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

Highlights

• Hybrid model outperforms ML and OK.

• No silver bullet is found among sampling designs.

• 180 calibration samples are required by topsoil Ca and Mg.

• FSCS enables 120 samples to predict subsoil Ca and Mg.

• DSM achieves a potential ~ 18 % and 86 % decrease in lime and Mg fertilisers cost.

Abstract

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⁻¹) and Mg (cmol(+) kg⁻¹). 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.

Introduction

Sugarcane requires large amounts of calcium (Ca) because it is essential for development of leaves and roots to strengthen cell walls. Magnesium (Mg) is important for photosynthesis and movement of phosphorus because it is required for respiration and nitrogen metabolism and assimilation. Deficiency in Ca can lead to leaves showing pale green/yellow mottling and primary shoot death (White and Broadley, 2003), while for Mg it may cause leaf chlorosis and retardation (Cakmak and Kirkby, 2008). Therefore, Ca and Mg fertilisation is necessary to maintain sugarcane productivity. However, Ca fertilisation inconsistent with nutritional needs may cause soil pH to rise, which restricts zinc and copper uptake (Dontsova and Norton, 2002); whereas excess Mg could interfere with potassium uptake, and make soil hard, reducing water infiltration and drainage (Zhang and Norton, 2002). To improve Ca and Mg management, the sugarcane industry formulated the Six-Easy-Steps nutrient management guidelines (Schroeder et al., 2010), which aims at determining suitable fertiliser rates (i.e., lime and Mg) based on topsoil (0–0.3 m) Ca and Mg (cmol(+) kg⁻¹). For example, Table 1 shows that small (<0.2) Ca requires a lime application rate of 4 t/ha, whereas large (>1.6) Ca requires 1 t/ha. Similarly, the guidelines indicate for small (<0.05) and large (>0.2) Mg, the rates should be 150 and 50 kg/ha, respectively. Therefore, knowledge about Ca and Mg is necessary to enable site-specific fertilisation to address infertility and mitigate environmental impacts.

While geostatistical models (e.g., ordinary kriging) have been implemented to map topsoil Ca and Mg (Behera and Shukla, 2015), increasingly digital soil mapping (DSM) approaches are being applied to predict Ca and Mg from limited soil data by augmenting this with easier to acquire digital data (Wang et al., 2020) using models. In terms of digital data, proximal sensing electromagnetic induction (EMI) and/or gamma-ray (γ-ray) spectrometer could be employed. For instance, in Australia Holland et al. (2017) quantified distribution of cation exchange capacity using γ-ray data in cropping lands of the Glenelg-Hopkins catchment. More recently, Li et al. (2019) made a DSM of topsoil (0–0.15 m) Ca and Mg in a sugarcane field in Burdekin, by synergistically combining γ-ray and EMI data. With respect to models, linear (e.g., linear mixed model [LMM]) and geostatistical (e.g., ordinary kriging [OK] and regression kriging [RK]) methods are commonly implemented (Keskin and Grunwald, 2018). When non-linear or multi-dimensional hierarchy relationships exist, machine learning (ML) techniques including, quantile regression forests (QRF) (Vaysse and Lagacherie, 2017), Cubist (Ma et al., 2017) and support vector machine (SVM) (Liao et al., 2014), and hybrid models that incorporate ML with geostatistical (e.g., CubistRK), may produce better prediction accuracy (Ma et al., 2017).

To fit these statistical models, sampling designs and number of calibration samples should also be considered (Brus, 2019). Regarding design of sampling, spatial coverage (SCS), feature space coverage (FSCS), conditioned Latin hypercube (cLHS) and simple random (SRS) are common (Brus, 2019). For example, Schmidt et al. (2014) evaluated several sampling designs, concluding cLHS with only 20 samples returned the most accurate predictions for topsoil (0–0.3 m) pH, soil organic carbon and particle fractions across a grassland in Germany, whereas Ng et al. (2018) inspected cLHS, FSCS and SRS at continental, regional, and local scale to predict CEC and clay and found FSCS was suitable when sample size was large (i.e., ~1000) but performed poorly when it was small. Moreover, cLHS appeared more robust regardless of sample size. However, the converse was shown by Wadoux et al. (2019) and Ma et al. (2020), who found the accuracy of FSCS was superior to cLHS and SRS over all sample sizes, for mapping topsoil (0–0.3 m) organic carbon and soil classes across continental and catchment scales, respectively.

In this study, we examine statistical models (i.e., OK, LMM, QRF, SVM, CubistRK) based on a large calibration sample size (i.e., n = 180) to predict topsoil (0–0.3 m) and subsoil (0.6–0.9 m) Ca and Mg, using digital data in combination (i.e., proximal sensing EMI, γ-ray spectrometry and DEM derivatives). Different sampling designs (i.e., SCS, FSCS, cLHS and SRS) were investigated, along with sample size (i.e., n = 180, 150, 120, 90, 60, 30) evaluated using an independent validation dataset (i.e., n = 40), by Lin's concordance correlation coefficient (LCCC) and ratio of performance to interquartile distance (RPIQ). DSMs of topsoil and subsoil Ca and Mg were produced to recommend lime and Mg application rates according to the Six-Easy-Steps management guidelines for Herbert Valley.