# Evaluation of Leaf N Concentration in Winter Wheat Based on Discrete Wavelet Transform Analysis

^{1}

^{2}

^{*}

## Abstract

**:**

_{705}alone, and was more stable in estimating LNC than models based on random forest regression (RF). The results indicated that narrowband reflectance spectroscopy (450–1350 nm) combined with DWT analysis and PLS regression was a promising method for rapid and nondestructive estimation of LNC for winter wheat across a range in growth stages.

## 1. Introduction

_{705}) and the modified simple ratio (mSR

_{705}), which effectively reduce the impact of differences in leaf surface reflectance and improve the sensitivity of pigment and N content estimation [19]. Chen et al. [20] developed the three-band double-peak canopy nitrogen index (DCNI) to predict the LNC of maize and wheat during the critical N management stage. However, these indices are calculated by utilizing a limited number of wavelengths in specific spectral regions, which have not exploited the entire range in hyperspectral data [21] and are calibrated against a specific database, which cannot be generalized to other databases [22]. There is an urgent need to propose an approach that could take advantage of the entire canopy spectral information as well as diminish the impacts of band autocorrelation and data redundancy.

## 2. Materials and Methods

#### 2.1. Data Acquisition

#### 2.1.1. Experimental Design

^{2}(3 m × 4 m) with a planting row spacing of 0.2 m and a plant density of 185 kgha

^{−1}. Six N rates (0, 30, 60, 90, 120 and 150 kg ha

^{−1}) and six P rates (0, 15, 30, 60, 75 and 90 kg ha

^{−1}) were employed with two replications. 30 kg ha

^{−1}P

_{2}O

_{5}and 60 kg ha

^{−1}N were applied as a basal fertilizer for N and P treatments, respectively. There was no K fertilizer application due to the K sufficiency in this area. Experiment 2 was conducted at Qian County (108°10’ E, 34°37’ N; elevation: 830 m) in Xianyang City during the years 2014 to 2015. A total of 36 plots were set and each plot was 36 m

^{2}(6 m × 6 m) with a similar cultivar as experiment 1. Six N rates (0, 45, 90, 135, 180 and 225 kg ha

^{−1}), six P rates (0, 22.5, 45, 67.5, 90 and 112.5 kg ha

^{−1}) and six K rates (0, 15, 30, 45, 60 and 75 kg ha

^{−1}) were applied and replicated twice. 60 kg ha

^{−1}K

_{2}O and 45 kg ha

^{−1}P

_{2}O

_{5}, 60 kg ha

^{−1}K

_{2}O and 90 kg ha

^{−1}N and 90 kg ha

^{−1}N and 45 kg ha

^{−1}P

_{2}O

_{5}were applied as a basal fertilizer for N, P and K treatments, respectively, before planting. For all the treatments, N, P

_{2}O

_{5}and K

_{2}O fertilizers were applied as urea, potassium chloride and superphosphate, respectively. All the plot crop planting and management patterns followed the local standard practices for wheat production.

#### 2.1.2. Canopy Spectral Measurement

_{4}calibration panel was used to calculate the black and baseline reflectance. To minimize the effects caused by the surroundings, the canopy spectrum in each plot was obtained by randomly selecting three sampling sites, and then averaging these into a single spectral sample. Each sample consisted of an average of ten scans at an optimized integration time. Canopy spectral data were measured during the main growth stages in each growing season. A total of 84, 84, 74 and 73 samples were obtained in tillering, jointing, booting and filling growth stages.

#### 2.1.3. Leaf Nitrogen Concentration Measurement

^{2}(0.2 m × 0.4 m) and 0.25 m

^{2}(0.5 m × 0.5 m) of each plot in experiments 1 and 2 were cut respectively at ground level. All green leaves were separated from stems, sealed in plastic bags and transferred to the laboratory with ice chests. Then, the samples were oven-dried at 105 °C for 30 min, followed by oven drying at 80 °C until a constant weight was achieved. Finally, dried leaves were finely ground and a subsample of ground leaves was taken to analyze for LNC (g per 100 g dry weight, %) using the Kjeldahl method [31].

#### 2.2. Spectral Transformation

#### 2.3. Analytical Methods

#### 2.3.1. Discrete Wavelet Transform Analysis

_{i}

_{,k}is a DWT coefficient; f(λ) is a signal; φ

_{i,k}(λ) is the discretized wavelet basis used to fit optimally the signal; i is the ith decomposition level or step and k is the kth wavelet coefficient at the ith level. With DWT analysis, signals are analyzed over a discrete set of scales, typically being dyadic (2

^{i}, i = 1, 2, 3, … i is the decomposition level) [25,28,30].

_{i}) plus the DCs at decomposition level 1 to level j (L

_{1}–L

_{i}).

_{i}denotes the wavelet energy value of the ith decomposition level (L

_{i}), w

_{i,k}is the kth wavelet coefficient at L

_{i}and K represents the total number of wavelet coefficients under each level. As shown in Figure 1, EV

_{3}will be calculated with the AC

_{3}, DC

_{1}, DC

_{2}and DC

_{3}according to expression (3). Five mother wavelet functions including db10, sym8, coif5, bior6.8 and rbio6.8 from the Daubechies, Symlet, Coiflet, Biorthogonal and Reverse biorthogonal wavelet families, respectively, were assessed in this study, which are commonly tested wavelet families in the canopy spectra decomposition [25,26,27,28,30].

#### 2.3.2. Existing Spectral Indices Calculation

_{705}), MERIS terrestrial chlorophyll index (MTCI), structurally insensitive pigment index (SIPI) and normalized pigment chlorophyll index (NPCI); (2) nitrogen indices: Nitrogen reflectance index (NRI), normalized difference red-edge index (NDRE) and double-peak canopy nitrogen index (DCNI); (3) greenness indices: Green normalized difference vegetation index (GNDVI), optimized soil-adjusted vegetation index (OSAVI) and modified triangular vegetation index (MTVI

_{2}). The definitions and reference sources for these ten spectral indices are summarized in Table 1.

#### 2.3.3. Modeling Method

^{®}7.0 (MathWorks, Inc., Natick, MA, USA).

#### 2.3.4. Calibration and Validation

^{2}), root mean square error (RMSE), relative error (RE, %) and the ratio of prediction to deviation (RPD) were used to measure the predictive performance of each estimation model by different methods. Higher values of R

^{2}and RPD, and lower values of RMSE and RE indicate better dependability and accuracy of the regression model in predicting LNC [21,47,48]. RPD is a ratio of standard deviation to RMSE. RPD values greater than 2.0 indicate a stable and accurate predictive model, an RPD value between 1.4 and 2.0 indicates a fair model that could be improved by more accurate prediction techniques and a value less than 1.4 indicates poor predictive capacity [21]. Rc

^{2}, Rv

^{2}, RMSEc, RMSEv, REc, REv, RPD

_{c}and RPD

_{v}in this paper represented R

^{2}, RMSE, RE and RPD in the calibration and validation data set, respectively. A 1:1 plot of observed vs. estimated values was drawn to demonstrate the degree of model fit.

## 3. Results

#### 3.1. LNC Estimation Models (SR-LNC) Based on Sensitive-Band Reflectance

#### 3.1.1. Correlations Between Canopy Spectra and LNC

#### 3.1.2. Construction of SR-LNC Estimation Models

_{c}

^{2}s in exponential prediction models were 0.73 and 0.79, respectively. The R

_{v}

^{2}s in validation samples were 0.72 and 0.85, RMSE

_{v}s were 0.42 and 0.35 and RE

_{v}s were 28.38 and 20.65 for LOGS and CRS, respectively. Scatter plots between predicted and measured LNC values indicated that higher LNC values were underestimated (Figure 4). CRS was superior to other spectra in predicting LNC at sensitive reflectance bands, with predicted and measured LNC values falling close to the 1:1 line.

#### 3.2. LNC Estimation Models (SI-LNC) Based on Spectral Indices

_{705}index was the best of ten spectral indices, which could explain 83% variability in LNC. The higher R

_{v}

^{2}(0.86), lower RMSE

_{v}(0.28) and RE

_{v}(18.81) also illustrated a better performance of mSR

_{705}. The NDRE index was the best of three nitrogen indices, which could explain 80% of variability in LNC. The GNDVI was the best among the three greenness indices. Both GNDVI and NDRE were exponentially related to LNC, while the accuracy of GNDVI was slightly worse than NDRE.

#### 3.3. LNC Estimation Models (DWT-LNC) Based on DWT Features

#### 3.3.1. Selection of Optimum Mother Wavelet and Decomposition Level

_{1}to L

_{12}, and the downward trend became stable at L

_{10}. Among five mother wavelets, sym8 had the strongest data compression ability, while coif5 was the weakest. For example, the total number of wavebands in this study was 951 (from 400–1350 nm). After DWT analysis at decomposition level 10, the number of DWT coefficients with mother wavelet function sym8 was 15, while coif5 had 29, which was determined from the wavelet basis length [25].

_{5}until leveling off at L

_{10}, which indicated that the explanatory and signal restoring ability of ACs to canopy spectra declined gradually from L

_{5}to L

_{10}. All the correlation coefficients were still above 0.7 at L

_{10}except with FDS, which went down to less than 0.6 rapidly after decomposition level 6. The mother wavelet db10 was more labile compared to the others, especially poor was the large fluctuation in CRS correlations. Taking into account the data compression effectiveness, stability of mother wavelet and ability to maintain the information quality of the canopy spectra, a mother wavelet sym8 at decomposition level of L

_{1}–L

_{10}was chosen to conduct the DWT to analyze the correlation with LNC.

#### 3.3.2. DWT-LNC Models Based on PLS Regression

#### PLS Regression Using Wavelet ACs

_{1}to L

_{10}passed the 0.01 significance level test. The number of latent variables (LVs) extracted by PLS regression increased and then decreased with the decomposition level (Figure 6). The maximum number of latent variables emerged at L

_{5}, which implied a lower convergence rate of the PLS regression at L

_{5}. As a whole, all the estimating models had high prediction accuracy (R

_{c}

^{2}was greater than 0.70). The general trend of R

_{c}

^{2}in each predicting model increased and then decreased gradually with an increasing decomposition level (Figure 7). The ACs could explain 90%–93% of the variability in LNC at L

_{1}to L

_{5}, except with CRS at L

_{1}. The variation of R

_{v}

^{2}was consistent with R

_{c}

^{2}, and all the R

_{v}

^{2}s were greater than 0.75. Table 5 shows the variation in RMSE and RE. LOGS had stronger prediction ability over other models, with the highest values of R

_{v}

^{2}and R

_{c}

^{2}, and lowest RE

_{v}and RMSE

_{v}values at L

_{1}–L

_{10}. All the RMSE

_{v}s were below 0.30. The R

_{v}

^{2}s were 0.93, 0.93 and 0.91 respectively for the LOGS at L

_{3}, L

_{4}and L

_{5.}Measured and predicted LNC values with ACs from LOGS at L

_{3}–L

_{5}closely approximated a 1:1 line (Figure 8), and the PLS model at L

_{4}yielded the optimal prediction accuracy (RMSE

_{v}= 0.20, RE

_{v}= 13.47).

#### PLS Regression Using Wavelet DCs

_{1}to L

_{5}were very small in amplitude (near zero) and could be removed without major loss in the information content of the signal. Table 6 summarizes the validation results of PLS models based on DCs at L

_{6}–L

_{10}. Prediction accuracy decreased with the decomposition level. The performance of LOGS was better than other spectral transformations, but it was still worse than PLS modeling with ACs (Table 5).

#### PLS Regression Using EVs

_{v}

^{2}increased and then decreased with OS and LOGS, while a general tendency of first increasing then decreasing and a conspicuous monotonic increase were found, respectively, with FDS and CRS (Table 7). However, all the R

_{v}

^{2}reached the maximum at L

_{10}. Energy value could explain over 80% of the variability of LNC at L

_{10}with fewer variables (number of variables was 11). LOGS still gave the best performance over the other transformations (with R

_{c}

^{2}of 0.85 and R

_{v}

^{2}of 0.88), but the overall accuracy was still lower than those using approximate coefficients at L

_{3}–L

_{5}(Figure 6). The RMSE and RE of validation set were 0.26 and 17.82 respectively, also a poorer correlation compared with the results in Table 5.

#### 3.3.3. DWT-LNC Based on RF Regression

_{10}were selected to build the RF regression models. As showed in Table 8, R

^{2}s in the validation set were slightly lower than the calibration set and most of them were less than 0.90, except for results using ACs of LOGS in L

_{4}and L

_{5}. After L

_{5}, the RMSE

_{v}and RE

_{v}tended to go up slightly for all transformations especially with FDS. In general, LOGS was better than other transformations in estimating LNC by ACs with RF regression. ACs at L

_{4}had the best RMSE

_{v}and RE

_{v,}being 0.24 and 16.08, respectively, while the ACs at L

_{10}were the worst in the RF regression models. The accuracy of RF models based on energy values of wavelet coefficients was improved compared with the PLS regression, but still poorer than using ACs.

#### 3.4. Estimation Accuracy Comparison

_{c}

^{2}and R

_{v}

^{2}increased to 0.79 and 0.85, and the RMSE

_{v}and RE

_{v}decreased to 0.35 and 20.65, respectively (Figure 2). The accuracy also was better than the results of LOGS and FDS at 645 nm and 447 nm, respectively (Figure 3 and Figure 4). However, it was still lower than the performance of some spectral indices especially mSR

_{705}(R

_{c}

^{2}= 0.83, R

_{v}

^{2}= 0.86, RMSE

_{v}= 0.28 and RE

_{v}= 18.81; Table 3). The LOGS was obviously distinguished from four transformed canopy spectra in the discrete wavelet transform analysis and exhibited a promising potential for revising LNC. For PLS modeling, LOGS combined with ACs at L

_{4}produced the best performance both in the calibration and validation sets. The prediction result of LNC in the high-value region was better than SR-based and SI-based LNC estimation models. DCs and EVs performed worse in LNC evaluation by using PLS regression. The best prediction accuracy of DCs was at the decomposition level 6 (R

_{v}

^{2}= 0.89, RMSE

_{v}= 0.26 and RE

_{v}= 17.53), which was slightly higher than the mSR

_{705}index. EVs at L

_{10}had similar prediction accuracy as DCs at L

_{6}. With RF regression, LOGS at L

_{4}showed the highest accuracy in LNC prediction on the basis of ACs, with the R

_{v}

^{2}, RMSE

_{v}and RE

_{v}being 0.91, 0.24 and 16.28, respectively, which were slightly worse than the PLS regression. LNC estimation result using energy values was improved by a RF regression, but it was still lower than the PLS and RF models with ACs at L

_{4}.

_{725}, which indicated all the estimation models in Table 9 had stable and accurate predictive abilities. The PLS model with AC

_{4}produced the best performance (RPD

_{c}= 3.97 and RPD

_{v}= 3.95), and followed by the RF regression model with AC

_{4}(RPD

_{c}= 3.04 and RPD

_{v}= 3.29). Overall, by comparing all the methods in this article with statistical indicators of R

^{2}, RMSE, RE and RPD, an integrated approach using DWT ACs and PLS regression exhibited the highest stability and reliability in LNC estimation.

## 4. Discussion

#### 4.1. Sensitive Band Reflectance and Spectral Transformation

_{c}

^{2}= 0.79) was higher than that of LOGS, FDS and OS (Figure 3) in winter wheat LNC prediction. The same conclusion was obtained in the grass foliar nitrogen retrieval reported by Ramoelo et al. [51], where an R

^{2}of 0.81 was based on a greenhouse experiment using continuum removal in combination with a PLS regression. As a whole, the exponential model was more suitable for delineating the quantitative relationship between sensitive band reflectance and LNC than a linear regression (Figure 3). This may be caused by the fact that the relationship between leaf N and chlorophyll concentration was not linear [10,52].

#### 4.2. Relationship Between Spectral Indices and LNC

_{705}index of chlorophyll indices, NDRE index of nitrogen indices and GNDVI of greenness indices in this paper were constructed on the basis of red edge reflectance, could explain 83%, 80% and 81% of the variability in LNC, respectively (Table 3), and had better performance than other spectral indices. This was consistent with the report that the GNDVI performed similarly as NDRE in estimating maize N concentration [52]. Green and red edge reflectance were sensitive to a wider range of chlorophyll levels than red reflectance. The predictive ability of NDRE in the category of nitrogen indices was higher than with NRI and DCNI in this study (Table 3). NDRE is similar in form to NDVI, but with the red band being replaced by a red edge band. NRI, a normalized near-infrared over green waveband reflectance ratio, has been used to assess in-season corn N status and to develop N variability maps [37,54], but in our study, the predictive ability (R

_{c}

^{2}= 0.50) of NRI was lower than NDRE (R

_{c}

^{2}= 0.80). These results demonstrated the importance of red edge vegetation indices for estimating winter wheat N status.

_{c}

^{2}= 0.63) explained 20% less variability in LNC than mSR

_{705}in this study (Table 3). The RMSE of mSR

_{705}(RMSE

_{v}= 0.28) indicated an ordinary performance of the LNC prediction model, and an RMSE

_{v}of 0.41 indicated poor model performance of DCNI [48].

#### 4.3. Features and Parameters Selection of the DWT Analysis

_{1}to L

_{5}could be used directly to predict the LNC, instead of using the whole reflectance spectra, while ignoring the high-frequency DCs.

_{4}with PLS regression could explain 83% (R

_{c}

^{2}= 0.83) of the variability in LNC. EVs had a poorer performance and ability to estimate LNC compared with the ACs. This might be due to excessive dimensionality reduction, resulting in a loss of some sensitive information in the canopy spectrum.

#### 4.4. Estimation Models of LNC

_{705}) explained 4% more variability in LNC estimation than the best performing single sensitive band CRS

_{725}. The advantage of multi-variable regression was obvious (Table 9). Approximation coefficients at decomposition level 4 using LOG-transformed spectra had the best prediction accuracy in PLS-LNC models. The prediction accuracy of the RF-LNC model with LOGS at L

_{4}was similar to the PLS-LNC model, while the R

^{2}, RMSE, RPD and RE of validation set were slightly worse than the PLS regression (Table 8 and Table 9). That is, the prediction and verification accuracy of the PLS model was more stable than that of the RF model. This is likely because the accuracy of the RF model was greatly influenced by the undefined input parameters, although it was efficient for large input variables and non-linear problems [42,43,44,45].

_{705}might alternatively be suggested to predict LNC, especially in multi-spectral remote sensing applications. Wavelet analysis of a reflectance spectrum was performed by scaling and shifting the wavelet function to produce wavelet coefficients that were assigned to different frequency components. It made the DWT analysis to have the potential to capture much more of the information contained within the canopy hyper-spectra [25,28,30,57,58,59]. Our results showed that using DWT coefficients and PLS regression together could overcome the limitations of individual variable technology and offer a practical approach to LNC detection. The model produced by using AC

_{4}with PLS regression had the best performance (RPD

_{c}= 3.97 and RPD

_{v}= 3.95) and was recommended for LNC estimation across all growth stages.

#### 4.5. Research Challenges

## 5. Conclusions

_{705}and was more stable in LNC estimation than the RF regression.

## Author Contributions

## Funding

## Conflicts of Interest

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**Figure 1.**Process of multi-level discrete wavelet transform decomposition of signal S. AC

_{i}and DC

_{i}denote the approximation coefficient (AC) and detail coefficient (DC) at the ith decomposition level (L

_{i}). Taking L

_{3}for example, the output wavelet decomposition vectors include AC

_{3}, DC

_{1}, DC

_{2}and DC

_{3}. The size of each box demonstrates the length of the successive approximation and detail coefficients vectors.

**Figure 2.**Correlation coefficients between leaf nitrogen concentration and transformed canopy spectra, including original spectrum (OS), first derivative spectrum (FDS), log-transformed spectrum (LOGS) and continuum removal spectrum (CRS).

**Figure 3.**Leaf nitrogen concentration prediction models based on sensitive band reflectance. The solid line represents the exponential fitting.

**Figure 4.**Scatter plots between the measured and predicted leaf nitrogen concentration based on sensitive band reflectance. The dash line is the 1:1 line.

**Figure 5.**Correlations between reconstructed signals and transformed spectra for different mother wavelets at each decomposition level. (

**a**) OS, (

**b**) FDS, (

**c**) LOGS and (

**d**) CRS.

**Figure 6.**The number of latent variables in a partial least squares regression based on approximation coefficients.

**Figure 7.**Relationships between determination coefficients and decomposition level of partial least squares regression models with approximation coefficients in the calibration (

**a**) and validation set (

**b**).

**Figure 8.**Relationships between measured and predicted leaf nitrogen concentration (%) based on the approximation coefficients of the log-transformed spectra (LOGS) at decomposition level 3, 4 and 5 in validation set.

Category | Index | Formula | Developed by |
---|---|---|---|

Chlorophyll indices | mSR_{705} | (R_{750} – R_{445})/(R_{705} − R_{445}) | [19] |

MTCI | (R_{754} − R_{709})/(R_{709} − R_{681}) | [35] | |

SIPI | (R_{800} − R_{445})/(R_{800} − R_{680}) | [36] | |

NPCI | (R_{430} − R_{680})/(R_{430} + R_{680}) | [36] | |

Nitrogen indices | NRI | (R_{570} − R_{670})/(R_{570} + R_{670}) | [37] |

NDRE | (R_{790} − R_{720})/(R_{790} + R_{720}) | [38] | |

DCNI | (R_{720} − R_{700})/(R_{700} − R_{670})/(R_{720} − R_{670} + 0.03) | [20] | |

Greenness indices | GNDVI | (R_{750} − R_{550})/( R_{750} + R_{550}) | [39] |

OSAVI | 1.16(R_{800}−R_{670})/(R_{800} + R_{670} + 0.16) | [40] | |

MTVI_{2} | 1.5(1.2(R_{800} − R_{550}) − 2.5(R_{670} − R_{550}))/sqrt((2R_{800} + 1)^{2} − (6R_{800} − 5sqrt(R_{670})) − 0.5) | [41] | |

R_{i} is the reflectance at i nm wavelength |

Data Set | No. of Samples | Min | Max | Range | Mean | SD | Variance | Skewness | Kurtosis | CV (%) |
---|---|---|---|---|---|---|---|---|---|---|

Whole | 315 | 0.22 | 3.87 | 3.64 | 1.47 | 0.77 | 0.59 | 0.76 | 2.98 | 52.03 |

Calibration | 252 | 0.22 | 3.60 | 3.38 | 1.46 | 0.76 | 0.58 | 0.73 | 2.88 | 51.88 |

Validation | 63 | 0.35 | 3.87 | 3.52 | 1.5 | 0.79 | 0.63 | 0.86 | 3.26 | 53.00 |

**Table 3.**Estimation models and prediction errors of leaf nitrogen concentration based on the spectral indices. ** at 0.01 significance level.

Category | Index | Correlation Coefficient | Equation | R_{c}^{2} | R_{v}^{2} | RMSE_{v} | RE_{v} |
---|---|---|---|---|---|---|---|

Chlorophyll indices | mSR_{705} | 0.91 ^{**} | LNC = 0.2702x − 0.6773 | 0.83 | 0.86 | 0.28 | 18.81 |

MTCI | 0.89 ^{**} | LNC = 0.5454x − 1.0901 | 0.78 | 0.84 | 0.31 | 20.94 | |

SIPI | 0.79 ^{**} | LNC = 1E − 06e^{15.28x} | 0.71 | 0.69 | 0.57 | 37.80 | |

NPCI | 0.80 ^{**} | LNC = 1.9583e^{4.13x} | 0.70 | 0.71 | 0.45 | 30.13 | |

Nitrogen indices | NRI | 0.70 ^{**} | LNC = 6.2342x − 0.5199 | 0.50 | 0.50 | 0.56 | 37.64 |

NDRE | 0.86 ^{**} | LNC = 0.046e^{6.28x} | 0.80 | 0.85 | 0.30 | 20.27 | |

DCNI | 0.79 ^{**} | LNC = 0.039x − 0.8904 | 0.63 | 0.74 | 0.41 | 27.06 | |

Greenness indices | GNDVI | 0.85 ^{**} | LNC = 0.002e^{8.44x} | 0.81 | 0.82 | 0.33 | 21.90 |

OSAVI | 0.69 ^{**} | LNC = 0.0099e^{6.61x} | 0.55 | 0.54 | 0.55 | 36.61 | |

MTVI_{2} | 0.60 ^{**} | LNC = 5.293x − 1.0551 | 0.36 | 0.42 | 0.60 | 40.08 |

**Table 4.**The number of wavelet coefficients under different mother wavelets and decomposition levels.

Mother Wavelet | L_{1} | L_{2} | L_{3} | L_{4} | L_{5} | L_{6} | L_{7} | L_{8} | L_{9} | L_{10} | L_{11} | L_{12} |
---|---|---|---|---|---|---|---|---|---|---|---|---|

bior6.8 | 484 | 250 | 133 | 75 | 46 | 31 | 24 | 20 | 18 | 17 | 17 | 17 |

coif5 | 490 | 259 | 144 | 86 | 57 | 43 | 36 | 32 | 30 | 29 | 29 | 29 |

db10 | 485 | 252 | 135 | 77 | 48 | 33 | 26 | 22 | 20 | 19 | 19 | 19 |

rbio6.8 | 484 | 250 | 133 | 75 | 46 | 31 | 24 | 20 | 18 | 17 | 17 | 17 |

sym8 | 483 | 249 | 132 | 73 | 44 | 29 | 22 | 18 | 16 | 15 | 15 | 15 |

**Table 5.**The coefficient of determination, root mean square error and relative error of the validation set based on a partial least squares regression with wavelet approximation coefficients.

OS | FDS | LOGS | CRS | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

R_{v}^{2} | RMSE_{v} | RE_{v} | R_{v}^{2} | RMSE_{v} | RE_{v} | R_{v}^{2} | RMSE_{v} | RE_{v} | R_{v}^{2} | RMSE_{v} | RE_{v} | |

AC_{1} | 0.86 | 0.29 | 19.59 | 0.88 | 0.27 | 18.07 | 0.91 | 0.24 | 15.78 | 0.83 | 0.33 | 22.06 |

AC_{2} | 0.86 | 0.30 | 19.68 | 0.89 | 0.26 | 17.22 | 0.92 | 0.23 | 15.19 | 0.84 | 0.33 | 22.13 |

AC_{3} | 0.84 | 0.32 | 21.24 | 0.92 | 0.23 | 15.50 | 0.93 | 0.20 | 13.59 | 0.87 | 0.33 | 22.18 |

AC_{4} | 0.87 | 0.29 | 19.09 | 0.87 | 0.27 | 18.18 | 0.93 | 0.20 | 13.47 | 0.84 | 0.33 | 22.20 |

AC_{5} | 0.88 | 0.28 | 18.45 | 0.88 | 0.29 | 19.49 | 0.91 | 0.23 | 15.60 | 0.88 | 0.28 | 18.37 |

AC_{6} | 0.85 | 0.31 | 20.98 | 0.85 | 0.31 | 20.76 | 0.88 | 0.27 | 17.95 | 0.88 | 0.27 | 18.24 |

AC_{7} | 0.82 | 0.34 | 22.62 | 0.85 | 0.31 | 20.52 | 0.87 | 0.30 | 20.11 | 0.88 | 0.27 | 17.99 |

AC_{8} | 0.83 | 0.33 | 22.28 | 0.81 | 0.31 | 20.84 | 0.86 | 0.30 | 19.83 | 0.84 | 0.31 | 20.87 |

AC_{9} | 0.77 | 0.38 | 25.13 | 0.81 | 0.35 | 23.07 | 0.85 | 0.30 | 20.29 | 0.85 | 0.31 | 20.74 |

AC_{10} | 0.78 | 0.37 | 24.90 | 0.83 | 0.32 | 21.64 | 0.86 | 0.29 | 19.59 | 0.85 | 0.30 | 20.14 |

**Table 6.**The coefficient of determination, root mean square error and relative error of the validation set based on a partial least squares regression with detail coefficients at decomposition level 6 to level 10. DC

_{i}denotes the detail coefficient (DC) at L

_{i}.

DC | OS | FDS | LOGS | CRS | ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

R_{v}^{2} | RMSE_{v} | RE_{v} | R_{v}^{2} | RMSE_{v} | RE_{v} | R_{v}^{2} | RMSE_{v} | RE_{v} | R_{v}^{2} | RMSE_{v} | RE_{v} | |

DC_{6} | 0.84 | 0.32 | 21.43 | 0.81 | 0.35 | 23.02 | 0.89 | 0.26 | 17.53 | 0.85 | 0.30 | 20.25 |

DC_{7} | 0.83 | 0.33 | 21.75 | 0.77 | 0.38 | 25.19 | 0.89 | 0.27 | 17.73 | 0.84 | 0.32 | 21.41 |

DC_{8} | 0.83 | 0.33 | 22.17 | 0.57 | 0.52 | 34.54 | 0.87 | 0.29 | 18.38 | 0.81 | 0.35 | 23.13 |

DC_{9} | 0.77 | 0.38 | 25.36 | 0.48 | 0.57 | 38.05 | 0.88 | 0.28 | 18.77 | 0.81 | 0.36 | 23.76 |

DC_{10} | 0.76 | 0.39 | 26.17 | 0.39 | 0.62 | 41.63 | 0.88 | 0.28 | 19.55 | 0.77 | 0.38 | 25.53 |

**Table 7.**The coefficient of determination, root mean square error and relative error of the validation set based on a partial least squares regression with wavelet energy values. EV

_{i}denotes energy value (EV) at decomposition level i.

EV | OS | FDS | LOGS | CRS | ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

R_{v}^{2} | RMSE_{v} | RE_{v} | R_{v}^{2} | RMSE_{v} | RE_{v} | R_{v}^{2} | RMSE_{v} | RE_{v} | R_{v}^{2} | RMSE_{v} | RE_{v} | |

EV_{1} | 0.14 | 0.73 | 49.02 | 0.46 | 0.58 | 38.83 | 0.47 | 0.57 | 38.22 | 0.64 | 0.47 | 31.61 |

EV_{2} | 0.25 | 0.69 | 46.14 | 0.43 | 0.59 | 39.80 | 0.72 | 0.42 | 28.67 | 0.71 | 0.43 | 28.43 |

EV_{3} | 0.19 | 0.71 | 47.34 | 0.41 | 0.61 | 40.58 | 0.71 | 0.44 | 29.36 | 0.72 | 0.41 | 27.66 |

EV_{4} | 0.19 | 0.71 | 47.34 | 0.36 | 0.63 | 42.08 | 0.65 | 0.46 | 31.14 | 0.74 | 0.40 | 26.74 |

EV_{5} | 0.29 | 0.67 | 44.42 | 0.32 | 0.65 | 43.47 | 0.69 | 0.43 | 29.05 | 0.75 | 0.39 | 26.34 |

EV_{6} | 0.74 | 0.42 | 27.93 | 0.65 | 0.47 | 26.41 | 0.81 | 0.34 | 22.85 | 0.75 | 0.39 | 26.41 |

EV_{7} | 0.79 | 0.36 | 23.99 | 0.66 | 0.47 | 31.49 | 0.81 | 0.34 | 22.91 | 0.76 | 0.38 | 25.88 |

EV_{8} | 0.87 | 0.29 | 19.22 | 0.74 | 0.41 | 27.61 | 0.83 | 0.32 | 21.56 | 0.80 | 0.35 | 23.56 |

EV_{9} | 0.87 | 0.29 | 19.15 | 0.76 | 0.40 | 27.02 | 0.84 | 0.32 | 21.35 | 0.81 | 0.34 | 23.19 |

EV_{10} | 0.87 | 0.29 | 19.28 | 0.82 | 0.35 | 23.23 | 0.88 | 0.26 | 17.82 | 0.83 | 0.33 | 22.17 |

**Table 8.**Validation of leaf nitrogen concentration estimation models based on a random forest regression with discrete wavelet transform features. AC

_{i}denotes approximation coefficient (AC) at Li; EV

_{10}is the energy value at L

_{10}.

OS | FDS | LOGS | CRS | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

R_{v}^{2} | RMSE_{v} | RE_{v} | R_{v}^{2} | RMSE_{v} | RE_{v} | R_{v}^{2} | RMSE_{v} | RE_{v} | R_{v}^{2} | RMSE_{v} | RE_{v} | |

AC_{1} | 0.86 | 0.29 | 19.64 | 0.87 | 0.29 | 19.30 | 0.89 | 0.26 | 17.53 | 0.89 | 0.27 | 17.93 |

AC_{2} | 0.86 | 0.30 | 19.86 | 0.87 | 0.29 | 19.25 | 0.89 | 0.27 | 17.91 | 0.89 | 0.28 | 18.38 |

AC_{3} | 0.87 | 0.29 | 19.34 | 0.87 | 0.29 | 19.20 | 0.89 | 0.26 | 17.21 | 0.88 | 0.28 | 18.41 |

AC_{4} | 0.86 | 0.29 | 19.52 | 0.86 | 0.29 | 19.52 | 0.91 | 0.24 | 16.08 | 0.89 | 0.27 | 17.78 |

AC_{5} | 0.87 | 0.28 | 18.89 | 0.87 | 0.29 | 19.01 | 0.90 | 0.25 | 16.35 | 0.89 | 0.28 | 18.44 |

AC_{6} | 0.86 | 0.28 | 18.91 | 0.86 | 0.29 | 19.44 | 0.86 | 0.28 | 18.40 | 0.88 | 0.29 | 19.25 |

AC_{7} | 0.88 | 0.29 | 19.41 | 0.71 | 0.43 | 28.76 | 0.86 | 0.30 | 20.12 | 0.86 | 0.31 | 20.77 |

AC_{8} | 0.83 | 0.33 | 21.84 | 0.69 | 0.45 | 29.85 | 0.85 | 0.31 | 20.84 | 0.84 | 0.32 | 21.57 |

AC_{9} | 0.85 | 0.31 | 20.67 | 0.64 | 0.49 | 32.45 | 0.80 | 0.36 | 24.02 | 0.81 | 0.35 | 23.27 |

AC_{10} | 0.83 | 0.32 | 21.49 | 0.51 | 0.56 | 37.15 | 0.74 | 0.41 | 27.17 | 0.76 | 0.39 | 26.23 |

EV_{10} | 0.82 | 0.35 | 23.34 | 0.77 | 0.38 | 25.36 | 0.86 | 0.29 | 19.43 | 0.84 | 0.32 | 21.16 |

**Table 9.**The ratio of prediction to deviation (RPD) values in the calibration models and validation models of leaf nitrogen concentration.

Model | OLS regression | PLS regression | RF regression | ||||
---|---|---|---|---|---|---|---|

CRS_{725} | mSR_{705} | AC_{4} | DC_{6} | EV_{10} | AC_{4} | EV_{10} | |

RPD_{c} | 1.95 | 2.43 | 3.97 | 2.81 | 2.61 | 3.04 | 2.38 |

RPD_{v} | 2.26 | 2.82 | 3.95 | 3.04 | 3.04 | 3.29 | 2.72 |

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## Share and Cite

**MDPI and ACS Style**

Li, F.; Wang, L.; Liu, J.; Wang, Y.; Chang, Q.
Evaluation of Leaf N Concentration in Winter Wheat Based on Discrete Wavelet Transform Analysis. *Remote Sens.* **2019**, *11*, 1331.
https://doi.org/10.3390/rs11111331

**AMA Style**

Li F, Wang L, Liu J, Wang Y, Chang Q.
Evaluation of Leaf N Concentration in Winter Wheat Based on Discrete Wavelet Transform Analysis. *Remote Sensing*. 2019; 11(11):1331.
https://doi.org/10.3390/rs11111331

**Chicago/Turabian Style**

Li, Fenling, Li Wang, Jing Liu, Yuna Wang, and Qingrui Chang.
2019. "Evaluation of Leaf N Concentration in Winter Wheat Based on Discrete Wavelet Transform Analysis" *Remote Sensing* 11, no. 11: 1331.
https://doi.org/10.3390/rs11111331