## 3 Methods
### Remote Sensing-Based Ecosystem Respiration Model  
Ecosystem respiration (R\({}_{\text{eco}}\)) comprises two main components: plant respiration (R\({}_{\text{GPP}}\)) and the respiration of organic matter and soil microorganisms within the ecosystem (R\({}_{\text{EOM}}\)), which includes contributions from litter and soil organic matter. This relationship can be expressed as:  
\[\text{R}_{\text{eco}}=\text{R}_{\text{GPP}}+\text{R}_{\text{EOM}}, \tag{8}\]  
According to [PERSON] et al. [44], R\({}_{\text{GPP}}\) is influenced by plant growth conditions and water availability, which are primarily represented by _EVI_ and _LSWI_. The relationship between R\({}_{\text{GPP}}\), the EVI influence function (\(EVI_{s}\)), and the water influence function on the maximum light use efficiency (\(W_{s}\)) can be expressed as:  
\[\text{R}_{\text{GPP}}=\alpha\times\text{PC}_{max}\times EVI_{s}\times W_{s}, \tag{9}\]  
In the equation, \(\alpha\) represents a model parameter to be calibrated through fitting. _PC\({}_{max}\)_ denotes the maximum photosynthetic capacity specific to each vegetation type, with its value varying across vegetation categories. _EVI\({}_{s}\)_ captures the variability in photosynthetic capacity among different vegetation types, and the product of _PC\({}_{max}\)_ and _EVI\({}_{s}\)_ reflects the effective photosynthetic capacity of each vegetation type. Finally, \(W_{s}\) quantifies the influence of water availability on the photosynthetic process.  
Where _EVI\({}_{s}\)_ is a function of _EVI_, expressed as:  
\[EVI_{s}=EVI-0.1, \tag{10}\]  
when the _EVI_ approaches 0.1, R\({}_{\text{GPP}}\) converges to 0. In the model proposed by [PERSON] et al. [45], \(W_{s}\) represents a modified form of \(W_{scalar}\), which is determined using the _LSWI_, and can be expressed as:  
\[W_{scalar}=\frac{1+LSWI}{1+LSWI_{max}}, \tag{11}\]  
Since the value of \(W_{scalar}\) depends on _LSWI\({}_{max}\)_, different vegetation types may exhibit similar or identical \(W_{scalar}\) values despite significant variations in actual canopy water content. Thus, \(W_{scalar}\) effectively captures the temporal dynamics and spatial patterns of moisture conditions. By setting _LSWI\({}_{max}\)_ to 1, spatial comparisons are simplified. Consequently, the equation for \(W_{scalar}\) is adjusted to \(W_{s}\), expressed as:  
\[W_{s}=\frac{1+LSWI}{2}, \tag{12}\]  
The relationship between R\({}_{\text{EOM}}\) and _LST_ can be described using the [PERSON] [46] equation, expressed as:\[\mathrm{R_{EOM}}=R_{ref}\times exp\left[E_{0}\left(\frac{1}{T_{ref}-T_{0}}-\frac{1 }{LST-T_{0}}\right)\right], \tag{13}\]  
In the equation, \(R_{ref}\) represents the respiration rate of ecosystem organic matter and soil microorganisms at the reference temperature \(T_{ref}\), \(E_{0}\) is a parameter associated with the activation energy; \(T_{0}\) is the temperature at which \(\mathrm{R_{EOM}}\) becomes 0; and \(LST\) refers to the land surface temperature. Typically, the reference temperature \(T_{ref}\) is set to 10 \({}^{\circ}\)C, and \(T_{0}\) is fixed at \(-\)46.02 \({}^{\circ}\)C. Accordingly, the remote sensing-based ecosystem respiration model can be expressed as:  
\[\mathrm{R_{eco}}=\alpha PC_{max}EVI_{s}W_{s}+R_{ref}\times exp\left[E_{0} \left(\frac{1}{T_{ref}-T_{0}}-\frac{1}{LST-T_{0}}\right)\right], \tag{14}\]