2.2.3. Super-Sampled Sun Correction

L-band observations of the Sun disk showed that its BT emissivity is not spatially homogeneous [16]. Sunspots tend to have much larger BT emissions than other Sun regions. The Sun correction applied to SMOS during the second mission reprocessing considered the Sun as a point source. The team considered this correction to be insufficient and derived a new method to correct for the Sun BT emissions to take into account those spatial inhomogeneities Figure 12.

**Figure 12.** L-band BT emission of the Sun [16].

The so-called super-sampled Sun correction applied in L1OP v724 estimates the BT of multiple spots within the Sun disk, minimising the differences between the simulated signal and the BT observations in an area around the Sun and in the Sun tails [17].

$$V\_{Sun} = \sum\_{i} V\_{1ki} T\_{i\nu} \tag{14}$$

where *VSun* are the visibilities of the Sun as a function of the 1K visibilities (*V*1*ki*) computed for each of the sub-sample points' times and *Ti* corresponds to the BT estimated for each of those points from the following equation:

$$\begin{bmatrix} F^{-1}(V - V\_{\zeta 2})\_1 - \left\{ F^{-1}(V - V\_{\zeta 2})\_0 \right\} \\ F^{-1}(V - V\_{\zeta 2})\_) - \left\{ F^{-1}(V - V\_{\zeta 2})\_0 \right\} \\ F^{-1}(V - V\_{\zeta 2})\_{n'} - \left\{ F^{-1}(V - V\_{\zeta 2})\_0 \right\} \\ \dots \\ \frac{\tilde{T}\_0}{\text{rowPOS}} \\ \dots \\ \dots \\ \frac{\tilde{T}\_0}{w} \end{bmatrix} = \begin{bmatrix} F^{-1}(V\_{1\mathcal{K}1})\_1 & F^{-1}(V\_{1\mathcal{K}1})\_1 & F^{-1}(V\_{1\mathcal{K}POS})\_1 \\ F^{-1}(V\_{1\mathcal{K}1})\_{n'} & F^{-1}(V\_{1\mathcal{K}1})\_{n'} & F^{-1}(V\_{1\mathcal{K}POS})\_{n^\*} \\ 1/w & \dots & 0 \\ \dots & 1/w & \dots \\ 0 & 0 & 1/w \\ 1/w & \dots & 1/w \end{bmatrix} \begin{bmatrix} & & & & & \\ & & & & & \\ & & & & & \\ & & & & & \\ & & & & & \\ & & & & & \\ & & & & & \\ & & & & & \\ & & & & & \\ & & & & & \\ & & & & & \\ & & & & & \\ & & & & & \\ & & & & & \\ \end{bmatrix} \begin{bmatrix} & & & & & & \\ & & & & & \\ & & & & & \\ & & & & & \\ & & & & & \\ & & & & & \\ & & & & & \\ & & & & & \\ & & & & & \\ & & & &$$

where:

⎡

⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣


This correction succeeds in better reducing the residuals of solar radiations, as shown in Figure 13.

**Figure 13.** Time standard deviation of 100 snapshots over the ocean, with the Sun alias present at approximately [0.4, −0.15], with the old Sun correction (**a**) and the super-sampled correction (**b**).

Figure 13 shows that the new super-sampled Sun correction reduces the variations in the measurements along the Sun tails and within the Sun alias disk.

2.2.4. Sun Correction in the Back

SMOS measurements showed that the radiation coming from the Sun is observed even in the case the Sun is behind the antenna plane, through the antenna back-lobes [18].

The team considered that it was important to correct for this foreign source radiation and applied the Sun correction algorithm described in [19] and later modified in [20], even in the case the Sun was behind the antenna. Figure 14 shows the bias observed in the data before and after the extension of the Sun correction in the back.

**Figure 14.** SMOS biases from a measurement in the Pacific after removing the expected forward model when the Sun is in the back of the instrument before (**a**) and after (**b**) the Sun BT correction in the back [18].

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

The changes applied in the v724 version of the processor have been analysed using a dedicated end-to-end processing campaign that involved 3 years of data. The results presented hereafter show the improvement of the data quality in different metrics, such as reduction of the spatial biases, improvement of stability, reduction of land–sea contamination biases for certain polarisations, better match to in-situ measurements and reduction of the χ<sup>2</sup> in the soil moisture retrievals.

#### *3.1. Orbital and Seasonal Stability*

The quality of the stability of the measurements is established by comparison with the ocean forward model. In this case, one of the metrics used by the SMOS team is the one provided by the Hovmoller plots showing the biases observed in the Pacific open ocean in time and latitude. This metric allows us to assess both the orbital stability (variation along the vertical axis) and the seasonal stability (variation along the horizontal axis). The analysis is done independently per polarisation and separately for ascending and descending passes.

Figure 15 shows an example of the stability of the measurements in the second mission reprocessing [21] and the expected behaviour for the third mission reprocessing, for both X and Y polarisations. Descending orbits suffer the most from larger instrument thermal dynamics and are always more prone to measurement instabilities.

**Figure 15.** Hovmoller plots showing the bias between measurement and model averaged over the entire extended alias-free field of view for descending orbits for (**a**) v620 X polarization, (**b**) v724 X polarization, (**c**) v620 Y polarization and (**d**) v724 Y polarization.

Figure 15 shows that both the orbital and seasonal instabilities have been reduced in the third mission reprocessing. A further metric to assess the improvement in stability is the standard deviation of these Hovmoller plots. The values in Table 2 show an important reduction of the instabilities.



#### *3.2. Spatial Biases*

Spatial biases have been one of the largest challenges in the SMOS image reconstruction process [21, 22]. The Level 2 Ocean Salinity Processor uses the ocean target transformation (OTT) technique to reduce them [23,24], but this technique only works well in scenes whose brightness temperature is roughly stable, such as measurements in the open ocean. Near the coastlines, or for any measurement over land, the technique does not work properly. Therefore, it is of utmost importance that the spatial biases are minimised at the image reconstruction level. The changes introduced in the v724 processor have considerably reduced the spatial biases in the extended alias-free field of view.

Figure 16 shows the spatial biases for X and Y polarisation. A very important aspect to note in the spatial bias improvement in Y polarisation is the reduction of a negative gradient from top to bottom of the OTT image.

**Figure 16.** Spatial biases for descending orbits in (**a**) v620 X polarization, (**b**) v724 X polarization, (**c**) v620 Y polarization and (**d**) v724 Y polarization.

#### *3.3. Land–Sea Contamination*

Another critical aspect of the SMOS radiometric measurements is the land–sea contamination. This refers to the increase in the bias that occurs in the ocean measurements near land masses and vice versa. The adjustments in calibration and the new Gibbs-2 image reconstruction technique have achieved a significant improvement in land–sea contamination, even though this is still substantially present in the third mission reprocessing. Figure 17 shows the biases, over ocean, in the global maps for one particular month of data (June 2016) for the four polarisations for the second [21] and third mission reprocessing. The improvements are most noticeable in Y polarisation and in the fourth Stokes parameter. On the other hand, the contamination in Tx has changed but remains at similar levels, and similarly for the third Stokes parameter.

In must be noted that the Level 2 Ocean Salinity Processor includes an empirical correction of the land–sea contamination. Being able to reduce the original bias is an important aspect of the *L*<sup>1</sup> processor, but almost more important is that the residual bias remains constant, which can then be corrected empirically at Level 2. For this reason, another metric assesses the variation of the land–sea contamination bias at Level 1 by means of the standard deviation. Figure 17 shows this metric, over ocean, for Y polarisations only. Similarly to Figure 17, the land–sea contamination variation is substantially reduced, mainly for Y polarisation (Figure 18) and for the fourth Stokes parameter.

**Figure 17.** Maps of bias between SMOS measurements and the ocean forward model, showing an increase excess of bias in regions near the coast, known as land–sea contamination. (**a**) all four polarizations for v620 and (**b**) all four polarisations in v724.

**Figure 18.** Standard deviation of the SMOS measurements in June 2016 for v620 (**a**) and v724 (**b**).

#### *3.4. Impact on Retrieved Soil Moisture and Vegetation Optical Depth (VOD)*

As part of our standard metric protocol, new versions of *L*<sup>1</sup> data are systematically processed with the Level 2 soil moisture processor to assess the changes compared to the previous *L*<sup>1</sup> processor version. This assessment is made through spatial monthly maps showing the changes on retrieved soil moisture and retrieved opacity along with χ<sup>2</sup> changes. A second perspective is obtained through time series of retrieved soil moisture corresponding to a collection of in-situ time series of measured soil moisture for the two-year period 2011–2012 and provides quantitative metrics but for a limited number of grid points.

For the purposes of this analysis, the same Level 2 Soil Moisture v650 processor has been used in order to assess only the improvements in the *L*<sup>1</sup> processor.

#### 3.4.1. Spatial Maps of Retrieved Soil Moisture and Opacity

Figure 19 displays the differences in soil moisture and opacity of v724 minus v620 for the month of June 2014, separated by ascending and descending orbit passes. The overall global change is rather neutral, with mean differences close to 0 but with a significant variability that appears very structured spatially. The significant changes correspond to specific areas, with contrasts between transition areas and forest in both retrieved soil moisture and opacity. Below dense forest v724, soil moisture and opacity tend to decrease, with patterns changing in position between ascending and descending orbits, e.g., the North American east coast, Amazonian forest, and African Congo forest. This is probably a signature of the Gibbs-2 correction, as the contrast of land/sea masses is not similar within the SMOS field of view for these locations depending on the orbit pass.

The L1C v724 data generate significant changes compared to the L1C v720, and the question whether those changes are in the right direction is addressed by the two following sections.
