The annual average ground temperature (MAGT) observation data at the depth of annual temperature variation in the permafrost regions of the Northern Hemisphere are based on the Global Permafrost Network (GTN-P) database (gtnpdatabase. org). Additionally, we have expanded the GTN-P data and added more MAGT observation data from relevant literature, including some MAGT>; 0 ℃ observation data, these observation data are key factors that help us predict the ground thermal state in future scenarios. For other related data, please refer to Jin et al., 2024

    The machine learning models used include logistic regression (LR), random forest (RF), and LightGBM (LGB). Considering that using a single method may lead to overfitting in the simulation, we used the set and average results of the three methods mentioned above when simulating MAGT. Using TDD, FDD, leaf area index, precipitation, snow cover, solar radiation, soil moisture content, soil organic matter, and gravel volume content as input variables, corresponding to station observations, the model was established with 90% of the data as the test set and 10% of the data as the validation set to evaluate the accuracy of the model. In order to reduce the uncertainty of a single run, this study ran the three machine learning models 100 times and used their ensemble average results to simulate the distribution changes of annual average ground temperature in permafrost areas at different periods by combining environmental variables at each period.

    The RMSE of the output result of the ensemble average mode is 1.01 ℃, MAE is 0.69 ℃, and R is 0.89.