Abstract
The freezing-thawing processes in soils are important components of terrestrial hydrology, which significantly influence energy and water exchanges between land surface and sub-surface. Long-term changes in frost and thaw depths are also an important indicator of climate change. A water-heat coupled movements model is established with frozen soil in this paper, which treats the freezing/thawing front as a moving interface governed by some Stefan problems with two free boundaries. The numerical simulation is conducted by using the modified finite difference method. The model is validated to compare its predictions with GEWEX Asian Monsoon Experiment(GAME)-Tibet observations at D66 site in Tibetan Plateau. The results show that the simulated soil temperature, soil water content and frost/thaw depth are in excellent agreement with the measured values. Finally, optimal error estimation for L^∞ norm is derived on the model problem by using coordinate transformation method. The numerical simulation system is established on the basis of rigorous mathematics and mechanics, which successfully solved the important and difficult problems of environmental science.
Highlights
The freezing-thawing processes in soils are important components of terrestrial hydrology, which significantly influence energy and water exchanges between land surface and sub-surface
A water-heat coupled movements model is established with frozen soil in this paper, which treats the freezing/thawing front as a moving interface governed by some Stefan problems with two free boundaries
The results show that the simulated soil temperature, soil water content and frost/thaw depth are in excellent agreement with the measured values
Summary
The freezing-thawing processes in soils are important components of terrestrial hydrology, which significantly influence energy and water exchanges between land surface and sub-surface. A water-heat coupled movements model is established with frozen soil in this paper, which treats the freezing/thawing front as a moving interface governed by some Stefan problems with two free boundaries. Water phase transition(ice formation) and heat transfer in soil freezing and thawing process affect each other. It is the coupled variation process (see Lei, Z.D. et al(1988)). The seasonal depth changes in frozen and thawed soil is described to the coupled water and heat moving boundary problem on two free moving boundaries.The proposed model explicitly tracks the variation and dynamics of the active layer by computing the moving interfaces between the frozen zone and the unfrozen zone, and obtains the soil temperature, humidity and freeze/thaw depth simultaneously. The whole soil column is supposed to be divided into three zones: a thawed layer from ground surface to the first phase-transition interface (namely thaw depth), a frozen layer from thaw depth to the second phase-transition interface (namely frost depth), and an unfrozen layer from frost depth to the soil bottom
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