# Evaluation of Water and Carbon Estimation Models in the Caatinga Biome Based on Remote Sensing
## 2 Material and Methods
### Data Processing and Analysis  
2.4.1 Atmospheric Parameters (Precipitable Water and Air Temperature) and Daily R\({}_{\mathrm{n}}\)  
Estimation  
The estimation of the instantaneous Rn was conducted using only MODIS data, aiming to develop an operational methodology. We understand that this approach can facilitate future analysis in similar ecosystems, given the significant lack of Rn estimates globally [31]. Rn is not usually measured at weather stations, meaning that its estimation is often restricted to experimental campaigns, which are more costly. The instantaneous Rn was used to estimate the evaporative fraction and the daily Rn to calculate the actual daily evapotranspiration (ET). The first step is to estimate the instantaneous Rn as follows:  
\[\mathrm{Rn}=\mathrm{Rs}(1-\alpha)+\mathrm{R_{L\downarrow}}-\mathrm{R_{L \uparrow}}-(1-\varepsilon_{0})\mathrm{R_{L\downarrow}} \tag{1}\]  
where \(\mathrm{R_{s}}\) (W\(\cdot\)m\({}^{-2}\)) is the downwelling shortwave radiation; \(\alpha\) (dimensionless) is the surface albedo; \(\mathrm{R_{L\downarrow}}\) (W\(\cdot\)m\({}^{-2}\)) is the downwelling longwave radiation; \(\mathrm{R_{L\downarrow}}\) (W\(\cdot\)m\({}^{-2}\)) is the upwelling longwave radiation; (\(1-\varepsilon_{0}\)) \(\mathrm{R_{L\downarrow}}\) (W\(\cdot\)m\({}^{-2}\)) represents the fraction of incident longwave radiation reflected by the surface; and \(\varepsilon_{0}\) is the surface emissivity (dimensionless). The term \(\alpha\)\(\mathrm{R_{s}}\) (W\(\cdot\)m\({}^{-2}\)) represents the shortwave radiation flux reflected by the surface (upwelling shortwave radiation). More detailed information about this methodology can be found in [32]. To investigate the impact of considering the water content in the atmosphere on the \(\mathrm{R_{n}}\) estimates, our methodology aimed to generate the \(\mathrm{R_{n}}\) spatial distribution in two ways: (a) using Equation (2), in order to estimate \(\mathrm{R_{n}}\) 1 (where the transmissivity only depends on altitude) [33], and (b) using Equation (3), to estimate \(\mathrm{R_{n}}\) 2 (where the transmissivity considers the water content in the atmosphere) [22]:  
\[\tau_{\mathrm{sw}}=0.75+2\cdot 10^{-5}\mathrm{z} \tag{2}\]  
where z represents each pixel's altitude in the image, obtained from the digital elevation model generated by the Shuttle Radar Topography Mission (SRTM), available at [[http://srtm.csi.cgiar.org](http://srtm.csi.cgiar.org)]([http://srtm.csi.cgiar.org](http://srtm.csi.cgiar.org)) (accessed on 23 October 2022). \[\tau_{\mathrm{sw}}=0.35+0.627\exp\left[\frac{-0.00146\mathrm{P}}{\mathrm{K_{ t}}\mathrm{cos}\,\theta_{\mathrm{z}}}-0.075\bigg{(}\frac{\mathrm{WP}}{\mathrm{ cos}\,\theta_{\mathrm{z}}}\bigg{)}^{0.4}\right] \tag{3}\]  
where \(\theta_{\mathrm{z}}\) is the solar zenith angle, obtained from the product MOD09A1, P is the average atmospheric pressure in kPa, \(\mathrm{K_{t}}\) is the atmospheric turbidity coefficient, set to 1 for a clear sky and set to 0.5 for extreme turbidity [34], and WP is the precipitable water, obtained from the MOD05 product. For validation purposes and aiming at greater operability when using only satellite data, a comparison was made between the WP values obtained by the MOD05 product and those estimated from surface data using the following equation [35]:  
\[\mathrm{WP}=0.14\mathrm{e_{a}}\mathrm{P_{air}}+2.1 \tag{4}\]  
where \(\mathrm{e_{a}}\) is the near-surface vapor pressure (KPa), \(\mathrm{P_{air}}\) is the atmospheric pressure, both obtained from surface data obtained according to [36].