2 Method

The method used to estimate the new CNES-CLS2022 MDT follows the same approach than the one detailed in Rio and Hernandez (2004), Rio et al. (2007, 2011 and 2014a), and Mulet et al. (2021). It is a three-step approach reminded and summarized below:
The first step is to compute a first guess MDT from the filtered difference between the MSS and the geoid model: a geodetic MDT. The effective resolution of this resulting field depends on the noise level of the raw differences between the MSS and the geoid height; it is around 125km (Bruinsma et al. 2014).
The second step is to compute synthetic estimates of the MDT and associated mean geostrophic velocities from in-situ data. The drifter data and High Frequency (HF) radar data are processed to keep only the geostrophic component. For the dynamic heights estimated from the T/S profiles, they are processed to add the missing components: the barotropic component and the deep baroclinic component. Temporal variability is removed from the dynamic heights and velocities, by subtracting the altimeter sea level anomalies and the associated geostrophic velocity anomalies respectively. Since the altimeter sea level anomalies referenced to the 1993-2012 reference period, the processed in-situ dynamic heights and velocities are then also referenced to the 1993-2012 period, and this allows the use of in-situ observations over a longer period than the reference period (Rio and Hernandez 2004). The processed dynamic heights are averaged by 1/4° boxes to obtain the synthetic mean heights and the processed velocities are averaged by 1/8° boxes to obtain the synthetic mean velocities. Velocities from HF radar are averaged per cell (6X6km resolution). Note that this version of the MDT uses only Mid Atlantic Bight HF radar data.
Finally, the third step consists in improving the large-scale MDT (from step 1) from the synthetic data (from step 2) through a multivariate objective analysis whose formulation was first introduced in oceanography by Bretherton et al. (1976). This analysis takes as input the a-priori knowledge of the MDT variance and zonal and meridional correlation scales.

2.1 Computation of first guess and comparison with previous first guess

The raw difference between the CNES-CL22 MSS and GOCO06s geoid height is filtered using the optimal filter fully described in Rio et al. (2011). For the MDT CNES-CLS22 computation, this step has been improved with the application of additional Lagrangian filter along the coast to avoid streamline going into land.
The geostrophic velocities associated with the first guess calculated from the raw differences between the CNES-CL22 MSS and GOCO06s geoid height optimaly filtered are compared with the drifter velocities (section 3); the drifter velocities have been processed to obtain a physical content comparable with the geostrophic velocities. Similarly, the geostrophic velocities associated with the first guess of the CNES-CLS18 MDT have been compared with the drifter velocities. Figure 1 shows the improvement (blue color) or degradation (red color) of the RMS of the differences with the drifter velocities of the CNES-CLS22 first guess compared with the CNES-CLS18 first guess, in current amplitude (a) and current direction (b). Figure 1 (a) shows that current amplitude is strongly enhanced near the coast, almost everywhere. In the open ocean, the differences between the two first guesses in comparison to drifters are minimal, except south of 45°S, particularly in the Indian Ocean, where there are degradation boxes for first guess 2022. For this comparison, Lagrangian filtering at the coast has not yet been applied. This improvement at the coast in the amplitude of the geostrophic currents associated with the first guess compared with the drifters is linked to the use of the new CNES-CLS22 MSS and the new GOCO06s geoid. As for the current direction shown in Figure 1 (b), there is no clear improvement or deterioration in the new first guess compared with the old one.