## 2 Materials and Methods
### Methodology
#### 2.3.3 Total Accounting of Carbon Budgets in Territorial Space  
The calculation of territorial carbon budgets depends on the difference between carbon emissions and carbon sequestration. This study uses direct and indirect estimation methods from the IPCC inventory to evaluate carbon emissions and sequestration across production-living-ecological spaces in the Dongting Lake region. Based on the IPCC inventory, the study incorporates multi-temporal and multi-source remote sensing data and statistical yearbooks to ensure accuracy and timeliness. To improve scientific rigor, carbon emission factors and sequestration coefficients are derived from authoritative literature and model data, with adaptive adjustments for the ecological characteristics of lake-dense regions. A systematic analysis of carbon source and sink characteristics across territorial space types ensures a comprehensive and accurate carbon budget calculation. The specific models for carbon emissions and sequestration are outlined below:  
(1) Territorial space carbon emission estimation model  
Carbon emissions in territorial space primarily focus on carbon sources in production and living spaces. This study considers farmland carbon emissions as non-construction land carbon emissions and fossil energy consumption emissions as construction land carbon emissions. Farmland carbon emissions are estimated using the direct estimation method. Based on [PERSON]'s research [29], the carbon emission coefficient is set at 0.4970 tC/hm\({}^{2}\)-a. Fossil energy consumption emissions are estimated using the indirect estimation method, considering the consumption of the top 10 fossil fuels [30; 31]. Carbon content, average lower heating values, and carbon oxidation rates are based on the IPCC [32] guidelines and the General Principles for Calculating Comprehensive Energy Consumption (Table 2). The formulas are as follows:  
\[C_{e}=C_{a}+C_{fue} \tag{3}\]  
\[C_{a}=5\times\gamma \tag{4}\]  
\[C_{fue}=\sum_{n=1}^{10}E_{n}\times b_{n}\times\beta_{n} \tag{5}\]  
where \(C_{e}\) is the total carbon emissions (t); \(C_{a}\) is the carbon emissions from farmland (t); \(C_{fue}\) is the carbon emissions from fossil energy consumption (t); \(S\) is the farmland area (hm\({}^{2}\)); \(\gamma\) is the farmland carbon emission coefficient (tC/hm\({}^{2}\)-a); \(E_{n}\) is the consumption of fossil fuel type \(n\) (t); \(b_{n}\) is the conversion factor for fuel type \(n\) to standard coal (tce/t or tce/10\({}^{3}\)-m\({}^{3}\)); \(\beta_{n}\) is the carbon emission coefficient for fuel type \(n\) (tC/tce).  
(2) Territorial space carbon sequestration estimation model  
Carbon sequestration in territorial space primarily focuses on carbon sinks in ecological spaces. This study employs the direct estimation method to calculate total carbon  
\begin{table}
\begin{tabular}{c c} \hline
**Energy Type** & **Carbon Emission Factor (tC/tce-a)** \\ \hline Raw coal & 0.5127 \\ Washed coal & 0.6292 \\ Coke & 0.7801 \\ Natural gas & 0.5390 \\ Crude oil & 0.8237 \\ Gasoline & 0.7977 \\ Kerosene & 0.8273 \\ Diesel & 0.8443 \\ Fuel oil & 0.8647 \\ Liquefied petroleum gas & 0.8458 \\ \hline \end{tabular}
\end{table}
Table 2: Carbon emission coefficients for major energy types in the Dongting Lake region.  
sequestration by summing the contributions of forests, grasslands, water bodies, and unused land within ecological spaces. The carbon sequestration coefficients are based on existing research and are detailed in Table 3[29]. The formula for estimating total carbon sequestration is as follows:  
\[C_{s}=\sum_{m=1}e_{m}=\sum_{m=1}T_{m}\times\delta_{m} \tag{6}\]  
where \(C_{s}\) is the total carbon sequestration of territorial space (t); \(e_{m}\) is the carbon sequestration of land type \(m\) (t); \(T_{m}\) is the area of land type \(m\) functioning as a carbon sink (hm\({}^{2}\)); \(\delta_{m}\) is the carbon sequestration coefficient of land type \(m\) (tC/hm\({}^{2}\)).