MSFDmap: A novel scheme to map monthly soil freeze depth in the pan-Arctic considering spatiotemporal heterogeneity in heat transfer capability

Accurately characterizing the spatiotemporal dynamics of soil freeze depth (SFD) is critical for understanding the response of frozen soils to climate change. Existing SFD mapping schemes mainly focus on annual maximum values, rarely address monthly variations, and fail to capture both spatiotemporal heterogeneity and physical constraints. We developed a monthly SFD mapping scheme (MSFDmap) that considers spatiotemporal heterogeneity in heat transfer capability. Based on the simplified Stefan equation, which is physically constrained by energy conservation, MSFDmap first predicts the spatial distribution of monthly heat transfer factor (HTF) using a random forest regression model driven by soil clay content, precipitation, soil bulk density, soil organic carbon content, soil water content, and leaf area index, and then maps monthly SFD. MSFDmap was implemented using 2123 site-month observations from 60 pan-Arctic sites over 20 years. Results show that MSFDmap achieves a root mean square error (RMSE) of 19.21 cm and an R² of 0.91 for monthly SFD estimates, reducing RMSE by 24–55 % and improving R² by 8–65 % over existing schemes. For monthly SFD averaged across sites, estimates exhibit strong temporal agreement with quasi-true SFD series (Pearson correlation coefficient r = 0.99, RMSE = 9.13 cm). The MSFDmap-derived SFD distribution exhibits expected latitudinal and altitudinal gradients, with r = 0.60 relative to an ERA5-Land-based reference distribution. These results demonstrate that MSFDmap effectively characterizes the spatiotemporal dynamics of monthly SFD and outperforms existing schemes. It is attributed to the capture of heterogeneous HTF, which enables the representation of SFD heterogeneity under physical constraints.