The freezing front depth (z(ff)) of annual freeze-thaw cycles is critical for monitoring the dynamics of the cryosphere under climate change because z(ff) is a sensitive indicator of the heat balance over the atmosphere-cryosphere interface. Meanwhile, although it is very promising for acquiring global soil moisture distribution, the L-band microwave remote sensing products over seasonally frozen grounds and permafrost is much less than in wet soil. This study develops an algorithm, i.e., the brightness temperature inferred freezing front (BT-FF) model, for retrieving the interannual z(ff) with the diurnal amplitude variation of L-band brightness temperature (?T-B) during the freezing period. The new algorithm assumes first, the daily-scale solar radiation heating/cooling effect causes the daily surface thawing depth (z(tf)) variation, which leads further to ?T-B; second, ?T-B can be captured by an L-band radiometer; third, z(tf) and z(ff) are negatively linear correlated and their relation can be quantified using the Stefan equation. In this study, the modeled soil temperature profiles from the land surface model (STEMMUS-FT, i.e., simultaneous transfer of energy, mass, and momentum in unsaturated soil with freeze and thaw) and T-B observations from a tower-based L-band radiometer (ELBARA-III) at Maqu are used to validate the BT-FF model. It shows that, first, ?T-B can be precisely estimated from z(tf) during the daytime; second, the decreasing of z(tf) is linearly related to the increase of z(ff) with the Stefan equation; third, the accuracy of retrieved z(ff) is about 5-25 cm; fourth, the proposed model is applicable during the freezing period. The study is expected to extend the application of L-band T-B data in cryosphere/meteorology and construct global freezing depth dataset in the future.

Nanofluid is an emerging heat transfer fluid with good heat transfer and thermal conductivity properties. It is important to investigate the phase change properties and morphological evolution during the freezing of nanofluid droplets to understand their practical applications. The effect of dynamic wettability on the deformation of a single droplet of aluminum trioxide (Al2O3-H2O) and graphene (CNT-H2O) nanofluids at different mass concentrations and substrate temperatures was investigated by visualizing the droplet freezing. The formation of solid-like and freezing front motions inside the droplet during the freezing process of these droplets was investigated. The solidification process was strongly influenced by the temperature gradient perpendicular to the cold surface and the change in the solid- liquid interface wettability during the phase change, resulting in volume redistribution at the top of the droplet. The freezing shape of Al2O3-H2O nanodroplets resembled a moon crater, and the influence of wettability decreased with increasing concentration, leading to a relative increase in the aperture of the top platform. The fully frozen state of the nanofluid droplet had an increasingly pointed tip, with a strong relationship between the substrate temperature and solidification time when the CNT-H2O concentration was 5 times higher and showed no change in the freezing droplet deformation rate under the experimental conditions. The contact angle of the two nanofluid droplets did not fluctuate significantly with increasing concentration, while that of the 1% nanofluid droplets remained at an average value of 85 degrees during freezing. Under different freezing conditions, the freezing shape of Al2O3-H2O droplets tended to increase in diameter as the subcooling temperature decreased, with the final deformation rate of 1% Al2O3-H2O being twice that at 5% concentration, while the contact angle of the same mass concentration of Al2O3-H2O decreased by 1 degrees as the subcooling temperature dropped. The CNT-H2O droplet became sharper at the tip as the subcooling temperature increased, and its contact angle did not change with temperature.