Complex EOF Analysis as a Method to Separate Barotropic and Baroclinic Velocity Structure in Shallow Water

Abstract

Defining the vertical depth average of measured currents to be barotropic is a widely used method of separating barotropic and baroclinic tidal currents in the ocean. Away from the surface and bottom boundary layers, depth-averaging measured velocity is an excellent estimate of barotropic tidal flow, and internal tidal dynamics can be well represented by the difference between the measured currents and their depth average in the vertical. However, in shallow and/or energetic tidal environments such as the shelf of the South Atlantic Bight (SAB), bottom boundary layers can occupy a significant fraction of the water column, and depth averaging through the bottom boundary layer can overestimate the barotropic current by several tens of centimeters per second near bottom. The depth-averaged current fails to capture the bottom boundary layer structure associated with the barotropic tidal signal, and the resultant estimate of baroclinic tidal currents can mimic a bottom-trapped internal tide. Complex empirical orthogonal function (CEOF) analysis is proposed as a method to retain frictional effects in the estimate of the barotropic tidal currents and allow an improved determination of the baroclinic currents. The method is applied to a midshelf region of the SAB dominated by tides and friction to quantify the effectiveness of CEOF analysis to represent internal structure underlying a strong barotropic signal in shallow water. Using examples of synthesized and measured data, EOF estimates of the barotropic and baroclinic modes of motion are compared to those made using depth averaging. The estimates of barotropic tidal motion using depth-averaging and CEOF methods produce conflicting predictions of the frequencies at which there is meaningful baroclinic variability. The CEOF method preserves the frictional boundary layer as part of the barotropic tidal current structure in the gravest mode, providing a more accurate representation of internal structure in higher modes. The application of CEOF techniques to isolate internal structure co-occurring with highly energetic tidal dynamics in shallow water is a significant test of the method. Successful separation of barotropic and baroclinic modes of motion suggests that, by fully capturing the effects of friction associated with the barotropic tide, CEOF analysis is a viable technique to facilitate examination of the internal tide in similar environments.