# Rice Yield Estimation Based on Vegetation Index and Florescence Spectral Information from UAV Hyperspectral Remote Sensing

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

^{2}) increasing from 0.748 to 0.799, and the mean absolute percentage error (MAPE) and the root mean squared error (RMSE) decreasing by 11.8% and 10.7%, respectively. Optimized by flowering information, the two-growth stage VIs-based model gave the best performance (R

^{2}= 0.869, MAPE = 3.98%, RMSE = 396.02 kg/ha). These results showed that introducing florescence spectral information at the flowering stage into conventional VIs-based yield estimation models is helpful in improving rice yield estimation accuracy. The usefulness of florescence spectral information for yield estimation provides a new idea for the further development and improvement of the crop yield estimation method.

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Study Area

#### 2.2. Data Collection and Processing

_{grey}is the radiation of the reference board, Rad

_{img}is the radiation of image, and Ref

_{grey}is the reflectivity of the reference board.

#### 2.3. Calculation of Vegetation Indices

_{i}is the reflectance of band i in the NIR spectral region (760 nm–900 nm), and RED

_{j}is the reflectance of band j in the red spectral region (620 nm–760 nm).

#### 2.4. Description of Florescence Spectral Information

#### 2.4.1. Florescence Ratio Reflectance, Difference Reflectance and Their First Derivative Reflectance

_{r_Fl(i)}) and florescence difference reflectance (R

_{d_Fl(i)}) were calculated as:

_{Fl(i)}is the canopy spectral reflectance at wavelength i during the flowering stage, and R

_{0_Fl(i)}is the canopy spectral reflectance of the exact day before flowering at wavelength i.

_{r_Fl(i)}) and the first derivative florescence difference reflectance (R′

_{d_Fl(i)}) were calculated using florescence ratio reflectance and difference reflectance. They were expressed as:

_{r_Fl(i+1)}and R

_{r_Fl(i−1)}are the florescence ratio reflectance at wavelength i + 1 and i − 1. R

_{d_Fl(i+1)}and R

_{d_Fl(i−1)}are the florescence difference reflectance at wavelength i + 1 and i – 1. Δγ is wavelength difference between wavelength i + 1 and wavelength i − 1.

#### 2.4.2. Formulation of Florescence Indices

#### 2.5. Model Construction and Evaluation

^{2}), average absolute percentage error (MAPE), and root mean square error (RMSE). R

^{2}reflected the fitting degree of estimated and measured yield. The higher R

^{2}was, the higher the reliability of the yield estimation model was. MAPE and RMSE reflected the error between estimated and measured yield, with lower values indicating higher accuracy. They were defined as:

## 3. Results

#### 3.1. Yield Estimation Basing on VIs

#### 3.2. Correlation Analysis between Florescence Ratio Reflectance, Florescence Difference Reflectance and Rice Yield

#### 3.3. Development of Florescence Difference Index (FDI) and Florescence Ratio Index (FRI)

#### 3.4. Yield Estimation Model

_{(740,768)(Booting)}at the booting stage, with R

^{2}of 0.748. The introduction of FDI1(

_{576,664)}, FDI2

_{(596,784)}and FDI4

_{(848,872)}into this model effectively improved the model performance, with R

^{2}increasing from 0.748 to 0.799, increasing by 6.8%, and MAPE and RMSE decreasing by 11.8% and 10.7%, respectively. For the two-growth stage model, the involved vegetation indices were NDVI

_{(740,768) (Booting)}at the booting stage and DVI(

_{752,864)(Filling)}at the filling stage. After introducing florescence spectral indices FRI1

_{(624,716)}, FRI4

_{(692,720)}and FDI5

_{(576, 608)}, the model R

^{2}increased by 4.1%, MAPE and RMSE decreased by 16.0% and 11.3%, respectively. For the three-growth stage model, RVI

_{(748,832)(Heading)}at the heading stage was added on the basis of the two-growth stage model and the introduction of FRI8

_{(692, 720]}and FDI4

_{(848,872)}at the flowering stage increased R

^{2}by 2.7%, and decreased MAPE and RMSE by 7.8% and 4.6%, respectively. It could be seen that the performance of estimation models using vegetation indices alone were improved when two or three florescence spectral indices were included. Among the involved florescence spectral indices, FDI4

_{(848,872)}was used in the single-growth stage model and three-growth stage model, and FRI4

_{(692,720)}was introduced in the two-growth stage model and three-growth stage model.

#### 3.5. Validation of Yield Estimation Models

^{2}, MAPE and RMSE of yield estimation models using vegetation indices alone (Table 7). Moreover, the fitting line of measured and estimated yields of models with flowering information were closer to the 1:1 line (Figure 7). R

^{2}of the single-growth stage model, two-growth stage model and three-growth stage model increased by 0.073, 0.037 and 0.012, respectively, with the largest increase obtained by the single growth stage model, whose MAPE and RMSE decreased by 27.3% and 19.2%, respectively.

## 4. Discussion

#### 4.1. The Mechanism of Spectral Information at Flowering Stage on Improving Yield Estimation Accuracy

#### 4.2. Comparisons between This Study and Previous Studies

#### 4.3. Shortcomings of the Study

## 5. Conclusions

- (1)
- For the first derivative florescence ratio reflectance, the sensitive bands to yield were centered at green bands 560 nm–568 nm, yellow bands 576 nm–588 nm, red-edge bands 680 nm–760 nm and NIR bands around 840 nm; the highly sensitive bands (top 50% of the sensitive bands) were located at 704 nm–760 nm (red-edge). For the first derivative florescence difference reflectance, the sensitive bands were yellow bands 580 nm–596 nm, red bands 664 nm, red-edge bands 688 nm–696 nm, 724 nm–768 nm, the NIR region 840 nm–864 nm, and the highly sensitive bands (top 50% of the sensitive bands) were 590 nm (yellow), 690 nm and 736 nm–748 nm, and 760 nm–768 nm.
- (2)
- The useful florescence spectral indices, FDI and FRI, were mainly constructed with NIR bands, red-edge bands and yellow bands as denominators and bands from those that closely relate to the yield as numerators.
- (3)
- The best date for monitoring the spectral information of rice flowering was at around the seventh day of the flowering stage.
- (4)
- The introduction of florescence information into VIs-based models could not only improve the accuracy of yield estimation, but is also helpful in realizing rice yield estimations at an earlier stage.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 3.**(

**a**) Time series florescence difference reflectance and florescence ratio reflectance (from 1st day to 11th day) (

**b**) florescence difference reflectance and florescence ratio reflectance at the 7th day of the flowering stage.

**Figure 4.**Correlation between rice yield and the difference florescence reflectance (FDR), the rice yield and the ratio florescence reflectance (FDR).

**Figure 5.**Correlation between rice yield and the first derivative florescence difference reflectance (FDFDR), rice yield and the first derivative florescence ratio reflectance (FDFRR) at the 7th day of flowering.

**Figure 6.**Correlation analysis of sensitive bands in the florescence ratio reflectance (FRR), the florescence difference reflectance (FDR), the first derivative florescence ratio reflectance (FDFRR) and the first derivative difference reflectance (FDFDR).

**Figure 7.**The combinations of high correlation florescence indices in the florescence ratio reflectance (FRR), the florescence difference reflectance (FDR), the first derivative florescence ratio reflectance (FDFRR) and the first derivative florescence difference reflectance (FDFDR).

**Figure 8.**Scatter plots of measured yield vs. estimated yield derived from the original vegetation index-based model and the optimization model introducing florescence spectral information for modeling datasets of (

**a**) single growth stage (

**b**) two-growth stage (

**c**) three-growth stage, and validation datasets of (

**d**) single-growth stage (

**e**) two-growth stage and (

**f**) three-growth stage.

WL | FWHM | WL | FWHM | WL | FWHM | WL | FWHM | WL | FWHM |
---|---|---|---|---|---|---|---|---|---|

504 | 8.18 | 592 | 7.24 | 680 | 9.80 | 733 | 6.39 | 816 | 9.10 |

512 | 8.18 | 596 | 7.72 | 685 | 5.82 | 736 | 6.68 | 824 | 7.69 |

520 | 8.51 | 600 | 7.76 | 688 | 6.06 | 740 | 6.14 | 832 | 13.62 |

528 | 7.58 | 604 | 7.26 | 692 | 6.50 | 744 | 6.23 | 840 | 14.49 |

536 | 8.55 | 608 | 9.24 | 696 | 7.45 | 748 | 5.87 | 848 | 13.53 |

544 | 7.63 | 616 | 10.21 | 700 | 6.99 | 752 | 6.59 | 856 | 13.61 |

552 | 7.77 | 624 | 9.20 | 704 | 5.89 | 760 | 5.96 | 864 | 12.42 |

560 | 7.98 | 632 | 8.93 | 709 | 6.00 | 768 | 6.09 | 872 | 12.75 |

568 | 7.27 | 635 | 9.29 | 712 | 6.44 | 776 | 8.71 | 880 | 12.83 |

576 | 8.30 | 650 | 8.36 | 716 | 6.91 | 784 | 7.38 | 888 | 10.51 |

580 | 8.16 | 656 | 9.37 | 720 | 6.86 | 792 | 8.51 | ||

584 | 7.24 | 664 | 8.75 | 724 | 6.22 | 800 | 8.72 | ||

588 | 6.51 | 672 | 9.43 | 728 | 5.81 | 808 | 8.16 |

Index | Equation | Index | Equation |
---|---|---|---|

FRIa | $\frac{{R}_{r\_Fl(i)}-{R}_{r\_Fl(j)}}{{R}_{r\_Fl(i)}+{R}_{r\_Fl(j)}}$ | FDIa | $\frac{{R}_{d\_Fl(i)}-{R}_{d\_Fl(j)}}{{R}_{d\_Fl(i)}+{R}_{d\_Fl(j)}}$ |

FRIb | $\frac{{R}_{r\_Fl(i)}}{{R}_{r\_Fl(j)}}$ | FDIb | $\frac{{R}_{d\_Fl(i)}}{{R}_{d\_Fl(j)}}$ |

FRIc | ${R}_{r\_Fl(i)}-{R}_{r\_Fl(j)}$ | FDIc | ${R}_{d\_Fl(i)}-{R}_{d\_Fl(j)}$ |

FRId | $\frac{{R}_{r\_Fl(i)}^{\prime}-{R}_{r\_Fl(j)}^{\prime}}{{R}_{r\_Fl(i)}^{\prime}+{R}_{r\_Fl(j)}^{\prime}}$ | FDId | $\frac{{R}_{d\_Fl(i)}^{\prime}-{R}_{d\_Fl(j)}^{\prime}}{{R}_{d\_Fl(i)}^{\prime}+{R}_{d\_Fl(j)}^{\prime}}$ |

FRIe | $\frac{{R}_{r\_Fl(i)}^{\prime}}{{R}_{r\_Fl(j)}^{\prime}}$ | FDIe | $\frac{{R}_{d\_Fl(i)}^{\prime}}{{R}_{d\_Fl(j)}^{\prime}}$ |

FRIf | ${R}_{r\_Fl(i)}^{\prime}-{R}_{r\_Fl(j)}^{\prime}$ | FDIf | ${R}_{d\_Fl(i)}^{\prime}-{R}_{d\_Fl(j)}^{\prime}$ |

Sensitive Bands | Booting | Heading | Filling | Ripening | |
---|---|---|---|---|---|

NDVI | band 1 | 740 | 733 | 752 | 748 |

band 2 | 768 | 832 | 880 | 792 | |

Correlation coefficient | 0.872 | 0.873 | 0.826 | 0.663 | |

RVI | band 1 | 740 | 748 | 752 | 748 |

band 2 | 768 | 832 | 880 | 792 | |

Correlation coefficient | 0.871 | 0.872 | 0.824 | 0.662 | |

DVI | band 1 | 748 | 748 | 752 | 748 |

band 2 | 800 | 840 | 864 | 816 | |

Correlation coefficient | 0.817 | 0.867 | 0.804 | 0.681 |

**Table 4.**The expressions of florescence difference index (FDI) and florescence ratio index (FRI) with high correlation with rice yield.

Index | Equation | CC | Index | Equation | CC |
---|---|---|---|---|---|

FRI1 | $\frac{{\rho}_{r\_Fl7th(624)}^{\prime}}{{\rho}_{r\_Fl7th(716)}^{\prime}}$ | −0.4852 | FDI1 | $\frac{{\rho}_{d\_Fl7th(576)}^{\prime}-{\rho}_{d\_Fl7th(664)}^{\prime}}{{\rho}_{d\_Fl7th(576)}^{\prime}+{\rho}_{d\_Fl7th(664)}^{\prime}}$ | −0.4671 |

FRI2 | $\frac{{\rho}_{r\_Fl7th(560)}^{\prime}}{{\rho}_{r\_Fl7th(748)}^{\prime}}$ | −0.4696 | FDI2 | $\frac{{\rho}_{d\_Fl7th(596)}^{\prime}-{\rho}_{d\_Fl7th(784)}^{\prime}}{{\rho}_{d\_Fl7th(596)}^{\prime}+{\rho}_{d\_Fl7th(784)}^{\prime}}$ | –0.4660 |

FRI3 | $\frac{{\rho}_{r\_Fl7th(696)}^{\prime}-{\rho}_{r\_Fl7th(716)}^{\prime}}{{\rho}_{r\_Fl7th(696)}^{\prime}+{\rho}_{r\_Fl7th(716)}^{\prime}}$ | 0.5149 | FDI3 | $\frac{{\rho}_{d\_Fl7th(709)}^{\prime}-{\rho}_{d\_Fl7th(768)}^{\prime}}{{\rho}_{d\_Fl7th(709)}^{\prime}+{\rho}_{d\_Fl7th(768)}^{\prime}}$ | 0.4756 |

FRI4 | ${\rho}_{r\_Fl7th(692)}^{\prime}-{\rho}_{r\_Fl7th(720)}^{\prime}$ | 0.5363 | FDI4 | $\frac{{\rho}_{d\_Fl7th(848)}^{\prime}-{\rho}_{d\_Fl7th(872)}^{\prime}}{{\rho}_{d\_Fl7th(848)}^{\prime}+{\rho}_{d\_Fl7th(872)}^{\prime}}$ | –0.4755 |

FRI5 | $\frac{{\rho}_{r\_Fl7th(716)}^{\prime}-{\rho}_{r\_Fl7th(800)}^{\prime}}{{\rho}_{r\_Fl7th(716)}^{\prime}+{\rho}_{r\_Fl7th(800)}^{\prime}}$ | 0.4589 | FDI5 | $\frac{{\rho}_{d\_Fl7th(576)}^{\prime}-{\rho}_{d\_Fl7th(608)}^{\prime}}{{\rho}_{d\_Fl7th(576)}^{\prime}+{\rho}_{d\_Fl7th(608)}^{\prime}}$ | 0.4746 |

**Table 5.**The expressions for the optimization model with single, two and three growth stages involved.

Growth Stage | Model Expression |
---|---|

Single-growth stage | Y = 29882.803 × NDVI_{(740,768) (Booting)}−3.017 × FDI1−78.851 × FDI2-7.921 × FDI4 + 2331.725 |

Two-growth stage | Y = 24173.141 × NDVI_{(740,768) (Booting)} + 33292.36 × DVI_{(752,864) (Filling)} + 24.836 × FRI1 + 43897.073 × FRI4 + 15.488 × FDI5−32.097 |

Three-growth stage | Y = 30193.832 × NDVI_{(740,768) (Booting)} − 15773.406 × RVI_{(748,832) (Heading)} + 73832.326 × DVI_{(752,864) (Filling)} + 41129.09 × FRI4−5.211 × FDI4 + 16010.301 |

**Table 6.**Comparisons of the yield estimation models with and without considering florescence spectral information for the modeling dataset.

Growth Stage Combination | Florescence Information | Assessment | ||
---|---|---|---|---|

R^{2} | MAPE (%) | RMSE (kg/ha) | ||

Single-growth stage | No | 0.748 | 5.74 | 548.61 |

Yes | 0.799 | 5.06 | 489.91 | |

Two-growth stage | No | 0.833 | 4.74 | 446.45 |

Yes | 0.869 | 3.98 | 396.02 | |

Three-growth stage | No | 0.838 | 4.7 | 439.7 |

Yes | 0.861 | 4.33 | 419.58 |

**Table 7.**Comparisons of the yield estimation models with and without considering florescence spectral information for the validation dataset.

Growth Stage Combination | Florescence Information | Assessment | ||
---|---|---|---|---|

R^{2} | MAPE (%) | RMSE (kg/ha) | ||

Single-growth stage | No | 0.738 | 7.04 | 405.92 |

Yes | 0.811 | 5.12 | 328.10 | |

Two-growth stage | No | 0.791 | 6.83 | 391.68 |

Yes | 0.828 | 6.04 | 376.16 | |

Three-growth stage | No | 0.795 | 6.17 | 360.54 |

Yes | 0.807 | 6.06 | 373.31 |

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**MDPI and ACS Style**

Wang, F.; Yao, X.; Xie, L.; Zheng, J.; Xu, T.
Rice Yield Estimation Based on Vegetation Index and Florescence Spectral Information from UAV Hyperspectral Remote Sensing. *Remote Sens.* **2021**, *13*, 3390.
https://doi.org/10.3390/rs13173390

**AMA Style**

Wang F, Yao X, Xie L, Zheng J, Xu T.
Rice Yield Estimation Based on Vegetation Index and Florescence Spectral Information from UAV Hyperspectral Remote Sensing. *Remote Sensing*. 2021; 13(17):3390.
https://doi.org/10.3390/rs13173390

**Chicago/Turabian Style**

Wang, Fumin, Xiaoping Yao, Lili Xie, Jueyi Zheng, and Tianyue Xu.
2021. "Rice Yield Estimation Based on Vegetation Index and Florescence Spectral Information from UAV Hyperspectral Remote Sensing" *Remote Sensing* 13, no. 17: 3390.
https://doi.org/10.3390/rs13173390