Spatial interpolation of soil moisture and nutrients using BME combined with BNN

Understanding spatial distribution characteristics of soil moisture and nutrients is an important step for precision agriculture and site-specific soil management. In order to improve the accuracy of soil spatial prediction, it is of great importance to predict and map soil spatial characteristics based on limited data and develop new methods by integrating different spatial analysis theories. By analyzing the advantages and disadvantages of the Bayesian maximum entropy method (BME) and the Bayesian neural networks (BNN), this study proposed a Bayesian maximum entropy method combined with the Bayesian neural networks (BMENN) to predict the spatial distributions of soil moisture and nutrients in farmlands. The BMENN method takes the following steps: first, the BNN is used to quantify the prediction uncertainties of soil moisture and nutrients at all predicted locations; then, the uncertainties expressed by 95% prediction limits are regarded as soft data of BME method to be interpolated in spatial distributions of soil variables. Six soil variables, including moisture content, organic matter, total nitrogen (N), alkali-hydrolyzable N, available phosphorus (P) and available potassium (K), were measured at 161 locations in agricultural field in the north of Yangzhou City, Jiangsu Province. The locations were selected on the basis of 5 m×5 m regular grid. Based on these soil data, the performance of the BMENN method for spatial prediction of soil moisture and nutrients was compared quantitatively with the BNN method and the ordinary Kriging (OK) using Pearson correlation coefficient (r), mean error (ME) and mean squared error (MSE). The sampling data from the 161 locations for each variable were divided into the calibration data set and the validation data set. The calibration data set was used to build prediction models of all 3 methods. The 3 methods were compared by the cross-validation using the validation data set. The MSE was divided further into 3 components revealing different aspects of the discrepancy between the observed and the estimated values of soil moisture and nutrients. The results showed that: 1) Compared to the other 2 approaches, the BMENN reduced MSE by 2.26%-23.54% and had the smallest MSE for all soil variables, indicating that the BMENN predictions had less estimation errors than those of the OK and BNN method because the BMENN incorporated the uncertainty estimated by the BNN into the BME method. 2) The Pearson correlation coefficients were of the same magnitude or close to 1 for the BMENN, which indicated that the linear relationship was stronger between the BMENN estimates and the observed values. 3) Although the BMENN method did not produce the largest unbias (ME was close to zero) for all soil variables compared with the other 2 approaches, the ME values of the BMENN were very small for all soil variables, especially for the alkali-hydrolyzable N and available K, which showed that the BMENN provided the unbiased estimates. 4) The contribution of the bias (ME) to the MSE was almost zero and the lack of positive correlation (LCS) was the factor that contributed the most to the MSE of the 3 interpolation methods for all soil variables. This indicated that the differences between the estimated and the measured values were mainly caused by the differences in the degree of their fluctuations. 5) The MSE decomposition showed that the BMENN method performed better than the other 2 approaches in reproducing the magnitude and degree of fluctuation observed in soil moisture and nutrients. 6) The soil spatial distribution maps generated by the BMENN approach had more continuous changes with a little less fragmentized polygons than those by the BNN and OK methods. The BMENN approach could more accurately express the regionalization characteristics of soil moisture and nutrients. In summary, the BMENN is a better prediction method than the OK and BNN, and the stronger the spatial autocorrelation of soil variable, the higher its prediction accuracy. The BMENN approach has great significance in improving the accuracy of soil spatial mapping based on limited soil data, and may provide the scientific evidence for the application of the soil management, precision agriculture and regional environment planning.