GWR模型在土壤重金属高光谱预测中的应用

目前土壤重金属高光谱反演模型大多忽视了重金属与光谱变量间相关关系的空间异质性,这与实际情况不相吻合,而地理权重回归（GWR）模型能有效地揭示变量间关系的空间异质性。本文以福州市土壤重金属Cd、Cu、Pb、Cr、Zn、Ni为对象,构建土壤重金属预测的GWR高光谱模型,并将预测结果与普通最小二乘法回归（OLS）结果进行比较分析,探讨GWR模型在土壤重金属高光谱预测中的适用性及局限性。结果表明：① GWR模型在土壤重金属高光谱预测中适用与否取决于重金属对光谱变量影响的空间异质性程度：对于Cr、Cu、Zn、Pb等对光谱变量影响空间异质性大的元素,其GWR预测精度较OLS提高明显,表现为GWR模型的调节R²较OLS模型有了明显提高,分别为OLS模型的2.69倍、2.01倍、1.87倍和1.53倍;而AIC值以及残差平方和较OLS模型却明显降低,AIC值减少量均大于3个单位,残差平方和则仅分别为OLS模型的25.33%、30.09%、47.22%和86.84%;对于Cd和Ni等对光谱变量影响空间异质性小的元素,相较于OLS模型,GWR模型的调节R²分别提高了0.015和0.007,残差平方和分别减少了5.97%和4.18%,但AIC值却分别增加了2.737和2.762,GWR预测效果改善不明显;② 光谱变换可以有效增强土壤重金属的光谱特征,其中以光谱的倒数变换效果最好,而且该变换及其微分形式可以很好地提高模型的预测效果;③ GWR模型的应用前提是变量间关系的空间非平稳性,适合在与土壤光谱变量间关系具有显著空间异质性的重金属高光谱预测中推广。

Application of GWR model in hyperspectral prediction of soil heavy metals

The inversion models applied in hyperspectral prediction of soil heavy metals include multiple linear regression, partial least squares regression, artificial neural network, and wavelet analysis. They are mostly based on the presumed homogeneous influence of heavy metal contents on spectral reflectance in different locations. This presumption, however, ignores the spatial heterogeneity of the correlation between heavy metal and spectral variables. In comparison, GWR model effectively reveals the spatial heterogeneity among different variables, which is well evidenced in the studies involving the spatial prediction of soil properties. But no publications can be found so far on the application of this model in hyperspectral prediction of soil heavy metals. In this paper, Cd, Cu, Pb, Cr, Zn and Ni were studied to establish GWR model for soil heavy metal prediction, with 132 soil samples taken from Fuzhou, a major city in southeastern China. Increasing soil pollution emerges in this area as a result of dense population and developed industrial and agricultural sectors. And the spatial distribution of soil heavy metals in the area features great heterogeneity because of complex and fragmented terrains. At first, metal concentrations of the samples were determined through inductively coupled plasma-mass spectrometry (ICP-MS) analysis, and reflectance was measured with an ASD (Analytical Spectral Devices) field spectrometer covering a spectral range of 350-2500 nm. Then a series of transformations were conducted to enhance the spectral features of heavy metals, such as derivative transformation, reciprocal transformation, absorbance transformation, and continuum removal. And then an analysis was made on the correlation between heavy metal contents and the transformed spectral data, and sensitive spectral bands were selected according to the highest correlation coefficient. With heavy metal contents as dependent variables, and sensitive spectral bands as independent variables, a stepwise regression analysis was conducted to select variables with low multi-collinearity, which were then used to establish prediction models. At last, the applicability and limitation of GWR model in the hyperspectral prediction of heavy metals was assessed by comparing the outcome of predictions based on GWR and OLS regression respectively. Some conclusions can be drawn as follows: (1) The applicability of GWR model is dependent on the spatial heterogeneity level of heavy metal influence on spectral variables: For Cr, Cu, Zn and Pb, whose influence on spectral variables features high-level spatial heterogeneity, GWR-based prediction performance was evidently better than that of OLS. It was shown in an obvious increase of adjusted R² (by 2.69, 2.01, 1.87 and 1.53 times respectively) and an obvious decrease of AIC (by over 3 units) and RSS (by 74.67%, 69.91%, 52.78% and 13.16% respectively); For Cd and Ni, whose influence on spectral variables features low-level spatial heterogeneity, GWR-based prediction displayed an increase of adjusted R² (by 0.015 and 0.007 respectively), a decrease of RSS (by 5.97% and 4.18% respectively) and a rise of AIC (by 2.737 and 2.762 respectively), with less significant improvement in prediction performance; (2) Heavy metal spectral properties are intensified by different spectral transformations, among which reciprocal transformation is most effective. And reciprocal transformation and its derivative patterns improve the performance of heavy metal prediction models; (3) With spatial non-stationarity as the prerequisite of application, GWR model is applicable in hyperspectral prediction of heavy metals that feature obvious spatial heterogeneity with soil spectral variables.