Quantifying Chlorophyll Fluorescence Parameters from Hyperspectral Reﬂectance at the Leaf Scale under Various Nitrogen Treatment Regimes in Winter Wheat

: Chlorophyll ﬂuorescence (ChlF) parameters, especially the quantum e ﬃ ciency of photosystem II (PSII) in dark- and light-adapted conditions (Fv / Fm and Fv’ / Fm’), have been used extensively to indicate photosynthetic activity, physiological function, as well as healthy and early stress conditions. Previous studies have demonstrated the potential of applying hyperspectral data for the detection of ChlF parameters in vegetation. However, the performance of spectral features that have been documented to estimate ChlF is not ideal and is poorly understood. In this study, ChlF parameters and leaf reﬂectance were collected in two ﬁeld experiments involving various wheat cultivars, nitrogen (N) applications, and plant densities, during the growing seasons of 2014 to 2015 and 2015 to 2016. Three types of spectral features, including vegetation indices (VIs), red edge position (REP), and wavelet features, were used to quantify ChlF parameters Fv / Fm and Fv’ / Fm’. The results indicated that traditional chlorophyll ﬂuorescence vegetation indices (ChlF VIs), such as the curvature index (CUR) and D705 / D722 were capable of detecting Fv / Fm and Fv’ / Fm’ under various scenarios. However, the wavelet-based REP (WREP-S4) and the wavelet feature (WF) (704 nm, scale 4) yielded higher accuracy than other spectral features in calibration and validation datasets. Moreover, the bands used to calculate WREP-S4 and WF (704 nm, scale 4) were all centered in the red edge region (680 to 760 nm), which highlighted the role of the red edge region in tracking the change of active ChlF signal. Our results are supported by previous studies, which have shown that the red edge region is vital for estimating the chlorophyll content, and also the ChlF parameters. These ﬁndings could help to improve our understanding of the relationships among active ChlF signal and reﬂectance spectra.


Introduction
Chlorophyll fluorescence (ChlF) is a reaction of the photosynthesis apparatus to cope with excess light energy, which is accompanied with photochemical reactions and heat dissipation [1]. When the maximum photosynthetic rate is impaired, ChlF increases under many non-optimal environments. Therefore, ChlF is a direct indicator of electron transport and photosynthetic activity [2]. The ChlF parameters have been measured using a pulse-amplitude modulation fluorometer with different active light sources under light-adapted or dark-adapted conditions. ChlF parameters which are widely used to express the energy transfer of plant photosynthesis are relevant ChlF variables that have been calculated based on standard methodologies as reported in the PAM-2000 manual [3].
In contrast to traditional remote sensing techniques, ChlF produced solely by plants, rapidly captures the specific and instantaneous change of plants' physiology status and response to various nutritional treatments, heat, and water conditions [4,5]. Among all the ChlF parameters, Fv/Fm, which is the ratio of variable to maximal fluorescence, is the initial maximal efficiency of photons captured by open photosystem II (PSII) reaction centers [6], and is a widely used parameter representing the health and growth of plants [7][8][9]. The Fv'/Fm' parameter, which is the efficiency of energy harvesting by oxidized (open) PSII reaction centers in light, serves as an indicator to assess plant stress, nutrient, and health status [10]. Both Fv/Fm and Fv'/Fm' are closely related to the actual activity of plant photosynthetic tissue, and have been applied to monitor the physiological status of plants and their reactions to the environment [11].
Given the small ChlF signal and low efficiency for monitoring, there has been limited progress in retrieving ChlF parameters at the leaf and canopy scales. Most studies have mainly focused on the vegetation indices (VIs) [12][13][14][15][16]. The essence of estimating ChlF parameters using VIs is based on the fact that ChlF emission is superimposed on the leaf reflectance in the red edge region (680 to 800 nm). The VIs used to monitor ChlF parameters is a reflectivity index reflecting fluorescence intensity, rather than a definite physical quantity. These ChlF VIs have been divided into two categories, the reflectance ratio VIs and the derivative VIs. For reflectance ratio VIs, the curvature index (CUR), R685/R655, and R680/R630 have shown good relationships with ChlF parameters [12,13]. Meanwhile, derivative VIs, such as (D688*D710)/D697 2 (DPi), D705/D722, and D730/D706, have been developed to detect the subtle ChlF signal, because it has been found that the double-peak feature at 690 to 710 nm in the derivative reflectance was related to the natural fluorescence in both short-term and long-term stress experiments [14,17]. Although the photochemical reflectance index (PRI) has been used as an interspecific index of photosynthetic radiation use efficiency for foliar and canopy leaves [18], there has been some predicted bias when estimating Fv/Fm using PRI [13].
The ChlF signal centers in the red edge region (680 to 800 nm) and the VIs used to estimate the ChlF parameters are mainly composed of bands in the red edge region, which can makes it possible to monitor ChlF parameters using the red edge position (REP). The REP, defined as the wavelength of inflection point in the red edge region, has been widely used as an indicator of chlorophyll (Chl) content of various plants [19]. Many techniques have been developed to extract REP including linear interpolation (LI) [20], linear extrapolation (LE) [21], polynomial fitting (PF) [22], inverted Gaussian (IG) [23], and wavelet-based REP extraction technique (WREP) [19]. In the past few decades, although REP has been successfully applied to monitor Chl content, it has never been used to monitor plant physiological parameters, especially ChlF parameters directly related to photosynthesis and plant function. Moreover, the most suitable algorithm of REP extraction for ChlF parameters estimation is still unclear.
In general, wavelength selection of ChlF VIs is mainly based on existing research or experience, and therefore the bands relevant to ChlF characteristics have not been fully explored and utilized. However, continuous wavelet analysis (CWA) can capture the rich and subtle changes of the reflectance by simulating the similarity between the wavelet function at different scales within a continuous region [24]. This approach improves the use of spectral libraries and gives a better performance for estimating plant traits relative to that of VIs, including Chl content, leaf water content, and leaf mass per area (LMA) [25,26]. However, to date, little is known regarding the selection of optimal spectral features using CWA to estimate plant ChlF parameters.
In this context, the objectives of this study included the following: (1) to identify the ChlF parameters in light-and dark-adapted conditions which are more related to plant physiological and biochemical status; (2) to investigate the potential of CWA and REP to exploit hyperspectral reflectance for ChlF parameter estimation under different treatments involving variable sowing densities, development stages, and N fertilization; and (3) to determine the sensitive features relevant to the representative ChlF parameters. It is projected that this research could provide an experimental basis and technical support for estimating ChlF parameters via hyperspectral reflectance.

Experimental Design
Two experiments of winter wheat were conducted at Rugao (32 • 15 N, 120 • 38 E) in Jiangsu Province, China, during the growing seasons of 2014 to 2015 and 2015 to 2016. The data collected during the 2014 to 2015 growing season was only dedicated to the calibration of spectral computations, whereas that of the 2015 to 2016 dataset was used mainly as validation. As shown in Table 1, the experimental variables included various nitrogen (N) applications, planting densities, cultivars, and growing stages. A completely randomized block design was used with three replications in each experiment. Prior to seeding, 120 kg ha −1 P 2 O 5 and 135 kg ha −1 KCl were applied for all treatments. For two winter wheat cultivars, the plant type of Shengxuan 6 is dispersed, and that of Yangmai 18 is erect. Then, 50% nitrogen (N) fertilizer was applied at the pre-planting stage and jointing period. Additional details about the experiments are provided in Table 1. The plot size was 6.5 × 5 m 2 for two experiments. The management of disease, pests, and weeds followed standard practices for chemical control in the local region.

Measurement of ChlF Parameters
The ChlF parameters (Table 2) of wheat leaves were measured using a portable modulated chlorophyll fluorometer PAM-2500 (Heinz Walz GmbH, Effeltrich, Germany) at several significant growth stages in two growing seasons. For each treatment, the top three fully expanded leaves of wheat were clamped at the center of PAM-2500 leaf clip holder. All light-adapted ChlF parameters were measured between 10:00 and 12:00 h in sunny conditions, whereas dark-adapted ChlF parameters (Fo, Fm, Fv/Fm), were obtained around 16:00 h after the leaves were subjected to dark adaptation for 30 minutes.

Measurement of Leaf Physiological Parameters
After the ChlF parameters were obtained, measurements of leaf gas exchange, including net photosynthetic rate (An) and stomatal conductance (gs), were taken on the same leaves under field conditions. These data were collected between 10:00 and 13:00 h on clear days using a LI-6400 portable photosynthesis system (LiCOR Inc., Lincoln, Nebraska, USA) during the 2014 to 2015 growing season. During the measurements, the photosynthetically active radiation (PAR) was set to 1200 µmol·m −2 ·s −1 , which corresponds to saturation in the field. The temperature and concentration of CO 2 in the chamber were maintained at 25 • C and 380 µmol·mol −1 , respectively. The airflow rate through the leaf chamber was held constant at 500 µmol·s −1 . Air pressure and relative humidity were adjusted to near ambient levels. Finally, the plant leaves to be measured were transported to the laboratory for measuring the reflectance spectra.

Measurement of Leaf Reflectance
Leaf reflectance spectra were measured using an ASD FieldSpec Pro FR2500 spectrometer coupled with a leaf clip accessory (Analytical Spectral Devices, Boulder, CO, USA). The spectrometer, operating in the 350 to 2500 nm spectral range, provided a sampling interval of 1.4 nm and a spectral resolution of 3 nm between 350 and 1050 nm, and 2 nm and 10 nm between 1050 and 2500 nm, respectively. The leaf clip, used to collect leaf reflectance, was combined with a high-intensity reflectance probe attachment. It was equipped with an internal artificial light source that was independent of solar illumination. The clip also provided white and black background panels, of which the reflectance was approximately 100% and 0%, respectively. The field of view was limited to a diameter of 1.3 cm for the leaf clip, therefore measurements of leaf reflectance were not conducted before the jointing stage of winter wheat. After the dark current correction and optimization, the reflectance of the white panel was recorded as the reference. Individual spectral measurements, based on an average of three scans, were determined by standardizing a sample spectrum to that of the white reference panel.

Optical Measurements of Pigments in Laboratory
After the reflectance measurements, the surface area and fresh weight were determined immediately. The leaf area was measured with LI 3000 (LI-COR, Inc., Lincoln, NE, USA). Then, the leaves were cut into pieces and put into a volumetric flask (25 ml). The pigment content was extracted by ethanol (95%) and determined using a V1200 spectrophotometer (MAPADA Co., Shanghai, China) following standard wet chemistry procedures [27]. Then, the concentration (µg/ml) of Chl a, Chl b, and carotenoid (Car) of samples were determined. Finally, the area based Chl ab (Chl a + Chl b, ug/cm 2 ) and Car (ug/cm 2 ) were calculated.

Calculation of VIs
Five groups of VIs (Table 3) were calculated using the reflectance data. The first group was the ChlF VIs, including reflectance ratio VIs and derivative Vis, which were classified according to the previous study [28]. The second group was about status VIs, involving PRI and REPs extracted by five algorithms. These indices were selected because the variation of ChlF parameters is influenced comprehensively by biological activity and environmental conditions (fertilizer, solar radiation, temperature, and water) [29,30]. Thus, several VIs related to Chl content, structure properties, and water content were involved in this study for the detection of ChlF parameters.

Methods for REP Extractions
The explanation of five algorithms for REP extractions (listed in Table 3) are as follows: (1) Linear Interpolation (LI) REP is determined using a simple four-point LI method near the midpoint of the region 670 to 780 nm, where the reflectance can be simplified to a straight line [21]. The calculation procedure is shown as below: where R re is the reflectance average of 670 nm and 780 nm.
(2) Polynomial Fitting (PF) A fifth-order PF function (shown below) was used to fit the reflectance curve over the red edge region 670 to 780 nm. The REP is defined as the wavelength corresponding to the maximum value of the first derivative spectra curve which is obtained by taking the first derivative of the fitted curve [23].
where λ represents 111 bands of the reflectance from 670 nm to 780 nm.
(3) Linear Extrapolation (LE) The first derivative spectra were obtained by a first difference transformation and then smoothing with the Savitzky-Golay method. Two points in the far-red region (680 to 700 nm) and two points in the near-infrared region (NIR) (725 to 760 nm) of the first derivative spectra were identified to construct two straight lines as follows [22]. FDR = m 1 λ + c 1 (4) where FDR is the first derivative spectra and m1, m2, c1, and c2 represent the slopes and intercepts of the two respective straight lines. The REP is determined as the wavelength corresponding to the intersection of the straight lines as below:

(4) Wavelet-Based Red Edge Position (WREP)
The WREP is extracted in the red edge region of wavelet spectra as follows [20]: where w 1 and w 2 are the wavelet coefficients of the two adjacent points below and above the horizontal zero line in the red edge region, respectively. λ 1 and λ 2 are the wavelengths corresponding to w 1 and w 2 , separately. The WREP has shown strong correlations with Chl content at the leaf level, especially at low scales [20]. Therefore, in this study, WREP was extracted at two low scales, such as scale 3 (WREP-S3) and scale 4 (WREP-S4).

Continuous Wavelet Analysis (CWA)
CWA is a powerful mathematical tool that processes spectroscopic signals and provides an effective approach for acquiring information about plant traits [31,32]. CWA is typically conducted in two steps, namely, continuous wavelet transform (CWT) and feature selection. In this study, CWT was analyzed using the "WV_CWT" function in IDL 8.3 (ITT Visual Information Solutions, Boulder, CO, USA).
A signal matrix (1×n) was generated by a wavelet function based on a given wavelet scale, a translational wavelet function, and a spectral signal. Thus, a n×m dimensional continuous wavelet transform coefficient matrix was produced after wavelet transformation at the m scale (where n represents the band and m is the scale). In this study, the mother wavelet function is the second derivative of the Gaussian function, because it has a similar shape to the leaf absorption features [33]. Each reflectance in the range 400-1000 nm where ChlF occurs was decomposed into continuous components at various scales. The CWT operations were conducted at a power of 2 (2 1 , 2 2 , . . . , 2 8 ) and are called by their respective power numbers (i.e., scale 1, scale 2, . . . scale 8). Random noise due to reflectance measurement can be contained in the low scale components [32], and hence only the wavelet features at scales 3 to 8 were analyzed to produce a correlation scalogram (coefficient of determination, R 2 ). The regions with the highest 1% of R 2 for wavelet feature and ChlF parameters (Fv/Fm and Fv'/Fm') were highlighted in red, and the wavelet features with the highest R 2 in each region were extracted.  [14] physiological VI Photochemical reflectance index (PRI) Enhanced vegetation index (EVI) 2.5 × (R810 -R690)/(R810 + 2.4 × R690 + 1) [38] Water VI Normalized difference water index (NDWI) (R850 − R1240)/(R850 + R1240) [39] Water index (WI) R850/R970 [40] REP Linear interpolation (REP LI ) Explained as below, [

Statistical Analysis
The VIs, REPs, and CWA were applied to build models to monitor the ChlF parameters of wheat leaf. The relationships among the spectral features and ChlF parameters were established from the data collected during the 2014 to 2015 growing season, which were validated using the data acquired during the 2015 to 2016 growing season. The 1:1 plot of the measured and predicted data was used to evaluate the model fitness. Calibration R 2 (R 2 C ), see Equation (8), and the root mean square error of calibration (RMSE C ), see Equation (9), were statistical parameters used to evaluate the performances of all models in calibration. For validation, they are validation R 2 (R 2 V ), see Equation (10); bias (Bias), see Equation (11); the root mean square error of prediction (RMSEv), see Equation (12); and the relative root mean square error of prediction (RRMSEv), see Equation (13). Higher values of R 2 C , R 2 V , and lower values of RMSE C , Bias, RMSEv, and RRMSEv indicate higher accuracy of the model.
where Y i is the measured value of samples, M i is the predicted value of samples in the calibration dataset, X is the average of X i , Y is the average of Y i , Y i is the predicted values, Y is the average of Y i for the validation dataset, and n is the number of samples.  Table 4 than other ChlF parameters. For instance, among the dark-adapted ChlF parameters, Fv/Fm was significantly related to Car, Chl ab , An, gs, Fm, Fm', Fv'/Fm', and Y(II) with R 2 > 0.5 and p value < 0.001. Other crop traits which showed moderately significant relationships with Fv/Fm (at p < 0.01) were Fs (R 2 = 0.20). Fo' and ETR had a remarkable relationship with Fv/Fm at the p < 0.05 level (R 2 = 0.13 and 0.15). For the steady-state ChlF parameters, Fv'/Fm' was significantly related with Car, Chl ab , An, gs, Fv'/Fm', Fm', Y(II), and ETR (R 2 = 0.34, 0.35, 0.47, 0.29, 0.58, 0.59, 0.45, and 0.41, respectively; p < 0.001). Fm and NPQ also had significant relationships with Fv'/Fm'. In general, Fv/Fm and Fv'/Fm' were the representative ChlF parameters in dark-and light-adapted conditions. Due to their fundamental significance and practical utility, they are the subjects of our research, and discussed in later sections.  However, the first expanded leaf under the N0 treatment, yielded a slightly different result ( Figure  S1A). The Fv/Fm kept increasing until DAS 179, and then decreased.

Dynamic
The temporal patterns of Fv'/Fm' measured during the 2014 to 2015 growing season were exhibited in Figure 1E-H, Figure S1D-F, Figure S2D-F, Figure S3D-F and Figure S4D-F). The Fv'/Fm' values under N4 applications were usually larger than that in N2 cases, but for the first leaves, it was slightly smaller than that in N2 cases from DAS 164 to DAS 179 ( Figure S1D), but slightly larger from DAS 179 to DAS 187. The Fv'/Fm' values of the second and third leaves in the N2 and N4 cases were relatively close to that in the N2 treatment from DAS 164 to DAS 172 ( Figure S1E,F), and higher than that in the N2 condition from DAS 172 to DAS 187. It was shown obviously that the Fv'/Fm' in the N2 and N4 treatments were higher than that in N0 case regardless of which leaf position. The Fv'/Fm' of the top three leaves increased gradually from DAS 164, and reached the maximum at DAS 172 or DAS 179. The Fv'/Fm' of the third leaves decreased more sharply than that of the first and second leaves.     Figure 3F.

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For the derivative VIs listed in  3.96%) depicted in Table 6, significantly better than that of the other derivative VIs.  Tables 5 and 6 show the performance of three types of spectral features (VIs, REP, and wavelet feature) for monitoring leaf Fv/Fm and Fv'/Fm' in calibration and validation datasets.

Performance of VIs-based Fv/Fm and Fv'/Fm' Models in Calibration and Validation Datasets
The best-fit functions for the relationships between the reflectance ratio VIs and wheat leaf Fv/Fm and Fv'/Fm' were mainly linear, with Rc 2 values ranging from 0.22 to 0.67 for Fv/Fm, and 0.35 to 0.56 for Fv'/Fm'. Only the R685/R655 showed logarithmic relationships with Fv/Fm. For both Fv/Fm and Fv'/Fm', the CUR exhibited the best goodness of fit among all the reflectance ratio VIs in the calibration dataset (Figure 2A,F), superior to R680/R630, followed by R685/R655 and R750/R800. When applying the reflectance ratio VIs regression models to the validation dataset, the RRMSEv produced ranged from 1.95% to 3.43% and from 4.28% to 5.51% for predictive Fv/Fm and Fv'/Fm', separately. The CUR yielded the best performance in validation for predicting Fv/Fm (Rv 2 = 0.50, Bias = 0.0056, RMSEv = 0.012, and RRMSEv = 1.95%) shown in Figure 3A and for Fv'/Fm' (Rv 2 = 0.38, Bias = 0.0072, RMSEv = 0.030, and RRMSEv = 4.28%) exhibited in Figure 3F.
For the derivative VIs listed in Table 3, the best fitness between Fv/Fm and D705/D722, Dλρ/D(λρ+12 nm), and DPi were linear, except for D730/D706 and Dλρ/D720 which were logarithmic. The Rc 2 values of the derivative VIs and leaf Fv/Fm ranged from 0.38 to 0.64. D705/D722, D730/D706, and Dλρ/D720 gave similar performances in the calibration dataset (R C 2 = 0.63) (  Table 5 and for Fv'/Fm' (R V 2 = 0.40, Bias = 0.0031, RMSEv = 0.028, and RRMSEv = 3.96%) depicted in Table 6, significantly better than that of the other derivative VIs.     The PRI, as a physiological VI, showed a little worse calibration performance than some ChlF VIs, and it did not yield a positive result in validation. The sensitivities of structure VIs and water VIs to Fv/Fm and Fv'/Fm' were much poorer than that of Chl VIs. The MTCI and CIred edge had similar performances for predicting Fv/Fm and Fv'/Fm' in the calibration dataset, with Rc 2 around 0.61 and 0.55, respectively. But with regards to the predictive accuracy of leaf Fv/Fm inversion, the best validation results were obtained by CIred edge (R V 2 = 0.39, Bias = −0.013, RMSEv = 0.022, and RRMSEv = 2.79%), which also was the most accurate Chl VIs to derive leaf Fv'/Fm' (R V 2 = 0.32, Bias = −0.011, RMSEv = 0.030, and RRMSEv = 4.07%). In addition, the VIs related to structure properties and water content were proven to be invalid to estimate Fv/Fm and Fv'/Fm' in the validation dataset.

Performance of REP for Predicting Leaf Fv/Fm and Fv'/Fm' in Calibration and Validation
The best relationships between the REPs and Fv/Fm all were linear except WREP-S3, and all linear functions for Fv'/Fm'. There are not much difference between the five REPs monitoring A Fv/Fm or Fv'/Fm'. However, with regards to the validation performance, WREP-S4 showed better performance in estimating leaf Fv/Fm and Fv'/Fm' than the other four REPs, with the highest predictive accuracy (R V 2 = 0.51 for Fv/Fm and R V 2 = 0.43 for Fv'/Fm') and the lowest error (RRMSEv = 1.80% for Fv'/Fm' and RRMSEv = 3.74% for Fv'/Fm') as shown in Figure 2C,H, followed by WREP-S3. Figure 4A shows the top 1% wavelet feature regions relevant to the ChlF parameter Fv/Fm for the dataset acquired during the 2014 to 2015 growing season. These wavelet features were formed in five feature regions in the visible and near-infrared regions. All of them occurred from scale 3 to scale 6. These five wavelet features were identified as significantly related to Fv/Fm (P < 0.0001) with Rc 2 values for the linear regressions ranging from 0.68 to 0.70 (Table 5). According to the Rc 2 values, the wavelet features sensitive to Fv/Fm were WF (702 nm, scale 3), WF (637 nm, scale 3), WF (704 nm, scale 4), WF (592 nm, scale 5), and WF (575 nm, scale 6) in sequence, which gave similar performances for the estimation of the Fv/Fm of winter wheat. When the regression models of the calibration dataset were used as the validation dataset, WF (704 nm, scale 4) showed the best transferability yielding the highest precision (Rv 2 = 0.55) and lowest predicted error (Bias = 0.0050, RMSEv = 0.014, and RRMSEv = 1.81%; Figure 3E and Table 5).

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RMSEv = 0.014, and RRMSEv = 1.81%; Figure 3E and Table 5).  The wavelength of the first feature was closed to the blue band, in which the N-carbon compounds have absorption characteristics. Other features were located in the red region and red edge area, including the 630 nm, 688 nm, and 702 to 707 nm, in which the reflectance is strongly absorbed by Chl. Among these six wavelet features, the top five features were selected to estimate the leaf Fv'/Fm'. All of the best-fit functions for the relationships between wavelet features and leaf Fv'/Fm' were linear, with Rc 2 values from 0.58 to 0.62. The WF (465 nm, scale 4) located in the blue region produced the worst agreement in the calibration dataset and the independent validation dataset as compared with the other four wavelet features. And regardless of which dataset, the best predictive accuracy and the lowest predictive error were found when using the WF (704 nm, scale 4), followed by WF (702 nm, scale 3), and WF (707 nm, scale 7).

Signature Components of Leaf Chlf Parameters and Their Variation with N Regimes
Compared with other ChlF parameters in dark-adapted and steady-state condition, Fv/Fm and Fv'/Fm', two ChlF parameters related to the photochemical efficiency of PSII, were more significantly correlated with leaf pigments, physiological indices, and other ChlF parameters (Table 4). Fv/Fm and Fv'/Fm', relevant to the quantum function of the PSII reaction center, have been used to study plant response to environmental factors [43][44][45], analyze the correlation to net photosynthesis and quantum yield, indicate leaf N and sulfur content, Chl concentration [46], and detect plant stress and evaluate the nutritional and healthy status of plants [47]. Therefore, Fv/Fm and Fv'/Fm' are seen as the subjects of this study due to their fundamental significance and practical utility.
Compared with the variation of L1, L2, and L3 under N0, N2, and N4 treatments ( Figure S1) for wheat leaf in V1D1, those in V1D2, V2D1, and V2D2 were similar overall. This seasonal trend is common, existing in multiple genotypes of wheat sown with different plant densities. In general, the changes of Fv/Fm and Fv'/Fm' for wheat leaves at different leaf positions and different N treatments were basically the same as the findings of other studies [4]. At the heading or anthesis stages, Fv/Fm and Fv'/Fm' reached a peak, and then decreased, which is mainly due to the exuberant growth and strong physiological activity of plants. Within a certain range of fertilizer applications (i.e., N0 to N2), Fv/Fm increased with an increase of N application [4]. It shows that the efficiency of light energy conversion and potential activity of photosynthetic reaction center were increased, with decreased damage on the photosynthetic apparatus. However, there was a slight decrease in Fv'/Fm' in the N4 treatment as compared with the N2 application ( Figure 1D), and similar Fv/Fm in the N4 and N2 cases ( Figure 1A) [48]. Photosynthetic capacity was not improved under excess N, which indicates that excessive N is not effective in photosynthetic performance. The reason why N can cause a change of ChlF parameters is because different N applications affect the photochemistry of PSII by altering the quantum yield of PSII electron transport [49].

Comparing VIs and REPs for Quantitatively Retrieving Fv/Fm and Fv'/Fm'
Many ChlF VIs have been proposed to exploit the effect of ChlF on the apparent reflectance spectrum in the red edge region (from 650 to 800 nm) [13]. By dividing the sample into different growth periods, it was concluded that phenological stages did not cause a significant impact on the performance of these spectral features for monitoring Fv/Fm and Fv'/Fm' (S5). Among the reflectance ratio VIs, the CUR yielded the best relationship with leaf Fv/Fm and Fv'/Fm' (Figure 3A), followed by R680/R630, which was also found in the case of tracking Fv/Fm variations under various Chl contents [12]. Both R680/R630 and CUR can well capture the reflectance changes centered around 680 nm, therefore, they can track the curvature of reflectance caused by ChlF emission (in the red edge region from 670 nm to 770 nm, with the central emission at 690 nm and 730 nm) as reported earlier [14]. Derivative VIs minimizing other confounding effects, can detect subtle changes due to the ChlF emission in the red edge region. Among all the derivative VIs listed in this study, the best predictive accuracy was found when using D705/D722 to estimate Fv/Fm and Fv'/Fm' in various N treatments, which is consistent with an independent study [13]. Our study provided confirmatory evidence that the inference of ChlF using reflectance ratio VIs and derivative VIs is feasible with acceptable accuracy.
The REP, the wavelength of the inflexion point in the red edge region of reflectance, has received much attention over the years for understanding the properties of plants, such as the Chl content, N content of the leaf, and the leaf area index [50,51]. Among five methods widely used to extract REP, WREP-S4 yielded more stable results than VIs relevant to ChlF, physiological status, Chl content, water content, and structure properties. In comparison with VIs related to physiological status, those for Chl content, water content, and structure properties were not effective for monitoring ChlF parameters. With respect to NDVI and PRI, they varied with the development of vegetation, but NDVI can be saturated before PRI [52]. And the bands sensitive to the photosynthesis and water content are definitely different. Although CIred edge showed acceptable performance in calibration, the transferability of CIred edge-based model was not ideal. However, REP can characterize signals in the red edge region, where ChlF exists. Therefore, according to the good agreement between REP and Fv/Fm, Fv'/Fm', it implies that REP can be used as the functions of ChlF emission bands in the red edge region, which is consistent with previous theoretical descriptions of ChlF effects on reflectance or the derivative spectra [14].

Comparison between CWA and Other Spectral Features for Estimating Fv/Fm and Fv'/Fm'
CWA, as an effective mathematical method, has been extensively used to retrieve useful information from hyperspectral data, such as leaf biochemical parameters [25]. Comparing the wavelet features associated with Fv/Fm and Fv'/Fm', we found that WF (702 nm, scale 3), WF (637 nm, scale 3), and WF (704 nm, scale 4) were their common wavelet features. Among these three wavelet features, WF (704 nm, scale 4) outperformed and exhibited the best stability, not only for Fv/Fm estimation but also for Fv'/Fm'. Therefore, WF (704 nm, scale 4) is considered to be a robust spectral feature for tracking Fv/Fm and Fv'/Fm' collected throughout various significant growth stages and different N treatment regimes.
According to a comprehensive evaluation of the performances in calibration and validation, the reflectance ratio VI CUR, the derivative VI D705/D722, the REP extracted by WREP-S4 technique, CIred edge related to Chl content, and WF (704 nm, scale 4) derived by CWA performed best and exhibited good reliability in their respective groups. The best wavelet feature WF (704 nm, scale 4) was superior to WREP-S4, but not significantly. Both of them were extracted at the fourth scale and centered around 704 nm. WF (704 nm, scale 4) has been used to retrieve the leaf Chl contents of cereal crops [19], and therefore it confirms that this wavelet feature is not only sensitive to Chl content but also ChlF signal. In summary, WREP-S4 and wavelet feature WF (704 nm, scale 4) permitted operational quantification of Fv/Fm and Fv'/Fm' using hyperspectral data.
On the basis of a comparison of the performance of these spectral features for detecting Fv/Fm and Fv'/Fm', we concluded that Fv/Fm could be estimated more accurately than Fv'/Fm'. This may be because the change of Fv/Fm is very small under non-stress conditions and it is not affected by species and growth conditions. The performance of WREP and wavelet feature for detecting ChlF parameters should be tested for more vegetation types. Moreover, at the leaf scale, ChlF signal is to a certain extent influenced by environmental factors, however, when these findings are extended to the canopy and regional scales, additional complexity should be considered, such as canopy structure, canopy heterogeneity, and the interaction of ChlF signal with atmosphere.

Conclusions
In this study, three reflectance-based approaches (VIs, REPs, and wavelet features) were used to extract the optimal spectra features from apparent reflectance for estimation of two significant ChlF parameters, Fv/Fm and Fv'/Fm'. They were related to photosynthetic apparatus, especially PSII activity, and were more relevant to pigment content and physiological parameters than other ChlF parameters. In each group, the spectral feature most relevant to Fv/Fm and Fv'/Fm' were the same, and all of them were calculated based on bands in the red edge region, where the ChlF signal occurs. The results also showed that the ChlF VIs (CUR and D705/D722) are effective indicators for the estimation of Fv/Fm and Fv'/Fm' under various treatment regimes. Meanwhile, the performance of REPs and wavelet feature for the estimation of Fv/Fm and Fv'/Fm' were evaluated and compared with that of traditional VIs related to ChlF, physiological status, Chl content, water content, and structure properties. The accuracy of WREP-S4 in both calibration and validation was better than REPs extracted by other algorithms. Among all wavelet features, WF (704 nm, scale 4) yielded the best predictive accuracy for Fv/Fm and Fv'/Fm' estimation. Additionally, both WREP-S4 and WF (704 nm, scale 4) were all centered around 704 nm. This work demonstrates that the use of WREP-S4 and WF (704 nm, scale 4) provide more reliable assessments of the ChlF parameters Fv/Fm and Fv'/Fm' than empirical methods based on traditional VIs. Therefore, the red edge region can be exploited for estimation of Fv/Fm and Fv'/Fm'. These findings provide new insight for quantifying ChlF signal more accurately using reflectance-based approaches.