Novel Combined Spectral Indices Derived from Hyperspectral and Laser-Induced Fluorescence LiDAR Spectra for Leaf Nitrogen Contents Estimation of Rice

: Spectra of reﬂectance ( S r ) and ﬂuorescence ( S f ) are signiﬁcant for crop monitoring and ecological environment research, and can be used to indicate the leaf nitrogen content (LNC) of crops indirectly. The aim of this work is to use the S r -S f features obtained with hyperspectral and laser-induced ﬂuorescence LiDAR (HSL, LIFL) systems to construct novel combined spectral indices ( NCI H-F ) for multi-year rice LNC estimation. The NCI H-F is in a form of FWs* Φ + GSIs* Φ , where Φ is the S r -S f features, and FWs and GSIs are the feature weights and global sensitive indices for each characteristic band. In this study, the characteristic bands were chosen in di ﬀ erent ways. Firstly, the S r -S f characteristics which can be the intensity or derivative variables of spectra in 685 and 740 nm, have been assigned as the Φ value in NCI H-F formula. Simultaneously, the photochemical reﬂectance index ( PRI ) formed with 531 and 570 nm was modiﬁed based on a variant spectral index, called PRI fraction , with the S f intensity in 740 nm, and then compared its potential with NCI H-F on LNC estimation. During the above analysis, both NCI H-F and PRI fraction values were utilized to model rice LNC based on the artiﬁcial neural networks (ANNs) method. Subsequently, four prior bands were selected, respectively, with high FW and GSI values as the ANNs inputs for rice LNC estimation. Results show that FW- and GSI-based NCI H-F are closely related to rice LNC, and the performance of previous spectral indices used for LNC estimation can be greatly improved by multiplying their FWs and GSIs. Thus, it can be included that the FW- and GSI-based NCI H-F constitutes an e ﬃ cient and reliable constructed form combining HSL ( S r ) and LIFL ( S f ) data together for rice LNC estimation.

contribution to LNC, can be considered in the estimation of LNC in a form of FWs*Φ, where Φ is the intensity or derivative variables of S r and S f . Global sensitivity analysis can generate global sensitivity indices (GSIs) that present the contributions from multiple interest biochemicals, such as Chl, water and so on, to the changes in each feature band [44,45]. GSIs were also formed in a similar way as GSIs*Φ for each prior ranked band. Then, the above FW-and GSI-based items are integrated finally in a form of FWs*Φ + GSIs*Φ for LNC estimation.
This work aims to construct a combined SIs for LNC estimation of rice by using S r -S f features obtained with HSL and LIFL systems. The rice leaf sampling and the data measurements of S r -S f are described in Section 2. An overview of the analysis methods in this study can be found in Section 3.1, and then two factor-calculated methods (FW analyses and global sensitivity analyses) are respectively presented in Section 3.2. Responding to the Results section, the NCI H-F models of rice LNC based on these two methods in specified bands (685 and 740 nm) are presented in Sections 4.1 and 4.2 respectively. The regression algorithm is ANN which has been described in Section 3.3. Being different with the designated variables in 685 and 740 nm, the first four bands ranked according to the FWs and GSIs are selected successively for the prediction of rice LNC (Section 4.3). Comparisons and discussions of the model performance are provided in Section 5, followed by the conclusions drawn in Section 6.

Samples Preparation
Leaf samples were collected in the Jianghan Plain of China (29 • [46]. The rice varieties were Yongyou 4949 (2014) and Yangliangyou 6 (2015). Different levels of urea fertilizer were used in the experimental fields which could be found in the study of Shi et al. [37] in detail. Three fertilization repetitions were performed for each cultivation condition in 2014 and 2015. The sample sizes in this experiment were 120 for 2014 and 144 for 2015. The rice leaves were the second ones from the canopy of the rice plant, which were destructively sampled by randomly cutting six leaves for each experimental field.

LiDAR Systems and Data Measurement
The HSL system used in this work consisted of some fundamental components, including laser emission, photovoltaic receiving and conversion and the data processing section ( Figure 1). The light emission section of the HSL mainly contained a supercontinuum laser source (SuperK EXTREME, NKT Photonics Inc., DEN), which can generate a wide-band laser with a frequency of 20-40 kHz, an average output power of 100 mW, a broadband spectrum white light of~450-2400 nm and a pulse duration of 1-2 ns [47,48]. The data collected by HSL represented the characteristic spectrum of the target in a range of 538-910 nm with the spectral resolution of 12 nm based on the APD array, which consisted of 32 separated channels with a spectral sensitive range of 300-920 nm (D1 in Figure 1). The components of LIFL system were similar to those of HSL, and the only difference with HSL was that the LIFL system had the ultraviolet excitation light source (355 nm, 20 Hz, Surelite OPO PLUS, USA) and a spectrograph with ICCD camera (D2 in Figure 1, Princeton Instrument SP2500i, USA) as the section of laser emission, and photovoltaic receiving and conversion, respectively. The laser source for LIFL is an Nd: YAG which has an output power of 1.5 mJ and width per pulse of 5 ns. The spectrograph can be controlled along with the direct commands through its USB or RS-232 port, so as to scan and then obtain S f characteristics with a wide-range (360-800 nm) and high spectral resolution (0.5 nm). In order to eliminate the effects of light reflected from the laser, we placed a 355 nm long-pass edge filter (M3 in Figure 1) between the spectrograph and the optics fiber during S f collection. The filter was 4 of 17 shunted to the other side during the measurement of S r . These two LiDAR systems, which had the same optics design, were used in collecting and focusing light signals into an achromatic telescope (with a diameter of 200 mm, MEADE, USA), and then transmiting the light signals reflected from the target surface to two photo-sensitive receiver ports on a SP2500i spectrometer (D1 for S r , red and D2 for S f , blue in Figure 1) through an optics fiber for photovoltaic conversion. Further details about the systems can be found in the study of Du et al. [40] and Yang et al. [49].
Remote Sens. 2019, 12, x FOR PEER REVIEW  4 of 17   systems, which had the same optics design, were used in collecting and focusing light signals into an  achromatic telescope (with a diameter of 200 mm, MEADE, USA), and then transmiting the light  signals reflected from the target surface to two photo-sensitive receiver ports on a SP2500i  spectrometer (D1 for Sr, red and D2 for Sf, blue in Figure 1) through an optics fiber for photovoltaic conversion. Further details about the systems can be found in the study of Du et al. [40] and Yang et al. [49]. With these two LiDAR systems, spectra of Sr and Sf were measured at three different positions off the rice leaf vein for one sample, and five replications were carried out at the same position. Then, the characteristic spectra for one leaf were represented with the average of 15 spectra obtained by the above process. The laser spots of HSL and LIFL resided onto the measured position perpendicularly and completely.
As shown in Figure 2, differences among rice LNC levels are easily distinguished on the basis of some feature positions on the Sr and Sf curves measured by HSL ( Figure 2a) and LIFL (Figure 2b) systems respectively. After the collection of the spectra, LNC values were determined using the Kjeldahl method [50], and then weighted and expressed as milligrams per gram of leaf dry matter. The LNC values in 2014 ranged from 2.5 to 4 mg/g, with an average (Ave) of 3.34 mg/g and standard deviation (SD) of 0.27 mg/g. In 2015, the LNC ranging from 1.1mg/g to 4.4mg/g had an Ave value of 2.84 mg/g and SD value of 0.61 mg/g. With these two LiDAR systems, spectra of S r and S f were measured at three different positions off the rice leaf vein for one sample, and five replications were carried out at the same position. Then, the characteristic spectra for one leaf were represented with the average of 15 spectra obtained by the above process. The laser spots of HSL and LIFL resided onto the measured position perpendicularly and completely.
As shown in Figure 2, differences among rice LNC levels are easily distinguished on the basis of some feature positions on the S r and S f curves measured by HSL ( Figure 2a) and LIFL ( Figure 2b) systems respectively. After the collection of the spectra, LNC values were determined using the Kjeldahl method [50], and then weighted and expressed as milligrams per gram of leaf dry matter. The LNC values in 2014 ranged from 2.5 to 4 mg/g, with an average (Ave) of 3.34 mg/g and standard deviation (SD) of 0.27 mg/g. In 2015, the LNC ranging from 1.1 mg/g to 4.4 mg/g had an Ave value of 2.84 mg/g and SD value of 0.61 mg/g.

Overview of the Analysis Method
In this study, a SIs, called NCIH-F, was constructed to estimate the rice LNC. This kind of SIs links the HSL and LIFL spectra to LNC through two factors ( 1 ω , 2 ω in Equation (1)) which are closely related to the characteristic bands.
On the basis of two calculation methods for these factors, the analysis methods in this study were organized as shown in Figure 3: (Ⅰ) FW-based NCIH-F were utilized for estimation of rice LNC, and then (Ⅱ) utilized based on GSIs. The results were respectively summarized in Section 4.1 and 4.2. (Ⅲ) Finally, four characteristic bands from Sr and Sf data were respectively ranked and then selected based on the values of FW and GSI for the calculation of NCIH-F, rather than designating them in 685,

Overview of the Analysis Method
In this study, a SIs, called NCI H-F, was constructed to estimate the rice LNC. This kind of SIs links the HSL and LIFL spectra to LNC through two factors (ω 1 , ω 2 in Equation (1)) which are closely related to the characteristic bands.
On the basis of two calculation methods for these factors, the analysis methods in this study were organized as shown in Figure 3: (I) FW-based NCI H-F were utilized for estimation of rice LNC, and then (II) utilized based on GSIs. The results were respectively summarized in Sections 4.1 and 4.2.
(III) Finally, four characteristic bands from S r and S f data were respectively ranked and then selected based on the values of FW and GSI for the calculation of NCI H-F , rather than designating them in 685, 740 nm. The estimation results were showed in Section 4.3. Meanwhile, a modified SI Remote Sens. 2020, 12, 185 6 of 17 named PRI fraction (Equations (7) and (8) in Section 4.1) [51] was proposed in steps (I) and (II) for the comparison experiment.  (7) and (8) in Section 4.1) [51] was proposed in steps Ⅰ) and Ⅱ) for the comparison experiment.

Two Methods for NCIH-F Factor Calculation
The NCIH-F values derived from HSL and LIFL data are linked in a linear form according to the contribution ratio of Sr ( 1 ω ) and Sf ( 2 ω ) to LNC, as determined with two methods described in

Feature Weights for Each Spectral Band
The FWs of each band represent the efficient indicators linking the spectra in wide-bands to biochemical contents. In this work, FWs were calculated on the basis of the divergence for each class divided according to vegetation species and biochemical contents. In the calculation process, a significant coefficient of band corresponding to class j, ( ) j η λ (j=1, 2, …, m), was ranked in descending order with Equation (3) according to band sensitivity to the different biochemistry parameters. Subsequently, the FWs for each band were calculated using Equation (2), where re-ranked P λ was the band position in the sequence of ( )

Two Methods for NCI H-F Factor Calculation
The NCI H-F values derived from HSL and LIFL data are linked in a linear form according to the contribution ratio of S r (ω 1 ) and S f (ω 2 ) to LNC, as determined with two methods described in Sections 3.2.1 and 3.2.2. The values of Φ HSL and Φ LIFL in Equation (1) may represent the intensity of S r and S f in a single band (685 or 740 nm), and can represent the SIs derived from LiDAR data.

Feature Weights for Each Spectral Band
The FWs of each band represent the efficient indicators linking the spectra in wide-bands to biochemical contents. In this work, FWs were calculated on the basis of the divergence for each class divided according to vegetation species and biochemical contents. In the calculation process, a significant coefficient of band corresponding to class j, η j (λ) (j = 1, 2, . . . , m), was ranked in descending order with Equation (3) according to band sensitivity to the different biochemistry parameters. Subsequently, the FWs for each band were calculated using Equation (2), where P λ re−ranked was the band position in the sequence of η j (λ) in Equation (3), Remote Sens. 2020, 12, 185 where n is the number of bands, µ i represents a divergence ratio of the ith band to all bands, and E λi denotes the elements of eigenvectors of the covariance matrix for each class.

Global Sensitivity Indices for Each Spectral Band
In this section, the sensitivity indices of parameters to the changes in total spectra in each band were noted as the new weights for constructing NCI H-F for LNC estimation. Given that k variables affect the variation characteristics of LNC in a spectrum, the set of parameter variables was defined as A = [a 1 , a 2 , . . . , a k ]. For A = [a 1 ], only one variable was present, and a i = a i , the variance of R(λ) was Var[R(λ)| a i ]. Generally, the value of a i was unpredictable. Hence, the variance was unavailable. However, the expectation for R(λ) can be calculated according to all the possible values of a i , which can be substituted with the variance, noted as E[R(λ)| a i ]. Then, the sensitivity of the single variable GSI s i to the reflection spectrum can be characterized using the following formula: This equation was used in a local sensitivity analysis called the first-order sensitivity index, which disregarded the influence of other parameters. In fact, a feature spectrum is not determined by a single variable but is the result of the interaction of many factors, and usually GSI s ij (λ) ≥ GSI s i (λ) + GSI s j (λ). In this work, a total sensitivity index (Equation (5)) with multivariable was calculated by taking the spatial autocorrelation coefficient γ(λ) as the input condition, and was used as the basis for the priority ranking of sensitive bands.
Each variable shows unique sensitivity in different bands, and even the spectral intensity in the same band depends on multiple parameters. This attribute is not only a powerful basis for constructing NCI H-F for LNC estimation, but also an essential analysis strategy for the inversion and extraction of specific biochemical parameters.

Artificial Neural Networks for LNC Estimation
In this section, an ANN with four training functions, namely, Levenberg-Marquardt Algorithm (trainlm), Bayesian regularization algorithm (trainbr), Quasi-Newton Algorithm (trainbfg), and one step secant algorithm (trainoss) were described, and then utilized for the prediction of rice LNC with the constructed NCI H-F values.
The feed forward ANNs in this work consisted of three layers, namely input, hidden, and output, which were created, trained, and implemented in the Matlab 2014b environment. Four commonly used training functions were adopted respectively. Additionally, the ANN conditions were set as follows: minimum mean square error (MSE) of 10 −3 , minimum gradient of 10 −6 , and maximum iteration number (epochs) of 100. After the conditions were met, the ANNs iteration process was stopped. Other details about ANNs can be found in the work of Yegnanarayana [52] and the documents of software Matlab 2014b.
The nonlinear activation function f non in Equation (6) was used in processing the iteration process. The function generated a y value as the predicted LNC, where b i is the network weight and c i is the bias, which were all adjusted along with the gradient-decreased MSE. Figure 2 shows the spectra of S r and S f collected by HSL and LIFL systems under four different LNC levels, and the distribution of prior LNC-sensitive bands on the S r and S f curves. The features of S r and S f in special bands were closely related to the LNC values of rice, which could be correctly measured by these two LiDAR systems, whether there was a positive or negative relationship. Thus, these two LiDAR systems were reliable remote sensing tools for rice feature spectra measurement, regardless of S r or S f characteristics under different LNC levels. Moreover, prior bands selected with FWs and GSIs were discretely distributed onto the S r and S f curves and covered most LNC-sensitive bands. This finding indicated that the analysis of feature weight and the global sensitivity of numerous factors to the spectral intensity in each special band was powerful potential method for selecting preferentially sensitive bands for vegetation biochemical estimation, especially N.

Results
On the basis of a series of spectra of S r and S f collected by HSL and LIFL system, we constructed numerous combined SIs linked by FWs and GSIs for LNC estimation, and finally obtained some SIs with high R 2 (that >0.7 have been in bold in Table 1, Table 2, and Table 4) for LNC prediction models. Generally, the combined SIs performed well in rice LNC modeling in the specified bands, i.e., 685 and 740 nm. Subsequently, we analyzed the ability of NCI H-F in four prior bands on LNC estimation (Section 4.3), and these ranked bands were selected according to FW and GSI values respectively.  Table 2 and Table 4.

LNC Estimation Using FW-Based NCI H-F
On the basis of the construction form of NCI H-F in Equation (1), four FW-based NCI H-F with high R 2 values were obtained during rice LNC estimation ( Table 1). The superscripts (a, b, c and d) of each R 2 in Table 1 indicates the four training functions of ANN models used in examining the relationship between LNC and NCI H-F . The obtained NCI H-F can be classified into two types, namely, the sum of HSL and LIFL variables in two specified bands (685 and 740 nm, marked with NCI H-F *_W in Table 1), that is, there are four variables (H685, H740, F685 and F740). Another type is the modified photochemical reflectance index (PRI), called PRI fraction (Equation (7)) which is also presented in Table 1. Similar to the combined form of NCI H-F , the bands used in PRI fraction , including 531, 570 and 740 nm, were also replaced with FWs*Φ, or GSIs*Φ in the subsequent analysis. PRI is commonly used as an indicator of vegetation photosynthesis process. In this study, the item k lif in Equation (7) was replaced with F740, which is expressed Equation (9) as follows: For NCI H-F 0_W in Table 1, we set a constant weight of 0.5, whereas ω 1 = ω 2 = 0.5 for each spectral variable, and obtained an R 2 of 0.74 in the booting stage and a R 2 of 0.7 in the heading stage of 2014.
Replacing ω 1 and ω 2 with the corresponding FWs for 685 and 740 nm alternatively (NCI H-F 1_W), the model results were improved by more than 0.8 and 0.72 in 2014 respectively. In 2015, the NCI H-F with a constant contribution weight of 0.5, had no outstanding performance in LNC estimation. By replacing the constant weights with their FWs, we could obtain an R 2 of 0.61 for NCI H-F 1_W. For NCI H-F 2_W, the spectral variables of NCI H-F were single band (H685, F685), which were different from those of NCI H-F 1_W. Table 1 shows that the R 2 of NCI H-F 1_W model can be more than 0.79 for 2015, while is less than 0.7 for both stages of 2014.

LNC Estimation Using GSI-Based NCI H-F
As shown in Section 4.1, the same kinds of NCI H-F obtained R 2 values of >0.7 in this section. The difference with FW-based NCI H-F was that the spectral variables are connected with GSIs, and some items used to construct NCI H-F in the same form had changed. For example, for NCI H-F 2_S the spectral variable was (H740, F740), and not the (H685, F685) in NCI H-F 2_W. The NCI H-F 2_S model for LNC estimation performed well in 2014-B, but obtained an unsatisfactory result in 2014-H, and even a bad performance in 2015-T. When the GSI-based NCI H-F in four spectral variables was used, the NCI H-F 1_S was available in 2014 and 2015 data, obtaining a mean R 2 of 0.76 (Table 2). However, for PRI fraction _S, the ANN model performed well with R 2 of 0.74 for the 2015-T data. The difference in performance can be found in Section 4.1, which shows a relatively good results in 2014-H and 2015-T. Thus, the spectra in different years can be a noteworthy issue in the LNC estimation of rice.
The PRI has been demonstrated to be a robust spectral index that is closely related to the vegetation photosynthesis process in leaf and canopy scales [2]. PRI has the same construction form as NDVI, which is calculated in 531 and 570 nm (Equation (8)). As well, PRI had been proved the available ability on LNC estimation with different training functions of ANNs in this study. In comparison with PRI, we found that the PRI fraction with FW-and GSI-based weights could be a more effective index for LNC estimation in rice. For example, the total mean R 2 of PRI was 0.68 for the 2015 data ( Figure 4); this value was slightly lower than the PRI fraction values represented in Tables 1 and 2. Thus, the FW-and GSI-based weights could be efficiently used in improving the performance of PRI in LNC estimation on the basis of S r -S f features obtained with HSL and LIFL systems. Notably, the mean R 2 of PRI was 0.69 in both stages of 2014, and these values were higher than the PRI fraction modified based on the FWs and GSIs in Tables 1 and 2. These results indicated that the growth stages and years of rice served as relatively sensitive factor which affected the model performance of combined SIs in LNC estimation. and years of rice served as relatively sensitive factor which affected the model performance of combined SIs in LNC estimation.

NCIH-F in Ranked Bands for LNC Estimation
In this section, the bands used to construct NCIH-F were selected preferentially based on the FW and GSI values. Then, the first four prior bands were selected as the spectral variables for the calculation of NCIH-F, and modeling of rice LNC with the ANN method. These prior bands are the LNC-sensitive characteristics to rice LNC, and they are discretely distributed onto some critical positions of HSL and LIFL spectra ( Figure 2). Concretely, the positive relationship between N level and Sr intensity can be changed to a negative relationship in approximately 700 nm. Alternatively, for Sf, the double-peak spectra in 650-750 nm regularly increased along with the N level.
Based on the positions of these selected bands, four FW-based prior variables for Sr were almost distributed in the near-infrared band. These variables were significantly important to the GSV because of the reflectance and absorption characteristics of pigments in vegetation leaf. In Sf curve, FW-based prior bands were distributed discretely over the whole interest range of 450-800 nm (Figure 2b). For the prior bands selected by GSI values, two bands located in the "red-edge" position of Sr curve, while all of them located in the bands centered about the double-peak characteristics in Sf curve.
With these selected bands, NCIH-F was calculated and then unitized in estimating LNC for the 2014-and 2015-year data based on ANNs method. The results could be found in Figure 5, which showed the optimal R 2 among these band-ranked NCIH-F. In comparison with the use of specified bands in the above section, the NCIH-F with ranked bands generally had an acceptable modeling accuracy for the 2014 and 2015 data, whereas for GSI-based NCIH-F the R 2 was less than 0.7 ( Figure  5b).

NCI H-F in Ranked Bands for LNC Estimation
In this section, the bands used to construct NCI H-F were selected preferentially based on the FW and GSI values. Then, the first four prior bands were selected as the spectral variables for the calculation of NCI H-F , and modeling of rice LNC with the ANN method. These prior bands are the LNC-sensitive characteristics to rice LNC, and they are discretely distributed onto some critical positions of HSL and LIFL spectra ( Figure 2). Concretely, the positive relationship between N level and S r intensity can be changed to a negative relationship in approximately 700 nm. Alternatively, for S f , the double-peak spectra in 650-750 nm regularly increased along with the N level.
Based on the positions of these selected bands, four FW-based prior variables for S r were almost distributed in the near-infrared band. These variables were significantly important to the GSV because of the reflectance and absorption characteristics of pigments in vegetation leaf. In S f curve, FW-based prior bands were distributed discretely over the whole interest range of 450-800 nm (Figure 2b). For the prior bands selected by GSI values, two bands located in the "red-edge" position of S r curve, while all of them located in the bands centered about the double-peak characteristics in S f curve.
With these selected bands, NCI H-F was calculated and then unitized in estimating LNC for the 2014-and 2015-year data based on ANNs method. The results could be found in Figure 5, which showed the optimal R 2 among these band-ranked NCI H-F . In comparison with the use of specified bands in the above section, the NCI H-F with ranked bands generally had an acceptable modeling accuracy for the 2014 and 2015 data, whereas for GSI-based NCI H-F the R 2 was less than 0.7 (Figure 5b). Remote Sens. 2019, 12, x FOR PEER REVIEW 11 of 17  ω are respectively calculated with the FWs and GSIs in bands of 531 and 570 nm following Equation (7) and (8).
Linking factors (ω1 and ω2) for NCIH-F in Equation (1) were listed in Table 3, in which the sum variables (H685 H740) and (F685 F740) for NCIH-F 1_W and _S had the comparative contribution to NCIH-F (approximately 0.5). However, for FW-based NCIH-F, the values of ω1 and ω2 for single variable, such as H685 and F685, were 0.27 and 0.73 respectively, indicating that the Sr features from HSL data had a weaker contribution to LNC than that using Sf from the LIFL data. For GSI-based NCIH-F, namely NCIH-F 2_S with variables of H740 and F740, had the near factor values (ω1 =0.50 and ω2 =0.50). For the PRIfraction, the variable in the denominator was replaced by F740, with FW and GSI values as the contribution ratios ω1 and ω1, and being less than 0.4 (0.35 and 0.24 respectively).

Comparison with Previously Published Methods
Both Sr and Sf features are the important indicators for GSV monitoring. Thus, we attempted to find an effective way to combine these two spectral properties together for LNC modeling. The first thing we could conceive was to construct a common SI based on the HSL and LIFL data, which is Linking factors (ω 1 and ω 2 ) for NCI H-F in Equation (1) were listed in Table 3, in which the sum variables (H685 H740) and (F685 F740) for NCI H-F 1_W and _S had the comparative contribution to NCI H-F (approximately 0.5). However, for FW-based NCI H-F , the values of ω 1 and ω 2 for single variable, such as H685 and F685, were 0.27 and 0.73 respectively, indicating that the S r features from HSL data had a weaker contribution to LNC than that using S f from the LIFL data. For GSI-based NCI H-F , namely NCI H-F 2_S with variables of H740 and F740, had the near factor values (ω 1 = 0.50 and ω 2 = 0.50). For the PRI fraction , the variable in the denominator was replaced by F740, with FW and GSI values as the contribution ratios ω 1 and ω 1 , and being less than 0.4 (0.35 and 0.24 respectively).  (7) and (8).

Comparison with Previously Published Methods
Both S r and S f features are the important indicators for GSV monitoring. Thus, we attempted to find an effective way to combine these two spectral properties together for LNC modeling. The first thing we could conceive was to construct a common SI based on the HSL and LIFL data, which is sensitive to rice LNC. Vegetation LNC is thought to be codetermined by S r -S f characteristics, and the values of ω 1 and ω 2 can be considered as their corresponding contribution ratios to LNC. Some combined indices derived from HSL and LIFL data had been proposed in some previous works. Shi et al. [40] developed a kind of combined index with the similar form as NDVI by combining HSL and LIFL spectral variables, called N(H685, F685) and N(H740, F740) in Equation (10). However, these combined indices performed poorly, and even had a weaker ability for LNC modeling than the ratio indices obtained by using HSL or LIFL spectra separately. In this work, we linked the HSL and LIFL variables to rice LNC as expressed in a form of Equation (1), and named as NCI H-F , which was constructed by significant factor, such as FWs and GSIs for each band. Accordingly, we improved the estimation results efficiently. In addition, we found that adding more characteristics entered as the model input did not necessarily improve the results. Conversely, the combined SIs with only two spectral variables showed the same good model R 2 , such as the NCI H-F 2_S in Table 2, and HL-NormIndex_W and _S in Table 4. Hence, multiplying the bands with their corresponding FWs or GSIs may efficiently combine S r and S f together for LNC estimation, and the ability of SIs for LNC estimation relies mostly on the combination forms of spectral variables. Moreover, with the purpose of supporting the above conclusion and further improving the SIs performance on LNC estimation [38], we replaced the spectral variables in Equation (9), including H685, F685, H740 and F740, by FWs and GSIs multiplied with the corresponding bands, and then conducted LNC modeling with these modified SIs. Table 4 showed that the model performance was improved, and some R 2 values distinctly reached 0.82 (HL-NormIndex_W and _S) while with a lower RMSE. Thus, the FW-and GSI-based methods in this work may be used to efficiently construct combined SIs for LNC estimation and improve the model performance significantly.

Prior Bands Selection
In Figure 5, the FW-based combined SIs performed better in linking NCI H-F to rice LNC than that SIs using GSI values. The selected bands from the HSL and LIFL spectrum in Figure 2 can also explain this result. The prior bands ranked based on FWs were regularly located in the major S r range, thereby covering more features related to LNC, such as the "red-edge" position, and Chl absorption area. Comparatively, the GSI-based NCI H-F in this work was usually calculated with the bands in the red-range but lacked some characteristics, which might decrease its universality in estimating LNC or other biochemicals. Meanwhile, the prior bands selected with mathematics (FWs) or physical model (GSIs) cannot consider all these variables from different experimental and environmental situations. However, the spectral variables in 685 and 740 nm are the important features for GSV, which has been determined by many researchers [53]. Thus, the results of NCI H-F in specified bands obtaining a better model performance for LNC estimation than that in four prior bands can be reasonable.
The spectra collected with optical sensors, even for the active LiDAR used in this work, are the direct indicators for Chl contents in vegetation leaf, and these indicators can be used as the basis of LNC monitoring by remote sensing method. However, the LNC and Chl of vegetation are not same parameters after all, even though they are closely related to each other. In this work, FWs for each band were calculated based on a mass of modeled and collected spectra [54,55] and LNC measurement in the laboratory, whereas the GSIs were analyzed based on the fluorescence model with inputs that do not contain LNC [56]. This may contribute to the prior bands being selected with GSIs are not Chl-sensitive for LNC. Thus, GSI-based bands do not cover the total characteristics for LNC in HSL and LIFL spectra in Figure 2, indicating that the GSI-based NCI H-F obtained a lower R 2 than that using FWs.

Limitation and Future Research
In this study, rice LNC was successfully estimated by NCI H-F . However, the model should be recalibrated when applied to other vegetations or even to rice grown under different environmental conditions. Moreover, the ANN model used in this study greatly depended on the selection of training and validation dataset, which would change during LNC modeling. Thus, a universal and dataset-independent method should be determined for the combination of the spectra of S r and S f for LNC or other biochemical estimation. This study attempted to solve this problem by forming a novel SI which linked S r and S f in a linear equation with two factors, namely, FWs and GSIs. However, we should admit that the FW-and GSI-based NCI H-F was conducted based on the spectra from two separate datasets, which might contribute errors to the ANN models of LNC estimation because of the non-uniform dataset.
Furthermore, the FW and GSI values of each band represented quite a contribution ratio of S r and S f to the LNC, although a certain physical significance was observed in the linear form NCI H-F to some extent. The two factors were calculated using a statistical method, especially for FWs, which greatly depended on sample spectra. In a recent study, the biochemical estimation of vegetation was conducted based on the radiative transfer models (RTMs), including the SCOPE model (Soil Canopy Observation, Photochemistry and Energy fluxes) proposed by Christiaan et al. [57,58] and one of the separated components of SCOPE, namely, the Fluspect-B model [59]. Unlike the PROSPECT model with leaf reflectance and transmittance spectra [55] and the FluorMODleaf model with leaf S f [60], both SCOPE and Fluspect-B can simulate the total spectra of S r and S f simultaneously, rather than being univocal for generating a special spectrum without considering all feature spectra together to estimate the vegetation biochemicals [61]. Based on the uniform spectra of S r and S f generated by SCOPE or Fluspect-B model, the FWs and GSIs for each band can be calculated, which might further improve the performance and universality of the ANN model in rice LNC estimation, and even for some other biochemicals, such as moisture, dry matter, and so on, which are important indicators for the GSV, as well as for land coverage and change detection, which are critically significant for the analysis of the carbon-nitrogen cycle [62], near surface atmosphere temperature [63][64][65], and dynamics variation in permafrost region [66,67] among other fields.

Conclusions
This study proposed a combined spectral index, namely, the NCI H-F for LNC estimation. The NCI H-F was constructed in a linear combination form linked spectra of S r and S f collected with HSL and LIFL systems to rice LNC based on two factors, namely FWs and GSIs for each feature band. By using an additive SI in two specific bands (685 and 740 nm), the NCI H-F values in this work could be utilized to estimate rice LNC accurately under multi-year rice samples. Thus, the NCI H-F is the available and reliable combined form for combining HSL and LIFL spectral characteristics for rice LNC estimation. Simultaneously, the modified PRI, called PRI fraction , demonstrated a satisfactory performance in rice LNC estimation by replacing some items with S f variables, multiplying corresponding FWs and GSIs in 740 nm. These results showed that FWs and GSIs could indicate the main contribution of each band to LNC, which were essential and valuable parameters for constructing novel SIs for LNC estimation of rice. Moreover, the FW and GSI values for each feature band were multiplied to some previous combined SIs, for instance, N(H685, F685) and N (H740, F740), and improved the model performance of LNC estimation significantly. This result further supported the above conclusion that FW-and GSI-based NCI H-F is efficient in remotely sensing rice LNC, and combining S r and S f features in a linear form is a reliable way to improve the model performance in LNC estimation based on the HSL and LIFL spectra.