Visible and near infrared (vis-NIR) diffuse reflectance and X-ray fluorescence (XRF) sensors are promising proximal soil sensing (PSS) tools for predicting soil key fertility attributes. This work aimed at assessing the performance of the individual and combined use of vis-NIR and XRF sensors to predict clay, organic matter (OM), cation exchange capacity (CEC), pH, base saturation (V), and extractable (ex-) nutrients (ex-P, ex-K, ex-Ca, and ex-Mg) in Brazilian tropical soils. Individual models using the data of each sensor alone were calibrated using multiple linear regressions (MLR) for the XRF data, and partial least squares (PLS) regressions for the vis-NIR data. Six data fusion approaches were evaluated and compared against individual models using relative improvement (RI). The data fusion approaches included (i) two spectra fusion approaches, which simply combined the data of both sensors in a merged dataset, followed by support vector machine (SF-SVM) and PLS (SF-PLS) regression analysis; (ii) two model averaging approaches using the Granger and Ramanathan (GR) method; and (iii) two data fusion methods based on least squares (LS) modeling. For the GR and LS approaches, two different combinations of inputs were used for MLR. The GR2 and LS2 used the prediction of individual sensors, whereas the GR3 and LS3 used the individual sensors prediction plus the SF-PLS prediction. The individual vis-NIR models showed the best results for clay and OM prediction (RPD ≥ 2.61), while the individual XRF models exhibited the best predictive models for CEC, V, ex-K, ex-Ca, and ex-Mg (RPD ≥ 2.57). For eight out of nine soil attributes studied (clay, CEC, pH, V, ex-P, ex-K, ex-Ca, and ex-Mg), the combined use of vis-NIR and XRF sensors using at least one of the six data fusion approaches improved the accuracy of the predictions (with RI ranging from 1 to 21%). In general, the LS3 model averaging approach stood out as the data fusion method with the greatest number of attributes with positive RI (six attributes; namely, clay, CEC, pH, ex-P, ex-K, and ex-Mg). Meanwhile, no single approach was capable of exploiting the synergism between sensors for all attributes of interest, suggesting that the selection of the best data fusion approach should be attribute-specific. The results presented in this work evidenced the complementarity of XRF and vis-NIR sensors to predict fertility attributes in tropical soils, and encourage further research to find a generalized method of data fusion of both sensors data.
Bayesian Model Averaging and Weighted-Average Least Squares: Equivariance, Stability, and Numerical Issues
