## 3 Results and Discussion
### Performance Analysis of Models  
At present, LIF technology has been widely applied in remote sensing for monitoring the growth status of vegetation. In this study, the effect of hidden layer sizes and train function of BPNN model on the accuracy of LNC estimation was analyzed. The results demonstrated that the effect of the selected training function on the accuracy of LNC estimation is more evident than that of the hidden layer sizes. In this study, the minimum number of hidden layers is varying for different fluorescence characteristics which may be related to the input layer sizes. The \"trainrp,\" \"trainbr,\" and \"trainlm\" of training functions are superior to other training functions based on BPNN model for different fluorescence characteristics. In addition, a fluorescence index based on the slope of fluorescence spectrum was proposed and used to estimate LNC. For \"traingd,\" \"traingdm,\" \"traingda,\" \"traingdx,\" and \"traincgf,\" the proposed fluorescence index (the mean of \(R^{2}\) are 0.407, 0.412, 0.626, 0.636, and 0.746 corresponding to Figure 5a-d, and 5f, respectively) is superior to the fluorescence ratios (the mean of \(R^{2}\) are 0.342, 0.337, 0.596, 0.594, and 0.738 corresponding to Figure 4a-d, and 4f, respectively) and fluorescence characteristics calculated by PCA (the mean of \(R^{2}\) are 0.239, 0.248, 0.517, 0.518, and 0.701 corresponding to Figure 3a-d, and 3f, respectively) based on the gradient descent algorithm to train the BPNN model for LNC estimation. In addition, the proposed fluorescence index exhibited better reliability and stability with lower SD values than other fluorescence characteristics. The possible interpretation is that the fluorescence index can efficiently eliminate the effect of background noise on the fluorescence signal [38; 39]. Fluorescence will be influenced by the fluctuation of environmental conditions and the leaf or canopy chlorophyll concentration. Although the fluorescence characteristics calculated based on PCA and fluorescence ratios cannot efficiently eliminate these influence factors, they can improve the detection of the differences of the fluorescence characteristics of different LNCs. However, the proposed fluorescence index based on the slope of fluorescence characteristic peaks can eliminate the effect of background noise on fluorescence characteristics to a certain extent [38; 40; 41]. Thus, the proposed fluorescence index exhibited promising potential due to its stability for LNC estimation.  
In this study, the performance of different fluorescence characteristics for LNC estimation was compared based on the BPNN model. In addition, the effect of hidden layer sizes and training function of BPNN model on the accuracy of LNC estimation was analyzed. However, some limitations of this investigation should be considered. For example, a method to confirm the minimum number of hidden layers should be discussed, and as only the BPNN model was used in this research, other algorithms also need to be considered. In addition, whether the proposed fluorescence index can eliminate the effect of crop varieties or growth seasons on the fluorescence characteristics should be discussed in future work.