# Effects of Cyclical Climate Change on Water Temperature Characteristics of Permafrost Slopes
## 3 Results and Discussion
### Freeze-Thaw Water Temperature Characteristics  
As shown in Figure 9, the freeze-thaw process of seasonal frozen soil slopes exhibits distinct stages and asymmetric rates. Taking one cycle as an example, the freezing process (dashed line) begins at 0 days and reaches a maximum depth of 0.98 m by day 215 of the following year. During the early stage, the freezing depth increases rapidly, indicating that the temperature drops quickly and the surface temperature falls below the freezing point, allowing cooling energy to transfer to the ground. In the later stages, the freezing depth growth slows, which is attributed to the reduced temperature difference between the surface and the deeper soil as freezing deepens, thus decreasing the efficiency of heat transfer. During the thawing process, the upper surface layer melts rapidly in the early stage, indicating a significant rise in air temperature and a faster melting rate. In the later stage, the lower soil layer's melting depth increases more slowly, likely due to a reduction in surface heat input or slower heat diffusion to deeper soil layers. Unlike permafrost, where freeze-thaw cycles are mainly influenced by surface temperature, seasonal frozen soil is affected by both surface temperature and underground heat flux. The process exhibits characteristics of unidirectional freezing (i.e., shallow soil begins to freeze from the surface downward) and bidirectional thawing (i.e., thawing occurs from the surface downward and from the bottom of the frozen layer upward), with the melting rate significantly higher than the freezing rate. During the thawing process, the primary thawing occurs in the shallow soil layers. Overall, the freezing process lasts approximately 1.35 times longer than the thawing process, and the thawing rate is notably higher than the freezing rate. This reflects the characteristics of unidirectional freezing and bidirectional thawing in seasonal frozen soil, with thawing being more sensitive to changes in surface temperature. Figure 10 illustrates the temperature variation with depth at different freeze-thaw stages of the slope. During the freeze-thaw process, the temperature of the slope changes significantly. In the early freezing stage, the surface temperature rapidly drops to near 0 \({}^{\circ}\)C, while the deeper layers remain relatively stable, exhibiting a clear temperature gradient. In the stable freezing stage, the environment continues to cool, with the surface temperature  
Figure 8: The moisture content profiles at the center of the slope in different freeze–thaw stages. dropping to a stable negative value. The deeper layers are also affected, and the gradient diminishes. In the thawing stage, the surface layer quickly rises to positive temperatures, while the deeper layers change more slowly and remain below zero, leading to a reduced overall temperature gradient. The temperature changes at different locations are influenced by topography, thermal conductivity, and ambient temperature, with the shallow layers being more sensitive to changes and the deep layers exhibiting a delayed response and smaller amplitude. In the early freezing stage, the surface loses heat due to contact with cold air, creating a temperature gradient within the slope, with heat transferring from the deeper to the shallower layers. Although soil moisture freezes and releases latent heat, the rapid cooling prevents uniform heat diffusion. Additionally, the formation of ice increases the soil's thermal conductivity, causing the temperature to drop rapidly with depth, especially in the shallow layers. During the stable freezing stage, the heat loss and the latent heat released during water freezing reach a balance, and the thermal conductivity of the ice-soil system stabilizes, leading to a reduced temperature variation. In the thawing stage, the warming of the surface causes soil ice to melt and absorb heat, with heat transferring to deeper  
Figure 10: Temperature variation with depth at different freeze-thaw stages of slope.