## 4 Results and Discussion
### SM-LST Relationship at the Daily Scale  
The correlation of SM acquired at SMOS morning/afternoon passes and LST-derived parameters is shown in Figure 5 (left). In the boxplot, the central mark indicates the median, and the bottom and top edges of the box indicate the 25 th and 75 th percentiles, respectively. The whiskers extend to the most extreme data points not considered outliers, and the outliers are plotted individually using red crosses. Considering the entire study period, SM and LST variables are in general anticorrelated: if SM decreases, LST increases, and vice versa. This result agrees with those obtained in Figure 3 (right). There is a single outlier with a very low correlation (R \(\approx-0.2\) to 0.1) corresponding to H7, a vineyard station that recorded extremely dry conditions (with SM ranging from 0 to 0.08 m\({}^{3}\)/m\({}^{3}\) along the four years). In the morning passes, the anticorrelation values (in median) sorted from strong to weak are obtained for: daily maximum LST and daily mean LST (R\({}_{T_{max},\overline{T}}\approx-0.71\)), daily median LST (R\({}_{T_{mod}}\approx-0.70\)), instantaneous LST and daily minimum LST (R\({}_{T_{i},T_{min}}\approx-0.68\)), and LST diurnal range (R\({}_{\Delta T}\approx-0.59\)). In the afternoon passes, the sorted R values are obtained for: daily median LST (R\({}_{T_{mod}}\approx-0.70\)), daily mean LST (R\({}_{\overline{T}}\approx-0.69\)), daily maximum LST and instantaneous LST (R\({}_{T_{max},T_{i}}\approx-0.68\)), daily minimum LST (R\({}_{T_{min}}\approx-0.66\)), and LST diurnal range (R\({}_{\Delta T}\approx-0.55\)). Note that the correlation obtained for instantaneous LST becomes equal to the correlation obtained for daily minimum LST in the morning, and equal to the correlation obtained for daily maximum LST in the afternoon. This could be due to \(T_{i}\) being closer in time and similar to \(T_{min}\) values at the morning, and to \(T_{max}\) values at the afternoon passes, respectively. Considering the percentiles and whiskers, the strongest anticorrelation is obtained for the daily maximum LST (\(T_{max}\)) both in morning and afternoon passes. This can be explained by the time of \(T_{max}\) being also the time of maximum potential evapotranspiration, i.e, when there is a higher atmospheric demand of water and the air turbulence (uplift) is maximum. When analyzing the detrended in situ time-series, Figure 5 (right) shows that, as expected, correlations are weaker than when using the variables directly. In the morning passes, the sorted anticorrelation values (in median) from strong to weak are: LST diurnal range (R\({}_{\Delta T}\approx-0.33\)), daily maximum LST (R\({}_{T_{max}}\approx-0.31\)), daily mean LST (R\({}_{\overline{T}}\approx-0.26\)), daily median LST (R\({}_{T_{md}}\approx-0.25\)), and instantaneous LST and daily minimum LST (R\({}_{T_{i},T_{min}}\approx-0.20\)). In the afternoon passes, the sorted anticorrelation values are obtained for: LST diurnal range (R\({}_{\Delta T}\approx-0.31\)), instantaneous LST (R\({}_{i}\approx 0.30\), daily maximum LST (R\({}_{T_{max}}\approx-0.29\)), daily mean LST and median LST (R\({}_{\overline{T},T_{md}}\approx-0.24\)), and daily minimum LST (R\({}_{T_{min}}\approx-0.19\)). The strongest anticorrelation is obtained for the LST diurnal range both in morning and afternoon passes. This agrees with previous literature [56; 57; 58], in which a relation between SM and near-surface air temperature diurnal range was reported. However, this air temperature is usually measured at 1.5 m above the ground level, not in the top 5 cm of the soil. Results indicate that maximum LST and LST diurnal range provide complementary information of the SM-LST relationship. Since results obtained at the SMOS morning and afternoon are very similar using both the direct variables and their anomalies, hereafter only results at morning passes are presented. Figure 4: Comparison of in situ SM (**left**) and LST (**right**) dynamic ranges with soil texture: sand content (red asterisks) and clay content (blue crosses).