红边位置改进算法的冬小麦叶绿素含量反演

植被反射光谱的红边位置对叶绿素含量高度敏感，利用遥感数据建立基于红边位置的作物叶绿素含量反演模型，可实现大范围作物及时的长势监测。该研究以冬小麦为研究对象，在学习6种经典红边位置求解算法的基础上，提出牛顿-切比雪夫插值法和牛顿八点插值法2种改进红边位置求解算法。根据不同算法的红边位置分布特征综合分析了改进算法的优缺点，并在此基础上建立基于红边位置的冬小麦叶绿素含量反演模型。结果表明，与传统算法相比，2种改进算法均显著改善了双峰现象和红边位移，且基于新算法的模型预测值与叶绿素含量实测值的决定系数>0.619，较最大一阶导数法提高了5.024%～10.480%，具有更高的精度。同时，在2种改进算法中，牛顿八点插值法具有更高的稳定性与实用性。研究结果为植被理化参数反演与农业生产应用提供理论与技术支撑。

Inversion of winter wheat chlorophyll contents based on improved algorithms for red edge position

Red Edge Position (REP) of vegetation spectral reflectance is highly sensitive to chlorophyll content. The inversion model of crop chlorophyll content based on REP enables timely growth monitoring of the crops on a large scale. The displacement of REP and bimodal phenomenon are ubiquitous in 6 traditional algorithms of REP. To reduce the adverse effects effectively, the Newton interpolation method was applied to calculate REP in this study. And two improved REP solving algorithms, Newton-Chebyshev-Node Interpolation (REP_NCNI) and Newton Eight-Point Interpolation (REP_NEPI) were proposed. The strengths and weaknesses of the old and improved algorithms were analyzed, according to the distribution characteristics of REP from different algorithms, and the comprehensive attribute information of the different algorithms was compared. It was found that: 1) Maximum First Derivative (REP_MFD) method and Lagrange Three-Point Interpolation (REP_LAGR) method had the largest variation of REP (41 nm), which was sensitive to chlorophyll content, however, there was an obvious bimodal phenomenon. 2) The REP calculated by an Inverted Gaussian (REP_IG) model method ranged from 695 nm to 729 nm with the lowest mean value (719.5 nm). The whole model moved towards the short-wave direction (blue shift) with the highest Relative Error (RE) (0.882%). 3) The REP calculated by the Linear Four-Point Interpolation method (REP_LFPI) were between 717 and 731 nm, with an average value of 725.4 nm. The whole result was clustered in the direction of a long wave, and the REP had the smallest variation (14 nm), which was not sensitive to the change of chlorophyll content. 4) The variation of the Linear Extrapolation (REP_LE) method was better (37.1 nm), but the average value was lower (721.9 nm). The whole value moved towards the short-wave direction (blue shift), and the RE was larger (0.551%). 5) The results of polynomial fitting of the ninth order (REP_POLY) were generally good, but the bimodal phenomenon was the most serious. 6) The REP_NCNI and REP_NEPI overcame the bimodal phenomenon and displacement of REP effectively with ideal mean value, amplitude, and RE. And the least square regression was adopted to establish the inversion model of chlorophyll content of winter wheat based on REP. The study revealed that compared with traditional algorithms, the improved algorithms exhibited the most accurate and robust performance, where the coefficient of determination of the chlorophyll content inversion model established by improved algorithms was higher than that of traditional algorithms with the coefficient of determination of 0.728 and 0.751, respectively. Moreover, in the improved algorithms, the coefficient of determination between the predicted value and the measured value was greater than 0.619, which was 10.480% higher than that of the REP_MFD method, and the standard root mean square error was less than 0.151, indicating that the goodness of the model was better. At the same time, the coefficient of determination of the inverse equation (0.455-0.758) was higher than that of the fitting equation (0.396-0.656). And the inversion model was ranked chlorophyll-a model, chlorophyll-ab model, and chlorophyll-b model, according to the coefficient of determination from large to small. Besides, the research showed that in the two improved algorithms, the REP_NEPI demonstrated the best and satisfactory performance than REP_NCNI. Considering that only 8 bands were needed to calculate REP by REP_NEPI, it provided a theoretical basis for making a simple sensor to determine the chlorophyll content of crops. The results showed that REP_NEPI was the optimal selection for the calculation of REP and the inversion of chlorophyll content of winter wheat. And this study should provide theoretical and technical support for the inversion of biophysical and biochemical parameters of vegetation and the application in agricultural production.