## 3 Results
### Spatiotemporal Variation of Carbon Budgets in Territorial Space  
3.2.1. Spatiotemporal Evolution of Carbon Budgets in Territorial Space  
Building on the analysis of territorial space evolution mechanisms, this section examines the spatiotemporal trends of carbon emissions, carbon sequestration, and carbon budgets. Figure 5 presents the numerical trends for the study area and individual cities. Overall, the region's territorial space carbon budgets exhibited an increasing trend, though the growth slowed between 2015 and 2020. Detailed results show the following:  
(1) Regarding land-use function categories, carbon emissions from production and living spaces increased between 2005 and 2020, with the highest growth occurring from 2005 to 2010 at an annual rate of 3.4%. Although the growth rate slowed to 0.69% between 2010 and 2015, total emissions increased by 2.78 \(\times\) 10\({}^{6}\) tC during this period. Carbon sequestration in ecological spaces declined annually, decreasing from 7.68 \(\times\) 10\({}^{6}\) tC in 2005 to 7.58 \(\times\) 10\({}^{6}\) tC in 2020, with an annual reduction rate of -0.19% between 2015 and 2020. The carbon budget trend followed carbon emissions, exhibiting a strong total growth rate of 19.13% between 2005 and 2010. However, from 2015 to 2020, the carbon budget growth rate slowed to 0.10%, indicating a converging trend. (2) Regarding regional differences, Jingzhou's territorial space carbon budget has increased. Between 2015 and 2020, the most significant changes occurred, with carbon emissions and sequestration rates of 9.22% and -1.77%, respectively. Changde's territorial space carbon budget exhibited an overall declining yet fluctuating trend. Carbon emissions varied, with rates of 12.52%, -5.74%, and 1.01% across different periods, while carbon sequestration remained relatively stable. Yueyang contributed the largest share of carbon budgets in the Dongting Lake region, accounting for 53.43%, 42.20%, 56.99%, and 56.59% between 2005 and 2020. The carbon budgets in Yiyang and Changsha peaked in 2010 before declining from 2.23 \(\times\) 10\({}^{7}\) tC to 1.24 \(\times\) 10\({}^{7}\) tC. Notably, most cities experienced significant growth between 2005 and 2010, but growth rates approached zero after 2010. This trend reflects the initial emphasis on economic growth, which drove substantial carbon emissions through increased energy consumption. This shift aligns with the transition in development priorities since 2010 from \"extensive development\" to \"intensive and efficient utilization\". However, the ecological carbon sequestration capacity of the Dongting Lake region remains weak relative to socioeconomic carbon emissions. The high baseline of net carbon emissions poses significant challenges for transitioning to a low-carbon and green economy. Carbon emissions, sequestration, and budgets across the five cities were analyzed through the ArcGIS map visualization approach, categorizing the data into five levels (I-V) from minimal to maximal. Figure 6 illustrates the spatial patterns and temporal trends of carbon budgets during the study period. The results show the following:  
(1) Carbon emissions from production and living spaces exhibit a radial \"core-periphery\" pattern, with elevated values concentrated in plains near water bodies, decreasing as distance from water sources increases. This pattern is related to clustering urban construction land and farmland along water bodies. The carbon emissions pattern was influenced by economic development, with peak values increasing year by year during the study period. Regarding individual cities, Jingzhou's carbon sources cover a broad area, with level V regions expanding southward yearly. This trend is intricately linked to  
Figure 5: Numerical trends of carbon budgets in the Dongting Lake region from 2005 to 2020. (**a**) shows the overall carbon budget trend; (**b**) shows the city-level carbon budget trends; (**c**) shows the carbon budget change rates. the southward relocation of Jingzhou's economic hub across the river.