Determining geostrophic velocity shear profiles with inverted echo sounders

It is known that vertical acoustic travel time (τ), round‐trip from the seafloor to the sea surface as measured by inverted echo sounders (IESs), can be interpreted in terms of dynamic height. This relationship is generalized and quantified in this paper for dynamic height (ΔDi, j) integrated between a variety of pressure limits (pi, pj) which span different portions of the main thermocline. The generalized form of the ΔDi,j(τ) relationships is nonlinear; the conventional linear relationship is valid when the limits of integration span the entire main thermocline. Velocity and temperature records are shown to be highly correlated vertically, indicating that the variability of the Gulf Stream and adjacent eddy field is dominated by the lowest baroclinic mode, which is called a gravest empirical mode (GEM). A “parallel isotherms model” is used to approximate the GEM and to develop analytic expressions for the observed ΔDi,j(τ) relationships in the Gulf Stream. The analytic expressions represent the observations well, with noise‐to‐signal variance ratios that are typically 1%. Using these new ΔDi,j(τ) relationships, the baroclinic velocity structure can be determined geostrophically by measuring the horizontal gradients with laterally separated τ measurements from IESs. Baroclinic velocities determined from a two‐dimensional array of IESs in the Gulf Stream during 1988–1990 agree with velocity shears directly measured by current meters. The rms velocity difference between these two measurements of velocity shear at 400 dbar relative to 1000 dbar was 12 cm s−1 in the presence of typical currents of 50 cm s−1. Ageostrophic motions (at both mesoscale and submesoscale), measured by the current meters but not by the IESs, contribute most of the velocity differences