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<p>We applied a machine learning model (MLM) and an empirical model (EM) based on the improved Stefan formula to study the freezing depth of seasonally frozen ground (SFG) from the northern to southwestern part of the Qinghai-Tibetan Plateau (QTP). The rationality and accuracy of the predicted freezing depths from the two models were compared, and their performance in identifying the maximum freezing depth (MFD) of SFG. Through a comparison of four MLMs, we found that the support vector machine regression (SVMR) model was more suitable for MFD simulation than the random forest (RF), k-nearest neighbor (KNN), and generalized linear regression (GLR) models. Having identified SVMR as the most suitable model, we then systematically compared its performance against the EM. In the comparison of the 50-year average maximum freezing depth (AMFD) prediction with the observed value, the coefficient of determination (<i>R</i><sup>2</sup>) of the EM based on Stefan improved formula decreased by 3.7%, while the root mean square error (RMSE), mean absolute error (MAE) and mean absolute percentage error (MAPE) increased by 5.43, 3.87 and 0.03, respectively, compared with the prediction performance of the SVMR model. From the statistical indicators, it can be seen that the freezing depth prediction based on the MLM performs well. From the regional performance of the MFD, it can be seen that the distribution area of each freezing depth line predicted by the EM is more extensive. The depth lines predicted by the MLM are close to the periphery of the permafrost area and extend to the southwest, and the depth lines are parallel to each other, and the closer to the boundary of the permafrost area, the greater the depth value. The paper proposes two methods for predicting freezing depth, and research on freezing depth not only reveals the impact of climate change on SFG but also provides a scientific basis for regional agroecological conservation. Changes in freezing depth disturb the soil environment, which directly affects agricultural production, ecological stability, and regional sustainable development. Therefore, accurate prediction of freezing depth is essential for developing climate change adaptation strategies.</p>

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Comparison of the seasonal freezing depth from the northern to southwestern surrounding regions of the Qinghai-Tibetan plateau over the past 50 years (1975–2024)

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  • 出版模式：

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  • 发表日期：

    2026年7月10日

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  • Shuo Wang,
  • Aihemaitijiang Tuerhong,
  • Chenyang Peng,
  • Zuojun Ning

摘要

We applied a machine learning model (MLM) and an empirical model (EM) based on the improved Stefan formula to study the freezing depth of seasonally frozen ground (SFG) from the northern to southwestern part of the Qinghai-Tibetan Plateau (QTP). The rationality and accuracy of the predicted freezing depths from the two models were compared, and their performance in identifying the maximum freezing depth (MFD) of SFG. Through a comparison of four MLMs, we found that the support vector machine regression (SVMR) model was more suitable for MFD simulation than the random forest (RF), k-nearest neighbor (KNN), and generalized linear regression (GLR) models. Having identified SVMR as the most suitable model, we then systematically compared its performance against the EM. In the comparison of the 50-year average maximum freezing depth (AMFD) prediction with the observed value, the coefficient of determination (R2) of the EM based on Stefan improved formula decreased by 3.7%, while the root mean square error (RMSE), mean absolute error (MAE) and mean absolute percentage error (MAPE) increased by 5.43, 3.87 and 0.03, respectively, compared with the prediction performance of the SVMR model. From the statistical indicators, it can be seen that the freezing depth prediction based on the MLM performs well. From the regional performance of the MFD, it can be seen that the distribution area of each freezing depth line predicted by the EM is more extensive. The depth lines predicted by the MLM are close to the periphery of the permafrost area and extend to the southwest, and the depth lines are parallel to each other, and the closer to the boundary of the permafrost area, the greater the depth value. The paper proposes two methods for predicting freezing depth, and research on freezing depth not only reveals the impact of climate change on SFG but also provides a scientific basis for regional agroecological conservation. Changes in freezing depth disturb the soil environment, which directly affects agricultural production, ecological stability, and regional sustainable development. Therefore, accurate prediction of freezing depth is essential for developing climate change adaptation strategies.