Landscape ecological integrity is a regionalized variability and has heterogeneity. Its heterogeneity varies over time and is driven by different factors in various years. In this paper, Geostatistical methods were used for isotropic variation and anisotropic variation of landscape ecological integrity (LEI) in Yulin using GS +9.0 software. Under isotropic conditions, the spatial heterogeneity caused by random factors accounted for 7.30%, 45%, 43.5% and 30.7% of the total in 2000, 2005, 2010 and 2015 respectively, mainly within the range of 10km. In these four years, the spatial heterogeneity caused by spatial autocorrelation factors accounted for 92.7%, 55%, 56.5% and 69.3% respectively, mainly between 10 km and 54.6 km, 153.6 km, 181.8 km and 119.4 km. Spatial heterogeneity was generated by spatial autocorrelation factors principally in recent years in Yulin. The ratio of nugget value to base value of LEI varied from 0.073 to 0.45, reflecting a moderate to strong spatial correlation of LEI. The simpler the spatial pattern of landscape ecological integrity, the stronger the spatial dependence. In anisotropic situations, the spatially structured variance dominated in ratio of 71.84%, 70.00%, 71.85% and 85.80% of the total independently in 2000, 2005, 2010 and 2015. The spatial pattern of Landscape ecological integrity is a synthetic expression of landscape characteristics influenced by random factors and structural factors. Geostatistics can be well used to express the spatial heterogeneity of landscape ecological integrity.

Inexpressible Island is an ice-free island located in Antarctica, characterized by a distribution of numerous thermokarst ponds, which serve as warning indicators of permafrost degradation, and their evolution can indirectly reveal local climate change. In this study, we explored changes in thermokarst ponds on Inexpressible Island over the period 1987–2023 using Landsat series dataset and Sentinel-2 data. Over the study period, the total pond area exhibited an 11.3% increase, with the lowest value recorded in 1990 and the highest in 2019. Cumulatively, 54 ponds were monitored during the period with their count rising from 37 in 1987 to 39 in 2023. Ponds were classified as either persistent or transient, the latter not continuously existing throughout the study period. Among the 22 persistent ponds, an overall increasing trend in their total area was observed, with most experiencing area augmentation. However, a few persistent ponds, situated in the higher elevations of the northwestern part of the island, exhibited a slight shrinkage. The number of transient ponds displayed considerable fluctuations, reaching its peak at 30 in 2018 and 2019, contrasting with only 5 transient ponds recorded in 1999. The occurrences of transient lake ponds varied, ranging from 2 to a maximum of 26. This study highlights the dominant influence of temperature on the monthly, seasonal, and long-term dynamics of these ponds, while precipitation significantly affected the short-term variations. Additionally, the melting of ice wedges and the subsequent seepage into thawed permafrost formations were identified as potential processes that may affect pond persistence and drainage.