*2.7. Assessment of MODIS ATI Surface Soil Moisture*

Prior to using the resulting ATI-derived SSM to estimate RZSM, all alternative SSM estimations based on MODIS data were tested, i.e., varying the albedo (*α*shortwave or *α*visible), the diurnal temperature range (Δ*LST*4values, Δ*LST*Aqua, Δ*LST*Terra, or Δ*LST*Aqua/Terra), and the reference dynamic range (SHD or CCI). The assessment of these SSM estimations was performed for the 22 stations in the REMEDHUS network. The in situ SSM time series were compared with the MODIS ATI-derived SSM time series of the 1 km pixel that overlapped the corresponding station. To evaluate the level of agreement of both time series, a set of statistical metrics—namely the Pearson correlation coefficient (R), the root mean square difference (RMSD), the unbiased or centered *RMSD* (cRMSD), and the bias—was used. They were computed following these equations:

$$\mathcal{R} = \frac{\sum\_{i=1}^{n} \left( y\_i - \overline{y} \right) \left( x\_i - \overline{x} \right)}{\sqrt{\sum\_{i=1}^{n} \left( y\_i - \overline{y} \right)^2} \sqrt{\sum\_{i=1}^{n} \left( x\_i - \overline{x} \right)^2}},\tag{7}$$

$$\text{RMSSD} = \sqrt{\frac{\sum\_{i=1}^{n} \left(y\_i - \mathbf{x}\_i\right)^2}{n}},\tag{8}$$

$$\text{cRMSD} = \sqrt{\frac{\sum\_{i=1}^{n} \left[ (y\_i - \overline{y}) - (x\_i - \overline{x}) \right]^2}{n}},\tag{9}$$

$$\text{bias} = \frac{\sum\_{i=1}^{n} (y\_i - x\_i)}{n},\tag{10}$$

where *y* is the soil moisture to be analyzed, *x* is the soil moisture used as benchmark, *i* corresponds to each day of the study period with coincident data; the average value of both soil moisture datasets are indicated by a bar.

Since the in situ soil moisture did not have data gaps along the study period, the number of coincident days—in which there are both in situ and satellite data (N, expressed in percentage referred to a total number of 642 days)—was also computed to give some insight about the coverage of each satellite dataset.

## *2.8. Estimation of Root Zone Soil Moisture from SMOS-BEC and MODIS ATI Surface Soil Moisture*

The SWI model was used to estimate the RZSM from the SMOS-BEC and MODIS ATI SSM. This model consists of two soil layers. The first corresponds to the surface topsoil, while the second extends from the bottom of the first layer downward [32]. These two layers are related by an exponential formulation, thus simulating the dynamics of water within the soil profile. The SWI is computed recursively, where each RZSM value depends on the previous one [33]. The advantage of the SWI compared to other models is its simplicity. Moreover, the SWI uses only the SSM as input, together with the exponential T parameter. This T is interpreted as the characteristic time length that defines the rate of water transfer of each type of soil, increasing with the thickness of the soil layer and decreasing with the soil diffusivity constant [32,33,40,43].

For this study, the method to obtain the optimal T values relies on the comparison of SSM and RZSM products from SMAP and SMOS. Two alternative T maps over the Iberian Peninsula were computed: TSMAP at 9 km from the SMAP L4 SSM and RZSM, and TSMOS at 25 km from the SMOS-CESBIO L3 SSM and L4 RZSM. First, different T values ranging from 1 to 100 days were introduced into the SWI model with the SSM (SMAP L4 SSM or SMOS-CESBIO L3 SSM), obtaining 100 SWI time series for each pixel. Later, all 100 SWI time series were compared with their corresponding RZSM (SMAP L4 RZSM or SMOS-CESBIO L4 RZSM). The optimal T of each pixel was selected from these comparisons based on the criterion of highest correlation [43]. The two resulting T maps were resampled into the regular 1 km grid using the nearest neighbor technique. Then, the TSMAP and TSMOS were combined with the SMOS-BEC L4 and MODIS ATI SSM, both at 1 km, into the SWI to obtain four possible RZSM estimates at 1 km.

For a comprehensive understanding, a flowchart (Figure 1) summarizes all the data and the methodology applied to obtain the six different RZSM estimates to be analyzed in this study: (1) SMAP L4 RZSM; (2) SMOS-CESBIO L4 RZSM; (3) SMOS-BEC SWI (TSMAP); (4) SMOS-BEC SWI (TSMOS); (5) MODIS ATI SWI (TSMAP); and (6) MODIS ATI SWI (TSMOS).

#### *2.9. Comparison of Root Zone Soil Moisture Estimates*

The RZSM measured in REMEDHUS was used as the benchmark dataset to be compared with the six different RZSM estimates. Owing to the different scales of in situ and remotely sensed datasets, two strategies were used. On the one hand, a comparison between each station-pixel pairwise was performed. Thus, the in situ RZSM time series of each station was compared with the satellite-based RZSM time series of the overlapping pixel at its spatial resolution (9 km for SMAP L4 RZSM, 25 km for SMOS-CESBIO L4 RZSM, and 1 km for SMOS-BEC and MODIS ATI SWI). On the other hand, a validation based on the area averages was done. Then, the average of the 14 RZSM stations was compared with the average of 10 pixels for SMAP L4 RZSM, 4 pixels for SMOS-CESBIO L4 RZSM, and 14 pixels of SMOS-BEC and MODIS ATI SWI. Similar to the assessment suggested for the MODIS ATI SSM, the R, RMSD, cRMSD, and bias were used to evaluate the agreement of the RZSM estimates with the in situ measurements as well as the number of coinciding data days.

In addition, with the aim of analyzing the impact of the exponential T parameter (TSMAP and TSMOS) in the SWI-based estimations, temporal correlation maps between the SMOS-BEC SWI (TSMAP), the SMOS-BEC SWI (TSMOS), the MODIS ATI SWI (TSMAP), and the MODIS ATI SWI (TSMOS) were obtained at 9 km and at 25 km. To do this, the four different SWI maps were aggregated from 1 to 9 km, using the average value of the 1 km pixels that span the 9 km SMAP pixel. Then, these SWI maps at 9 km were compared with the SMAP L4 RZSM product and between them at this spatial resolution. The same aggregation technique was also applied for the comparison with the SMOS-CESBIO L4 RZSM product at 25 km.

**Figure 1.** Flowchart showing all data and methodology applied to obtain the RZSM estimates.
