*2.5. Recovered VTEC Maps with Simulated Data*

The descending SMOS overpass in the Pacific Ocean on March 20th, 2014 was processed in the simulator using the methodology described and the results are shown in Figure 8. The recovered VTEC is shown at the left and the error of the retrieval with respect to the database is shown at the right. The retrieved VTEC follows the variation of the database VTEC with a RMSE of 0.48 TEC units. It can be seen that the error in the retrieval does not follow any systematic pattern. The highest error is found close to where the geomagnetic field is orthogonal to the wave propagation direction (indetermination in Equation (1)).

**Figure 8.** VTEC of a descendent orbit over the Pacific Ocean, March 21st, 2011 processed with the simulator applying the proposed methodology: (**a**) recovered VTEC, (**b**) VTEC error with respect to the database VTEC.

By applying Equation (1) with the database VTEC, an FRA reference can be obtained. Likewise, the FRA can be computed from the retrieved VTEC for all the pixels in the EAF-FoV. Figure 9 shows the database FRA (red) and the simulated retrieved FRA (green) as a function of latitude of a pixel with ξ = 0 and η = 0.2, as well as the error of the FRA retrieval with respect to the database FRA. The gap in the retrieval comes from the rejected pixels in the zone of the orthogonality that is between the geomagnetic field and the wave propagation direction (incidence angle), where it can be seen how the FRA vanishes.

The methodology is able to recover the FRA following the geophysical and temporal variation with a negligible error (with a RMSE of 0.07◦), showing good performance.

**Figure 9.** FRA vs. latitude of a pixel along the descending orbit: (**a**) database FRA (red) and retrieved simulated FRA (green), (**b**) error of the retrieved simulated FRA with respect to the database.

#### **3. Results and Discussion**

Considering the promising results obtained when assessing the methodology with the simulated data, SMOS radiometric data were processed to derive VTEC maps.

#### *3.1. VTEC Retrievals from SMOS Data*

Results of the retrieved VTEC with SMOS radiometric data, and the difference between the retrieved VTEC and the database VTEC (used here as a reference) are shown in Figure 10 (top). The recovered VTEC presents a systematic pattern with higher differences in the edges of the swath. This pattern did not appear in the retrieved VTEC from simulated TB. It needs to be characterized at some point in future research.

In order to mitigate the effect on the swath laterals, some empirical approaches were assessed. The first approach used only the alias free-field of view (AF-FoV) instead of using the EAF-FoV region. By doing so, the retrieval of FRA could only be performed over a much narrower swath after a complete SMOS overpass. Hence, a second attempt was based on assigning the average VTEC of the AF-FoV to the entire EAF-FoV in each snapshot [9], disregarding the TEC variability along the snapshot. The third and selected approach consists of extending the value of the VTEC in the pixels of the AF-FoV closest to the EAF-FoV to the latter. The processed orbit using that approach and its difference with respect to the database VTEC are shown in Figure 10 (bottom).

The lateral bands of the southern hemisphere become softened. In the northern hemisphere, a similar softening happens, though not as noticeably as in the southern hemisphere. Additionally, the retrieved VTEC is generally lower than the database VTEC, something that in the simulation does not happen. Table 2 shows the root mean square of the difference (RMSD) between the retrieved and the database VTEC in the EAF-FoV and the difference between the retrieved VTEC in the AF-FoV extended to the EAF-FoV with respect to the database VTEC. For a reference, the statistics of the simulated retrieval are also presented. The statistics are calculated in a range of latitudes between 60◦ N and 60◦ S.

**Table 2.** Statistics of the VTEC retrieval with respect to the database VTEC: (**a**) with simulated data, (**b**) with the retrieval in the EAF-FoV, (**c**) with the retrieval in the AF-FoV extended to the EAF-FoV.


**Figure 10.** VTEC of a descendent orbit over the Pacific Ocean, March 20th, 2014 obtained from SMOS radiometric data: (**a**) retrieved VTEC, (**b**) VTEC difference with respect to the database VTEC, (**c**) retrieved VTEC with the refined methodology (extension of alias free-field of view (AF-FoV) to the laterals), (**d**) difference of the retrieved VTEC with the refined methodology and the database VTEC.

Figure 11 shows the retrieved FRA (from the VTEC shown in Figure 10c) as a function of the latitude. The database FRA (red) is compared against the retrieved FRA (green) at a pixel in the center of the swath (ξ = 0 and η*x*0.2) and its difference is shown in Figure 11b. When processing SMOS radiometric data with the proposed methodology, even though it is possible to recover the FRA geophysical and temporal variation, there is a difference with respect to the database FRA.

Greater differences are perceived in the southern hemisphere. In the northern hemisphere and up to 10◦ S, both FRAs are very similar, a scenario that does not happen when analyzing pixels in the laterals of the overpass (not shown). This is noticeable in Figure 10d. Still, the root mean square of the difference between the retrieved FRA and the FRA database (Figure 11b) is 1.5◦, which represents only 6.50% of the dynamic range of the database FRA.

**Figure 11.** FRA vs. latitude of a pixel along the descending orbit: (**a**) database FRA (red) and retrieved FRA with SMOS radiometric data (green), and (**b**) retrieved FRA difference with respect to the database.

#### *3.2. Comparison of Retrieved VTEC from SMOS with Other External VTEC Sources*

In this section, a comparison of the VTEC retrieved with the proposed methodology and that from other sources shown in Section 2 is presented in Figure 12 shows the VTEC of the middle pixel of the swath as a function of the latitude provided by different sources. The line in red corresponds to the database VTEC, the green line to the recovered VTEC using the proposed methodology, the magenta line to the A3TEC (VTEC from the DTBXY product), and the blue line to the IONEX VTEC coming from GPS data [23].

**Figure 12.** Comparison of the VTEC coming from different sources.

The retrieval with the proposed methodology (green line) follows the temporal-geophysical variation that the A3TEC (magenta) presents. Both of them come from SMOS radiometric data. The gap around 20◦ N corresponds to the zone where the geomagnetic field is orthogonal to the wave propagation direction causing the Faraday rotation to vanish. The A3TEC provides data in that zone but tends to the value of the database VTEC, which is expected, because in the procedure to retrieve it, that auxiliary database is used as a first guess, and in that zone, the sensitivity of the TB to TEC is very low. The retrieved VTEC with the proposed methodology has fewer ripples than the A3TEC. It was found that the origin of those ripples is due to the remaining noise as reported in [11]. IONEX is always above the VTEC value retrieved from SMOS data, both using the methodology proposed in this paper and the VTEC from DTBXY products, which is in agreement to [11]. The presented methodology proposes an alternative to the current methodology used in order to eliminate the dependency on any external database VTEC.

#### *3.3. Impact of RFI Contamination in the Retrieved VTEC*

In order to analyze the performance of the proposed methodology on a global scale, the analysis was extended to all the descending orbits over the ocean on March 21st, 2011. This particular year was chosen because it opened up the possibility to evaluate the impact in the presence of radio-frequency interference (RFI). The RFI contaminates the TB, which has an impact in the recovered VTEC. The retrieved VTEC with the proposed methodology and the one provided by the database VTEC (used as a reference) are shown in Figure 13 as well as the difference between them.

**Figure 13.** VTEC of all descending orbits on March 20th, 2011: (**a**) database VTEC, (**b**) retrieved VTEC using radiometric SMOS data with the proposed methodology, and (**c**) differences between the retrieved VTEC and the database VTEC with a RMSD of 17.84 total electron content units (TECU).

Greater differences between the recovered and the database VTEC are concentrated at northern, high latitudes, close to ice edges. There were significant differences over the Bering, the Beaufort, and the Barents Seas on that date (see zoomed in portions of Figure 14a,c, respectively). We analyzed whether this was related to TB contamination by RFIs (radio-frequency interferences) sources. In 2011, there were RFIs affecting the Bering Sea, which were switched off in 2012 [27]. The VTEC retrieval of a descending orbit over the same region on March 20th, 2012 was processed and it is shown in Figure 14b. When the RFI was shut down, it was possible to recover a VTEC that was less affected by errors. Similarly, a descending orbit over the Barents Sea on March 22nd, 2019 was processed (when the RFI source was already switched off) and it is shown in Figure 14c. Once again, it was confirmed that RFIs were affecting the VTEC retrieval in 2011 (Figure 14c).

**Figure 14.** Recovered VTEC of descending orbits over (**a**) the Bering Sea in March 21st, 2011, (**b**) the Bering Sea on March 20th, 2012, (**c**) the Barents Sea on March 21st, 2011, and (**d**) Barents Sea on March 22nd, 2019.

#### **4. Conclusions**

Measuring the Faraday rotation from radiometric data allows for the estimation of the total electron content of the ionosphere by using an inversion procedure. This allows for the possibility of creating a VTEC product from SMOS data. Eventually, this product can then be re-ingested in the SMOS level 2 processor in order to improve the geophysical retrievals.

The proposed methodology works independently of the target seen by the instrument. This is an important improvement with respect to the current methodology that also derives VTEC maps from SMOS radiometric data [11], which use a forward radiative model and are focused only over the ocean because SMOS's main purpose is to improve salinity measurements. Moreover, the developed methodology estimates the VTEC for all the pixels in the EAF-FoV with information from different incidence angles, instead of using only the FoV region with the highest sensitivity to TEC, and extending this value across the FoV as does the methodology detailed in [8].

The analysis of the retrieved VTEC maps has been focused over the ocean, where the impact of ionospheric corrections is stronger. These maps have been inter-compared with the database VTEC, the IONEX GPS data, and the A3TEC products. The retrieved VTEC maps provide values generally lower than those of the external VTEC database and the IONEX GPS data, which is in agreement with the differences found when comparing the other SMOS-derived product (A3TEC) with the same two external data sources [8]. However, SMOS-derived VTEC products cannot be fully validated by comparing them with the external VTEC database and the IONEX GPS data, since the spatial resolution of the latter ones is much coarser than that provided by the SMOS products. The comparison between both SMOS-derived VTEC products reveals greater differences in the northern hemisphere. The origin of these discrepancies needs to be investigated.

Further work is needed to evaluate the feasibility of providing global SMOS-derived VTEC maps, including ocean, land, and ice. The main challenge is to obtain accurate TEC retrievals over land areas in (i) regions where SMOS TB measurements are degraded by strong RFI contamination and (ii) regions where TB at horizontal and vertical polarizations are very similar (such as in dense forests), making the TEC retrieval ill-conditioned. A dedicated study of retrieved VTEC over land to assess the performance of the proposed method on a global scale is currently on-going. Besides, the Faraday rotation vanishes in regions of the earth where the geomagnetic field is orthogonal with the signal path. Therefore, the retrieval of VTEC in these regions is not possible and maps will present data gaps. Improvements over the ocean also need to be addressed. The retrieved VTEC maps present a remaining systematic pattern (more noticeable in the northern hemisphere, as shown in Figure 14c) that might be introduced by the instrument when measuring the Faraday rotation (not present in the simulation experiments). Ongoing work is focused on characterizing this FRA systematic pattern in a region and for a period with very low FRA values, so the measurement can be assumed as a systematic error of the instrument, and a correction can be built upon that.

The recovered VTEC maps could be used in the SMOS Level-2 processor to correct the Faraday rotation, which could potentially improve geophysical retrievals, as reported when using the A3TEC method [11]. As a preceding step to analyze the impact of using these VTEC maps on salinity retrievals, the computation of the OTT (ocean target transformation) will be evaluated and used in order to correct the spatial bias presented in the TB as is done by the SMOS ocean salinity team [28]. If an improvement in the stability of the OTT is achieved, more accurate salinity retrievals by using these VTEC maps would be expected.

**Author Contributions:** Conceptualization, F.T., Investigation, R.R., N.D., V.G.-G., and I.C., methodology, R.R., N.D., V.G.-G., I.C., and I.D., supervision, N.D., V.G.-G., and I.C., writing—original draft, R.R., writing—review an editing, N.D., V.G.-G., I.G., and M.M.-N. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was supported by the European Space Agency and Deimos Engenharia (Portugal), SMOS P7 Subcontract DME CP12 no. 2015-005; ERDF (European Regional Development Fund); by the Spanish public funds, projects TEC2017-88850-R and ESP2015-67549-C3-1-R; and through the award "Unidad de Excelencia María de Maeztu" MDM-2016-0600, financed by the "Agencia Estatal de Investigación" (Spain) and by the European Regional Development Fund (ERDF).

**Conflicts of Interest:** The authors declare no conflict of interest.
