Inference of Soil Freezing Front Depth During the Freezing Period From the L-Band Passive Microwave Brightness Temperature

Abstract

The freezing front depth ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">zff</i> ) of annual freeze- thaw cycles is critical for monitoring the dynamics of the cryosphere under climate change because <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">zff</i> 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 seasonal 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 freezing front depth ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">zff</i> ) with the diurnal amplitude variation (DAV) of L band brightness temperature ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ΔTB</i> ) during the freezing period. The new algorithm assumes 1) the daily-scale solar radiation heating/cooling effect causes the daily surface thawing depth ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ztf</i> ) variation, which leads further to <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ΔTB</i> ; 2) Δ <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">TB</i> can be captured by an L-band radiometer; 3) <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ztf</i> and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">zff</i> 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 <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">TB</i> observations from a tower- based L-band radiometer (ELBARA-III) at Maqu are used to validate the BT-FF model. It shows that: 1) <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ΔTB</i> can be precisely estimated from <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ztf</i> during the daytime; 2) the decreasing of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ztf</i> is linearly related to the increase of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">zff</i> with the Stefan Equation; 3) the accuracy of retrieved freezing front depth is about 5-25 cm; 4) the proposed model is applicable during the freezing period. The study is expected to extend the application of L -band <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">TB</i> data in cryosphere/meteorology and construct global freezing depth data set in the future.