福州市土壤铬含量高光谱预测的GWR模型研究

通过系统分析不同光谱分辨率和光谱变换对土壤铬高光谱预测模型的不确定性影响,筛选出最优的光谱分辨率及光谱变量进行土壤铬含量预测的地理权重回归(GWR)模型构建,利用该模型进行福州市土壤铬含量预测,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模型在土壤铬高光谱预测中的适用性及局限性。结果表明:(1)在10 nm分辨率尺度下,以土壤全铬含量为因变量,反射率的二阶微分和反射率倒数的二阶微分为自变量构建的GWR模型对土壤铬预测的效果最好。GWR模型的R~2和调节R~2分别为0.821和0.716,较OLS模型分别提高了0.529和0.450,而AIC值为720.703,较OLS模型减少了22个单位,残差平方和仅为OLS模型的1/4,说明GWR模型的预测效果较OLS模型有了显著提高。(2)土壤铬预测模型的精度受光谱分辨率影响。对于OLS预测模型来说,3 nm分辨率的模型预测效果最好,而对于GWR预测模型来说,10nm分辨率的模型不仅预测效果最好,其相较于OLS模型的改善作用显著,为土壤铬含量GWR预测的最佳光谱分辨率。(3)光谱的一阶微分变换可以有效增强土壤铬的光谱特征,而其余的光谱变换对土壤铬的光谱特征则未起到增强作用,但可以很好地提高模型的预测效果。(4)研究得出土壤铬GWR模型预测的最佳光谱分辨率为10 nm,为EO-1 Hyperion影像的光谱分辨率,而且随着采样点的增加,GWR模型的预测效果趋于稳定,适合空间异质性大的区域尺度土壤铬预测。故该模型与高光谱影像结合,实现模型从实验室尺度向区域尺度的推广,为格网尺度土壤铬的空间预测提供可能。

Study on GWR model applied for hyperspectral prediction of soil chromium in Fuzhou City

Inversion models applied for hyperspectral prediction of soil chromium include univariate regression, multiple linear regression, principal component regression, and partial least squares regression models. They are mostly based on the presumed homogeneous influence of heavy metal content on spectral reflectance at different locations. This presumption, however, ignores the spatial heterogeneity of correlation between soil chromium and spectral variables. In contrast, Geographically Weighted Regression(GWR) model effectively reveals the spatial heterogeneity among different variables, as is evidenced in many studies involving the spatial prediction of soil properties. In this study, we first analyzed the influence of different spectral resolutions and transformations on soil chromium-targeted hyperspectral prediction model. Thereafter, optimal spectral resolution and variables were selected to establish the GWR model for prediction of soil chromium content in Fuzhou City. In addition, the applicability and limitations of the model were assessed by comparing the predictions based on GWR and Ordinary Least Squares Regression(OLS)models separately. The conclusions finally drawn from the study are as follows:(1) At a resolution of 10 nm, with soil chromium content as a dependent variable and the second derivative of reflectance and reflectance reciprocal as independent variables, the GWR model displayed the best prediction performance. The values of R² and the adjusted R² were 0.821 and 0.716, respectively, which showed an increase of 0.529 and 0.450, respectively, above the corresponding values in the OLS model. The AIC was decreased by 22 units to 720.703, and the residual sum of squares was decreased by three quarters, an indication of significant improvement of the prediction performance. (2) The spectral resolution exerted obvious influence on the accuracy of chromium prediction models. The GWR model, with a spectral resolution of 10 nm, as against the OLS model, with a resolution of 3 nm, showed optimal prediction outcome and an evident increase in accuracy. The best resolution for the GWR model was 10 nm. (3) The spectral transformation of first-order differential effectively enhanced the spectral features of soil chromium. Whereas other spectral transformations failed to enhance the features, they significantly improved the prediction performance. (4) The optimal spectral resolution of 10 nm for GWR-based soil chromium prediction was up to the level of EO-1 Hyperion images. Moreover, the prediction performance of the GWR model showed a tendency to stabilize with the increase in the number of sample sites, which is suitable for soil chromium prediction in the regions featuring great spatial heterogeneity. Therefore, with hyper-spectral images, the application of GWR model can be extended from laboratory to the regional scale, making the spatial prediction of soil chromium on grid basis feasible.