## 3 Results
### Spatiotemporal Variation of Carbon Budgets in Territorial Space
In Changde, regions classified as level III and above are predominantly found in the flat eastern areas of Wuling District, Dingcheng District, and Lixian County. In Yiyang, carbon emissions are high in the northeastern Ziyang and Heshan Districts, while values are lower in the peripheral mountain areas farther from water bodies. Yueyang's central urban area mainly falls into levels IV and V. Over the past decade, agricultural production bases in Huarong County have shifted from traditional methods to modern processing technologies, gradually increasing carbon emissions and forming large-scale carbon-source farming areas. With the most concentrated carbon sources, Changsha shows a high-value core along both sides of the Xiang River, radiating outward throughout the study period. (2) Carbon sequestration patterns within ecological spaces demonstrate distinct spatiotemporal variations, with peripheral areas in the south, west, and east consistently showing higher values than the central regions. The spatial extent of the carbon sequestration pattern remained essentially unchanged during the study period. Regarding individual cities, Jingzhou has the smallest carbon sequestration area among the five cities, with only a tiny proportion of level III and IV regions distributed along the mountain edges. In Changde, high carbon sequestration values are found in the southwestern and northwestern areas, with a few high-value areas in Lini County. In Yueyang, extensive forest and grassland areas concentrated in the southeast exhibit high carbon sequestration. The Dongting Lake water body in the northwest also exhibits high carbon sequestration. In Yiyang,  
Figure 6: Spatiotemporal evolution patterns of carbon budgets in the Dongting Lake region from 2005 to 2020. (**a**) shows carbon emissions; (**b**) shows carbon sequestration; (**c**) shows carbon budgets. high-value areas are concentrated in southern Anhua County, where forest coverage reaches 76.17%, designating it as a key national ecological function county. In Changsha, carbon sequestration is distributed in patches across the southeastern Xiang Mountain ranges (Dawushan, Luoxiao, and the Wuling ridges) and the northwestern hills (Weishan and Huitang Mountains). (3) The carbon budget distribution across territorial space closely follows the carbon emissions pattern, exhibiting a U-shaped distribution, with low-value areas surrounding high-value areas. At the city level, Jingzhou's level IV carbon budget expanded rapidly southward during the study period, with low-value areas remaining minimal. In Changde, levels III and IV carbon budgets are concentrated in construction areas with dense water networks, with high values emerging between 2015 and 2020. The distribution of low-value areas remained essentially unchanged. Yueyang's levels II to IV carbon budgets expanded rapidly between 2005 and 2010, but growth slowed from 2010 to 2020. Additionally, level III expanded rapidly near the southwestern water bodies. In Yiyang, high-value areas of level IV and above exhibited limited expansion, while level III zones spread outward from government centers. In Changsha, levels III and above of the carbon budget gradually decrease outward from the government center. The Xiang River waterfront remained the high-value core during the study period, gradually expanding into the inland suburbs. In summary, the spatiotemporal dynamics of carbon emissions, sequestration, and budgets indicate a pronounced imbalance. The ipheral forest areas' high ecological carbon sequestration capacity has alleviated overall carbon budget saturation. Conversely, carbon emissions from active land development in water-adjacent areas directly threaten water body stability, intensifying carbon budget pressures in the five cities' northern lakeside plains and waterfront government centers.