*2.5. Estimation of MODIS ATI*

The MODIS ATI was computed as the ratio of the daily surface albedo and the diurnal temperature range [10]:

$$ATI = \mathbb{C} \frac{1-\alpha}{\Delta LST} \,\,\,\,\,\tag{1}$$

where *C* is the solar correction factor, *α* is the broadband albedo and Δ*LST* corresponds to the diurnal temperature range.

The correction factor *C* is related to the solar flux and therefore compensates for seasonal variation in solar insolation. This factor was obtained following the expression [10]:

$$\mathcal{L} = \sin\varrho \sin\delta (1 - \tan^2\varrho \tan^2\delta)^{1/2} + \cos\varrho \cos\delta \arccos(-\tan\varrho \tan\delta),\tag{2}$$

where *ϕ* corresponds to the latitude and *δ* to the solar declination of each pixel for each Julian day of the year.

The broadband albedo can be computed in two different spectral ranges—shortwave and visible in Equations (3) and (4), respectively—from daily Aqua MODIS surface reflectance at 1 km [54]:

$$
\mu\_{\text{shortwave}} = 0.160\rho\_1 + 0.291\rho\_2 + 0.243\rho\_3 + 0.116\rho\_4 + 0.112\rho\_5 + 0.081\rho\gamma - 0.0015,\tag{3}
$$

$$
\alpha\_{\text{visible}} = 0.331\rho\_1 + 0.424\rho\_3 + 0.246\rho\_{4'} \tag{4}
$$

where *ρ*1, *ρ*2, *ρ*3, *ρ*4, *ρ*<sup>5</sup> and *ρ*<sup>7</sup> are reflectance in bands 1, 2, 3, 4, 5 and 7, respectively. These two albedo approaches were analyzed.

The diurnal temperature range can be approximated in four different ways. The first method consists of estimating the LST through time as a sinusoid defined by its amplitude, its average temperature, the angular velocity of Earth, and the phase angle (Ψ) corresponding to the time of daily maximum LST [11,13], which coincides with the time of highest correlation between the LST and soil moisture behavior [55]. MODIS provides up to four observations for each day: Aqua nighttime LST at 1:30 h, Terra daytime LST at 10:30 h, Aqua daytime LST at 13:30 h, and Terra nighttime LST at 22:30 h, local time. These four LST at 1 km were used to compute Δ*LST* as the solution of the amplitude of the sinusoid by means of the least squares method (Δ*LST*4values). In this case, the four LST values are required to derive Ψ. Nonetheless, if Ψ was known, the amplitude could be calculated using only 2 LST values, preferable a day-night LST pair, because the difference between 2 daytime or 2 nighttime LSTs is usually low and would result in unrealistic Δ*LST* estimates. The second method is based on the difference between the Aqua daytime and nighttime LSTs (Δ*LST*Aqua). The third way employs the same methodology as the second but uses Terra daytime and nighttime LSTs (Δ*LST*Terra). The fourth way estimates the Δ*LST* as the difference between the daily maximum LST—computed from Terra or Aqua daytime LST—and the daily minimum LST—computed from Aqua or Terra nighttime LST (Δ*LST*Aqua/Terra). Therefore, four different approaches of the MODIS-based ATI are calculated, and their performances are assessed.

#### *2.6. Estimation of ATI-Derived Surface Soil Moisture*

The rationale of the ATI-derived SSM is that high ATI values correspond to maximum soil water content while low ATI values are related to minimum soil water content. The Soil Moisture Saturation Index (SMSI) was used to normalize the MODIS ATI time series at 1 km [12]:

$$MSSI(t) = \frac{ATI(t) - ATI\_{\text{min}}}{ATI\_{\text{max}} - ATI\_{\text{min}}},\tag{5}$$

where *ATI*(*t*) is the ATI at time *t*, and *ATImax* and *ATI*min represent the maximum and minimum values, respectively, of the ATI time series during the study period.

Because the SMSI varies from 0 to 1, the ATI-derived SSM was finally estimated after applying a change of dynamic range [12]:

$$SSM(t) = SMSI(t)(SSM\_{\text{max}} - SSM\_{\text{min}}) + SSM\_{\text{min}} \tag{6}$$

where *SSM*max and *SSM*min are the maximum and minimum SSM values of a reference soil moisture dynamic range, respectively.

To obtain an adequate soil moisture dynamic range and to account for a SSM dataset independent of SMAP and SMOS, two different data sources were used. The first data were the saturation (SAT), field capacity (FC), and wilting point (WP) water content maps at 1 km from the European 3D Soil Hydraulic Database (SHD) at 5 cm depth [56]. For each pixel over the Iberian Peninsula, the *SSM*max was calculated as the mean of SAT and FC, whereas the *SSM*min was calculated as the half value of the WP. This was similar to previous studies [12,57]. The second dataset was the combined CCI SSM v3.2 product at 25 km from 1978 to 2015 [58]. In this case, the *SSM*max and *SSM*min were computed as the maximum and minimum values, respectively, of the long-term time series of each pixel over the Iberian Peninsula. These *SSM*max and *SSM*min maps from CCI were resampled from 25 to 1 km resolution using the nearest neighbor method. Thus, the two different reference dynamic ranges were assessed.
