Abstract
Permafrost, being an important component of the cryosphere, is sensitive to climate change. Therefore, it is necessary to investigate the change of temperature within permafrost. In this study, we proposed a Fourier series model derived from the conduction equation to simulate permafrost thermal behavior over a year. The boundary condition was represented by the Fourier series and the geothermal gradient. The initial condition was represented as a linear function relative to the geothermal gradient. A comparative study of the different models (sinusoidal model, Fourier series model, and the proposed model) was conducted. Data collected from the northern Da Xing’anling Mountains, Northeast China, were applied for parameterization and validation for these models. These models were compared with daily mean ground temperature from the shallow permafrost layer and annual mean ground temperature from the bottom permafrost layer, respectively. Model performance was assessed using three coefficients of accuracy, i.e., the mean bias error, the root mean square error, and the coefficient of determination. The comparison results showed that the proposed model was accurate enough to simulate temperature variation in both the shallow and bottom permafrost layer as compared with the other two Fourier series models (sinusoidal model and Fourier model). The proposed model expanded on a previous Fourier series model for which the initial and bottom boundary conditions were restricted to being constant.
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Acknowledgements
This work was founded by the Key Joint Program of National Natural Science Foundation of China (NSFC) and Heilongjiang Province for Regional Development (No. U20A2082), National Natural Science Foundation of China (No. 41971151), Natural Science Foundation of Heilongjiang Province (No. TD2019D002).
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Zhang, Yy., Zang, Sy., Zhao, L. et al. Estimation of permafrost thermal behavior using Fourier series model. J. Mt. Sci. 19, 715–725 (2022). https://doi.org/10.1007/s11629-021-6796-1
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DOI: https://doi.org/10.1007/s11629-021-6796-1