## 2 Materials and Methods
### Field Data  
Table 1 shows the variables from the Ozflux sites considered in our analysis. In situ daily average SM, LST (K), and GPP were used in the present study and can be accessed from [37]. Quality control was carried out as part of the data delivery process, and details on methods of measurements, corrections, and gap filling can be found in previous studies, such as [37]. SM was measured with TDR probes arranged horizontally in two arrays within different habitats: under Mulga, in bare soil between trees, and beneath Mulga and understory (grass, Mulga, and spinifex in the case of Ti Tree) [33]. The sensors measured volumetric soil moisture content (m\({}^{3}\)/m\({}^{3}\)) at four depths: 0-10 cm (named SSM), 10-30 cm (named 10 cm), 60-80 cm (named 60 cm), and 100-130 cm (named 100 cm). We considered data from the array under Mulga (the most representative cover type) for both stations, which included the unconsolidated soil (at a 100 cm depth) above the hardpan in ASM. The sensors' calibration for the specific soil type was previously carried out by [14], comparing probe measurements with laboratory analysis of soil texture and bulk density.  
LST from the station was calculated to test the relationship with SM and to check the correlations obtained from MODIS LST data. For the calculation of LST, upwelling long-wave broad band hemispherical radiances measured by the pyrgeometer CNR1, averaging records from 10:30 a.m. to 2:30 p.m, were considered [38] (Equation (2)). This sensor was located at a 11.6 m height in ASM (9.8 m in the Ti Tree station) and included different cover types.  
\[LST=\left(\frac{L_{up}-(1-\varepsilon)L_{down}}{\varepsilon\sigma}\right)^{ \frac{1}{4}} \tag{2}\]  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Instrument Type** & **Brand** & **Model/Make** & **Location (Named)** \\ \hline \multirow{3}{*}{Volumetric soil moisture} & \multirow{3}{*}{Campbell Scientific} & \multicolumn{2}{c}{0–10 cm (SSM)} \\  & & CS616 and CS605 & 10–30 cm (10 cm) \\  & & (Campbell Scientific Inc) & 60–80 cm (60 cm) \\ \hline Net radiometer & Kipp and Zonen & CNR1 (Kipp and Zonen) & 12.2 m from ground level \\ \hline \hline \end{tabular}
\end{table}
Table 1: Sensors and variables from the ASM and Ti Tree OzFlux sites considered in this study.  
where \(L_{top}\) and \(L_{down}\) are the upwelling and downwelling longwave radiances (w/m\({}^{2}\)), respectively; \(\sigma\) is the Stefan-Boltzmann constant (5.67 \(\times\) 10\({}^{-8}\) W/m\({}^{2}\)K\({}^{4}\)); and \(\varepsilon\) is the surface emissivity. \(\varepsilon\) was calculated as [39] follows:  
\[\varepsilon=\varepsilon_{v}F_{c}+\varepsilon_{s}(1-F_{c}) \tag{3}\]  
where \(\varepsilon_{v}\) and \(\varepsilon_{s}\) are emissivity values for vegetation (0.985) and bare soil (0.960) [40; 41], respectively, and \(Fc\) is the fractional vegetation cover.  
\[F_{c}=\left(\frac{NDVI_{i}-NDVI_{s}}{NDVI_{v}-NDVI_{s}}\right)^{2} \tag{4}\]  
where \(NDVI_{i}\), \(NDVI_{s}\), and \(NDVI_{v}\) are NDVI values for each day, for bare soil (0.11), and for vegetation (0.45), respectively, obtained from the MCD43A4 MODIS product (see Section 2.3). \(NDVI_{i}\) values were obtained from a 3 \(\times\) 3 pixel window centered in the station. \(NDVI_{s}\) and \(NDVI_{v}\) were calculated as the minimum and maximum NDVI values for the analyzed data series.  
Finally, estimates of daily mean GPP (gC/m\({}^{2}\)d) from eddy covariance and meteorological data were considered to test the relationship between field and satellite variables during the wet pulses. These data had previously been processed by different authors for the OzFlux sites (more details are included in [14; 34]), including quality control assessment, the removal of outliers, and gap-filling and have been used in several studies [5; 11; 42].