## 1 Introduction  
The photosynthesis ability of vegetation is closely related to vegetation growth status, which is influenced by biochemical concentrations. The leaf nitrogen concentration (LNC) is one of the most important biochemical parameters closely related to the photosynthetic efficiency and crop yields [1]. Therefore, LNC can serve as a major indicator for monitoring crop growth status based on passive or active technology in the field of remote sensing [2, 3], wherein related investigations have been conducted by many researchers.  
For passive remote sensing technology, the reflectance spectrum of crops was measured, and the relationship between spectral characteristics and LNC or crop status was established. Thus, numerous investigations regarding LNC estimation have been done due to the non-destructive, fast, and large-scale advantages of passive remote sensing technology [4; 5; 6]. These investigations found that LNC was closely related to the visible and near-infrared regions of reflectance spectrum. Relative metrics (such as vegetation indices and spectral characteristics) based on reflectance spectra were then proposed for LNC estimation [1; 7; 8]. [PERSON] et al. [9] analyzed the sensitivity of spectral bands for LNC estimation. In addition, [PERSON] et al. [10] discussed the correlation between CO\({}_{2}\) and LNC and found that the efficiency of solar energy utilization was influenced by the LNC from the canopy scale. What's more, the three-dimensional information of crops can be measured by using light detection and ranging (LiDAR), which is an active remote sensing technique. Several metrics calculated based on spatial information can be efficiently applied in the monitoring of crop status. At present, passive and active remote sensing technologies have been maturely applied in the monitoring of crop growth status based on proposed relative metrics, which can provide guidance for precision agricultural management [11; 12; 13; 14].  
Laser-induced chlorophyll fluorescence spectrometry (LICFs) serves as another remote sensing technology for crop growth status monitoring and has attracted considerable attention from numerous investigators [15; 16; 17; 18; 19; 20]. Chlorophyll fluorescence can be efficiently applied in nutrient stress estimation and photosynthetic ability monitoring. [PERSON] and [PERSON] [21] analyzed the performance of chlorophyll fluorescence for nutrient stress monitoring in rice and found that the ratios of fluorescence intensity have considerable potential for remote sensing of stress effects in plants. [PERSON] et al. [22] used the fluorescence intensity ratio F685/F730 (the fluorescence intensity at 685 nm divided by that at 730 nm) to monitor chlorophyll concentration when evident reduction was not observed. [PERSON] et al. [23; 24; 25] compared the performance of published fluorescence metrics for LNC estimation and discussed the effect of fluorescence parameters combined with multivariate analysis on the accuracy of LNC monitoring. [PERSON] [26] utilized the chlorophyll fluorescence intensity ratio F690/F735 to analyze the changes in chlorophyll concentration and found that it was linearly related to fluorescence concentration. These investigations displayed the potential of chlorophyll fluorescence for LNC monitoring.  
However, understanding of the effect of kernel function or internal parameters of multivariate analysis on the LNC estimation is still limited. In addition, the fluorescence index is restricted by the fluorescence intensity ratio chosen. Thus, the main aims of this study are (1) to analyze the effect of kernel function of multivariate analysis on the accuracy of LNC estimation and select the optimal internal parameters; and (2) to discuss the performance of the proposed fluorescence index based on the slope characteristics of fluorescence spectrum for LNC estimation.