Clarifying the Distinction Between Steric and Baroclinic Sea Surface Height

One of the most fundamental uses of ocean models is for the prediction of sea level. Vertical integration of the hydrostatic equation leads to the partitioning of sea level in terms of atmospheric pressure, steric height, and bottom pressure. In an effort to validate the baroclinic wave dynamics of numerical ocean models, some researchers have compared the steric height from models with the sea level anomaly derived from satellite altimetry. The use of steric height in these comparisons captures the qualitative aspects of the baroclinic waves, but it neglects a non-negligible contribution from bottom pressure. A more accurate evaluation of baroclinic wave dynamics using sea level would involve projecting the pressure field onto orthogonal barotropic and baroclinic components to isolate the baroclinic sea level anomaly. This note illustrates the quantitative difference between steric height and baroclinic sea level, which amounts to approximately a 20% bias of steric height over baroclinic sea level, depending on location.