Soil Moisture Mapping Based on Multi-Source Fusion of Optical, Near-Infrared, Thermal Infrared, and Digital Elevation Model Data via the Bayesian Maximum Entropy Framework

This paper proposes a combined approach wherein the optical, near-infrared, and thermal infrared data from the Landsat 8 satellite and the Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER) global digital elevation model (GDEM) data are fused for soil moisture mapping under sparse sampling conditions, based on the Bayesian maximum entropy (BME) framework. The study was conducted in three stages. First, based on the maximum entropy principle of the information theory, a Lagrange multiplier was introduced to construct general knowledge, representing prior knowledge. Second, a principal component analysis (PCA) was conducted to extract three principal components from the multi-source data mentioned above, and an innovative and operable discrete probability method based on a fuzzy probability matrix was used to approximate the probability relationship. Thereafter, soft data were generated on the basis of the weight coefficients and coordinates of the soft data points. Finally, by combining the general knowledge with the prior information, hard data (HD), and soft data (SD), we completed the soil moisture mapping based on the Bayesian conditioning rule. To verify the feasibility of the combined approach, the ordinary kriging (OK) method was taken as a comparison. The results confirmed the superiority of the soil moisture map obtained using the BME framework. The map revealed more detailed information, and the accuracies of the quantitative indicators were higher compared with that for the OK method (the root mean squared error (RMSE) = 0.0423 cm3/cm3, mean absolute error (MAE) = 0.0399 cm3/cm3, and Pearson correlation coefficient (PCC) = 0.7846), while largely overcoming the overestimation issue in the range of low values and the underestimation issue in the range of high values. The proposed approach effectively fused inexpensive and easily available multi-source data with uncertainties and obtained a satisfactory mapping accuracy, thus demonstrating the potential of the BME framework for soil moisture mapping using multi-source data.