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.

Environmental interference factors affecting detection range in acoustic telemetry studies using fixed receiver arrays

“…Throughout the rest of our paper, stratification is defined by 2 indices calculated based on depthvarying currents within the sanctuary. Synergism between the sea breeze and the Coriolis force drive diurnal band currents at Gray's Reef with a 3-layer flow pattern under stratified conditions and a 2-layer pattern under unstratified conditions (Edwards & Seim 2008). Thus differences in diurnal band currents among depths can be used as a proxy for strati- Large open circles represent the determined reliable 200 m 50% detection range (Carroll 2010).…”

“…Latitude and longitude are not shown so that the location of the acoustic array within the sanctuary remains confidential fication. The general approach was to remove all semidiurnal and long-term variability from the raw current data and compare currents among depths, based on the methods of Edwards & Seim (2008).…”

Coupled physical, chemical, and microbiological measurements suggest a connection between internal waves and surf zone water quality in the Southern California Bight

“…Being a complex vector, the mode shape, or eigenvector, of each principal component was oriented such that its bottom-most component pointed shoreward, and its crossshore component of the mode shape was found by taking its real part. The barotropic, density-independent contribution was defined as the first principal component and the baroclinic, density dependent contribution as summation of the second through fifth components (Stacey et al, 2001;Edwards and Seim, 2008).…”

Upper layer current variability in the Central Ligurian Sea

“…Spatial EOF decomposition (Emery and Thomson, 2001) is often used to analyse geophysical data characterized by a spatial patternin this case the ADCP current profile -evolving with time. The profile at each temporal step is represented as a linear combination of a limited number of profiles (modes) which can be associated to different dynamical mechanisms; the coefficients of the linear combination indicate the relative importance of each mode.…”

“…Hisaki, 2006;Edwards and Seim, 2008;Cappelletti et al, 2010). The first two mode profiles and the temporal evolution of mode coefficients are reported in figure 10.…”