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Variability in sea surface height (SSH) can be decomposed into two contributions: one from changes in mass in the water column (barotropic) and the other from purely steric changes (baroclinic). Both contributions can be determined from data recorded by a pressure sensor–equipped inverted echo sounder (PIES). PIES data from the Agulhas South Atlantic Thermohaline Experiment (ASTTEX) were used, collected in the Cape Basin off South Africa, along 1000 km of an eddy corridor where Agulhas eddies carry cores of warm, salty Indian Ocean waters into the South Atlantic. The paper presents in detail the method used to convert PIES measurements into barotropic, baroclinic, and total SSH, and discusses the error budget. The baroclinic contribution is geopotential height (reference 4500 dbar), which can be determined from the measured vertical acoustic travel time together with a lookup curve based on the regional hydrography. The main error source is scatter about this curve that depends on the extent to which water masses advecting along each geopotential streamline may derive from different ocean regions. The barotropic contribution can be determined from the bottom pressure measurements of the mass variation in the water column and has an uncertainty due to sensor calibration drift in two years corresponding to 1-cm water column height. The barotropic component accounts for 20% of the overall SSH variance and 47% during large signal intervals exceeding 15 cm. PIES data demonstrate via the two measurements that barotropic and baroclinic contributions may work independently or in concert in different mesoscale eddies. The combined structure need not be equivalent barotropic. In particular, deep barotropic eddies exhibit mesoscale spatiotemporal scales and may or may not be systematically tilted or aligned in space or time relative to baroclinic eddies.