The influencing factors of rural residential areas have always been a key research direction in addressing rural problems in China. By introducing a spatial regression model combined with Kernel Density Estimation and Buffer Analysis, this study made a comparative study on the quantification of the influencing factors of rural residential areas in 2009, 2012, and 2015 in Lishan Township, Hubei Province, China. The results showed that the elevation and slope of Lishan Township have always played a decisive role in the distribution of rural residential areas, that the influence of the water system is abnormal, and that the influence of roads and townships has been strengthened based on the spatial statistical analysis. Then, based on spatial econometric regression analysis, the coefficients of “Topographic indices” (CTI) were 0.666, 0.719, and 0.439 in 2009, 2012, and 2015, respectively. The coefficients of Road (CR) were 0.170, 0.112, and 0.108, respectively. The coefficients of Town (CT) were 0.120, 0.127, and 0.166, respectively. The coefficients of Water system (CWS) were 0.166, 0.124, and 0.173, respectively. With the change of time, the influence of road decreased and the influence of town increased gradually. Furthermore, the influence of the water system and topography showed volatility.

Cultivated land is a basic resource that is related to the sustainable development of the global economy and society. Studying the spatial and temporal distribution of cultivated land and its influential factors at the township scale is an important way to improve its sustainable use. Based on the land use data in 2009 and 2015, this paper comprehensively uses kernel density estimation, spatial autocorrelation analysis, and the spatial autoregressive model to analyze the spatial distribution characteristics and influential factors of cultivated land. The results show that in 2009 and 2015, the maximum kernel density of cultivated land in Lishan Town was 31/km² and 38/km², respectively, and there is an increasing tendency for it in the future. The global spatial autocorrelation Moran’s I of the proportion of cultivated land area in the administrative villages of Lishan Town in 2009 and 2015 was 0.5251 and 0.3970, respectively. Cultivated land has significant spatial self-positive correlation agglomeration characteristics in spatial distribution. Based on spatial error model (SEM) analysis, the regression coefficients of the village were 0.236 and 0.196 in 2009 and 2015, respectively. The regression coefficients of the road were 0.632 and 0.630, respectively. The regression coefficients of the water system were 0.481 and 0.290, respectively. The regression coefficients of the topographic position index were −0.817 and −0.672, respectively. By comparing 2015 with 2009, the regression coefficients of each influential factor have been reduced to varying degrees.

Optimizing agricultural carbon compensation zoning is crucial for establishing robust mechanisms in agricultural carbon compensation management, with significant implications for achieving national “dual carbon” strategic objectives. This study employs K-means and the three-dimensional magic cube approach to construct a novel evaluation index system for comprehensive carbon compensation zoning. By combining spatial land-use zoning, we delineate carbon compensation zones in Guangshui City, Hubei Province, and analyze the spatiotemporal variations of agricultural carbon balance, proposing optimization strategies. The results show that (1) from 2000 to 2021, agricultural carbon emissions and absorption exhibit a trend of increasing followed by decreasing, with spatial patterns of “higher in the northwest, lower in the southeast” and “higher in the southwest, lower in the northeast”; (2) the Gini coefficient of agricultural carbon emissions averages at 0.24, with economic contribution coefficients and ecological carrying coefficients ranging from 0.04–16.1 and 0.39–1.99, respectively, from 2000 to 2021; and (3) in 2021, Guangshui City comprises seven payment zones, four balance zones, and six compensation zones, ultimately forming eight optimized agricultural carbon compensation zones in alignment with regional agricultural carbon balance objectives. This study provides theoretical references for enhancing county-level agricultural carbon comprehensive compensation management mechanisms.