A Novel Teacher–Student Framework for Soil Moisture Retrieval by Combining Sentinel-1 and Sentinel-2: Application in Arid Regions

Abstract

Soil moisture (SM) is an important parameter used to control a broad range of environmental applications. An increasing attention has been recently given to machine learning (ML) methods for SM retrieval that provide promising performance. Nevertheless, most of them are based on a supervised learning strategies that depend on the used labeled training samples. In fact, they are unaffordable or costly. In this letter, new teacher–student for SM estimation, called (TS-SME), relying on teacher–student (TS) framework using synthetic aperture radar (SAR) and optical data, was proposed to estimate SM. The main advantage of this framework is to enroll a large amount of unlabeled data together with a small amount of labeled data. Experiments were carried out on two arid areas in southern Tunisia. The input data include the backscatter coefficient in two-mode polarization ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\sigma ^{\circ }_{\textrm {VV}}$ </tex-math></inline-formula> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\sigma ^{\circ }_{\textrm {VH}}$ </tex-math></inline-formula> ) for Sentinel-1A, normalized difference vegetation index (NDVI) and normalized difference infrared index (NDII) for Sentinel-2A and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">in situ</i> measurements. Extensive experimental results demonstrated that TS-SME framework is capable of generating a well-performed student model, with the estimation accuracy is superior to all teacher models [artificial neural network (ANN), eXtreme gradient boosting (XGBoost), random forest regressor (RFR), and water cloud model (WCM)]. It was highly correlated with the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">in situ</i> measurements with high Pearson’s correlation coefficient <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$R$ </tex-math></inline-formula> ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${R}_{\textrm {RF}} =0.86$ </tex-math></inline-formula> , <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${R}_{\textrm {ANN}} =0.75$ </tex-math></inline-formula> , <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${R}_{\textrm {XGBoost}} =0.77$ </tex-math></inline-formula> , <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${R}_{\textrm {WCM}} =0.77$ </tex-math></inline-formula> , <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${R}_{{\,\,\textrm {TS-SME}}} =0.96$ </tex-math></inline-formula> ) and low root mean square error (RMSE) ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\textrm {RMSE}_{\textrm {RF}} =1.09$ </tex-math></inline-formula> %, <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\textrm {RMSE}_{\textrm {ANN}} =1.49$ </tex-math></inline-formula> %, <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\textrm {RMSE}_{\textrm {XGBoost}} =1.39$ </tex-math></inline-formula> %, <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\textrm {RMSE}_{\textrm {WCM}} =1.12$ </tex-math></inline-formula> %, <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\textrm {RMSE}_{\,\,\textrm {TS-SME{} }} =0.8$ </tex-math></inline-formula> %), respectively.