# Evaluation of Water and Carbon Estimation Models in the Caatinga Biome Based on Remote Sensing
## 2 Material and Methods
### Data Processing and Analysis
#### 2.4.3 Gross Primary Production (GPP) (Modeled versus MOD17A2H) Estimation  
GPP is the total carbon assimilated by vegetation, of which a part is lost to the atmosphere because of autotrophic respiration. Thus, GPP is the primary regulator of carbon exchange from the atmosphere to the Earth. Consequently, a better understanding of the spatiotemporal dynamics of GPP provides a valuable measure of ecosystem health and the impacts of regional LULC disturbances and climate change, thus improving carbon cycle estimates [12].  
In this study, the GPP product from MOD17A2H (called GPP MOD17A2H) was used. This product was based on [21], which relates gross photosynthesis to the amount of photosynthetically active radiation (PAR) absorbed by photosynthetic biomass and a conversion efficiency term [51]:  
\[\text{GPP}=\epsilon\times\text{fPAR}\times\text{PAR} \tag{14}\]  
where \(\epsilon\) is the radiation use efficiency (RUE) of vegetation (kg\(\cdot\)C\(\cdot\)M)\({}^{-1}\)), PAR is the photosynthetically active radiation (MJ\(\cdot\)d\({}^{-1}\)), and fPAR is the fraction of incident PAR absorbed by the canopy. Equation (14) was also used to estimate the GPP on a smaller scale (GPP Modeled), as described in the following:  
The fPAR estimate was obtained according to [52] as follows:  
\[\text{fPAR}=(-0.161+1.257\text{NDVI}) \tag{15}\]  
The acquisition of MODIS products was performed using the Google Earth Engine (GEE) platform, available at [[https://code.eartheengine.google.com](https://code.eartheengine.google.com)]([https://code.eartheengine.google.com](https://code.eartheengine.google.com)) (accessed on 23 October 2022). The \(\epsilon\) parameter was estimated using:  
\[\epsilon=\epsilon_{\text{max}}.\text{T}_{1}.\text{T}_{2}.\Lambda \tag{16}\]  
where \(\epsilon_{\text{max}}\) is the maximum efficiency of light use by vegetation, whose value was set to 2.15 g\(\cdot\)C\(\cdot\)M]\({}^{-1}\)[21; 53]). T\({}_{1}\) and T\({}_{2}\) are estimated as follows:  
\[\text{T}_{1}=0.8+0.02\text{T}_{\text{opt}}-0.005\text{T}_{\text{opt}}{}^{2} \tag{17}\]  
\[\text{T}_{2}=\frac{\frac{1}{1+\exp(0.2\text{T}_{\text{opt}}-10-\text{T}_{\text {day}})}*1}{1+\exp\left[0.3\left(-\text{T}_{\text{opt}}-10+\text{T}_{\text{ day}}\right)\right]} \tag{18}\]  
where T\({}_{\text{opt}}\) and T\({}_{\text{day}}\) are, respectively, the average air temperature during the maximum leaf area index, or maximum NDVI, and the daily average temperature. The T\({}_{1}\) factor is essentially responsible for reducing the cooler regions' effect on plant growth. In contrast,the T\({}_{2}\) factor reduces the light use efficiency (\(\epsilon\)) if the ambient temperature deviates from the optimal temperature, which is relevant for arid and semiarid regions.  
To estimate PAR, a model modified by [52] and applied in the Northeastern region of Brazil by [53] was used. It combines the model proposed by [21], which is based on PAR, with the light use efficiency model of [54] and the energy balance model of [23]. Thus, PAR is estimated as:  
\[\text{PAR}=0.48.\text{R}_{\text{s24h}} \tag{19}\]  
with R\({}_{\text{s24h}}\) in W\(\cdot\)m\({}^{-2}\).