综合BME和BNN法的农田土壤水分与养分分布空间插值

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

掌握农田土壤水分和养分的空间分布特征是实现农田土壤精确管理及实施精确农业的重要依据。以有限的采样信息为基础,通过多种空间分析理论的融合,形成优势互补的综合方法,对提高土壤变量空间分布模拟和绘图精度具有重要意义。该文将贝叶斯最大熵法（Bayesian maximum entropy,BME）和贝叶斯人工神经网络方法（Bayesian neural networks,BNN）结合形成一种空间插值新方法,即用BNN法表达估值的不确定性,并将其结果融入现代地质统计学BME法中,用融入BNN法结果的BME法（Bayesian maximum entropy method combined with Bayesian neural networks,BMENN）模拟土壤变量的空间分布。以江苏省扬州市区北部某田块的土壤水分、有机质、全氮、碱解氮、速效钾和速效磷6种土壤特性的采样数据为例,运用交叉验证法,将BMENN法对土壤变量的估值精度与BNN法、普通克立格法（ordinary Kriging,OK）进行了比较。结果表明：与OK法和BNN法相比,BMENN法将估计方差（mean squared error,MSE）缩小2.26%~23.54%,具有最小的估计方差和接近于0的平均绝对误差（mean error,ME）;BMENN法的估计值与实测值相关系数更大（r=0.62~0.89）,具有更高的相关程度;MSE的组成分析表明,BMENN法再现变量波动程度和波动大小的能力更强;从模拟的空间分布图来看,BMENN法绘制的空间分布图更连续,＂牛眼＂较少,更符合土壤变量的地学规律。BMENN法对于利用有限数据信息提高土壤变量空间分布模拟精度具有重要意义,并可为土壤管理、精准农业的实施以及区域环境规划等提供科学依据。

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 mx5 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.