Data Fusion of XRF and Vis-NIR Using Outer Product Analysis, Granger–Ramanathan, and Least Squares for Prediction of Key Soil Attributes

Abstract

Visible-near-infrared (vis-NIR) and X-ray fluorescence (XRF) are key technologies becoming pervasive in proximal soil sensing (PSS), whose fusion holds promising potential to improve the estimation accuracy of soil attributes. In this paper, we examine different data fusion methods for the prediction of key soil fertility attributes including pH, organic carbon (OC), magnesium (Mg), and calcium (Ca). To this end, the vis-NIR and XRF spectra of 267 soil samples were collected from nine fields in Belgium, from which the soil samples of six fields were used for calibration of the single-sensor and data fusion models while the validation was performed on the remaining three fields. The first fusion method was the outer product analysis (OPA), for which the outer product (OP) of the two spectra is computed, flattened, and then subjected to partial least squares (PLS) regression model. Two versions of OPA were evaluated: (i) OPA-FS in which the full spectra were used as input; and (ii) OPA-SS in which selected spectral ranges were used as input. In addition, we examined the potential of least squares (LS) and Granger–Ramanathan (GR) analyses for the fusion of the predictions provided by the single-sensor PLS models. Results demonstrate that the prediction performance of the single-sensor PLS models is improved by GR in addition to the LS fusion method for all soil attributes since it accounts for residuals. Resorting to LS, the largest improvements compared to the single-sensor models were obtained, respectively, for Mg (residual prediction deviation (RPD) = 4.08, coefficient of determination (R2) = 0.94, ratio of performance of inter-quantile (RPIQ) = 1.64, root mean square error (RMSE) = 4.57 mg/100 g), OC (RPD = 1.79, R2 = 0.69, RPIQ = 2.82, RMSE = 0.16%), pH (RPD = 1.61, R2 = 0.61, RPIQ = 3.06, RMSE = 0.29), and Ca (RPD = 3.33, R2 = 0.91, RPIQ = 1, RMSE = 207.48 mg/100 g). OPA-FS and OPA-SS outperformed the individual, GR, and LS models for pH only, while OPA-FS was effective in improving the individual sensor models for Mg as well. The results of this study suggest LS as a robust fusion method in improving the prediction accuracy for all the studied soil attributes.

Optimization of sample preparation and data evaluation techniques for X‐ray fluorescence prediction of soil texture, pH, and cation exchange capacity of loess soils

“…Although methods of spectral pretreatment are well‐developed for soils measured by infrared spectroscopy, standardized approaches have not yet been established for XRF (Xu et al., 2019). Transformations with the Savitzky–Golay algorithm have, however, shown some usefulness for XRF (Javadi & Mouazen, 2021; O'Rourke, Stockmann et al., 2016; Xu et al., 2019). Thus, 13 spectral pretreatments were carried out with the “prospectr” package (Stevens et al., 2022), including use of the full spectra without manipulation, calculation of moving averages (calculated over 5, 11, 17, or 23 data points), and application of the Savitzky–Golay algorithm for the reduction of noise applied with the polynomial degree (PD) set to 2, the order of the derivative (DER) ranging from 1 to 2 (with PD–DER: 2–1 or 2–2), and a window smoothing size of 5, 11, 17, or 23 (Table 1).…”

“…While elemental contents are typically determined using a single spectrum with optimal voltage for a given atomic number, the optimal approach using spectral intensities as predictors is unclear. While O'Rourke, and O'Rourke, analyzed both single and concatenated spectral intensities measured at three voltages (15, 40, and 50 kV), some studies do not specify the voltage(s) of the measurements used in modeling with ED-XRF (Xu et al, 2019) or do not specify whether spectra measured at both 15 and 40 kV were utilized in modeling (Javadi & Mouazen, 2021;Kandpal et al, 2022). Due to the time-consuming nature of consecutive analyses of multiple single spectrum or concatenated spectra, more information on the improvements from including measurements with various voltages may be beneficial.…”

“…Recent studies have therefore explored application of XRF for the estimation of soil texture (Silva et al., 2020), pH (Javadi & Mouazen, 2021), and cation exchange capacity (CEC) (Tavares et al., 2020) with promising results. The mechanisms by which XRF can predict contents of the soil particle size classes are based on the unique assemblages of elements present in soil minerals associated with coarse versus fine particles.…”

“…For example, infrared spectroscopy studies have demonstrated high model robustness in independent validation for spectrally active soil properties (e.g., clay), but that local calibration is often essential for spectrally inactive properties (e.g., pH and CEC) (Soriano‐Disla et al., 2014). While a large number of XRF studies predicting soil properties have been conducted, typically only one model calibration/validation strategy has been applied in each study (e.g., Javadi & Mouazen, 2021; Kandpal et al., 2022; Li et al., 2022; O'Rourke, Minasny et al., 2016, O'Rourke, Stockmann et al., 2016; Sharma et al., 2015; Tavares et al., 2020; Zhu et al., 2011). Thus, a mechanistic investigation of the robustness of XRF predictions for various soil properties with and without independent validation is required.…”

“…Rather than calculating elemental contents first to use as model predictors, an alternative approach is to directly use intensities across the XRF spectra (Javadi & Mouazen, 2021; Kandpal et al., 2022; Xu et al., 2019). Direct use of the spectral intensities can be considered an empirical modeling approach with a high number of correlated predictors, containing both useful information as well as spectral artifacts and noise.…”