*3.2. Temporal Analysis of Root Zone Soil Moisture Estimates*

The pixel-average time series of the different RZSM estimates across REMEDHUS were compared against the station-average time series (Figure 2). At first glance, it is remarkable that all satellite datasets followed a temporal pattern similar to that of the in situ RZSM evolution, in agreement with the seasonality and climate of this region. It is highlighted that SMAP L4 RZSM and SMOS-BEC SWI had the best agreement with the dry-down and wetting-up events indicated by the in situ RZSM. To a lesser extent, this agreement also occurred for the MODIS ATI SWI, which fluctuated less. The SMOS-CESBIO L4 RZSM exhibited a certain time lag, especially during the rising periods, compared to the rest of the estimates. The reason could be the three-day window average of this product, which also smoothed the curve. While the SMOS SSM has proven more variable than the ground-based SSM itself [45,64], the SMOS RZSM showed more stability, which is consistent with the expected behavior of the deep soil moisture [43] that is typically more steady than the SSM.

In general, the SMAP L4 RZSM slightly overestimated the in situ RZSM but captured its overall variability well, with the bias almost constant. By contrast, the SMOS-CESBIO L4 RZSM underestimated the in situ RZSM, and the differences are higher during the dry season compared to the other estimates except for the SMOS-BEC SWI. This fact could be explained from the SMOS SSM underestimation previously detected in this area [45,64,65] and in other regions [66–68]. Both MODIS ATI SWIs also underestimated the in situ RZSM, although to a minor degree, while their agreement was better than with the other estimates, particularly during the dry season.

**Figure 2.** Average time series of the different RZSM estimates across REMEDHUS.

Regarding the impact of the T parameter, there were no differences in the use of TSMAP and TSMOS to derive the SWI, both with SMOS-BEC and MODIS ATI. This result could have occurred because they were very similar in the REMEDHUS area. Indeed, when computing the statistics of the T maps, the mean values of TSMAP and TSMOS were 14.5 and 17 days, the median values were 13 and 16.5 days, and the mode values were 13 and 16 days, respectively. It has been demonstrated that the T parameter is the response time of the autocorrelation function of soil moisture [37]. The T was affected by soil depth, soil hydraulic properties, and different physical processes such as evaporation and runoff. However, other processes such as transpiration or the soil hydraulic conductivity variation depending on soil moisture conditions were not considered in the SWI model [32,33]. Additionally, the potential dependence of T on soil texture was previously suggested [69]. Unfortunately, no significant relations were observed between T and soil properties (sand and clay fractions, bulk density, and organic matter content) [33]. The variability of the T parameter has previously been shown in several studies [32,33,37–40,42,43,69]. However, the SWI performed with similar good results in all cases. The robustness of SWI on the T parameter may rely on the recursive expression of the exponential filter, where the SSM has the highest influence and T only represents a timescale value.

The statistics obtained from the validation of the different RZSM estimates across REMEDHUS showed very similar correlation coefficients for all the estimates (by stations; Table 2 and Figure 3), although the correlations for MODIS ATI SWI (area-average) were slightly lower (R ~0.75 to 0.77). All correlations were significant at a 95 % confidence level. Similar correlation coefficient values were found in previous research when the SWI model was used. For instance, R ~0.45 to 0.88 was obtained when the SWI was applied to in situ SSM measurements of the Soil Climatic Analysis Network (SCAN) and compared to soil moisture measurements at 10–90 cm depth [34]. Likewise, R ~0.49 to 0.75 was obtained when the SWI was applied to the SMOS SSM and compared to the soil moisture of the 25–60 cm profile layer at the Oklahoma Mesonet and the Nebraska Automated Weather Data Network (AWDN) [42] and also compared to the soil moisture of the 0–50 cm depth of the same REMEDHUS network [43].

Regarding the differences from the in situ RZSM (Table 2), the values obtained for MODIS ATI SWI (RMSD ~0.031 to 0.110 m3/m3 and cRMSD ~0.017 to 0.054 m3/m3, by stations) were slightly lower than those for the other estimates (RMSD ~0.027 to 0.180 m3/m3 and cRMSD ~0.019 to 0.058 m3/m3) except for the SMAP L4 RZSM product, as expected from Figure 2. Both SMAP L4 RZSM and MODIS ATI SWI had the lowest differences (RMSD ~0.044 m3/m3 and cRMSD ~0.020–0.021 m3/m3, area-average), while SMOS-CESBIO L4 RZSM and SMOS-BEC SWI had the highest. These results suggested that MODIS ATI SWI could be a good estimator of RZSM at a spatial resolution of 1 km.

The bias (Table 2) of SMAP L4 RZSM exhibited positive values (by stations and area-average), indicating an overestimation of the in situ RZSM, whereas SMOS-CESBIO L4 RZSM, SMOS-BEC SWI and MODIS ATI SWI had dry biases in both cases, as observed in Figure 2. Different studies

have shown that SMAP overestimates the SSM [2,59]. In this line, the SMAP L4 RZSM showed a slightly higher positive bias (0.063 m3/m3) during the validation of this product over the Little River. The irrigated crops and wetlands in the surroundings of this site, which are not considered in the SMAP model system, were first assumed as possible reasons for this wet bias, but REMEDHUS has no wetlands in its vicinity. Moreover, the wet bias over the Little River also appeared in the SMAP model-only simulations, suggesting that errors in the NASA catchment model parameters may be the main reason [30]. By contrast, the SMOS-derived RZSM estimates exhibited a dry bias (−0.15 to +0.05 m3/m3), with values similar to those previously observed [43].


**Table 2.** Statistics obtained from comparison of the six RZSM estimates (by stations and area-average) with the in situ RZSM across REMEDHUS. N indicates the number of coincident data days.

All values are significant (*p*-value < 0.05).

**Figure 3.** Pearson's correlation coefficients (R) between the in situ RZSM and the six RZSM estimates across REMEDHUS (by stations).

In summary, it is remarkable that the results for the SMAP RZSM and SMOS SWI (R > 0.8 and cRMSD ~0.02 m3/m3) were better than those found in some works about SSM over the REMEDHUS network. For the SMOS L2 SSM product, the correlation was R ~0.78, and the errors were beyond cRMSD ~0.04 m3/m3 [45]. In the case of the SMAP L2 SSM product, the correlation was R ~0.58, and the errors were also close to cRMSD ~0.04 m3/m3 [2]. Moreover, the results obtained for SMAP RZSM in this research were near those found for the SSM product in REMEDHUS (R ~0.9) but for a longer period of validation [59].

A previous study suggested that the inherent differences between SMOS and in situ were larger than the errors produced by the SWI model [42]. This situation was also true here, where the RMSD and bias were smaller for the SWI-derived estimations than for the SMOS RZSM product itself. The impact of using TSMOS or TSMAP in the SWI model was negligible for both SMOS-BEC and MODIS ATI, and non-significant differences were found during the validation across REMEDHUS. It is highlighted that the coverage of MODIS ATI SWI was clearly lower than that of the other estimations by both stations and area-average, which evidenced the most important drawback of the MODIS ATI-derived RZSM owing the use of VIS/IR observations.

## *3.3. Spatial Analysis of Root Zone Soil Moisture Estimates*

Six maps of RZSM over the Iberian Peninsula—one for each different RZSM estimate—are displayed during a summer and a winter day (9 July and 31 December 2016) in Figures 4 and 5, respectively. No significant differences were observed between the SMOS-BEC and MODIS ATI SWI calculated with TSMAP and TSMOS, as it was seen in the REMEDHUS area (Table 2 and Figure 3). This result suggests that the T parameter could have a very small influence in the SWI model results.

On both dates, there was a high similarity between the SMOS-CESBIO L4 RZSM and the SMOS-BEC SWI maps because both estimations used data from the same radiometer and similar approaches were employed to obtain the RZSM. Note that the higher spatial resolution of the SMOS-BEC SWI maps allowed observing more details than that of the SMOS-CESBIO L4 RZSM maps. In general, although the SMOS-BEC SWI used both ascending and descending orbits to increase its coverage, the SMOS orbital path of a unique day usually does not cover the entire Iberian Peninsula and some data gaps are still present. Instead, the SMOS-CESBIO L4 RZSM covered the entire spatial domain since it was produced by a three day composite.

**Figure 4.** RZSM maps corresponding to a summer day (9 July 2016): (**a**) SMAP L4 RZSM; (**b**) SMOS-BEC SWI (TSMAP); (**c**) MODIS ATI SWI (TSMAP); (**d**) SMOS-CESBIO L4 RZSM; (**e**) SMOS-BEC SWI (TSMOS); and (**f**) MODIS ATI SWI (TSMOS).

In general, the SMAP L4 RZSM product displayed wetter values than all the other estimates on both days, confirming the overestimation found in REMEDHUS. Additionally, the SMAP L4 RZSM maps clearly exhibited wetter values in the north than in the south, which was in accordance with the climatic patterns over the Iberian Peninsula. This effect was especially noticeable for the Pyrenees and the Cantabrian ranges in the north and the Galicia region and the northern part of Portugal in the northwestern Iberian Peninsula. The SMOS-CESBIO L4 RZSM maps also displayed this synoptic situation in the summer. In summer as well as winter, both SMAP and SMOS-CESBIO L4 RZSM were able to detect the Doñana National Park—the most important wetland in Spain—located at the Guadalquivir River mouth (southern Spain). This area was also captured by the SMOS-BEC SWI, whereas the MODIS ATI SWI did not show these distinctive features. There was no marked spatial contrast in RZSM for the MODIS ATI SWI maps throughout the Iberian Peninsula on both days except the high values in the north during the wet period. The MODIS ATI SWI can be masked not only by clouds but also by fog banks due to the use of optical observations. This effect was captured in the MODIS ATI SWI maps for the winter day where some river valleys in the center of the Iberian Peninsula did not have data.

**Figure 5.** RZSM maps corresponding to a winter day (31 December 2016): (**a**) SMAP L4 RZSM; (**b**) SMOS-BEC SWI (TSMAP); (**c**) MODIS ATI SWI (TSMAP); (**d**) SMOS-CESBIO L4 RZSM; (**e**) SMOS-BEC SWI (TSMOS); and (**f**) MODIS ATI SWI (TSMOS).

The temporal correlation maps of the SMAP and SMOS-CESBIO L4 RZSM with both SMOS-BEC and MODIS ATI SWI aggregated to 9 km and 25 km are shown in Figures 6 and 7, respectively. Only pixels with significant correlation (*p*-value < 0.05) are shown. It can be seen that microwave-based RZSM estimates (the SMAP L4 RZSM product at 9 km against SMOS-BEC SWI estimates) were highly correlated over most parts of the Iberian Peninsula (*R* ≥ 0.7), regardless of the T parameter used. Only some areas displayed low values of correlation (*R* ~0.2 to 0.3). These areas, such as the Pyrenees, had a low number of days with data because the abrupt topography decreased the number of soil moisture retrievals for these pixels. However, when comparing the SMAP L4 RZSM against the MODIS ATI SWI, the correlations over all the extreme north of the peninsula were low and even reached negative values, especially in regions with abundant and dense vegetation such as the Pyrenees and Cantrabrian ranges. The same patterns were obtained when comparing the MODIS ATI SWI against the SMOS-BEC SWI with both T parameter values. This result may be related to the distinctive vegetation of these regions because there are other mountainous areas in the Iberian Peninsula, but the north ranges are also the more densely forested ones.

**Figure 6.** Temporal correlation maps at 9 km between: (**a**) SMAP L4 RZSM and SMOS-BEC SWI (TSMAP); (**b**) SMAP L4 RZSM and MODIS ATI SWI (TSMAP); (**c**) MODIS ATI SWI (TSMAP) and SMOS-BEC (TSMAP); (**d**) SMAP L4 RZSM and SMOS-BEC SWI (TSMOS); (**e**) SMAP L4 RZSM and MODIS ATI SWI (TSMOS); and (**f**) MODIS ATI SWI (TSMOS) and SMOS-BEC (TSMOS).

**Figure 7.** Temporal correlation maps at 25 km between: (**a**) SMOS-CESBIO L4 RZSM and SMOS-BEC SWI (TSMAP); (**b**) SMOS-CESBIO L4 RZSM and MODIS ATI SWI (TSMAP); (**c**) MODIS ATI SWI (TSMAP) and SMOS-BEC (TSMAP); (**d**) SMOS-CESBIO L4 RZSM and SMOS-BEC SWI (TSMOS); (**e**) SMOS-CESBIO L4 RZSM and MODIS ATI SWI (TSMOS); and (**f**) MODIS ATI SWI (TSMOS) and SMOS-BEC (TSMOS).

In addition, a similar comparison was made with the SMOS-CESBIO L4 RZSM at 25 km, and the same patterns were distinguished irrespective of its lower spatial resolution compared to SMAP. The same patterns were found in the evapotranspiration and Fractional Vegetation Cover products from the Spinning Enhanced Visible and Infrared Imager (SEVIRI) sensor on board the Meteosat Second Generation (MSG) [70]. Then, the VIS/IR-based observations produced negative correlations in northern Spain. This result could be due to the MODIS variables involved in the ATI-derived soil moisture estimation (reflectance or LST). The reflectance was directly linked to the MODIS NDVI that was used to obtain the SMOS-BEC L4 SSM from its downscaling algorithm but not the MODIS LST. However, the observed correlation patterns were not seen in the correlations maps of the SMOS-BEC SWI with other passive RZSM estimates. Due to this fact, the reflectance was discarded as the cause of the negative correlations. Therefore, the reason for these correlation patterns may be the different characterization of the MODIS LST reflecting the north-south temperature gradient compared with the LSTs from the NASA catchment model and the ECMWF ERA-Interim model used in SMAP L4 RZSM and SMOS-BEC L4 SSM, respectively.

#### **4. Conclusions**

In recent years, the use of RZSM has become increasingly important in several hydrological and agricultural applications. In this research, six different RZSM estimates provided by three satellites—SMAP and SMOS operating at the microwave L-band and MODIS operating at the optical frequency range—were evaluated across the Iberian Peninsula from 31 March 2015 to 31 December 2016.

A preliminary analysis of the MODIS ATI-derived SSM estimation was carried out. It correctly reproduced the in situ SSM measurements with slightly lower correlations but a similar performance in terms of errors and bias than estimates obtained from the L-band. Because there were no remarkable differences between all possible alternatives to calculate the ATI-derived SSM, the approach that was easiest to implement, had the lowest computational cost, and with the best available spatial and temporal resolution was selected. This approach used the visible albedo reflectance, the combination of the Aqua/Terra LST, and the Soil Hydraulic Database to set the reference thresholds for soil moisture.

In the temporal analysis of the six RZSM estimates performed across the REMEDHUS area, all of them followed a similar evolution. The SMOS-CESBIO L4 RZSM product, the SMOS-BEC SWI, and MODIS ATI SWI showed underestimations with respect to the in situ measurements, while the SMAP L4 RZSM product showed overestimation. The different alternatives for T parameters used in the SWI model did not seem to impact the results.

In the spatial analysis performed across the Iberian Peninsula, a high level of similarity was observed between the SMOS-based estimations, with clearly higher spatial detail for the SMOS-BEC SWI than for the other estimates. The most distinctive spatial variability between wet and dry regions was displayed by the SMAP L4 RZSM, whereas the MODIS ATI SWI had the lowest spatial variability.

Regarding the correlation spatial patterns, the RZSM estimates from the microwave sensors were highly correlated across the Iberian Peninsula except in areas with low amounts of data. The comparison between microwave and optical observations showed low or negative correlation values all over the extreme north of the peninsula, coinciding with the location of higher mountains and more densely forested areas.

Although two different spectral regions were used (microwave or optical frequencies), all six different RZSM estimates reproduced the temporal patterns of the in situ RZSM well and could be considered as good RZSM estimators. The SWI model, which required only SSM and the T parameter as inputs, worked as well as more complex land surface or hydrological models for estimating RZSM, as in the cases of the SMOS and SMAP L4 RZSM products. The good results based on the MODIS ATI must be highlighted, despite its lesser temporal coverage, given MODIS is not a satellite mission specifically devoted to soil moisture retrieval.

The use of remote sensing as an alternative to ground-based measurements for RZSM monitoring offers a new opportunity for hydrological studies and agricultural applications at the global scale, improving their spatial coverage and temporal resolution.

**Author Contributions:** The initial idea for this research was conceived by J.M.-F. and N.S. The in situ data were prepared by Á.G.-Z. The satellite data were downloaded by M.P. The exponential T parameters were computed by Á.G.-Z. All other data processing was performed by M.P., who also collected all the results. The four authors have equally contributed to the interpretation of the results. The first manuscript was prepared by M.P. in collaboration with the other authors. All the authors revised the final manuscript and approved it.

**Funding:** This research was supported by the Junta de Castilla y León (Project SA007U16), the Spanish Ministry of Economy and Competitiveness (Projects ESP2015-67549-C3-3-R and ESP2017-89463-C3-3-R), and the European Regional Development Fund (ERDF).

**Acknowledgments:** The in situ SSM data are available at the International Soil Moisture Network (ISMN) database (https://ismn.geo.tuwien.ac.at) and the rest of in situ soil moisture data are available upon request. The SMAP L4 soil moisture (both SSM and RZSM variables within the SPL4SMGP v.3 product) are accessible at the National Snow and Ice Data Center Distributed Active Archive Center (NSIDC DAAC, https://nsidc.org/data/SPL4SMGP/ versions/3). The SMOS-CESBIO L3 SSM (SM\_RE04/OPER\_MIR\_ CLF31A/D v.300 product) was distributed by the Centre Aval de Traitement des Données SMOS (CATDS, http://www.catds.fr/Products/Available-productsfrom-CPDC). The SMOS-CESBIO L4 RZSM (SM\_SCIE\_MIR\_ CLF4RA/D v.300 product) was also disseminated by CATDS (http://www.catds.fr/Products/Available-products-from-CEC-SM/L4-Land-research-products). The authors especially thank Gerard Portal and Mercè Vall-llossera from the Technical University of Catalonia (UPC) and the Barcelona Expert Centre (BEC, http://bec.icm.csic.es) for providing the new cloud-free SMOS-BEC L4 SSM v.3 product. The Aqua MODIS surface reflectance (MYD09GA v.6 product) and both Aqua and Terra LST (MYD11A1 and MOD11A1 v.6 products) were provided by the NASA Land Processes Distributed Active Archive Center (LP DAAC, https://lpdaac.usgs.gov).

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