Hindcast
As detailed in “Model setup & assimilation method (4DVAR)” section, the 4DVAR simulation have been made for April 2020 and our analysis therefore target this periods. In the following the ROMS geostrophic velocities have been derived from surface elevation following Eq. 1 (where g represent the acceleration due to gravity, f the coriolis parameter and \(\eta\) the surface elevation) for both 4DVAR and FREE simulations and are compared to altimeter derived geostrophic currents after being interpolated on the ROMS grid.
$$\begin{aligned} u=-\frac{g}{f} \frac{\partial \eta }{\partial y} v=\frac{g}{f} \frac{\partial \eta }{\partial x } \end{aligned}$$
(1)
Spatially averaged Root Mean Square Error (RMSE) between both simulations and altimeters derived geostrophic currents are shown on Fig. 4. Top panel of Fig. 4 represents the spatial average of the RMSE over the whole domain (hereafter global area), while bottom panel represents the RMSE averaged over the area corresponding to the HF radar observation zone (hereafter local area). Both panels show a significant decrease of the RMSE for the geostrophic currents with data assimilation, but while the local improvements are almost immediate it takes about 15 days to propagate them over the whole domain.
Figure 5 represents the temporal and spatial evolution of the RMSE’s differences between FREE, 4DVAR simulations during April 2020. April has been split in three periods; days 1 to 10 (panel a), days 11 to 20 (panel b) and days 21 to 30 (panel c). As expected from Fig. 4, panel (a) shows an improvement (blue color) mostly located in the HF radar area. Panel (b) shows an extension of the RMSE decrease to the south west and to the east and panel (c) a strengthening of this improvement when compared to altimetry data and highlight the positive impact of the data assimilation outside the area where HF radar data are assimilated.
While previous RMSE times series (Fig. 4) and maps (Fig. 5) illustrated a global improvement of the geostrophic currents over the whole April month, Fig. 6 focuses on a daily averaged (23 of April 2020). Panels (a) and (b) show the daily averaged geostrophic currents for FREE and 4DVAR respectively. Panels (c) and (d) show the averaged geostrophic currents derived from altimeter data and the surface currents measured by the HF radar and assimilated in the model during this day. This figure illustrates the improvement between FREE and 4DVAR experiments. Indeed, west of \(24^{\circ }\hbox { E}\) the current is curving southward in FREE while 4DVAR is able to reproduce the northward bent seen by altimeters (panel (c)). Also, the area east of \(24^{\circ }\hbox { E}\) and north of \(36^{\circ }\hbox { S}\) is characterised by the presence of an anticyclonic eddy matching the eddy detected by altimeters. Finally 4DVAR also reproduces the intensity of the current in the southern branch of the eddy. It is furthermore interesting to note once again that beside the scarcity of the assimilated data (depicted on panel (d)) the 4DVAR assimilation is able to correct the circulation almost in the whole simulated domain.
Forecast
In the previous section, it has been shown that assimilating HF radar currents allows to improve the geostrophic circulation when compared to satellite-derived velocities. However, those altimeter data are at low resolution (25 km) with daily data only, while HF radar are available at 6 km resolution every 30 min. Since HF radar currents are assimilated in the model and therefore cannot be used for further validations, some forecast have been made starting from assimilated initial condition and FREE condition. This allow to validate the forecast against the HF radar data and explore the benefits of the assimilation on smaller scales and on the forecast capabilities of the current configuration.
To achieve this goal 48 h forecasts were performed during 9 consecutive days from the 21 to the 29 of April and were compared with the same forecasts initiated from FREE run. RMSE time series of both forecast against HF radar data are presented on Fig. 7. They show a strong improvement in intensity (top panel) and direction (bottom panel) when the forecast is initiated from 4DVAR simulation with a better performance of the first 24 hr of forecast (yellow curve) than the next ones (green curve).
When considering the first day of forecast, a reduction of more than 20% for both surface current intensity and direction is achieved for 87% and 99% of the time respectively. For the second day of forecast, those values change to 51% and 91% for intensity and direction respectively. When considering the averaged improvement of the current intensity RMSE, it is shown to move from 39 to 19% from the first to the second day of forecast. For directions, this RMSE improvement change from 42% to 28% from the first to the second day of forecast. Therefore, while the averaged forecast improvement is equivalent and around 40% during the first day of forecast, during the second day the averaged improvement is greater for the currents direction.
Figure 8 represents the maps of RMSE differences between forecast issued from 4DVAR and FREE for surface current intensity (Fig. 8a, b) and direction (Fig. 8c, d) along the 10 days of forecast. Right panels represent the first day of forecast and the left panels the second day of forecast. It confirms both forecast improvement of intensity and direction of the surface current. It also shows that current intensity and direction were significantly improved in the center of the area covered by the HF radar measurement. By comparing forecast day 1 and day 2, this figure also confirms that the faster degradation of the forecast is related to the current intensity rather than the direction.
Figure 9 shows the surface circulation of FREE, 4DVAR and HF radar currents averaged for two distinct first day of forecast as a superposition of arrows. It illustrates that the use of an assimilated initial condition allows to dramatically correct the path of the surface currents. Indeed on the forecast of the \(21^{th}\) april 2020 (Fig. 9, left panel) while the FREE forecast is characterized by a southward deviation and an cyclonic circulation between \(23^{\circ }\hbox { E}\) and \(24^{\circ }\hbox { E}\), the 4DVAR forecast surface circulation is almost the opposite. Indeed it is characterized by a northward shift inducing a anti-cyclonic circulation between \(22^{\circ }\hbox { E}\) and \(24^{\circ }\hbox { E}\). While the whole eddy cannot be depicted by the HF radar measurement, the northward shift of the Agulhas corresponds to what it is observed by the HF radar. On the forecast of the \(25^{th}\) of april 2020 (Fig. 9, right panel) while the eddy previously depicted seems to be dissipating, the northward bending of the 4DVAR forecast is once again coherent with the HF radar data and opposite to the southward bending of the FREE solution. This southward shift, seen in the FREE forecast is therefore an artefact of the model which can be corrected by using an assimilated initial condition.