*4.3. Mapping and Trajectory Analysis of Land Use Changes around Typical Rural Settlement Types*

The study introduces a geographic information mapping trajectory model to analyze the spatial and temporal trajectories of land use change around typical settlements in the LangXi trough valley (Figure 6). From 1964 to 1999, the land use around the trough dam of ES showed an expansion of steep-slope arable land, flat-dam arable land, grassland, and rural residential area, and a contraction of forestland and low-cover grassland in the time-series change characteristics. The trajectory mapping of land use change is as follows: forestland→steep-slope arable land, forestland→flat dam arable land, forestland→irrigated grassland, gently sloping arable land→irrigated grassland, low-cover grassland→steepslope arable land, low-cover grassland→rural residential areas. The land use at the trough valley top and the trough slope of the AS is mainly steep-slope arable land, flat dam arable land, irrigated grassland expansion, and forestland shrinkage. The trajectory of land use change around the settlement is mainly forestland→steep-slope arable land, forest land→flat dam arable land, forest land→gently sloping arable land. BS at the top of the trough valley is dominated by the expansion of steep-slope arable land, flat dam arable land, grassland, and rural residential area, and the contraction of forestland and low-cover grassland. The trajectory mapping of land use change is mainly: forestland→steep-slope arable land, forestland→flat dam arable land, forestland→irrigated grassland; gently sloping arable land→irrigated grassland, low cover grassland→steep-slope arable land, low cover grassland→rural residential area. The trough slope of the DS is mainly dominated by the expansion of arable land and the shrinkage of forestland grassland, and the land use change trajectory is mainly: forestland→steep-slope arable land, forestland→flat dam arable land, forestland→irrigated grassland, steep-slope arable land→gently sloping arable land; the intensity of arable land use is higher in the trough slope in this period.

From 2004 to 2014, the land use types of the ES were mainly forestland, abandoned land, grassland expansion, steep slope arable land, irrigated grassland, flat-dam arable land, and gently sloping arable land contraction. The land use change trajectory is mainly steepslope arable land→abandoned land, gentle slope arable land→abandoned land, flat dam arable land→abandoned land, low cover grassland, and irrigated grassland→abandoned land. The land use types of the AS are mainly an expansion of grassland and abandoned land, and contraction of forestland, irrigation grass, gently sloping arable land, and steep sloping arable land, and the trajectory mapping of the surrounding land use changes are mainly forestland→steep sloping arable land, forestland→flat dammed arable land, and forestland→gently slope arable land. The types of land use around the BS are mainly gently sloping arable land, abandoned land, irrigated grassland, low cover grassland, high cover grassland, rural road expansion, steep-slope arable land, forest land, and flat dam arable land contraction. The trajectory of land use change is as follows: steep-slope arable land to fallow land, steep-slope arable land to grassland, forest land to irrigated grassland, forest land to gently sloping arable land, forest land→irrigated grassland, forest land→country

roads, gently sloping arable land→abandoned land. The land use types around the DS are mainly arable land, grassland expansion, and forest land contraction, and the land use change trajectory mainly shows forestland→arable land, forest land→irrigated grass, forestland→high cover grass, and irrigated grass→high cover grass.

**Figure 6.** *Cont*.

**Figure 6.** Mapping of land use transfer trajectories in typical rural settlement types.

From 2014 to 2021, the land use types of the ES were forestland, flat dam arable land, rural road expansion, abandoned land, and steep-slope arable land, and slow slope arable land contraction was dominant, and the land use change trajectory around the settlement

is mainly: abandoned land→flat dam arable land, irrigated grass→forestland, low cover grass→forestland, abandoned land→forestland. The AS mainly focuses on expanding forestland, abandoned land and grassland, flat dam arable land, gently sloping arable land, and steep sloping arable land shrink. The BS is dominated by the expansion of forest land, rural roads, tea gardens, flat dam arable land, and the shrinkage of arable land and grassland. The land use types of the DS are mainly forestland, abandoned land, grassland expansion, steep-slope arable land, irrigated grassland, flat dam arable land, and slow slope arable land contraction. The trajectory of land use change is mainly steep-slope arable land→abandoned land, gentle slope arable land→abandoned land, flat dam arable land→abandoned land, low cover grassland, and irrigated grassland→abandoned land; the overall trend of land types around the settlement showed shrinkage at this stage.

#### *4.4. Coupled Analysis of Land Use Evolution around Typical Rural Settlement Types*

The evolution of land use around different settlement types in the karst trough valley has a mutual influence relationship, and different settlement types in the trough valley were divided into three time periods according to the land use change patterns around different settlements: 1964–2004, 2004–2014, and after 2014. There are dynamic evolutionary coupling processes and dynamic coupling strengths between different settlement types and their surrounding land use changes in the three time periods (Figure 7). Among them, the ES at the bottom of the trough, such as ZengJia, SanCun, Chuangyan, and the surrounding land use coupling process, show a complete coupling situation. The settlement area showed a local expansion from 1964 to 2004, a balanced expansion from 2004 to 2014, and a significant core expansion after 2014. The land use change around the settlement showed different trends with the settlement expansion, the land use area of steep-slope arable land and gentle slope arable land expanded, and the flat dam arable land decreased. The clusters and their surrounding land use showed an increasing linear trend in coupling intensity.

**Figure 7.** Schematic diagram of the coupling evolution of different settlement types and land use.

Regarding the BS of HeXi and GaoZhai in 1964–2021, the coupling process between the settlement and its surrounding land use showed a remote continuous coupling state, and the core of the settlement and the land use around the settlement its coupling intensity showed an inverse linear growth trend. The AS and the surrounding land use changed in this period, and the coupling process of surrounding land use with the settlement as the core showed a local coupling, which exhibited a local expansion from 1964 to 2004. From 2004 to 2014, it showed local shrinkage; after 2014, it showed rapid shrinkage. The land use

changes around shrinking settlements showed a gradual decrease in cultivated land on gentle slopes, steep slopes, and flat dams; minor changes in the surrounding forest land; and an increase in the irrigation and grassland areas, and overall, the coupling intensity of shrinking settlements and their surrounding land use changes showed a trend of increasing first and then decreasing. The area of DS showed local expansion from 1964 to 2004; balanced shrinkage from 2004 to 2014; and after 2014, the settlement center transitioned into a significant extinction phenomenon, the settlement and the surrounding land use showed a fundamental coupling disorder, and the coupling intensity of the settlement core and the surrounding land use of the settlement decreased linearly.

#### **5. Discussion**
