# Comparison of Citrus Leaf Water Content Estimations Based on the Continuous Wavelet Transform and Fractional Derivative Methods

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## Abstract

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## 1. Introduction

- (1)
- Use the CWT and FOD methods to process the raw spectral data of citrus leaves to explore and compare the roles of the CWT and FOD in the inversion accuracy of citrus leaf water content.
- (2)
- Use the SPA to explore sensitive band regions for inverting citrus leaf water content and then combine spectral vegetation indices to explore whether the ability to predict citrus leaf water content information can be enhanced.
- (3)
- Based on the SPA combined with the spectral vegetation index, compare the CWT and FOD inversion models to determine the best model for inverting the water content of citrus leaves.

## 2. Data and Methods

#### 2.1. Overview of the Study Area

#### 2.2. Data and Spectral Collection

#### 2.2.1. Sample Collection

#### 2.2.2. Spectral Acquisition

#### 2.2.3. Water Content Measurement

#### 2.3. Research Methods

#### 2.3.1. CWT

#### 2.3.2. FOD

#### 2.3.3. SPA

#### 2.4. Spectral Vegetation Indices

#### 2.5. Regression Model and Accuracy Evaluation

## 3. Results and Analyses

#### 3.1. Comparison of Inversion Accuracy between CWT and FOD Spectral Preprocessing of Citrus Leaves

#### 3.2. SPA-Based Analysis of Water Content-Sensitive Bands in Citrus Leaves

#### 3.3. Inversion Results of Citrus Leaf Water Content Using the Joint Spectral Vegetation Index

## 4. Discussion

## 5. Conclusions

- (1)
- Compared with the original spectral inversion of the citrus leaf water content, the inversion accuracy of the CWT improved at most scales, while that of the fractional-order derivatives of the FOD method decreased, and the inversion accuracy of the CWT was approximately 5% greater than that of the FOD method, which indicates that the CWT was able to improve the inversion accuracy of the water content of the citrus leaves and outperformed the FOD method.
- (2)
- The feature bands selected by the SPA were mostly located in the infrared region, indicating that the feature bands in the infrared region were more sensitive to inverting the water content of the citrus leaves. After the application of the joint spectral vegetation index, compared to those of the original spectra, the inversion accuracies of the CWT and FOD methods for citrus leaf water content increased by 9.61% and 9.29%, respectively. This indicates that the SPA joint spectral vegetation index can improve the ability to predict citrus leaf water information.
- (3)
- By comparing the best models for the FOD and CWT, it was ultimately found that the CWT method is superior to the FOD method, with the Gaus1 wavelet function having the best inversion effect. The use of the spectral vegetation index can provide a new prediction method for citrus leaf water content prediction.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**Overview of the study area: (

**a**) the specific location of Guilin; (

**b**) growth of fruit trees; (

**c**) collection location of leaf blades; (

**d**) specification of the device; (

**e**) placement of leaf blades; (

**f**) in situ hyperspectral curves of leaf blades; (

**g**) spectral reflectance of leaf blades at 401~2400 nm.

**Figure 2.**PLSR inversion model results: (

**a**) ${\mathrm{R}}^{2}$ at different wavelet scales; (

**b**) ${\mathrm{R}}^{2}$ for different fractional derivatives; (

**c**) RMSE values of different wavelet scales; (

**d**) RMSE values of different fractional derivatives.

**Figure 3.**The proportions of bands in different spectral ranges: (

**a**) the proportions of different wavelet scale bands; (

**b**) the proportions of different fractional derivative bands.

**Figure 4.**The screening results of the SPA and the results of the PLSR inversion model: (

**a**) the number of bands selected at different wavelet scales; (

**b**) the number of bands screened for different fractional derivatives; (

**c**) ${\mathrm{R}}^{2}$ values at different wavelet scales; (

**d**) ${\mathrm{R}}^{2}$ values for different fractional derivatives.

**Figure 5.**Test set determination coefficients ${\mathrm{R}}^{2}$ of the LWC and vegetation indexes at different wavelet scales using the PLSR model.

**Figure 6.**Regression curves of the inversion model: (

**a**) PLSR plot of CWT-SPA combined with the NDVI; (

**b**) PLSR plot of FOD-SPA combined with the SRWI.

Spectral Vegetation Index | Computational Formula | Pearson Correlation |
---|---|---|

NDVI | $({\mathrm{R}}_{800}-{\mathrm{R}}_{680})/({\mathrm{R}}_{800}+{\mathrm{R}}_{680})$ | 0.4739 |

MSI | ${\mathrm{R}}_{1600}/{\mathrm{R}}_{820}$ | −0.4787 |

NMDI | $({\mathrm{R}}_{860}-({\mathrm{R}}_{1640}-{\mathrm{R}}_{2130})$$)/({\mathrm{R}}_{860}+({\mathrm{R}}_{1640}-{\mathrm{R}}_{2130})$) | 0.4125 |

PWI | $({\mathrm{R}}_{900}/{\mathrm{R}}_{970})/\left[\right({\mathrm{R}}_{800}-{\mathrm{R}}_{680})/({\mathrm{R}}_{800}+{\mathrm{R}}_{680}\left)\right]$ | −0.3547 |

${\mathrm{N}\mathrm{D}\mathrm{W}\mathrm{I}}_{1200}$ | $({\mathrm{R}}_{860}-{\mathrm{R}}_{1200})/({\mathrm{R}}_{860}+{\mathrm{R}}_{1200})$ | 0.6063 |

${\mathrm{N}\mathrm{D}\mathrm{W}\mathrm{I}}_{1240}$ | $({\mathrm{R}}_{860}-{\mathrm{R}}_{1240})/({\mathrm{R}}_{860}+{\mathrm{R}}_{1240})$ | 0.6305 |

${\mathrm{N}\mathrm{D}\mathrm{W}\mathrm{I}}_{1640}$ | $({\mathrm{R}}_{860}-{\mathrm{R}}_{1640})/({\mathrm{R}}_{860}+{\mathrm{R}}_{1640})$ | 0.4923 |

WI | ${\mathrm{R}}_{900}/{\mathrm{R}}_{970}$ | 0.6716 |

VARI | $({\mathrm{R}}_{555}-{\mathrm{R}}_{645})/({\mathrm{R}}_{555}+{\mathrm{R}}_{645}-{\mathrm{R}}_{450})$ | 0.5641 |

SRWI | ${\mathrm{R}}_{860}/{\mathrm{R}}_{1240}$ | 0.6367 |

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## Share and Cite

**MDPI and ACS Style**

Dou, S.; Zhang, W.; Deng, Y.; Zhang, C.; Mei, Z.; Yan, J.; Li, M.
Comparison of Citrus Leaf Water Content Estimations Based on the Continuous Wavelet Transform and Fractional Derivative Methods. *Horticulturae* **2024**, *10*, 177.
https://doi.org/10.3390/horticulturae10020177

**AMA Style**

Dou S, Zhang W, Deng Y, Zhang C, Mei Z, Yan J, Li M.
Comparison of Citrus Leaf Water Content Estimations Based on the Continuous Wavelet Transform and Fractional Derivative Methods. *Horticulturae*. 2024; 10(2):177.
https://doi.org/10.3390/horticulturae10020177

**Chicago/Turabian Style**

Dou, Shiqing, Wenjie Zhang, Yuanxiang Deng, Chenhong Zhang, Zhengmin Mei, Jichi Yan, and Minglan Li.
2024. "Comparison of Citrus Leaf Water Content Estimations Based on the Continuous Wavelet Transform and Fractional Derivative Methods" *Horticulturae* 10, no. 2: 177.
https://doi.org/10.3390/horticulturae10020177