Spectral fusion by Outer Product Analysis (OPA) to improve predictions of soil organic C

Soil organic carbon (C) is an important indicator of agricultural and environmental quality. It improves soil fertility and helps to mitigate greenhouse gas emissions. Soil spectroscopy with either vis–NIR (350–2500 nm) or mid-IR (4000–400 cm−1) spectra have been used successfully to predict organic C concentrations in soil. However, research to improve predictions of soil organic C by simply combining vis–NIR and mid-IR spectra to model them together has been unsuccessful. Here we use the Outer Product Analysis (OPA) to fuse vis–NIR and mid-IR spectra by bringing them into a common spectral domain. Using the fused data, we derived models to predict soil organic C and compared its predictions to those derived with vis–NIR and mid-IR models separately. We analyzed 1259 tropical soil samples from surface and subsurface layers across agricultural areas in Central Brazil. Soil organic C contents were determined by a modified Walkley-Black method, and vis–NIR and mid-IR reflectance spectra were obtained with a FieldSpec Pro and a Nicolet 6700 Fourier Transformed Infrared (FT-IR), respectively. Reflectances were log-transformed into absorbances. The mean content of soil organic C was 9.14 g kg−1 (SD = 5.64 g kg−1). The OPA algorithm was used to emphasize co-evolutions of each spectral domain into the same one by multiplying the absorbances from both sets of spectra to produce a matrix with all possible products between them. Support Vector Machine with linear kernel function was used for the spectroscopic modeling. Predictions of soil organic C using vis–NIR, mid-IR, and fused spectra were statistically compared by the Tukey's test using the coefficient of determination (R2), root mean squared error (RMSE), and ratio of performance to interquartile distance (RPIQ). Absorbances in vis–NIR and mid-IR were emphasized in the common spectral domain presenting stronger correlations with soil organic C than individual ranges. Soil organic C predictions with the OPA fused spectra were significantly better (R2 = 0.81, RMSE = 2.42 g kg−1, and RPIQ = 2.87) than those with vis–NIR (R2 = 0.69, RMSE = 3.38 g kg−1, and RPIQ = 2.08) or mid-IR spectra (R2 = 0.77, RMSE = 2.90 g kg−1, and RPIQ = 2.43). Fusing vis–NIR and mid-IR spectra by OPA improves predictions of soil organic C.