3.4.2. χ<sup>2</sup> Test

χ<sup>2</sup> is an important metric to assess the quality of the soil moisture retrievals and is used widely in many retrieval processes. It provides a measure of the agreement (best fit) between the geophysical modelling that resulted in the retrieved parameters and the *L*<sup>1</sup> data that were used accounting for the expected noise on the observed data. In this study, we considered rather the reduced χ<sup>2</sup> *<sup>r</sup>* form, which is χ<sup>2</sup> divided by the number of degrees of freedom. Using χ<sup>2</sup> *<sup>r</sup>* introduces a normalisation, which is preferable as the Level 2 processor includes *L*<sup>1</sup> data filtering that may result in slightly different numbers of degrees of freedom between the two *L*<sup>1</sup> datasets.

Figure 20 shows the changes of the χ<sup>2</sup> *<sup>r</sup>* between v620 and v724, computed as the ratio χ<sup>2</sup> *<sup>r</sup>* v724 divided by χ<sup>2</sup> *<sup>r</sup>* v620 for June 2014 for ascending and descending orbits. Very similar maps are observed at other months of the year. Ratios >> 1 (toward red colours) indicate degraded (increased) v724 χ<sup>2</sup> *r*

with respect to v620 and ratios << 1 (toward blue colours) indicate improved (decreased) v724 χ<sup>2</sup> *<sup>r</sup>* with respect to v620.

The team analysed the changes in χ<sup>2</sup> *<sup>r</sup>* from v620 to v724 over land and concluded that χ<sup>2</sup> *<sup>r</sup>* has improved (reduced) significantly over most of the globe. Most exceptions are either neutral (light blueish/reddish area) or are related to presence of radio frequency interference (RFI), especially in the Middle East region and South Asia. All maps report a significant improvement (decrease) in v724 χ<sup>2</sup> *r* compared to v620 at global scale with distribution ratio modes marker always below 1 and strong negative asymmetry. Many continental areas show a deep blue colour, which indicates very significant improvements that also appear to be very stable in time for different seasons and different years. Similar to Figure 19, Figure 20 patterns show some differences between ascending and descending orbits. It is important to notice the good match of these blue spatial patterns in Figure 20 with the most significant change patterns in retrieved soil moisture and opacity reported in Figure 19; where v724 introduced the strongest changes in retrieved parameters is also where the best fit has improved the most with reduced χ<sup>2</sup> *<sup>r</sup>*. Finally, using the v724 data increases the number of successful retrievals by 2% to 3%.

(**b**) **Figure 19.** *Cont.*

**Figure 19.** Maps of averaged difference, v724–v620, over the month of June 2014 in (**a**) soil moisture for ascending orbits, (**b**) soil moisture in descending orbits, (**c**) VOD in ascending orbits and (**d**) VOD in descending orbitsBlue (resp., red) indicates a decrease (resp., an increase) in V724 soil moisture, VOD compared to v620.

#### 3.4.3. In-Situ Soil Moisture

Several networks of in-situ soil moisture measurements stations (ISMN) can be used to assess the quality of SMOS-retrieved soil moisture. SMOS coarse resolution observations and ultra-local in-situ measurement are not necessarily fully comparable, but become useful when assessing relative differences between two versions of processing of the same satellite data. SMOS soil moisture retrievals obtained from L1OP v620 data and from L1OP v724 data are compared against in-situ soil moisture time series of 250 validation sites taken from 11 in-situ soil moisture networks (Figure 21).

SMOS retrieval data and in-situ data are first co-located in space and time by taking the SMOS grid-points closest to the stations and by pairing in time SMOS and in-situ data of less than 7.5 min to a maximum of 30 min of absolute time difference, depending on the in-situ network temporal sampling characteristics. We denote the SMOS and in-situ collocated time series (*St*, *It*) and the associated difference time series (Δ*<sup>t</sup>* = *St* − *It*).

The 68.3% and 95.4% percentiles are shown by the inner and outer markers, respectively.

**Figure 21.** The 11 in-situ soil moisture networks and the position of their sites. The legend reports the network name, its associated colour and the number of the sites we considered for a total of 250 sites.

We computed the usual statistics and their 95% confidence intervals (CI95) obtained by bootstrap x to assess the two processor versions. For (*St*, *It*), we computed their means and standard deviations, μ<sup>S</sup> and σ<sup>S</sup> for SMOS and μ<sup>I</sup> and σ<sup>I</sup> for in-situ data and the correlation R. For the Δ*<sup>t</sup>* differences, we computed the bias, the standard deviation (STDD) and the root mean square (RMSD).

The results vary from site to site, but most of them show a better correspondence between the in-situ measurements and the data than the v724 processor or similar performance to the v620 processor. This is reflected by the overall performances, which are obtained by computing the statistics on the concatenation of all sites' time series (*St*, *It*), which are reported in Tables 3 and 4 along with their graphic representation using Taylor diagrams (Figure 22).

**Figure 22.** Taylor diagram of overall retrieved soil moisture time series with respect to in-situ measurement time series for ascending orbits (**a**) and descending orbits (**b**).


**Table 3.** Δ time series statistics and their CI95, 95% confidence intervals, given between parentheses.

**Table 4.** SMOS and in-situ time series statistics and their CI95, 95% confidence intervals, given between parentheses.


A Taylor diagram is a convenient 2D graphical representation focusing on the statistics R, σ and STDD, which are by nature debiased (mean-subtracted). The so-called 3D version given in Figure 22 makes the bias information available as a colour scale. Such a diagram is a polar coordinate representation of (σ, R). The standard deviations of series σ are used as the radius, and the correlation, R, with respect to a common reference is converted into an angle using acos(R). It is worth noting that the relation between the correlation and angle is highly non-linear; a 45◦ angle is already a 0.7 correlation. The reference data is always located at the x axis (correlation 1 with itself) and with a white marker (0 bias with itself) at the position σI, the reference being the in-situ data.

Figure 22 shows the performance of the overall retrieved soil moisture time series obtained from L1C V620 (1) and from L1C V724 (2) against the reference in-situ time series (0). Thanks to the concatenation, a large number of points (~40,000) allow computing reliable statistics, which result in a narrow CI95 that does not overlap for R, bias and STD making the separation of plots significant.

Compared to v620, v724 increases the correlation with respect to in-situ data and obtains an σ<sup>S</sup> closer to σI. As usual, this is more prominent for ascending morning orbits, where Level 2 retrievals always perform better, with better thermodynamic equilibrium at the surface and a calmer ionosphere in the mornings than in the evenings. Different RFI contamination patterns are also likely playing a role.

These two results indicate an increase in signal-to-noise ratio for v724, generating less noisy retrieved soil moisture and possibly better long-term stability. However, for the latter, two years of data is probably too short, and it is necessary to wait for the full *L*<sup>1</sup> and *L*<sup>2</sup> 10-year reprocessed data availability. Finally, similarly to the spatial maps, using the v724 data, provides here ~1% more successful retrievals in these time series.

#### **4. Conclusions**

The SMOS team has started a new reprocessing campaign, the third, after several improvements have been introduced in calibration and image reconstruction. In calibration, the changes mainly affect the NIR calibration parameters, the NIR antenna losses, the PMS sensitivities and the correction of the thermal coupling in one important thermistor. In image reconstruction, the changes focus on reducing the spatial biases induced by the dissimilarities of the antenna patterns, and on reducing the Sun effects in the image, which cannot be considered as a point source at L-band. These corrections improve the quality of the data, as indicated by several metrics that analyse spatial biases, measurement stability, and other image reconstruction errors, as well as by comparisons against in-situ measurements and χ<sup>2</sup>

metrics from soil moisture retrievals. This reprocessing campaign comes just after SMOS has been in orbit for over 10 years.

**Author Contributions:** NIR calibration, R.O. and I.C.; Antenna losses, I.C., J.K. and R.O., PMS Sensitivities, J.C., I.C. and A.Z.; PMS Heater correction, J.C., I.C. and A.Z.; Antenna patch thermistor correction, J.K. and R.O.; Gibbs-2, A.K. and F.C.; Ice-sea mask, F.C.; Super-sample Sun correction, F.C.; Sun correction in the back, A.K., Software, J.B. and G.L.; Supervision, M.M.-N., R.O. and R.C.; Validation, J.T., P.R., R.O., R.D.-G., V.G.-G.; Writing—original draft, R.O., V.G.-G.; Writing—review & editing, I.C., J.K., J.C., P.R., J.T., J.B., G.L., R.C., M.M.-N., A.K., V.G.-G. All authors have read and agreed to the published version of the manuscript.

**Funding:** This work has been funded by the European Space Agency under the SMOS programme.

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