Deterministic and geostatistical models for predicting soil organic carbon in a 60 ha farm on Inceptisol in Varanasi, India

Soil organic carbon (SOC) is the regulatory soil property for soil fertility. The SOC status and its variability pattern can be studied through spatial interpolation techniques. In the current study we compared deterministic (Inverse Distance Weightage, IDW), geostatistical (spherical and exponential kriging (OK) and Empirical Bayesian Kriging, EBK) and Machine Learning (Random Forest, RF, Support Vector Machine, SVM) method for samples collected at four grid spacings (20, 40, 60 and 80 m) to find out the combination of best interpolation method and sample spacing to produce a variability map for SOC. Geostatistical models with corresponding highest R2 (31.9%), Lin CCC (0.49) and Pearson Correlation Coefficient (0.57) performed better than deterministic and machine learning models. A more precise prediction technique of geostatistical methods than deterministic interpolation may be due to differences in weightage calculation technique and a higher biasness in terms of Mean Error associated with IDW as compared to EBK. The presence of higher local uncertainty and lack of auxiliary supporting parameters e.g., crop and nutrient management) made ML (R2 19.4%, 21.7% in case of RF and SVM respectively) to be a poor predictor than EBK. Among the six interpolation methods, EBK was found to be the best interpolation method in each sample grid spacing [31.9% (p < 0.001), 10.5% (p < 0.01), 13.5% (p < 0.01), 10.5% (p < 0.05)]. Better simulation technique of variogram generation through EBK makes it the best fit model among the three geostatistical techniques. A 20 m grid spacing was found to be the best minimum spacing for studying SOC at a small scale as a higher density sampling could better capture the variability pattern of a heterogenous field having moderate autocorrelation. High local variability and lack of covariates have resulted in poor performance of ML as compared to kriging. However, the prediction performance of models can be improved by using covariate data which has a high correlation with soil properties combined with intense sampling in regions of high variability.

Automated summary

Geostatistical models outperformed deterministic and machine learning models in predicting SOC, likely due to differences in weightage calculation and higher bias in IDW compared to EBK. Geostatistical methods had a more precise prediction technique compared to deterministic interpolation. Machine learning performed poorly compared to EBK in the absence of auxiliary supporting parameters.