Under the trend of climate warming, the high-latitude permafrost in Heilongjiang Province is becoming seriously degraded. The question of how to quantitatively analyze the spatial and temporal trends of multi-year permafrost has become fundamental for current permafrost research. In this study, the temporal and spatial variations of annual mean air temperature (MAAT), annual mean ground temperature (MAGST) and freezing/thawing index based on air and surface temperature data from 34 meteorological stations in Heilongjiang Province from 1971-2019, as well as the variation characteristics of permafrost distribution, were analyzed based on the freezing index model. The results showed that both MAAT and MAGST in Heilongjiang Province tended to decrease with the increase of altitude and latitude. For interannual variation, the MAAT and MAGST warming rates tended to be consistent across Heilongjiang Province, with multi-year variation from -8.64 to 5.60 degrees C and from -6.52 to 7.58 degrees C, respectively. From 1971-2019, the mean annual air freezing index (AFI) and ground surface freezing index (GFI) declined at -5.07 degrees C center dot d center dot a(-1) and -5.04 degrees C center dot d center dot a(-1), respectively, whereas the mean annual air thawing index (ATI) and ground surface thawing index (GTI) were elevated at 7.63 degrees C center dot d center dot a(-1) and 11.89 degrees C center dot d center dot a(-1), respectively. The spatial distribution of the multiyear mean AFI, ATI, GFI and GTI exhibited a latitudinal trend, whereas the effect of altitude in the northern mountainous areas was greater than that of latitude. Permafrost was primarily discovered in the Daxing'an and Xiaoxing'an Mountains in the north, and sporadically in the central mountainous regions. The southern boundary of permafrost shifted nearly 2 degrees to the north from 1970 to 2010s, while the southern boundary of permafrost in Heilongjiang Province was stable at nearly 51 degrees N. The total area of permafrost narrowed from 1.11 x 10(5) km(2) in the 1970s to 6.53 x 10(4) km(2) in the 2010s. The results of this study take on a critical significance for the analysis of the trend of perennial permafrost degradation at high latitudes in Heilongjiang Province and the whole northeastern China, as well as for mapping the distribution of large areas of permafrost using the freezing index model. This study provides a reference for natural cold resource development, ecological protection, climate change and engineering construction and maintenance in permafrost areas.

The soil freeze-thaw phenomenon is one of the most outstanding characteristics of the soil in Heilongjiang Province. Quantitative analysis of the characteristics of changes in key variables of the soil freeze-thaw processes is of great scientific importance for understanding climate change, as well as ecological and hydrological processes. Based on the daily surface temperature and air temperature data in Heilongjiang Province for the past 50 years, the spatial-temporal distribution characteristics of key variables and their correlations with air temperature and latitude in the freeze-thaw process of soil were analyzed using linear regression, the Mann-Kendall test, the local thin disk smooth spline function interpolation method, and correlation analysis; additionally, the spatial-temporal distribution of key variables and the changes in the surface temperature during the freeze-thaw process are discussed under different vegetation types. The results show that there is a trend of delayed freezing and early melting of key variables of the soil freeze-thaw process from north to south. From 1971 to 2019 a, the freezing start date (FSD) was delayed at a rate of 1.66 d/10 a, the freezing end date (FED) advanced at a rate of 3.17 d/10 a, and the freezing days (FD) were shortened at a rate of 4.79 d/10 a; with each 1 degrees C increase in temperature, the FSD was delayed by about 1.6 d, the FED was advanced by about 3 d, and the FD was shortened by about 4.6 d; with each 1 degrees increase in latitude, the FSD was delayed by about 2.6 d, the FED was advanced by about 2.8 d, and the FD was shortened by about 5.6 d. The spatial variation in key variables of the soil freeze-thaw process under the same vegetation cover was closely related to latitude and altitude, where the lower the latitude and altitude, the more obvious the variation trend; among them, the interannual variation trend of key variables of soil freeze-thaw under meadow cover was the most obvious, which varied by 9.65, 16.86, and 26.51 d, respectively. In addition, the trends of ground temperature under different vegetation types were generally consistent, with the longest period of unstable freeze-thaw and the shortest period of stable freeze in coniferous forests, compared to the shortest period of unstable freeze-thaw and the longest period of stable freeze in meadows. The results of the study are important for our understanding of soil freeze-thaw processes and changes in Heilongjiang Province, as well as the evolution of high-latitude permafrost; they also promote further exploration of the impact of soil freeze-thaw on agricultural production and climate change.