Figure 2: Fine scales of synthetic mean heights, all reference depths averaged by 1/8° by 1/8° boxes in cm, equivalent to mean synthetic heights minus first guess (input to optimal analysis).

2.3 Computation of the synthetic mean velocities

The objective of this estimation is to process the velocities estimated from drifters (section 3) and surface Argo float drifts to obtain the physical content of the geostrophic currents associated with the MDT. This is achieved by removing from the drifter velocities the ageostrophic components of the current, as well as the temporal variability of the geostrophic component of the velocities:
\begin{equation} U_{\text{synth}}=U_{\text{drifter}}-U_{\text{Ekman}}-U_{\text{Stokes}}-U_{\text{inertial}}-U_{\text{tidal}}-U_{ageo-hf}-U_{\text{slippage}}-U_{\text{alti}}^{{}^{\prime}}\nonumber \\ \end{equation}
First, wind-driven currents (\(U_{\text{Ekman}}\)) is removed from the drifter velocity, as well as the wind slippage (\(U_{\text{slippage}}\)), which is the direct effect of wind on undrogued drifters. \(U_{\text{Ekman}}\) is taken from the Copernicus-Globcurrent product (MULTIOBS_GLO_PHY_REP_015_004, https://data.marine.copernicus.eu/product/MULTIOBS_GLO_PHY_REP_015_004/description) while wind slippage correction (\(U_{\text{slippage}}\)) is available in the CMEMS INSITU_GLO_PHY_UV_DISCRETE_MY_013_044 product (https://data.marine.copernicus.eu/product/INSITU_GLO_PHY_UV_DISCRETE_MY_013_044/description). These products are consistent as they use same upstreams for computation: ERA5 wind and wind stress (section 3), and Mixed Layer Depth as a proxy to the Ekman layer thickness (from CMEMS ARMOR3D: MULTIOBS_GLO_PHY_TSUV_3D_MYNRT_015_012, https://data.marine.copernicus.eu/product/MULTIOBS_GLO_PHY_TSUV_3D_MYNRT_015_012/description). Then the temporal variability of the geostrophic component of velocities (\(U_{\text{alti}}^{{}^{\prime}}\)) is removed. Next, the tide, inertial oscillations and residual ageostrophic signal (as Ustokes) are removed by high-frequency filtering. Finally, the mean synthetic velocities obtained are averaged in boxes 1/8° by 1/8°.
This method, the estimation of the wind-driven component of the current and slippage, and the filtering applied are fully described in Mulet et al. (2021, section 5) and build on previous work by Rio and Hernandez (2004), Rio et al. (2007, 2011 and 2014a).
For this new MDT, we are also using velocities data estimated from High Frequency radars located in the Mid Atlantic Bight area, on the East Coast of the USA, from Cape Hatteras to Cape Cod. In the same way as for drifter data, the aim is to process these velocities to obtain synthetic velocities with the physical content of geostrophic MDT velocities. We used the cleaned, detited, high-frequency signal-filtered and mean currents over the period 2006-2016, processed by Rutgers University (Roarty et al. 2020). Then the mean wind-driven currents over the same period (\(U_{\text{Ekman}}\) taken from the Copernicus-Globcurrent product MULTIOBS_GLO_PHY_REP_015_004) were removed and finally these mean currents were re-referenced to the 1993-2012 reference period.
Figure 3 shows these mean synthetic velocities estimated from (a) drifters (at 1/8° resolution) and (b) HF radar data, over the Mid Atlantic Bight area off New Jersey and Delaware (USA). The figure also shows the 100m and 2000m isobaths that mark the limit of the continental shelf. The average synthetic velocities estimated by drifters are much noisier, with more intense currents, than those estimated from HF radars. However, both maps show a recirculation current to the south-east at the 100m isobath. The drifters (Figure 3 a) show this current as narrow and intense (15 to 20 cm/s), whereas the HF radars (Figure 3 b) show a broad current of between 5 and 10 cm/s. Very close to the coast, velocities are generally low (below 5 cm/s), but currents can be perpendicular to the coast (e.g. Figure 3 b at 74.5°, 75° and 75.5°W). Between 74.9° and 75°W, the outflow of the Delaware River could explain these cross-shore currents.
These differences can be explained by the very different sampling of the two types of data:
- HF radar: at least 50% of data every hour over 10 years
- Drifters (1 or 2 drifters per box near the coast).
Moreover, it is likely that drifters tend to converge at the center of the current due to convergence and subduction, resulting in a sampling bias in favor of a narrow jet.