土壤钾元素含量是评价土壤营养程度重要的指标之一。 利用热红外发射率(TASI)数据对钾元素的反演研究较少且模型精度较低。 利用在黑龙江海伦地区采集的热红外航空成像光谱仪TASI数据, 经过预处理和温度与发射率分离后, 探究黑土土壤热红外发射率与钾元素含量关系。 在对比了常规的多元逐步回归与偏最小二乘建模方法后, 使用了一种新的逐步回归方法-全二次多元逐步回归建立模型, 相对于常规多元逐步回归, 引入了更多的参数进行模型的建立, 有效提高反演精度。 研究发现, 土壤发射率数据对于选用有效特性波段建立的模型对钾元素具有较高的反演精度, 所选特征波段均为负相关, 波段分别为6（8.602 μm）, 11（9.150 μm）, 15（9.588 μm）, 23（10.464 μm）, 相关系数依次为-0.658, -0.673, -0.645和-0.627。 钾元素通过多元逐步回归建模与预测的均方根误差RMSE: 0.027和0.032, 判定系数R2: 0.667和0.82, 相比于常规多元逐步回归建模与预测的均方根误差RMSE: 0.031和0.031, 判定系数R2: 0.569和0.78与偏最小二乘法建模与预测的均方根误差RMSE: 0.033和0.037, 判定系数R2: 0.45和0.51评价指标精度均有所提高, 说明该方法有效提高了利用发射率数据对钾元素的反演精度。 在利用学生化残差对模型进行去除异常值的改进后发现, 建模精度有了明显提高但是测试精度却有所降低, 过度拟合训练集数据导致模型泛化性下降, 因此不建议对模型过度拟合。

Potassium content in soil is one of the important indicators for evaluating soil nutrient levels. There are few studies using thermal infrared emissivity data to invert potassium, and the model accuracy is low. In this paper, the Thermal Airborne Hyperspectral Imager (TASI) data collected in the Hailun region of Northeast China is used to investigate the relationship between soil emissivity and potassium content in black soil after pretreatment and separation of temperature and emissivity. Compared with the constant multiple stepwise regression and partial least-square regression model, a new stepwise regression method- quadratic multiple stepwise regression is innovatively used to enhance the model. Compared with the constant multiple stepwise regression, more parameters are introduced to establish the model, which can effectively improve the inversion accuracy. It is found that the model which uses effective special selected bands has a higher inversion accuracy to the potassium element and the selected bands are negatively correlated. The bands are 6 (8.602 μm), 11 (9.150 μm), 15 (9.588 μm), and 23 (10.464 μm)and the correlation coefficients are -0.658, -0.673, -0.645, -0.627, respectively. The quadratic multiple stepwise regression model’s RMSE of the training and testing data are 0.027 and 0.032, the decision coefficient R2 are 0.667 and 0.82. Compared to the constant multiple stepwise regression model’s RMSE of the training and testing data: 0.031 and 0.031, the decision coefficient R2: 0.569 and 0.78 and the least squares model’s RMSE: 0.033, 0.037, the judgment coefficient R2: 0.45, 0.51, the precisions of evalution indexes have been improved, it is indicated that this method effectively improved the inversion accuracy of the potassium element using the emissivity data. After using the studentized residuals to improve the model to remove the outliers, it is found that the training accuracy is significantly improved but the test accuracy is reduced. Over-fitting the training set data leads to the decline of the model generalization. Therefore, the model is not recommended to improve.