Quantifying uncertainty in soil moisture retrieval using a Bayesian neural network framework

Soil moisture (SM) is an important parameter for precision agriculture and water cycle. Recent studies of using Global Navigation Satellite System-Reflectometry (GNSS-R) to retrieve SM have shown that the joint use of data and models is an effective method. However, data and models are often accompanied by two types of uncertainties (i.e., data uncertainty and model uncertainty), which can lead to retrieved results with high uncertainty resulting in false reliability. In this study, we propose a new Bayesian neural network (BNN) framework composed of two techniques: Monte-Carlo (MC)-dropout and Deep Ensembles. It quantifies the uncertainty and feeds it back to the framework to ultimately reduce the uncertainty in the retrieved results and improve accuracy. To verify the proposed framework, we conduct experiments using in situ data sets and Global Land Data Assimilation System (GLDAS) data sets respectively. The results show that MC-dropout can improve the correlation coefficient (R) and root-mean-square error (RMSE) by 8%-21% and 7%-20%, compared to basic multilayer perceptron (MLP). Deep Ensembles can improve the R and RMSE by 9%-36% and 11%-25%. Concerning uncertainty, MC-dropout and Deep Ensembles can decrease the uncertainty by 37%-60% and 82% -84% relative to maximum a posteriori (MAP), respectively. This study demonstrates that BNN framework can be used to quantify the uncertainty in retrieving SM and reduce the uncertainty as well as improve the accuracy.

Automated summary

This study proposes a new Bayesian neural network framework that quantifies the uncertainty in retrieving soil moisture (SM) and ultimately reduces the uncertainty and improves accuracy using techniques such as Monte-Carlo dropout and Deep Ensembles.