# Satellite-Based Estimation of Carbon Dioxide Budget in Tropical Peatland Ecosystems
## Materials and Methods
### Methods  
#### 2.3.1 Gwt Calculations  
The KBDI was originally developed by [PERSON] and Byram in 1968 for a wildfire monitoring system [20]. It explains how the interaction between P (mm) and air temperatures (\(T_{air}\), \({}^{5}\)C) changes and how the evapotranspiration differs in specific vegetation types interpreting in situ measurements from various fire events:  
\[\text{dQ}\ =\ \frac{(800-Q_{0})(0.968\ \exp{(0.0486\ T_{air})}-0.830)d\tau}{1+10. 88\exp{(-0.0441P)}}\times 10^{-3} \tag{1}\]  
where dQ is a drought factor, \(Q_{0}\) is the initial moisture deficiency (mm) at time zero, \(T_{air}\) is air temperature, \(P\) is precipitations, and \(d\tau\) is a time interval (1 day in this study). The index ranges from 0 (moist) to 800 (dry) (unitless) [20]. The range of the index is determined by assuming that fully saturated soil has 8 inches of moisture readily available to vegetation [21]. The original index was derived from field observations. For further application to satellite-based data, a previous study-modified KBDI referring to in situ measurements of the _GWT_[21] and the equations were used in this study:  
\[mKBDI=mKBDI0\times 100p_{day}+\ \frac{0.968(800-mKBDI0)\exp{(0.486 LST_{max})}}{1.00+10.88\exp{(-0.441P_{ann})}} \tag{2}\]  
\[GWT\ (\text{m})\ =\ -0.0045\ \times\ mKBDI \tag{3}\]  
where \(mKBDI\) is the modified KBDI for using satellite-based data; \(mKBDI0\) is an initial value that was calibrated with in situ measurements of the GWT, \(p_{day}\) is a daily precipitation (mm/day), \(LST_{max}\) is maximum daily LST (degrees in Celsius), \(P_{ann}\) is an annual precipitation in each year (mm/year), and the previous study [21] added it to account for spatial variations in regional climatic moisture conditions. The initial value (\(mKBDI0\)) was determined by comparing a consistency of estimated inundation timing (i.e., \(GWT>0\)) and the AMSR-E inundation map. CO\({}_{2}\) emissions are associated with changes in local hydrology, such as fluctuations in groundwater levels. CO\({}_{2}\) emissions from peatlands are highly related to the _GWT_[25], and this study used the _GWT_ as an explanatory variable of \(R_{e}\) (Figure 2). Exponentially regressed \(p_{day}\), \(LST_{max}\), and \(P_{ann}\) are factors that represent the daily water recharge, evaporation, and climatic long-term water recharge, respectively. In this study, the \(T_{air}\) of original KBDI (Equation (1)) was altered by the satellite-based LST in the mKBDI (Equation (2)), since it is straightforward to use satellite-based LST, and the usefulness has been evaluated for substituting with \(T_{air}\), showing high correlation coefficient over 0.80 (r\({}^{2}\)) [48; 49].  
A linear regression function, established by the relationship between the satellite-based daily mKBDI and in situ _GWT_ measurements, was used to estimate the _GWT_ spatial variation (Equation (3)) [21]. The AMSR-E-based LSWC, which represents land surface inundation, was used as supplemental data to generate the _GWT_ map [21]. If an LSWC existed and the modelled _GWT_ showed above 0 m, the initial value of the _GWT_ of the day was set to 0.  
A bilinear method was used to generate the 1 km _GWT_ data from P (10 km) and LST (4 km). The discrepancy of spatial resolutions between the input data sources might cause the presence of mixed information at the sub-pixel scale in complex terrain, e.g., mountainous areas. Notably, most of the target areas in this study are located coastal or lowland regions, and the response of the _GWT_ to the surface moisture condition was relatively rapid and simple once we considered that the KBDI-_GWT_ represents a shallow _GWT_[50].