Hybridization of cokriging and gaussian process regression modelling techniques in mapping soil sulphur

Abstract

As a widely used soil mapping method, the kriging method involves a high sampling point to generate quality and accurate maps. Combining kriging and machine learning (ML) can produce soil maps with fewer number sampling points. This study's objective was to implement a hybrid approach based on the Cokriging (Cok) and an ML technique [i.e., Gaussian process regression (GPR)]. The hybrid method (called the Cok-GPR method) uses the Cok (Coki, i = 1 to n) as a predictor method of the soil sulphur and then uses GPR to improve the prediction accuracy. The proposed method was compared with the Cok and the GPR models, respectively, in a case study. Soil samples (n = 115) were collected from the topsoil (0–20) at the agricultural site of approximately 889.8 km2 size. S, Ca, K, Mg, Na, P, and V were estimated via Inductively Coupled Plasma Optical Emission Spectroscopy (ICP-OES) equipment and presented as S_ICP-OES (response variable), and predictors (Ca_ICP-OES, K_ICP-OES, Mg_ICP-OES, Na_ICP-OES, P_ICP-OES, and V_ICP-OES), respectively. For GPR and Cok-GPR, an 80% (calibration) to 20% (validation) random dataset split was performed. The calibration dataset was implemented under k = 10-fold cross-validation, repeated five times. All the models were evaluated by MAE, RMSE and R2 criteria. According to the model and map performances. Cok1 model via Ca_ICP-OES, K_ICP-OES, Mg_ICP-OES gave the best model (MAE = −1.28 mg/kg RMSE = 164.42 mg/kg, R2 = 0.85). Its corresponding GPR1 approach, modelled with the same predictors produced the best (MAE = 85.43 mg/kg, RMSE = 137.59 mg/kg, R2 = 0.83). While the hybrid Cok1-GPR model produced MAE = 76.84 mg/kg, RMSE = 102.11 mg/kg, and R2 = 0.91. The model outperformed both the Cok and GPR models, respectively. The proposed Cok-GPR model can be applied to efficiently predict soil nutrient element levels at the regional level and be useful during policymaking.