## 1 Introduction  
The atmospheric CO\({}_{2}\) concentration has risen sharply due to intensive industrial activities, making climate warming a critical global challenge [1]. To control CO\({}_{2}\) emissions,China aims to peak carbon emissions by 2030 and achieve carbon neutrality by 2060 [2]. Lake-intensive regions are areas where urban development is closely linked to rivers, lakes, and other water bodies. These regions show a more potent synergy and trade-off between human carbon sources and ecosystem carbon sinks than other areas [3]. In recent years, benefiting from developed water network ecosystems and convenient waterway transportation, lake-intensive regions have experienced rapid socioeconomic growth [4]. However, this development has intensified carbon reduction pressures in these watershed regions. At the same time, production and urban expansion have eroded blue-green ecological barriers, reducing the carbon sequestration potential of forests, wetlands, and aquatic ecosystems. Therefore, the conflict between socioeconomic carbon emissions and environmental carbon sequestration in territorial space intensifies, making the balance between protection and development increasingly prominent [5]. Researchers worldwide have extensively studied land-use carbon emissions, analyzing spatiotemporal patterns and underlying drivers to address imbalanced carbon dynamics in territorial spaces [6; 7; 8; 9]. Developing a carbon budget assessment framework for lake-intensive regions is the first step in identifying carbon imbalance risks. Key land-use carbon emissions accounting methods include model simulation, plot inventory, and emission coefficient approaches. Model simulation results are susceptible to parameter selection, making this method suitable for large-scale carbon emissions studies [10]. The plot inventory method estimates carbon emissions by measuring carbon density in vegetation and soil across land types [11]. Although effective, this method is resource-intensive, making it more suitable for small-scale analyses. The emission coefficient method estimates carbon emissions using land-use remote sensing and human activity data [12]. Due to its simplicity and data accessibility, this method is widely used. For instance, [PERSON] applied a carbon source-sink coupling model, integrating diverse datasets, to calculate land-use carbon budgets across different scales in the Pearl River Basin [13]. [PERSON] analyzed the carbon source-sink balance in northwest China's Bosten Lake region using a combined top-down and bottom-up approach, identifying areas with heightened carbon emission risks from land-use changes [14]. These diverse methodologies provide a quantitative foundation for examining carbon budget dynamics in lake-dense regions from multiple perspectives. Exploring the evolution of carbon budgets in territorial space is crucial for lake-intensive regions to achieve carbon reduction and sequestration goals. Earlier studies on carbon budget evolution primarily analyzed trends in emissions and sequestration, proposing macro-level carbon balance strategies. For instance, [PERSON] examined land-use carbon emission trends in Jiangxi Province, China, by integrating remote sensing data with statistical yearbook information [15]. Scholars have recently employed exploratory spatial data analysis (ESTDA) and regression models to investigate the mechanisms underlying carbon budget imbalances. For instance, [PERSON] combined ESTDA with vector autoregression models to reveal significant spatial variations in carbon emissions across the Guangdong-Hong Kong-Macao Greater Bay Area [16]. Similarly, [PERSON] applied kernel density estimation and spatial autocorrelation methods to assess the spatiotemporal characteristics of carbon emission efficiency along the Yangtze River Economic Belt [17]. These visualization and analytical techniques advancements have significantly enhanced the understanding of spatiotemporal evolution trends in carbon budgets within lake-intensive regions.