Evaluation of Total Nitrogen in Water via Airborne Hyperspectral Data: Potential of Fractional Order Discretization Algorithm and Discrete Wavelet Transform Analysis

Controlling and managing surface source pollution depends on the rapid monitoring of total nitrogen in water. However, the complex factors affecting water quality (plant shading and suspended matter in water) make direct estimation extremely challenging. Considering the spectral response mechanisms of emergent plants, we coupled discrete wavelet transform (DWT) and fractional order discretization (FOD) techniques with three machine learning models (random forest (RF), bagging algorithm (bagging), and eXtreme Gradient Boosting (XGBoost)) to mine this potential spectral information. A total of 567 models were developed, and airborne hyperspectral data processed with various DWT scales and FOD techniques were compared. The effective information in the hyperspectral reflectance data were better emphasized after DWT processing. After DWT processing the original spectrum (OR), its sensitivity to TN in water was maximally improved by 0.22, and the correlation between FOD and TN in water was optimally increased by 0.57. The transformed spectral information enhanced the TN model accuracy, especially for FOD after DWT. For RF, 82% of the model R2 values improved by 0.02~0.72 compared to the model using FOD spectra; 78.8% of the bagging values improved by 0.01~0.53 and 65.0% of the XGBoost values improved by 0.01~0.64. The XGBoost model with DWT coupled with grey relation analysis (GRA) yielded the best estimation accuracy, with the highest precision of R2 = 0.91 for L6. In conclusion, appropriately scaled DWT analysis can substantially improve the accuracy of extracting TN from UAV hyperspectral images. These outcomes may facilitate the further development of accurate water quality monitoring in sophisticated global waters from drone or satellite hyperspectral data.


Introduction
Total nitrogen (TN), as an essential element in water, not only impacts the water quality of inland waters around the world but also has a crucial bearing on the achievement of the United Nations' sustainable development goals of water conservation and water pollution management [1][2][3]. Water quality issues remain a chronic problem of inland wetland ecosystems [4]. Due to the special characteristics of inland wetland water cycle retardation, environmental pollution caused by unreasonable human production activities and life processes, and the lack of effective monitoring and assessment methods for water bodies, water quality issues such as eutrophication in inland water bodies have arisen, affecting the increase the workload and complexity of data processing and modeling [32][33][34]. It is urgent to develop fast and reliable preprocessing methods to extract useful spectral information.
The enriched spectral information captured by hyperspectral data can obscure valuable information regarding some target variables, which is why many scholars note that preprocessing hyperspectral data is obligatory [31,35,36]. Fractional order discretization (FOD) is one of the frequently applied and more efficient methods for preprocessing hyperspectral data [37]. The FOD has a narrow interval compared to the integer order derivative, which ensures a slow change in the signal-to-noise ratio and provides a spectral enhancement [38,39]. It has the capability to reduce the effect of information loss due to multiple noise partly [40]. Nowadays, FOD has become an acknowledged method in spectral data denoising. Thus, we opt for the FOD method to extract the crucial information of UAV hyperspectral reflectance data as well. Meanwhile, the combination of FOD with other preprocessing algorithms to identify the vital spectral curve information has acquired considerable attention. Bhadra et al. explored the fractional order Savitzky-Golay derivation (FOSGD) for hyperspectral data analysis, where they found that FOSGD could better balance the conflict between resolution and signal intensity and effectively extract information variables [41]. However, studies on FOD-expend are scarce, especially in processing UAV hyperspectral reflectance data. Thus, we proposed FOD combined with discrete wavelet transform (DWT), a new method to denoise hyperspectral data.
DWT is a spectral analysis method for extracting spectral features, and a variety of denoising algorithms (Daubechies N (dbN), Symlets N (symN), Coiflets N (coifN), etc.) have been developed to accomplish different noise elimination effects [42][43][44][45]. Many studies have investigated the processing of hyperspectral data by DWT, which can reveal key target information via low-scale decomposition reconstruction [46,47]. For example, Li et al. rapidly and nondestructively estimated the nitrogen concentration (LNC) of winter wheat at each fertility stage using DWT decomposition of hyperspectral canopy reflectance spectra (450-1350 nm) at 12 scales and obtained the best results at L4 (R 2 = 0.91) [47]. Meng et al. applied DWT in the processing of satellite hyperspectral data at 10 scales, and the resulting decomposed and reconstructed first derivative reflectance (FDR) spectra greatly improved the precision of soil moisture prediction at L6 (R 2 = 0.83) [48]. However, there is limited research on the application of DWT to airborne hyperspectral data processing. Whether such application is feasible in the study of TN in water and whether it has advantages over the well-known pretreatment methods of emergent vegetation data is worth exploring. In addition, we investigate the effectiveness of the combination of FOD and DWT to process hyperspectral reflectance data based on the existing studies.
Therefore, the paper aims to explore three questions: (1) How can DWT analysis potentially extract information from airborne hyperspectral data? (2) Which is more advantageous, pretreatment by DWT analysis or pretreatment by DWT combined with FOD? (3) Which combination of preprocessing methods and models can best improve the accuracy of hyperspectral prediction of TN in water, thus providing scientific support and reference information for water quality monitoring, other related research, and local precision agriculture?

Study Area
The study area is the Ebinur Lake Wetland National Nature Reserve. The Ebinur Lake Oasis (82 • 33 -83 • 53 E, 44 • 31 -45 • 09 N) is located in the Xinjiang Uygur Autonomous Region of northwestern China (Figure 1). The study area is far from the sea and has a typical continental arid climate (sunshine time is more than 2722 h and annual precipitation is less than 200 mm). The main wetland plants are P. australis and Typha orientalis Presl which are distributed widely and evenly at 0-5 m from the riverbank. The seasonal river confluence in the area that slowly renews the water, coupled with frequent human activities, typical continental arid climate (sunshine time is more than 2722 h and annual precipitation is less than 200 mm). The main wetland plants are P. australis and Typha orientalis Presl which are distributed widely and evenly at 0-5 m from the riverbank. The seasonal river confluence in the area that slowly renews the water, coupled with frequent human activities, causes serious eutrophication of the water bodies [49]. However, wetland plants are widely distributed and have an important purifying effect on the eutrophication of the water. To prevent continuous deterioration of the water environment and improve the quality of the ecological environment, the Ebinur Lake Wetland National Nature Reserve was established in 2007 and is included in the list of China's national nature reserves.

UAV Data Acquisition and Processing
Data were acquired by using the DJI Matrice 600 PRO ® (Shenzhen DJI Technology Co., Ltd., Shenzhen, China) hexacopter UAV platform, equipped with a Nano-Hyperspec ® hyperspectral sensor (Headwall Photonics Inc., Bolton, MA, USA), it is lightweight (less than 0.6 kg), ranging from 400-1000 nm with 272 spectral bands. The spectral resolution is 6 nm, the resampling interval is 2 nm, and the field of view is 22°. The sensor features a combined global positioning system/inertial measurement unit (GPS/IMU) navigation system that can acquire altitude information for the UAV platform in real time to enhance georeferencing and reflectivity calibration, respectively. To ensure data quality, dark current correction and spectral calibration were performed prior to takeoff. Hyperspectral images were collected at 15:00 (UTC/GMT+08:00) on 15 July 2018, on a clear and windless day. Preprocessing (including radiation correction and splicing) of the UAV data was based on Hyperspec ® III (version 3.1) and SpectralView ® (version 3.1) software. The extraction of hyperspectral reflectance information was performed with the ENVI5.3 remote sensing image processing platform.

Sample Collection and Experiments
On 15 July 2018, UAV hyperspectral data were acquired, accompanied by field surveys and sampling at 45 water sampling sites along the Aqikesu River. The sampling times met the requirements for single analysis of the river. Most importantly, July is representative of the dry season in the study area, when the river is narrow and flow velocities are extremely slow, and there are no strenuous agro-pastoral or human activities at any of the sampling sites, which are therefore representative of local natural conditions.

UAV Data Acquisition and Processing
Data were acquired by using the DJI Matrice 600 PRO ® (Shenzhen DJI Technology Co., Ltd., Shenzhen, China) hexacopter UAV platform, equipped with a Nano-Hyperspec ® hyperspectral sensor (Headwall Photonics Inc., Bolton, MA, USA), it is lightweight (less than 0.6 kg), ranging from 400-1000 nm with 272 spectral bands. The spectral resolution is 6 nm, the resampling interval is 2 nm, and the field of view is 22 • . The sensor features a combined global positioning system/inertial measurement unit (GPS/IMU) navigation system that can acquire altitude information for the UAV platform in real time to enhance georeferencing and reflectivity calibration, respectively. To ensure data quality, dark current correction and spectral calibration were performed prior to takeoff. Hyperspectral images were collected at 15:00 (UTC/GMT+08:00) on 15 July 2018, on a clear and windless day. Preprocessing (including radiation correction and splicing) of the UAV data was based on Hyperspec ® III (version 3.1) and SpectralView ® (version 3.1) software. The extraction of hyperspectral reflectance information was performed with the ENVI5.3 remote sensing image processing platform.

Sample Collection and Experiments
On 15 July 2018, UAV hyperspectral data were acquired, accompanied by field surveys and sampling at 45 water sampling sites along the Aqikesu River. The sampling times met the requirements for single analysis of the river. Most importantly, July is representative of the dry season in the study area, when the river is narrow and flow velocities are extremely slow, and there are no strenuous agro-pastoral or human activities at any of the sampling sites, which are therefore representative of local natural conditions. Specifically, in accordance with the water sample collection specifications, we rinsed the water sample collection bottles (1000 mL) three times with river water at each sampling site, after which samples were collected at a depth of 0-5 cm from the water surface, sealed, labeled, recorded, and rapidly refrigerated (at 2 • C) after collection. To guarantee that UAV-based hyperspectral data collection was performed at each sampling location, the precise geographic location of the samples was recorded using a portable GPS (G120, Beijing UniStrong Science and Technology Co., Ltd., Beijing, China) during sampling. The ultraviolet spectrophotometric method (HJ 535-2009) was applied to determine the TN concentration in water using an ultraviolet-visible light spectrophotometer (UV-6100, Shanghai Mapada Instruments Co., Ltd., Shanghai, China).

Data Processing
In addition to exhibiting redundancy, hyperspectral reflectance data are affected by factors such as water surface reflection and various forms of environmental noise [50]. It has been demonstrated that FOD is a more efficient preprocessing method for spectral analysis than the common integer-order derivative and can perform fine interpolation between the original spectrum (OR) and the integer-order derivative, thus providing a suitable solution for UAV hyperspectral data preprocessing [37,51]. Hyperspectral data are processed with FOD, which reduces the impacts of random noise on model calibration, enhances the peaks and valleys of spectral features, and reduces the effects of multiple scattering of irradiation [52,53]. In this study, the Grünwald-Letnikov method is adopted to define FOD. FOD is a generalization of integer-order differentiation and is defined as: where the function f (x) is the reflectance of the spectral curve; ν is the order; t and k are the upper and lower wavelength ranges of the FOD, respectively; h is the step length; n is a constant; and Γ(α) is the gamma function, whose expression is: As described in the above equation, an FOD equation of arbitrary order can be derived as: The FOD interval was set to 0.1 to 2.0 orders (0.1 is the interval step), and FOD was implemented in MATLAB 2018b.

Discrete Wavelet Transform
DWT can typically lower high spectral noise while retaining valuable spectral details in hyperspectral data, which is particularly applicable to spectral local noise reduction [54]. Compared with other hyperspectral data preprocessing methods, DWT analysis can more extensively decompose spectral information at different scales and reconstruct the corresponding spectrum after decomposition [48,55]. Moreover, different transform scales for wavelets can be selected according to different objectives [56]. Generally, DWT includes two processes: spectral decomposition and spectral reconstruction [57]. Decomposition refers to the process of decomposing a spectral signal into low-and high-frequency components based on a set of fundamental wavelets, which is normally performed iteratively by removing the noise from the high-frequency components with filters. Spectral reconstruction is the reconstruction of the low-frequency components at each scale, with the objective of representing different sub-bands of the signal in the spatial domain [58,59].
DWT can be expressed as: where WT f (j,k) is the f (n) wavelet transform coefficient, f (n) is the length of the signal sequence, ϕ , j,k (n) is the ϕ j,k (n) conjugate, and ϕ j,k (n) is the wavelet mother function. In DWT analysis, we selected the db4 mother wavelet after repeatedly testing several mother wavelet functions (dbN, sym, and coif) in the MATLAB wavelet toolbox and considering previous research results [46,60]. DWT decomposition was performed only on a binary scale in accordance with previous suggestions and preliminary experiments of hyperspectral data preprocessing. Eight scales, represented by L1-L8, were selected, and DWT was implemented using MATLAB R2018a.

Grey Relation Analysis
Previous studies have suggested that the selection of a suitable band position is essential to improving the correlation between TN concentration and chlorophyll concentration [61]. The grey relation analysis (GRA) is a dimensionless quantity that corresponds to the correlation between the TN concentration of the water column and the hyperspectral reflectance [62]. The greater the GRA is, the greater the sensitivity between hyperspectral reflectance and TN in the water column. The top 80 reflectance data points were used to construct the prediction model based on order of importance. The GRA was performed in Python 3.7.

Modeling of Total Nitrogen Monitoring
In this study, we selected three models to monitor the TN concentration: random forest (RF), bagging algorithm (bagging), and eXtreme Gradient Boosting (XGBoost). RF is a model that integrates multiple decision trees to invert water quality parameter predictions, and the combination of decision trees it constructs increases the ability of the hyperspectral reflectance model to predict the target variable [63][64][65]. Bagging is a prototype of the parallel integrated learning method that is directly based on the selfsampling method taking randomized bootstrapping with put-back sampling [66]. This approach ensures high model performance and a statistically reliable estimation of the generalization ability of the model without the risk of overfitting [67,68]. XGBoost is extensively applied in the field of data mining thanks to its unique advantages (efficient, flexible and lightweight) [69]. It admits sparse inputs from tree boosters and linear boosters, has an optimization algorithm that can be extended with user requirements, and is a gradient-enhanced implementation [70,71].
Despite the similarities of the three algorithms, RF, bagging, and XGBoost all have their own unique characteristics. All three models utilize the train_test_split function in the Sklearn module of the machine learning library in the Python 3.7 programming language to randomly divide the data into a modeling set (70%, n = 30) and a validation set (30%, n = 15), and fix the selected dataset with the random_state function. Before building the prediction model, the important parameters in the model need to be optimized (hyperparameter optimization) to improve the model performance [72]. Therefore, this study applies the grid search method to optimize the hyperparameters of the model. The prediction performance of different models was evaluated using a fivefold cross-validation method. All measurements were randomly divided into five groups, four of which were used as the training set and one as the validation set. Compared with the random division of the training and validation sets, fivefold cross-validation makes the models more reliable.

Statistical Analysis
The accuracy of the established prediction model was evaluated by calculating the determination coefficient (R 2 ), root mean square error (RMSE), and residual prediction deviation (RPD) [73]. R 2 takes values between 0 and 1; the larger the value is, the better the model fit and the higher the accuracy. RMSE indicates the inverse capability of the model, and its value is inversely proportional to the model accuracy, where higher values mean lower model accuracy. When RPD ≥ 2, the model prediction is excellent; when 1.4 ≤ RPD < 2, the model prediction is relatively balanced; and when RPD < 1.4, the model prediction is not credible.
where x i is the measured value of TN in water, X i is the predicted value of TN in water, Y i is the average value of TN in water, and n is the number of samples.

Modeling Dataset Division
The descriptive statistics of the whole sample, modeling set, and validation set were analyzed as follows ( Table 1). The average value of TN for all samples was 1.37, while the corresponding average values of TN for the modeling set and validation set were 1.45 and 1.33, respectively. The standard deviation (SD) and coefficient of variation (CV) between samples were similar. The TN concentrations in water in the calibration and validation datasets were considered representative enough to build and validate the regression models, respectively.
In addition, for the water samples taken this time, nearly half of the sample values (N = 21) were higher than 2.0 mg L −1 , and the water quality was Grade V (TN > 2.0 mg L −1 ) according to China's environmental quality standards for surface water (GB 3838−2002). According to this water environment standard (GB 3838−2002) classification, the spectral response curves corresponding to different TN concentrations are shown in the figure. The reflectance of P. australis increases sharply between visible and near-infrared wavelengths (700-760 nm), forming a "red edge" phenomenon. From Figure 2, it is obvious that the P. australis "redshifts" and the reflectance decrease as the TN concentration increases.

Average Reflectance and Wavelet Power Spectrum of Emergent Plants
The mean OR reflectance, mean FOD spectrum (1st and 2nd order integers), and mean wavelet power spectrum of 1st order FOD (scales 1-8 (L1~L8)) are shown in Figure  3. The OR has 49 peaks and 50 troughs ( Figure 3A1), while the FOD spectrum has 95 peaks

Average Reflectance and Wavelet Power Spectrum of Emergent Plants
The mean OR reflectance, mean FOD spectrum (1st and 2nd order integers), and mean wavelet power spectrum of 1st order FOD (scales 1-8 (L1~L8)) are shown in Figure 3. The OR has 49 peaks and 50 troughs ( Figure 3A1), while the FOD spectrum has 95 peaks and 95 troughs ( Figure 3A2). These numbers (peaks and troughs) intuitively reveal that the FOD spectrum contains more detailed information than the OR curve ( Figure 3).

Correlation Analysis of Preprocessed Spectral and TN Concentration in Water
The correlation coefficients of the preprocessed spectral reflectance and the TN concentration in water are shown in Figure 4. For the OR data, the sensitive spectral wavelengths are mainly concentrated between 400 and 720 nm, while the strongest correlation (0.61) is observed at 690 nm in the OR without DWT treatment. After DWT preprocessing, the FOD results for order 0.1-0.9 exhibit more continuous dark red regions, which better highlight the spectral details and reduce noise. DWT analysis was applied to the FOD spectra with order 0.3-0.8; the red regions from 400-720 nm are extended to 400-800 nm, and the correlation between the spectral reflectance of the extended spectral region (750-800 nm) and the TN concentration of water improves, where the highest correlation (0.80) is found for L8 at 586 nm. The clustering region in the sensitive spectral band is more discrete (especially between 500 and 720 nm) when the FOD order reaches or exceeds 1.0. Nevertheless, the sensitivity of the spectral region from 800-900 nm gradually becomes apparent. The spectral region between 900 and 1000 nm is decomposed and reconstructed, Affected by various environments, the OR spectral curve data will contain a lot of noise manifested as many "small burrs" on the spectral curve, which can be visualized in Figure 2. Noise removal is required to reduce the impact of these small burrs. The decomposition and reconstruction process of DWT analysis is carried out iteratively by removing the noise of high-frequency components with filters to finally reconstruct the different signal sub-bands in the spatial domain. Taking the DWT of 1st order FOD as an example, compared with the spectrum of OR/FOD ( Figure 3A1-A3), the wavelet power spectrum of FOD (L1~L8) showed more simplified information on the number of peaks and valleys as the decomposition proceeded ( Figure 3B1-B9), which intuitively indicated that the high frequency signal was further removed, and the noise transfer phenomenon was becoming weaker. Up to L5 (Figure 3B6), there is relatively little noise, and the reflection peak in the green band and the absorption valley in the red band are evident. By L7 and L8 ( Figure 3B8,B9), as the spectral details are continuously removed and the spectral curves gradually smooth out, certain absorption peaks characterizing the correlation between TN and P. australis chlorophyll in water disappear. The OR wavelet power spectra and other FOD wavelet power spectra (L1~L8) exhibit similar behavior, where DWT removes noise while simplifying differences in the spectral bands.

Correlation Analysis of Preprocessed Spectral and TN Concentration in Water
The correlation coefficients of the preprocessed spectral reflectance and the TN concentration in water are shown in Figure 4. For the OR data, the sensitive spectral wavelengths are mainly concentrated between 400 and 720 nm, while the strongest correlation (0.61) is observed at 690 nm in the OR without DWT treatment. After DWT preprocessing, the FOD results for order 0.1-0.9 exhibit more continuous dark red regions, which better highlight the spectral details and reduce noise. DWT analysis was applied to the FOD spectra with order 0.3-0.8; the red regions from 400-720 nm are extended to 400-800 nm, and the correlation between the spectral reflectance of the extended spectral region (750-800 nm) and the TN concentration of water improves, where the highest correlation (0.80) is found for L8 at 586 nm. The clustering region in the sensitive spectral band is more discrete (especially between 500 and 720 nm) when the FOD order reaches or exceeds 1.0. Nevertheless, the sensitivity of the spectral region from 800-900 nm gradually becomes apparent. The spectral region between 900 and 1000 nm is decomposed and reconstructed, shifting from relatively discrete, negatively correlated spectral reflectance to relatively concentrated, positively correlated spectral reflectance. For different decomposition layers (L1-L8) of DWT, the correlation coefficients between the spectra of each layer treated with wavelets and the concentration of TN in the water column were improved compared with the spectral information before treatment. The sensitivity of 45% of the OR spectra to TN in water was increased by 0.01-0.22, whereas the correlation between 54% of the FOD spectra and TN was increased by 0.01-0.57.

Grey Relation Analysis
GRA was performed for each layer of the wavelet analysis feature spectra, and all correlation degrees are 0.6 and above. The spectra with a correlation degree of 0.8 or higher and high aggregation between the characteristic spectra of each layer and the TN concentration in water are concentrated in five spectral regions, including 400-420 nm, 440-510 nm, 530-610 nm, 630-710 nm, and 750-830 nm, which indicates that the wavelet analysis could amplify sensitive spectral information while removing noise. For the OR of L1-L8 and the spectral analysis results after FOD transformation, we selected the spectral data with a GRA degree of 0.8 and above (the number distribution is shown in the figure) as the input of the model, and the number distribution ( Figure 5) confirms that the spectral region with high sensitivity to the TN concentration in water is between 400 and 700 nm. Overall, the combination of DWT and differential processing techniques not only retains  For different decomposition layers (L1-L8) of DWT, the correlation coefficients between the spectra of each layer treated with wavelets and the concentration of TN in the water column were improved compared with the spectral information before treatment. The sensitivity of 45% of the OR spectra to TN in water was increased by 0.01-0.22, whereas the correlation between 54% of the FOD spectra and TN was increased by 0.01-0.57.

Grey Relation Analysis
GRA was performed for each layer of the wavelet analysis feature spectra, and all correlation degrees are 0.6 and above. The spectra with a correlation degree of 0.8 or higher and high aggregation between the characteristic spectra of each layer and the TN concentration in water are concentrated in five spectral regions, including 400-420 nm, 440-510 nm, 530-610 nm, 630-710 nm, and 750-830 nm, which indicates that the wavelet analysis could amplify sensitive spectral information while removing noise. For the OR of L1-L8 and the spectral analysis results after FOD transformation, we selected the spectral data with a GRA degree of 0.8 and above (the number distribution is shown in the figure) as the input of the model, and the number distribution ( Figure 5) confirms that the spectral region with high sensitivity to the TN concentration in water is between 400 and 700 nm. Overall, the combination of DWT and differential processing techniques not only retains spectral details, but also removes noise.

Performance of Models Based on Reflectance, Derivative, and Wavelet Power Spectrum
To investigate the strengths of DWT analysis in extracting the TN concentration in water from hyperspectral reflectance data, we summarized and compared the accuracy of 567 models for the OR hyperspectral reflectance, FOD, and wavelet power spectra ( Figure  6 and Table 2).
Compared to the OR (Table 2), the model R 2 mean values were lower at wavelet scales of L1 to L4 with average model performance ability, while the R 2 mean values at scales L5 to L8 indicated a better performance than the OR model, and the best model prediction ability was achieved at L8 (R 2 = 0.71, RMSE = 0.62, RPD = 1.74). The same results were obtained for the FOD spectra, where the low-scale (L1) model had average performance. As the decomposition scale increased, the model predictions improved, and the best integrated prediction ability was obtained at L6 (R 2 = 0.69, RMSE = 0.44, RPD = 1.78).
Overall, the prediction model with the DWT applied has better regression performance than the OR model. Furthermore, at the eight scales of DWT analysis (Figure 6), the GRA results indicate that the three models follow the order bagging > XGBoost > RF. However, the accuracy values (R 2 , RMSE, and RPD) of these prediction models do not differ significantly from each other, indicating that the input selection process is objectively accurate. The highest accuracy among the RF models appears in L3 with R 2 = 0.86; likewise, the best accuracy of the bagging models appears in L4 with R 2 = 0.85. The best-performing model among the XGBoost models appears in L6 with R 2 = 0.91.
The regression performance of the different models (RF, bagging, and XGBoost) were assessed based on the wavelet power spectra. Among the 27 models developed for the OR and its DWT hyperspectral data, 12.5% of the RF model accuracy (

Performance of Models Based on Reflectance, Derivative, and Wavelet Power Spectrum
To investigate the strengths of DWT analysis in extracting the TN concentration in water from hyperspectral reflectance data, we summarized and compared the accuracy of 567 models for the OR hyperspectral reflectance, FOD, and wavelet power spectra ( Figure 6 and Table 2).    OR and FOD are the original reflection spectra and fractional order derivative spectra, respectively, and OR_scale and FOD_scale (L = 1, 2, 3, 4, 5, 6, 7, 8) represent the wavelet power spectra of OR and FOD at specific scales, respectively. SD is the standard deviation.
Compared to the OR (Table 2), the model R 2 mean values were lower at wavelet scales of L1 to L4 with average model performance ability, while the R 2 mean values at scales L5 to L8 indicated a better performance than the OR model, and the best model prediction ability was achieved at L8 (R 2 = 0.71, RMSE = 0.62, RPD = 1.74). The same results were obtained for the FOD spectra, where the low-scale (L1) model had average performance. As the decomposition scale increased, the model predictions improved, and the best integrated prediction ability was obtained at L6 (R 2 = 0.69, RMSE = 0.44, RPD = 1.78). Overall, the prediction model with the DWT applied has better regression performance than the OR model. Furthermore, at the eight scales of DWT analysis (Figure 6), the GRA results indicate that the three models follow the order bagging > XGBoost > RF. However, the accuracy values (R 2 , RMSE, and RPD) of these prediction models do not differ significantly from each other, indicating that the input selection process is objectively accurate. The highest accuracy among the RF models appears in L3 with R 2 = 0.86; likewise, the best accuracy of the bagging models appears in L4 with R 2 = 0.85. The best-performing model among the XGBoost models appears in L6 with R 2 = 0.91.
The regression performance of the different models (RF, bagging, and XGBoost) were assessed based on the wavelet power spectra. Among the 27 models developed for the OR and its DWT hyperspectral data, 12.5% of the RF model accuracy ( elements to confirm that emergent plant characteristics (especially chlorophyll) are the critical reflection of water quality [74,75]. Xing et al. concluded that the nitrogen removal and water purification functions of the typical emergency plant P. australis are due to its high nitrogen and phosphorus requirements during growth [15]. Despite the nitrogen absorption by vegetation growth, nitrification and denitrification remain the major denitrification mechanisms [76]. More than 45% of total nitrogen removal occurs via microbial nitrification and denitrification [77]. The root system of P. australis provides an adhesion interface and a habitat for microorganisms. These microorganisms greatly accelerate the interception of organic matter around the roots and the decomposition of suspended matter under favorable conditions (e.g., higher temperatures and a stable water column), doing so, for example, by breaking down large amounts of high molecular, weight-dissolved organic matter into plant-absorbable substances (especially ammonium nitrogen). The sampling time was July in this study, when the water temperature was high and during the growing season of wetland vegetation in the area, providing a hotbed for microbial metabolic action. In addition, P. australis, a wetland plant, is widely distributed and has a well-developed root system with strong enrichment capacity, whose combined action with microorganisms can better absorb TN elements in the water body. Chlorophyll in vegetation characteristics not only indicates the abundance of TN in water, but also is a significant factor affecting the spectral characteristics of vegetation. The study by Li et al. indicated that the chlorophyll concentration of plants is closely related to the TN supply in water [78]. This also provides a reasonable reference for this study to obtain water quality parameters using the vegetation characteristics profile.
Hyperspectral reflectance of airborne emergent vegetation is a comprehensive expression of the various ecological and environmental factors contained in emergent vegetation and a means of indirectly extracting essential information based on the radiant/scattered energy of the target feature [79]. The estimation of hyperspectral reflectance for surface water composition is attributed to the superior sensitivity of TN concentration to hyperspectral reflectance characteristics of specific wavelength spectra. As chlorophyll concentration increases, plant photosynthetically active radiation (PAR) becomes intense and green band reflectance decreases [80]. Sun et al. applied plant spectra to the diagnosis of TN concentration in water and obtained better estimation results, which verified that hyperspectral reflectance data from aquatic plant canopies are workable in monitoring water composition information [23]. In this study, the reflectance of plants decreased with increasing TN concentration levels ( Figure 3). Because there are clear spectral mechanisms [81][82][83] to support us in this operation, this paper is reliable for monitoring water quality based on airborne hyperspectral reflectance. In addition, TN concentration inversion results can be improved by airborne hyperspectral reflectance denoising and other processing methods. Notably, the selection of representative training and validation sets in conjunction with the GRA method is also important to produce reliable algorithm results.

Prerequisites for Accurate Estimation
The hyperspectral reflectance of the canopy contains redundancy. Hence, the db4 mother wavelet function was employed in decomposition and reconstruction on a binary scale to remove noise [84][85][86]. The db4 mother wavelet function decomposes the hyperspectral reflectance into feature spectra of different sub-bands, where each layer characterizes specific details of the original signal; the reconstructed spectra emphasize the relevant dominant signals and attenuate or filter minor signals [87]. Many works have reported DWT processing of hyperspectral data and the consequent identification of key target features with mediumscale decomposition reconstruction [47]. The present study obtained optimal results at L6 (R 2 = 0.91, Figure 6), which is consistent with the medium scale mentioned above.
Notably (Table 2), poor predictions were observed at lower scales, both in the OR decomposition layer (L2, R 2 = 0.50) and in the FOD (L1, R 2 = 0.58). This poor predictive ability probably lies in the fact that noise still exists in the spectrum after wavelet firstlayer decomposition and reconstruction, which is not sensitive to the spectral absorption characteristics of the internal structure of P. australis leaves [88]. The results of DWT analysis of hyperspectral data at low scales studied by Cai were also unsatisfactory, and they pointed out the poor denoising ability at low scales and the reduced interpretation ability at high scales [87]. Therefore, the optimal scale is still under the medium scale. In this study, the same problem occurs at the high scale (L7-L8), and its interpretation ability decreases.
The combinations of OR with DWT and FOD with DWT both strengthen the difference of spectral bands with increasing scale to improve model prediction accuracy (Table 2), indicating that the higher the scale is, the more prominently it reflects the effective information of leaf reflection spectra. However, in the decomposition layer at scales of up to L7 (Figure 3B8), the wave peak and trough features progressively disappear from the spectra with the continuous stripping of high-frequency signals, resulting in a decrease in information in the P. australis canopy reflection spectra. Existing studies stated that the spectral information interpretation ability was insufficient at both low and over decomposition scales [89] and the optimum scale of DWT at low scales required further study. In Table 2, the mean performance of some models with FOD is weaker than the results of DWT analysis of the OR at low scales, which seems to be because the FOD amplifies spectral noise while strengthening spectral differences. However, the effective denoising results exhibited by the combination of FOD and DWT provide a new reference method for the processing of UAV airborne hyperspectral data.

Vegetation Canopy Spectral Response Mechanisms
The researchers concluded that the spectral response regions between the emergency vegetation canopy spectra and TN elements were concentrated in the visible and red-edge regions. Haboudane et al. evaluated N concentrations in winter wheat at different growth stages and found that the 405-418 nm, 670-700 nm, and 761-763 nm regions were sensitive areas for TN [90]. Fava et al. found that the best spectral response region for estimating N concentration involved the long wavelength (740-770 nm) and near infrared (775-820 nm) of the red-edge band [91]. Due to the effect of TN elements, the vegetation reflectance spectral properties were "red-shifted" (630-780 nm) and the reflectance decreased in the red-edge region [92]. Unsurprisingly (Figure 4), the sensitivity of the OR and 0.1-0.9-order FOD after DWT is comparatively strong in the visible region (400-750 nm), as is that of 1st-2nd-order FOD in the near-infrared region (near 950 nm). The internal chlorophyll of plants absorbs the majority of the radiant energy in the visible range [24,93], which is why vegetative spectra can confirm the abundance of various elements in water. When the FOD order reaches or exceeds 1.0, the clustered regions of the sensitive spectral bands become more discrete, and the red-edge band (800-1000 nm) exhibits greater sensitivity. This spectral reflectance feature has a strong correlation with the internal structure of plant leaves (water, protein, chlorophyll, sugar, etc.) [94].
Some insignificant spectral bands are apparent after correlation analysis of the preprocessed spectra (Figure 4). If all discrete wavelet feature spectra are individually considered as independent variables to build the TN inversion model in water, the sensitive bands of certain decomposition layers could be ignored, resulting in the selected sensitive bands not fully explaining the TN in water bodies and limitations of the constructed model [47,95]. In this study, the optimal sensitive bands are selected by GRA as independent variables to build the optimal estimation model of TN in water. We regarded the spectral regions with high relation coefficients and GRA above 0.8 as sensitive bands (Figures 4 and 5). The sensitive bands were focused in mostly four spectral regions, including blue (450 nm), green (550 nm), red (670 nm), and near-infrared regions (950 nm). The results of this study are coherent with the existing research results. In summary, the combination of wavelet transform and GRA can better highlight sensitive band information related to TN concentration.

The Potential of the Developed Model
Three integrated learning models (RF, XGBoost, and bagging) were employed to predict TN. For all three models, the independent variables are randomly divided into a modeling set (70%, n = 30) and a validation set (30%, n = 15) and fixed by a function, which also ensures the reasonableness of the input samples. Figure 6 shows that all three models exhibited clear explanatory power (RPD mean > 1.5). However, the variation among the modeling results is substantial, and the optimal result was obtained with XGBoost, which can best describe the quantitative relationship between the reflectivity of the sensitive band and TN in water. The modeling accuracy is comparatively balanced for the bagging model; in the RF model based on the reflectance of the sensitive band, higher-sensitivity information is underestimated, although the RF are valid for this nonlinear issue [63,65]. Therefore, the XGBoost model is recommended to explain the relationship between the TN concentration in water and hyperspectral reflectance. The results of this study indicate that the combination of DWT and GRA generally enhances the accuracy of TN estimation in water (Table 2). Considering the difficulty of raw spectral feature extraction, it is recommended that DWT be applied to preprocess spectral reflectance data, especially in hyperspectral applications. A practical approach is provided for airborne hyperspectral data monitoring of water body components.

Research Challenges
DWT processing of hyperspectral reflectance data is analyzed in detail in this study. However, the wavelet mother function, reconstruction methods and threshold selection rules, wavelet decomposition scale, and other factors affect the denoising effectiveness to some degree; moreover, information decomposed at too high a scale is difficult to interpret. In future work, it will be critical to investigate the selection methods of the above wavelet factors and their combination techniques to further improve the hyperspectral reflectance denoising effect and thus enhance the analysis capability of DWT spectra. We compared the results of the three models and found that DWT combined with GRA produced the best prediction accuracy; however, it was not easy to determine exactly which wavelength range contributed optimally to the TN model of water. The presented inversion model, which is based on the spectral reflectance of the canopy of inland lake wetland vegetation, and the applicability of the model in other regions or in monitoring water bodies dependent on different wetland vegetation warrants further validation. Moreover, the influences of environmental factors (such as surrounding soil properties, leaf biochemical composition, and canopy structure) and complex interactions between substances within the water of water quality information extraction need to be further investigated.

Conclusions
The potential of discrete wavelet transform (DWT) combined with grey relation analysis (GRA) and different machine learning approaches for TN monitoring in water was explored using leaf hyperspectral data. The results of this study in hyperspectral data processing and extraction of water quality parameters once again demonstrated that the application of hyperspectral reflectance to water quality remote sensing is effective and provides a new technological approach for global water environmental protection. The following conclusions can be drawn: (1) DWT with appropriate scales is an outstanding technique for preprocessing hyperspectral data. The preprocessing method of fractional order discretization (FOD) combined with DWT may provide basic technical support for hyperspectral signal denoising and could enrich the preprocessing methods of UAV or satellite hyperspectral images.
(2) The hyperspectral information of emergent vegetation can be efficiently used for the estimation of TN in water. This approach offers a novel reference method for hyperspectral reflectance data monitoring and the protection of global inland water quality, serving the goals of water resource protection and water pollution management for sustainable development. (3) The XGBoost model shows remarkable explanatory power for the intrinsic relationship between TN in water and the spectrum of aquatic vegetation.
These results may contribute to further mining of airborne hyperspectral data information, which also provides a new reference for accurate water quality monitoring of complex global waters using UAV or satellite hyperspectral data. In the future, we need to further explore both the method of DWT and the influence of the complexity of water and their environment on water quality extraction.