grid point is generally obtained by differencing the sea surface heights at adjacent grid points. This is called a “three‐point stencil centered difference”. Here the stencil width is increased from three to five, seven, and nine points, using well‐known formulae from the numerical analysis literature. The discrepancies between velocities computed with successive stencils decreases with increasing stencil width, suggesting that wide stencil results are more reliable. Significant speed‐dependent biases (up to 10–20%) are found between results computed from three‐point stencils versus those computed from wider stencils. The geostrophic velocity, and the variance of geostrophic velocity, are underestimated with thin stencils. Similar results are seen in geostrophic velocities computed from high‐resolution model output. In contrast to the case when three‐point stencils are used, wider stencils yield estimates of the anisotropy of velocity variance that are insensitive to the differences in grid spacing between two widely used altimeter products. Three‐point stencils yield incorrect anisotropies on the 1/4° anisotropic AVISO grid; we recommend the use of 7‐point stencils. Despite the demonstrated inadequacies of the three‐point stencils, the conclusions of earlier studies based on them, that the zonally averaged midlatitude eddy kinetic energy field is nearly isotropic, are found to pertain also with wider stencils. Finally, the paper also examines the strengths and limitations of applying noise‐suppressing differentiators, versus classic centered differences, to altimeter data.