Selecting optimal calibration samples using proximal sensing EM induction and γ-ray spectrometry data: An application to managing lime and magnesium in sugarcane growing soil.

Calcium (Ca) and magnesium (Mg) are essential for growth of sugarcane leaves and roots, as well as respiration and nitrogen metabolism, respectively. To assist farmers decide suitable application rates of lime and Mg fertiliser, respectively, the Australian sugarcane industry established the Six-Easy-Steps nutrient management guidelines based on topsoil (0-0.3 m) Ca (cmol(+) kg) and Mg (cmol(+) kg). Given the heterogeneous nature of soil, digital soil mapping (DSM) methods can be employed to allow for the precise application rate to be determined. In this study, we examine statistical models (i.e., ordinary kriging [OK], linear mixed model [LMM], quantile regression forests [QRF], support vector machine [SVM], and Cubist regression kriging [CubistRK]) to predict topsoil and subsoil (0.6-0.9) Ca and Mg, employing digital data in combination (i.e., proximal sensing electromagnetic induction (EMI) [e.g., 1mPcon, 1mHcon, etc.], gamma-ray [γ-ray] spectrometry [i.e., TC, K, U and Th] and digital elevation model [DEM] derivatives). We also investigate various sampling designs (i.e., spatial coverage [SCS], feature space coverage [FSCS], conditioned Latin hypercube [cLHS] and simple random sampling [SRS]) and calibration sample size (i.e., n = 180, 150, 120, 90, 60 and 30). The predictions are assessed using Lin's concordance correlation coefficient (LCCC) and ratio of performance to interquartile distance (RPIQ) with an independent validation dataset (i.e., n = 40). The best results were for prediction of subsoil Mg, utilising CubistRK (LCCC = 0.82) with the largest calibration sample size (n = 180), followed by LMM (0.79), SVM (0.76), QRF (0.70) and OK (0.65). This was generally the case for topsoil and subsoil Ca. We also conclude that no single sampling design was universally better, and 180 samples were necessary for predicting topsoil Ca and Mg with moderate agreement (0.65 < LCCC < 0.80). However, with FSCS, a minimum of 120 samples were enough to calibrate a CubistRK model and achieve substantial (LCCC > 0.80) agreement for predicting subsoil Ca and Mg. With respect to soil use and management according to the Six-Easy-Steps, the sandy soil in the north and south require large application rate of lime (3.5 t/ha) and Mg (125 kg/ha), respectively. Conversely, varying amounts of fertiliser rates of lime (2.0, 1.5 and 1 t/ha) and Mg (50 kg/ha) were recommended where Vertosols were previously mapped.