Coupled water transport and heat flux in seasonally frozen soils: uncertainties identification in multi-site calibration

The modeling of seasonally frozen soils is significant for understanding the hydrological process in cold regions. The water and heat transports of two seasonally frozen sites in northern China were simulated with the process-oriented CoupModel, and a more efficient Monte Carlo based method was employed to identify the uncertainties in multi-site calibration. Results showed that water and heat measured at different sites could be explained by 15 merged parameters including FreezepointFWi (d1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$d_{1}$$\end{document}), EquilAdjustPsi (ψeg\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\psi_{eg}$$\end{document}), AlbedoKExp (ka\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k_{a}$$\end{document}), RoughLBareSoilMom (z0M\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$z_{0M}$$\end{document}) etc. with common ranges to some extent and three parameters MinimumCondValue (kmin,uc\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k_{\min ,uc}$$\end{document}), WindLessExchangeSoil (ra,max-1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$r_{a,\max }^{ - 1}$$\end{document}), and SThermalCondCoef (sk\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$s_{k}$$\end{document}) related to soil hydraulic conductivity, surface aerodynamic resistance and snow thermal conductivity respectively were identified to be site-dependent with site-specific ranges. The promotion in performance indices of interest variables indicated that the proposed systematic method had the potential to improve the multi-site simulation of heat and water in frozen soils based on CoupModel. However, the range ratios and posterior distributions of the merged parameters indicated the model structural uncertainty in CoupModel. And the comparison of the simulated variables between two sites demonstrated that the model structure uncertainty originated from the lack of consideration for the detailed processes related to ice cover and freezing point depression induced by soil solute. More detailed information on study sites as well as consideration of more detailed processes in frozen soil water-energy balance will expand the scope of model application in cold regions.