Blind Source Separation for Alleviating the “Ill-Posedness” of Estimating Soil Moisture From Nonstationary Time Series of Passive Microwave Brightness Temperatures

The effective use of observational constraints to mitigate the impacts of surface roughness and vegetation cover and the quantitative estimation of soil moisture from nonstationary microwave signals present critical challenges. Integrating the temporal constraints imposed by observations can provide additional information for achieving improved soil moisture estimation accuracy. Considering the time-dimensional autocorrelation of time-series passive microwave brightness temperatures, blind source separation (BSS) was introduced for soil moisture estimation. The single-channel BSS was used to decompose the brightness temperature into several intrinsic mode functions (IMFs). The Akaike information criterion and average silhouette width were used to recognize the number of blind sources based on the IMFs for multidimensional signal reconstruction. The multichannel BSS was carried out to decompose the reconstructed multidimensional signals to determine the trends of their blind sources to estimate soil moisture. An experiment conducted in Naqu demonstrated that the BSS-based method effectively estimated soil moisture, with an RMSE of 0.027 cm<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup>/cm<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup>. Through 1000 experiments, an error-bound analysis indicated that the method is robust, maintaining an average soil moisture estimation error of 0.032 cm<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup>/cm<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> [range 0–0.074 cm<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup>/cm<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup>]. Additionally, decomposing the SMAP brightness temperature for soil moisture estimation in Tianjun, Maqu, and Pali yielded good performance, with RMSEs of 0.037 cm<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup>/cm<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup>, 0.047 cm<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup>/cm<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup>, and 0.041 cm<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup>/cm<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup>, representing a significant improvement over the traditional inversion algorithms. Moreover, the proposed method bypasses the challenges of remote sensing-based soil moisture estimation, which is affected by variables such as surface roughness and vegetation cover. This changes the limitations of traditional soil moisture estimation methods that rely on microwave models.