Heat equation-based temperature profiles retrieval in frozen tundra soil using dual-polarized multi-angular brightness temperature observations in L-band

https://doi.org/10.1080/01431161.2024.2440670

In this theoretical paper, a method for temperature profile retrieval in frozen tundra soil is proposed based on the thermoevolutionary relationship between polarimetric multi-angular brightness temperature (TB) at 1.4 GHz, observed in sliding time window with a fixed duration, and the time series of soil temperature profiles, predicted by the heat equation. For TB modelling, the profiles of volumetric moisture, dry bulk density, and organic matter content in the active layer, measured at the Franklin Bluffs test site (North slope of Alaska, U.S.) from 12 December 2022 to 5 May 2023, were used. When solving the inverse problem, the retrieving temperature profiles were specified as a linear interpolation function between four known depths 0 cm, 25 cm, 50 cm, and 95 cm. The thermodynamic properties of the frozen active layer were considered independent of soil temperature, time, and vertical coordinates, which made it possible, based on weather station data, to determine the apparent value of the thermal diffusivity coefficient in the heat equation. The practically significant accuracy of retrieving soil temperature up to a depth of 70 cm with a root-mean-square error of 0.5–1.8°C and a coefficient of determination of 0.877–0.988 was demonstrated by the proposed method. The pursued research shows the advantage of the synergy of the heat equation and polarimetric multi-time compared to only single-moment TB observations for temperature profile retrieval in frozen tundra soil.