# Hyperspectral Estimation of Winter Wheat Leaf Water Content Based on Fractional Order Differentiation and Continuous Wavelet Transform

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## Abstract

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^{2}were 0.86 and 0.87 in modeling and verification, which indicated that the flowering period could be used as the best estimation period for LWC. Compared with the differential spectrum and wavelet coefficients, LWC estimation based on mixed variables performed best. The average values of R

^{2}in modeling and verification were 0.78 and 0.79. Among them, the ANN model had the highest estimation accuracy, and the R

^{2}in modeling and verification could reach 0.92 and 0.91. This showed that fractional differential and continuous wavelet transform could effectively promote the sensitivity of spectral information to LWC and enhance the prediction ability and stability of wheat LWC. The outcomes of the present study have the potential to provide new ideas for the water monitoring of crops.

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Overview of the Study Area

#### 2.2. Data Collection and Processing

#### 2.2.1. Hyperspectral Data Collection and Processing

_{4}whiteboard calibration was performed every 10–20 min. Each plot randomly selected three sample points that could represent the overall growth of wheat. For each sample point, 10 spectral curves were collected, and the average reflectance of the three sample points was regarded as the spectral reflectance value of the plot. After data acquisition, the spectral data were preprocessed by the Savitzky–Golay filtering method. Moreover, to eliminate the influence of noise in the spectral data, hyperspectral reflectance data in the range of 350–1350 nm were selected for analysis and modeling.

#### 2.2.2. LWC Data Measurement

#### 2.3. Data Processing Methods

#### 2.3.1. Fractional Order Differentiation

#### 2.3.2. Continuous Wavelet Transform

#### 2.4. Modeling Methods

#### 2.4.1. Gaussian Process Regression

#### 2.4.2. Classification and Regression Tree

#### 2.4.3. Artificial Neural Network

#### 2.5. Correlation Analysis

#### 2.6. Model Performance Evaluation

## 3. Results

#### 3.1. Statistical Characteristics of LWC in Wheat

#### 3.2. Estimation of Wheat LWC Based on Fractional Order Differential

#### 3.2.1. Analysis of Correlation between Original Hyperspectral and Fractional Order Differential Spectrum and LWC

- In the jointing period, the correlation between the original hyperspectral data and the LWC was analyzed. It could be seen from Figure 2a that there was a significant negative correlation with the LWC at a level of 0.01 within the wavelength from 350 to 721 nm. When the negative correlation was the strongest, the wavelength was 708 nm, and the correlation coefficient ρ was −0.54. The correlation between the differential spectrum and the LWC was analyzed. It could be seen from Figure 3a that the absolute value of the |ρ| of each order of the differential spectrum and LWC was greater than 0.54. When the order was 1.0, the |ρ| reached a maximum of 0.69 at a wavelength of 926 nm. Except for orders 1.0 and 2.0, more than 347 differential spectral bands reached a significant level of 0.01. At the jointing period, 10 differential spectra were selected as follows: J1.0R926, J2.0R735, J1.0R1022, J2.0R736, J1.1R733, J1.0R785, J1.1R732, J1.2R720, J1.3R720, and J1.9R713, respectively. The correlation results were shown in Figure 4a.
- In the booting period, the correlation between the original hyperspectral data and the LWC was analyzed. It could be seen from Figure 2b that there was a significant negative correlation with the LWC at a level of 0.01 within the wavelength from 353 to 735 nm and 1149 to 1350 nm. The negative correlation was the strongest at 355 nm, and the ρ value was −0.75. Then, the correlation between the differential spectrum and the LWC was analyzed. It could be seen from Figure 3b that the |ρ| value of each order of the differential spectrum and LWC were greater than 0.73. When the order was 1.1, the wavelength was at 433 nm, and the |ρ| value was up to a maximum of 0.80. Except for order 1.0 and order 2.0, more than 558 differential spectral bands reached a significance level of 0.01. At the booting period, 10 differential spectra were selected as follows: J1.1R433, J1.4R357, J1.8R432, J1.2R433, J1.5R357, J1.9R432, J1.7R432, J1.3R357, J1.6R432, and J0.9R418, respectively. The correlation results are shown in Figure 4b.
- In the flowering period, the correlation between the primitive hyperspectral data and the LWC was analyzed. According to Figure 2c, there was a significant negative correlation with the LWC at a level of 0.01 at wavelengths from 350 to 725 nm and 1316 to 1350 nm, and a significant positive correlation with the LWC at a level of 0.01 from 760 to 828 nm. When the correlation was strongest, the wavelength was 356 nm, and the ρ value was −0.74. Then, the correlation between the differential spectrum and the LWC was analyzed. According to Figure 3c, the |ρ| value of each order of the differential spectrum and LWC was greater than 0.72. When the order was 1.1, the |ρ| value was up to a maximum of 0.79 at a wavelength of 434 nm. Except for orders 1.0 and 2.0, more than 518 differential spectral bands reached a significance level of 0.01. At the jointing period, 10 differential spectra were selected as follows: J1.1R434, J0.9R374, J1.9R433, J1.2R409, J1.3R409, J1.6R351, J1.7R351, J0.8R374, J1.5R351, and J1.8R351, respectively. The correlation results are shown in Figure 4c.
- In the filling period, the correlation between the primitive hyperspectral data and the LWC was analyzed. It could be seen from Figure 2d that there was a significant negative correlation with the LWC at a level of 0.01 at wavelengths from 350 to 725 nm and 1316 to 1350 nm, and a significant positive correlation with the LWC at a level of 0.01 from 736 to 1137 nm; the strongest correlation was obtained at 680 nm, with the ρ value of −0.76. Then, the correlation between the differential spectrum and the LWC was analyzed. As shown in Figure 3d, the maximum value of |ρ| was greater than 0.72. When the order was 1, the |ρ| value reached a maximum of 0.78 at a wavelength of 675 nm. Except for orders 1.0 and 2.0, more than 792 differential spectral bands achieved a significant level of 0.01. At the jointing period, 10 differential spectra were selected as follows: J1.0R675, J1.0R1299, J1.0R720, J1.1R693, J1.1R689, J1.0R561, J1.9R688, J1.2R693, J1.0R564, and J1.3R693, respectively. The correlation results are shown in Figure 4d.

#### 3.2.2. Construction and Analysis of LWC Estimation Model

- In the jointing period, the modeling accuracy of the GPR model was R
^{2}= 0.72, RMSE = 1.05%, and nRMSE = 1.38%, and the validation accuracy was R^{2}= 0.75, RMSE = 0.97%, and nRMSE = 1.26%. Compared with the CART model and the ANN model, the modeling and validation R^{2}of the GPR increased by 0.11 and 0.13, and 0.11 and 0.06, the RMSE decreased by 0.02% and 0.30%, and 0.01% and 0.01%, and the nRMSE decreased by 0.02% and 0.42%, and 0.01% and 0.02%, respectively. The GPR model achieved higher modeling and verification accuracy than the other two models. A comprehensive analysis indicated that the GPR model had a better estimation effect in the jointing period. - In the booting period, the modeling accuracy of the GPR model was R
^{2}= 0.79, RMSE = 0.91%, and nRMSE = 1.19%, and the validation accuracy was R^{2}= 0.84, RMSE = 0.83%, and nRMSE = 1.08%. Compared with the CART model and the ANN model, the modeling and validation R^{2}of the GPR increased by 0.05 and 0.08, and 0.08 and 0.15, the RMSE decreased by 0.03% and 0.30%, and 0.09 and 0.19%, and the nRMSE decreased by 0.03% and 0.42%, and 0.12% and 0.27%, respectively. The GPR model achieved higher modeling and verification accuracy than the other two models. Through a comprehensive analysis, it was shown that the GPR model had a better estimation effect in the booting period. - In the flowering period, the modeling accuracy of the ANN model was R
^{2}= 0.89, RMSE = 0.80%, and nRMSE = 1.09%, and the validation accuracy was R^{2}= 0.88, RMSE = 1.14%, and nRMSE = 1.56%. Compared with the GPR model and the CART model, the modeling and validation R^{2}of the ANN increased by 0.02 and 0.03, and 0.11 and 0.02, and the RMSE decreased by 0.23% and 0.10%, and 0.28% and 0.37%, and the nRMSE decreased by 0.31% and 0.12%, and 0.38% and 0.47%, respectively. The ANN model achieved higher modeling and verification accuracy than the other two models. Through a comprehensive analysis, it was found that the ANN model had the highest estimation accuracy in the flowering period. - In the filling period, the modeling accuracy of the ANN model was R
^{2}= 0.85, RMSE = 3.82%, and nRMSE = 6.25%, and the validation accuracy was R^{2}= 0.83, RMSE = 2.89%, and nRMSE = 4.61%. Compared with the GPR model and the CART model, the modeling and validation R^{2}of the ANN increased by 0.00 and 0.05, and 0.13 and 0.02, and the RMSE decreased by 0.54% and 2.45%, and 1.32% and 1.49%, and the nRMSE decreased by 0.77% and 4.02%, and 2.13% and 2.21%, respectively. The ANN model achieved higher modeling and verification accuracy than the other two models. A comprehensive analysis indicated that the ANN model had a better estimation effect in the filling period.

#### 3.3. Estimation of Wheat LWC Based on Continuous Wavelet Transform

#### 3.3.1. Correlation Analysis between Wavelet Coefficients and LWC

- In the jointing period, the correlation between the wavelet coefficient and the LWC was analyzed. It could be seen from Figure 5a that the correlation between the wavelet coefficient and the LWC was stronger at first and then weakened as the decomposition scale increased from 1 to 10. Within the decomposition scale of 1 to 8, the maximum sizes of the wavelet coefficients and the LWC at each scale |ρ| were greater than 0.60. When the scale was 3, the |ρ| value reached the maximum of 0.70 at a wavelength of 1142 nm. Then, the 10 wavelet coefficients with a strong correlation with LWC were chosen as the independent variables, and their decomposition scales and bands were C3R1142, C2R972, C1R734, C2R733, C3R733, C4R732, C6R732, C5R731, C3R731, and C2R918, respectively. The correlation results are shown in Figure 6a.
- In the booting period, the correlation between the wavelet coefficient and the LWC was analyzed. According to Figure 5b, the correlation between the wavelet coefficient and the LWC first became stronger and then weakened as the decomposition scale increased from 1 to 10. The maximum values of |ρ| between the wavelet coefficient and the LWC within the decomposition scale of 1 to 8 were greater than 0.71. When the scale was 4, the |ρ| was up to 0.78 at 403 nm. The 10 wavelet coefficients with a strong correlation with LWC were chosen as the independent variables of the model, and their decomposition scales and bands were C4R403, C2R352, C4R396, C3R443, C2R353, C4R445, C6R1226, C4R464, C3R445, and C4R463, respectively. The correlation results are shown in Figure 6b.
- In the flowering period, the correlation between the wavelet coefficient and the LWC was analyzed. It could be observed from Figure 5c that the correlation between the wavelet coefficient and the LWC was first stronger and then weakened as the decomposition scale increased from 1 to 10. Within the decomposition scale of 1 to 8, the maximum sizes of the wavelet coefficients and LWC at each scale |ρ| were greater than 0.70. When the scale was 8, the |ρ| reached the maximum of 0.80 at the wavelength of 1321 nm. Then, the 10 wavelet coefficients with a strong correlation with LWC were selected as the independent variables of the model, and their decomposition scales and bands were C8R1321, C3R1326, C8R1328, C8R1309, C7R1288, C7R1282, C8R1307, C6R1223, C4R840, and C6R1216, respectively. The correlation results are shown in Figure 6c.
- In the filling period, the correlation between the wavelet coefficient and the LWC was analyzed. According to Figure 5d, the correlation between the wavelet coefficient and the LWC was stronger at first and then weakened as the decomposition scale increased from 1 to 10. The maximum values of |ρ| between the wavelet coefficient and LWC at the decomposition scale within 1 to 8 were greater than 0.77. When the scale was 3, the |ρ| was up to 0.80 at a wavelength of 450 nm. Then, the 10 wavelet coefficients with a strong correlation with LWC were selected as the independent variables of the model, and their decomposition scales and bands were C3R450, C1R743, C6R764, C2R742, C3R742, C6R768, C4R746, C8R1347, C6R775, and C5R755, respectively. The correlation results are shown in Figure 6d.

#### 3.3.2. Construction and Analysis of LWC Estimation Model

- In the jointing period, the modeling accuracy of the ANN model was R
^{2}= 0.72, RMSE = 0.86%, and nRMSE = 1.13%, and the validation accuracy was R^{2}= 0.76, RMSE = 0.98%, and nRMSE = 1.28%. Compared with the GPR model and the CART model, the modeling and validation R^{2}of the ANN increased by 0.10 and 0.13, and 0.11 and 0.15, and the RMSE decreased by 0.27% and 0.04%, 0.26% and 0.10%, and the nRMSE decreased by 0.36% and 0.07%, and 0.34% and 0.16%, respectively. The ANN model achieved higher modeling and verification accuracy than the other two models. Through a comprehensive analysis, it was found that the ANN model achieved a better estimation effect in the jointing period. - In the booting period, the modeling accuracy of the GPR model was R
^{2}= 0.78, RMSE = 1.00%, and nRMSE = 1.32%, and the validation accuracy was R^{2}= 0.83, RMSE = 0.93%, and nRMSE = 1.23%. Compared with the CART model and the ANN model, the modeling and validation R^{2}of the GPR increased by 0.08 and 0.08, and 0.09 and 0.10, and the RMSE decreased by 0.02% and 0.47%, and 0.00% and 0.03%, and the nRMSE decreased by 0.02% and 0.63%, and 0.00% and 0.03%, respectively. The modeling and validation accuracy of the GPR model was higher than that of the other two models. A comprehensive analysis indicated that the GPR model achieved a better estimation effect in the booting period. - In the flowering period, the modeling accuracy of the ANN model was R
^{2}= 0.91, RMSE = 0.71%, nRMSE = 0.97%, and the validation accuracy was R^{2}= 0.89, RMSE = 0.85%, and nRMSE = 1.16%. Compared with the GPR model and the CART model, the modeling and validation R^{2}of the ANN increased by 0.03 and 0.01, and 0.16 and 0.12, and the RMSE decreased by 0.40% and 0.81%, and 0.38% and 1.02%, and the nRMSE decreased by 0.54% and 1.10%, and 0.51% and 1.36%, respectively. The modeling and validation accuracy of the ANN model was higher than that of the other two models. Through a comprehensive analysis, it was found that the ANN model had the highest estimation accuracy in the flowering period. - In the filling period, the modeling accuracy of the ANN model was R
^{2}= 0.85, RMSE = 3.57%, and nRMSE = 5.84%, and the validation accuracy was R^{2}= 0.86, RMSE = 3.27%, and nRMSE = 5.27%. Compared with the GPR model and the CART model, the modeling and validation R^{2}of the ANN increased by 0.01 and 0.01, and 0.11 and 0.09, and the RMSE decreased by 1.10% and 0.98%, and 1.36% and 4.34%, and the nRMSE decreased by 1.71% and 1.59%, and 2.27% and 7.65%, respectively. The modeling and validation accuracy of the ANN model was higher than that of the other two models. A comprehensive analysis indicated that the ANN model achieved a better estimation effect in the filling period.

#### 3.4. Estimation of Wheat LWC Based on Mixed Variables

- In the jointing period, the modeling accuracy of the GPR model was R
^{2}= 0.77, RMSE = 1.04%, and nRMSE = 1.37%, and the validation accuracy was R^{2}= 0.77, RMSE = 0.93%, and nRMSE = 1.22%. Compared with the CART model and the ANN model, the modeling and validation R^{2}of the GPR increased by 0.15 and 0.11, and 0.17 and 0.10, and the RMSE decreased by 0.06% and 0.29%, and 0.03% and 0.37%, and the nRMSE decreased by 0.08% and 0.40%, and 0.04% and 0.49%, respectively. The GPR model achieved higher modeling and verification accuracy than the other two models. Through a comprehensive analysis, it was found that the GPR model achieved a better estimation effect in the jointing period. - In the booting period, the modeling accuracy of the GPR model was R
^{2}= 0.83, RMSE = 0.86%, and nRMSE = 1.12%, and the validation accuracy was R^{2}= 0.81, RMSE = 0.72%, and nRMSE = 0.94%. Compared with the CART model and the ANN model, the modeling and validation R^{2}of the GPR increased by 0.08 and 0.06, and 0.10 and 0.07, and the RMSE decreased by 0.06% and 0.46%, and 0.07% and 0.19%, and the nRMSE decreased by 0.09% and 0.61%, and 0.09% and 0.25%, respectively. The modeling and validation accuracy of the GPR model was higher than that of the other two models. A comprehensive analysis indicated that the GPR model achieved a better estimation effect in the booting period. - In the flowering period, the modeling accuracy of the ANN model was R
^{2}= 0.92, RMSE = 0.64%, nRMSE = 0.87%, and the validation accuracy was R^{2}= 0.91, RMSE = 0.82%, and nRMSE = 1.12%. Compared with the GPR model and the CART model, the modeling and validation R^{2}of the ANN increased by 0.02 and 0.02, and 0.09 and 0.05, and the RMSE decreased by 0.31% and 0.18%, and 0.30% and 0.68%, and the nRMSE decreased by 0.43% and 0.25%, and 0.41% and 0.90%, respectively. The modeling and validation accuracy of the ANN model was higher than that of the other two models. Through a comprehensive analysis, it was found that the ANN model had the highest estimation accuracy in the flowering period. - In the filling period, the modeling accuracy of the ANN model was R
^{2}= 0.86, RMSE = 3.14%, and nRMSE = 5.09%, and the validation accuracy was R^{2}= 0.83, RMSE = 6.01%, and nRMSE = 9.57%. Compared with the GPR model and the CART model, the modeling and validation R^{2}of the ANN increased by 0.01 and 0.04, and 0.10 and 0.08, and the RMSE decreased by 0.94% and 0.43%, and 1.68% and 1.84%, and the nRMSE decreased by 1.46% and 0.68%, and 2.81% and 4.14%, respectively. The modeling and validation accuracy of the ANN model was higher than that of the other two models. A comprehensive analysis indicated that the ANN model achieved a better estimation effect in the filling period.

## 4. Discussion

^{2}of modeling and verification reached 0.92 and 0.91, and the mean value reached 0.77 and 0.78, respectively. This is because the hyperspectral data have a high resolution and strong band continuity, which can correctly mirror the spectral characteristics and differences of crops and correctly obtain some agricultural information. Thus, the method is suitable for monitoring the physiological and biochemical parameters of crops. The difficulty of estimating crop LWC by adopting hyperspectral data lies in the influence of external interference factors when collecting data, which leads to noise in spectral data and affects the extraction of susceptible information [35]. After processing with fractional differential and continuous wavelet transform, the influence of noise can be eliminated, and the sensitive messages in spectral data can be deeply mined, further improving the estimation accuracy of crop LWC. This is consistent with the research results in the literature [14,36,37].

^{2}in modeling and verification was only 0.66 and 0.70, respectively. In the booting period, the mean values of R

^{2}were 0.75 and 0.77, respectively, which was slightly better than that in the jointing period. In the flowering period, the average values of R

^{2}for modeling and verification were 0.86 and 0.87, and those in the filling period were 0.81 and 0.81, respectively. It showed that the LWC estimation accuracy in the flowering period was higher than that in the filling period. This may be because the LWC of wheat in the flowering period gradually decreases and changes greatly, and the sensitivity of LWC to hyperspectral data is relatively strong. This is consistent with the research results in the literature [20,40].

^{2}of modeling and testing could reach 0.92 and 0.91, and the average value could reach 0.78 and 0.79. This is because fractional differential and wavelet transform can eliminate the influence of noise in spectral information, improve the sensitivity of LWC to spectral data, and further enhance the stability and robustness of the model. This is compatible with the study results in the literature [13,16,41].

^{2}of modeling and testing was 0.77 and 0.77, respectively. In the booting period, the mixed variables combined with the GPR model performed better in estimating LWC, and the R

^{2}of modeling and testing was 0.83 and 0.81, respectively. In the flowering period, using the mixed variables combined with the ANN model to estimate LWC obtained the highest accuracy, the R

^{2}of modeling and testing was 0.92 and 0.91, respectively. In the filling period, using the wavelet coefficient combined with the ANN model to estimate LWC contributed to high accuracy, and the R

^{2}of modeling and testing was 0.85 and 0.86, respectively.

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 2.**Correlation analysis of the raw hyperspectral with LWC in four growth periods. (

**a**) Jointing period; (

**b**) booting period; (

**c**) flowering period; (

**d**) filling period.

**Figure 3.**The relevance between the spectra of different growth periods and LWC. (

**a**) Jointing period; (

**b**) booting period; (

**c**) flowering period; (

**d**) filling period.

**Figure 4.**The relevance matrix of the selected fractional order differential spectra with LWC in four growth periods. (

**a**) Jointing period; (

**b**) booting period; (

**c**) flowering period; (

**d**) filling period.

**Figure 5.**The relevance between the wavelet coefficient of different growth periods and LWC. (

**a**) Jointing period; (

**b**) booting period; (

**c**) flowering period; (

**d**) filling period.

**Figure 6.**The relevance matrix of the selected wavelet coefficient with LWC in four growth periods. (

**a**) Jointing period; (

**b**) booting period; (

**c**) flowering period; (

**d**) filling period.

Growth Periods | LWC (%) | |||||||
---|---|---|---|---|---|---|---|---|

2020 | 2021 | |||||||

MAX | MIN | MEAN | SD | MAX | MIN | MEAN | SD | |

Jointing period | 79.89 | 71.04 | 76.19 | 1.70 | 81.87 | 72.97 | 77.11 | 2.05 |

Booting period | 79.48 | 71.85 | 76.42 | 1.80 | 82.20 | 73.86 | 78.71 | 2.06 |

Flowering period | 78.44 | 68.94 | 73.40 | 2.35 | 75.27 | 60.53 | 67.43 | 3.94 |

Filling period | 71.80 | 29.85 | 61.38 | 9.26 | 67.97 | 46.09 | 60.39 | 5.21 |

**Table 2.**The LWC estimation results obtained by adopting differential spectra combined with GPR, CART, and ANN for different growth periods.

Growth Periods | Method | Modeling Accuracy | Verification Accuracy | ||||
---|---|---|---|---|---|---|---|

R^{2} | RMSE (%) | nRMSE (%) | R^{2} | RMSE (%) | nRMSE (%) | ||

Jointing period | GPR | 0.72 ** | 1.05 | 1.38 | 0.75 ** | 0.97 | 1.26 |

CART | 0.61 ** | 1.07 | 1.40 | 0.62 ** | 1.27 | 1.68 | |

ANN | 0.61 ** | 1.06 | 1.39 | 0.69 ** | 0.98 | 1.28 | |

Booting period | GPR | 0.79 ** | 0.91 | 1.19 | 0.84 ** | 0.83 | 1.08 |

CART | 0.74 ** | 0.94 | 1.22 | 0.76 ** | 1.13 | 1.50 | |

ANN | 0.71 ** | 1.00 | 1.31 | 0.69 ** | 1.02 | 1.35 | |

Flowering period | GPR | 0.87 ** | 1.03 | 1.40 | 0.85 ** | 1.24 | 1.68 |

CART | 0.78 ** | 1.08 | 1.47 | 0.86 ** | 1.51 | 2.03 | |

ANN | 0.89 ** | 0.80 | 1.09 | 0.88 ** | 1.14 | 1.56 | |

Filling period | GPR | 0.85 ** | 4.36 | 7.02 | 0.78 ** | 5.34 | 8.63 |

CART | 0.72 ** | 5.14 | 8.38 | 0.81 ** | 4.38 | 6.82 | |

ANN | 0.85 ** | 3.82 | 6.25 | 0.83 ** | 2.89 | 4.61 |

**Table 3.**The LWC estimation results obtained by adopting wavelet coefficients combined with GPR, CART, and ANN for different growth periods.

Growth Periods | Method | Modeling Accuracy | Verification Accuracy | ||||
---|---|---|---|---|---|---|---|

R^{2} | RMSE (%) | nRMSE (%) | R^{2} | RMSE (%) | nRMSE (%) | ||

Jointing period | GPR | 0.71 ** | 1.13 | 1.49 | 0.74 ** | 1.02 | 1.35 |

CART | 0.61 ** | 1.12 | 1.47 | 0.61 ** | 1.08 | 1.44 | |

ANN | 0.72 ** | 0.86 | 1.13 | 0.76 ** | 0.98 | 1.28 | |

Booting period | GPR | 0.78 ** | 1.00 | 1.32 | 0.83 ** | 0.93 | 1.23 |

CART | 0.70 ** | 1.02 | 1.34 | 0.74 ** | 1.40 | 1.86 | |

ANN | 0.70 ** | 1.00 | 1.32 | 0.73 ** | 0.96 | 1.26 | |

Flowering period | GPR | 0.88 ** | 1.11 | 1.51 | 0.88 ** | 1.66 | 2.26 |

CART | 0.75 ** | 1.09 | 1.48 | 0.77 ** | 1.87 | 2.52 | |

ANN | 0.91 ** | 0.71 | 0.97 | 0.89 ** | 0.85 | 1.16 | |

Filling period | GPR | 0.84 ** | 4.67 | 7.55 | 0.85 ** | 4.25 | 6.86 |

CART | 0.74 ** | 4.93 | 8.11 | 0.77 ** | 7.61 | 12.92 | |

ANN | 0.85 ** | 3.57 | 5.84 | 0.86 ** | 3.27 | 5.27 |

**Table 4.**The LWC estimation results obtained by using differential spectrum and wavelet coefficients combined with GPR, CART, and ANN for different growth periods.

Growth Periods | Method | Modeling Accuracy | Verification Accuracy | ||||
---|---|---|---|---|---|---|---|

R^{2} | RMSE (%) | nRMSE (%) | R^{2} | RMSE (%) | nRMSE (%) | ||

Jointing period | GPR | 0.77 ** | 1.04 | 1.37 | 0.77 ** | 0.93 | 1.22 |

CART | 0.62 ** | 1.10 | 1.45 | 0.66 ** | 1.22 | 1.62 | |

ANN | 0.60 ** | 1.07 | 1.41 | 0.67 ** | 1.30 | 1.71 | |

Booting period | GPR | 0.75 ** | 0.92 | 1.21 | 0.75 ** | 1.18 | 1.55 |

CART | 0.83 ** | 0.86 | 1.12 | 0.81 ** | 0.72 | 0.94 | |

ANN | 0.73 ** | 0.93 | 1.21 | 0.74 ** | 0.91 | 1.19 | |

Flowering period | GPR | 0.90 ** | 0.95 | 1.30 | 0.89 ** | 1.00 | 1.37 |

CART | 0.81 ** | 0.94 | 1.28 | 0.86 ** | 1.50 | 2.02 | |

ANN | 0.92 ** | 0.64 | 0.87 | 0.91 ** | 0.82 | 1.12 | |

Filling period | GPR | 0.85 ** | 4.08 | 6.55 | 0.79 ** | 6.44 | 10.25 |

CART | 0.76 ** | 4.82 | 7.90 | 0.75 ** | 7.85 | 13.71 | |

ANN | 0.86 ** | 3.14 | 5.09 | 0.83 ** | 6.01 | 9.57 |

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## Share and Cite

**MDPI and ACS Style**

Li, C.; Xiao, Z.; Liu, Y.; Meng, X.; Li, X.; Wang, X.; Li, Y.; Zhao, C.; Ren, L.; Yang, C.;
et al. Hyperspectral Estimation of Winter Wheat Leaf Water Content Based on Fractional Order Differentiation and Continuous Wavelet Transform. *Agronomy* **2023**, *13*, 56.
https://doi.org/10.3390/agronomy13010056

**AMA Style**

Li C, Xiao Z, Liu Y, Meng X, Li X, Wang X, Li Y, Zhao C, Ren L, Yang C,
et al. Hyperspectral Estimation of Winter Wheat Leaf Water Content Based on Fractional Order Differentiation and Continuous Wavelet Transform. *Agronomy*. 2023; 13(1):56.
https://doi.org/10.3390/agronomy13010056

**Chicago/Turabian Style**

Li, Changchun, Zhen Xiao, Yanghua Liu, Xiaopeng Meng, Xinyan Li, Xin Wang, Yafeng Li, Chenyi Zhao, Lipeng Ren, Chen Yang,
and et al. 2023. "Hyperspectral Estimation of Winter Wheat Leaf Water Content Based on Fractional Order Differentiation and Continuous Wavelet Transform" *Agronomy* 13, no. 1: 56.
https://doi.org/10.3390/agronomy13010056