# Satellite-Based Estimation of Carbon Dioxide Budget in Tropical Peatland Ecosystems
## Materials and Methods
### Methods
#### 2.3.3 GPP Calibration  
The MODIS-based GPP (MOD17A2H) time series underestimated the GPP derived from flux towers when it was validated with the GPP of flux towers for three conditions (i.e., _UF_, _DF_, and _BF_) in Palangkaraya. In all cases, the MODIS GPP underestimated flux tower one, and the \(R^{2}\) in _DF_ was around 0.29 based on the least squares regression [52] between the MODIS GPP and the flux tower-derived GPP (Equation (7), and Figure 4). It has also been reported that the least squares regression method is sensitive to outliers [52]. To overcome this problem, we applied the robust regression method. This method has the following advantages. The robust regression method judges whether a point is an outlier or not. The coefficients of regression function are calculated by minimizing the absolute error. Furthermore, a weight function derived by the data distribution was applied to remove the excessive effects that were induced by outliers [53]. Hence, the weight function of each data point in a robust regression is useful to represent a best fitting line. Consequently, the linear equation with the robust regression method can reflect a more robust data distribution, removing the effects of outliers. In this study, some ranges in the MOD17A2H GPP, when the flux tower GPP was from 4 to 6 g C/m\({}^{2}\)/day, distributed likely outliers on the scatter plot (Figure 4). Underestimation in the low-end ranges of the MOD17A2H GPP compared with the flux tower GPP (e.g., the MOD17A2H GPP showed almost 0 g C/m\({}^{2}\)/day, but the flux tower GPP was more than 4 g C/m\({}^{2}\)/day), might have been caused by diffuse PAR [54]. Diffuse PAR generally provides more photosynthesis activity than that of direct PAR, and the MOD17 GPP algorithm does not account for this effect. On the other hand, higher values in the MODIS than flux the tower GPP could be produced by an overestimation of the MOD17 GPP algorithm. A clear sky condition with excess solar radiation might increase the potential GPP of MODIS, which is induced by incident PAR; however, the real photosynthesis activity would be saturated [55]. If a robust regression method [53] was applied to generate the linear regression for the calibration of the MODIS GPP, the \(R^{2}\) would  
Figure 3: Relationships between the groundwater table (_GWT_) and ecosystem respiration (\(R_{e}\)), in three different types of peatlands; (**a**) undrained forest (_UF_), (**b**) drained forest (_DF_), and (**c**) burned forest (_BF_). The regression equations were applied to estimate \(R_{e}\) by using a satellite-based _GWT_ in this study. be increased around 0.37 (Equation (8), and Figure 4). A function in MATLAB software named the \"_robustdemo_\" was used to perform a robust regression method. The two regressions were applied to the empirical parameter calibration in this study. As a result, the linear fitting function of robust regression (Figure 4) seemed to explain more plots than that of the least squares regression method. The root mean squared error (RMSE) and standard deviation values of the original MODIS GPP data, _Modified GPP\({}_{\text{test}}\)_, and _Modified GPP\({}_{\text{robust}}\)_ were 3.91 \(\pm\) 2.95, 1.47 \(\pm\) 1.59, and 1.33 \(\pm\) 1.40 g C/m\({}^{2}\)/day (\(\pm\) standard deviation), respectively. We concluded the linear fitting equation of robust regression was more suitable for explaining flux tower GPP when using MOD17A2H. Based on the comparison, we modified the MODIS GPP by using the result of the robust regression method (Equation (8));  
\[Modified\ GPP_{\text{\emph{least}}}=1.8584(MOD17A2H\ GPP)-10.4237 \tag{7}\]  
\[Modified\ GPP_{\text{\emph{robust}}}=2.1142(MOD17A2H\ GPP)-12.589 \tag{8}\]  
where _Modified GPP\({}_{\text{\emph{least}}}\)_ and _Modified GPP\({}_{\text{\emph{robust}}}\)_ are the results from modification with the flux tower GPP by using the least squares and the robust regression method, respectively, and _MOD17A2H GPP_ is results of the MODIS GPP product (Figure 4).