Estimating the spatial distribution of soil available trace elements by combining auxiliary soil property data through the Bayesian maximum entropy technique

Trace elements are essential nutrients for plant growth. An accurate prediction of soil available trace elements is necessary for scientifically based fertilization and soil environmental protection. In total, 670 surface soil samples were collected across the study area to analyze the relationship between soil properties and available trace elements (Cu, Zn, Fe, Mn, B, and Mo). Moreover, the Bayesian maximum entropy (BME) technique was employed to predict the spatial distribution of the trace elements by combining soil property information as auxiliary data. In addition, the prediction accuracy of the BME technique was compared with that of the conventional cokriging (CK) method. The results showed that soil macronutrients, especially organic matter, available P, available K and slow-release K, were significantly correlated with the content of the available trace elements. Soil texture also had great influences on trace elements and was generally represented as clay > heavy loam > medium loam > light loam. The BME technique combined with auxiliary soil property information (both categorical and numerical) performed better than the traditional CK technique, which was supported by the smaller MAE and RMSE and higher R-2 from the ten-fold cross validation. By mapping the spatial prediction error difference between the BME and CK methods across the study area, in comparison to the CK method, the BME technique provided consistently more accurate spatial predictions of trace element concentrations. In conclusion, with the advantages of combining categorical and numerical auxiliary data, the BME technique is a suitable spatial prediction method, and the results obtained in local regions could provide an important reference for the scientific application of microfertilizers.