## 4 Discussion
### Spatiotemporal Variation Patterns of Territorial Space Carbon Budgets in Lake-Intensive Regions  
Lake-intensive regions are pivotal for advancing regional green and low-carbon transitions. Clarifying the mechanisms of regional carbon budget imbalances is the first step in formulating carbon balance regulation strategies. Previous studies have highlighted diverse carbon budget trends across regions in China [40; 41]. Unlike prior studies, this study introduces a novel territorial space carbon source-sink measurement system integrating production-living-ecological functions. Building on this, the study employs ESTDA models to examine the variation and clustering effects of territorial space carbon budgets. This study fills gaps in research subject selection and accounting methodologies by uncovering the spatiotemporal evolution of carbon budgets in lake-intensive regions.  
The spatiotemporal evolution of carbon budgets reveals an annual increase in the territorial space carbon budget within the Dongting Lake region, though the growth rate has slowed from 19.13% to 0.10%. Despite this deceleration, the region remains short of achieving its \"carbon neutrality\" target. The recent plateau in carbon budget growth may be attributed to policies such as converting farmland to forests and lakes. As a key grain production base, the Dongting Lake region's agricultural production space has experienced significant spatial shifts in recent years. Converting farmland to ecological land has partially alleviated the region's carbon deficit. Spatially, variations in the carbon budget arise from differences in resource endowments and economic development among cities [42]. High-carbon budget areas are typically plains with well-developed water networks and higher economic development. Carbon sources from production and living spaces are primarily on the lake's outskirts in Yueyang and along both banks of the Xiangjiang River in Changsha. Carbon sinks in ecological spaces are found in forested areas, vegetation cover, and the main lake body, including western Changde, southern Yiyang, and western and eastern Yueyang. These high carbon source-sink areas shape the Dongting Lake region's carbon budget pattern and are critical for achieving China's future carbon balance goals. This finding aligns with [PERSON]'s research [43].  
Using ESTDA, this study uncovers the spatiotemporal variation and clustering effects of carbon budgets in the Dongting Lake region. SDE analysis highlights how the orientation of water systems and the layout of construction land in the Dongting Lake basin influence carbon budget patterns at both the regional and city levels. The water-adjacent ecological advantages of the Dongting Lake region spur economic activities, leading to a spatial divergence in carbon budgets with water bodies as the central axis, radiating outward toward forested areas. For example, Changsha's carbon budget center gradually shifts toward the central Xiangjiang River. The declining SDE flattening ratio reflects the convergence of carbon budgets from the periphery to the riverbanks. Jingzhou shows a similar trend to Changsha, with the carbon budget pattern gradually converging toward the Songzi River. At the spatiotemporal clustering level, H-H clusters concentrate in the government-seat areas of each city. L-L clusters occur in peripheral forest areas. H-L and L-H clusters are scattered on the outskirts of L-L and H-H areas, respectively, and are easily assimilated by them. Notably, H-H clusters show distinctly different development trends across government-seat areas. This suggests that although carbon budgets cluster clearly in government-seat areas, development trends are shaped by local economic structures, policies, and regional cooperation. Therefore, lake regions should adopt location-specific, differentiated, and precise carbon reduction and sequestration management strategies [44; 45].