# Synchronous Retrieval of LAI and Cab from UAV Remote Sensing: Development of Optimal Estimation Inversion Framework

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Modeling of UAV Observations

#### 2.1. Atmospheric Radiative Transfer

#### 2.2. Crop Canopy Reflectance

#### 2.3. The Coupling Model for Crop Parameter Inversion

#### 2.3.1. Coupling of Models

#### 2.3.2. Calculation of Jacobians

## 3. Method for the Synchronous Retrieval of LAI and Cab

**H**is the inverse matrix of the Hessian matrix constructed with successive gradient vectors in the quasi-Newton method, and ${\alpha}_{\mathrm{p}}$ is the step factor of the iteration.

## 4. Model Analysis for UAV Multispectral Measurements

#### 4.1. The Sensitivity of the Model to Crop Parameters

#### 4.2. Parameters Information Content Analysis

#### 4.3. Setting of State Vectors and Boundary Conditions

## 5. Results

#### 5.1. Validation of the Forward Model

^{2}in Qixian County, Henan Province (114.17° E, 35.6° N), where winter wheat was cultivated annually from October to June, approximately. The region has a warm temperate humid monsoon climate with warm and rainy summer and cold and dry winter. The measured data were derived from the FieldSpec Handheld (a handheld geophysical spectrometer, Analytica Spectra Devices, Inc., Boulder, CO, USA). The spectral range of the measuring instrument is 325~1075 nm, and the spectral resolution was 3 nm at wavelengths 325~700 nm. We collected the test data on 4 March 2021 at about 12:00 when the solar light intensity was stable and the weather was clear and cloudless. The measurement results can represent the true reflectance of the vegetation canopy because the instrument is closer to the target and less influenced by aerosols and water vapor. Figure 7 compares the results between the simulated data at a solar zenith angle of 5° and the measured data at a sampling test point.

#### 5.2. Retrieval Demonstration and Self-Consistency Tests

^{2}) and root-mean-square error (RMSE) are used to verify the consistency of the optimized algorithm. A larger R

^{2}and a smaller RMSE indicate the higher accuracy of the forward model and the better consistency of the inversion framework. The retrieved Cab and LAI synchronously under different observation geometries were compared to the true value as shown in Figure 9a,b.

^{2}value for Cab was 0.9999, while the RMSE was 0.1007, which indicated that the Cab had good retrieval results. Similarly, the verification results of LAI were consistent with Cab. Meanwhile, it is worth noting that the slopes of the fit lines were all close to 1. With the variation of solar zenith angle, the error lines of Cab and LAI were within E = x ± 0.02x ± 0.08 and E = x ± 0.08x ± 0.08, respectively. The error line is defined as a correlation range between the true value and the inversion value. The results showed the final model retrieval values were in good agreement with the real values.

^{2}value and RMSE for Cab were 0.9998 and 0.205, which indicated the uncertainty of the retrieved Cab increased weakly with the varying aerosol loading compared with Figure 9a. It can be seen from Figure 10b that the retrieved LAI value is lower than the true value when the LAI is larger than 6. However, the validation results were almost similar to Figure 9a,b, with the R

^{2}values all larger than 0.99. The results indicated that the developed inversion framework showed good performance regardless of the varied aerosol-loading situation.

## 6. Discussion

## 7. Conclusions

^{2}) between the inversion values and the true values were above 0.99, indicating that UAV multispectral observations can support the inversion of LAI and Cab. It also indicated that the inversion framework can make full use of the available radiation spectral information and has good stability. The findings from this study suggest that our proposed forward model has a strong coupling between vegetation reflectance and atmosphere. Moreover, there were good convergence and consistency for the inversion framework in obtaining inversion LAI and Cab. The optimal inversion framework for the synchronous retrieval of crop phenotypic parameters is expected to be performed on actual observation data in the future and can be applied to the monitoring of crop parameters in the field environment.

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**Diagram of the coupling model (where ${\mu}_{\mathrm{s}}$ and ${\mu}_{\mathrm{v}}$ are cosine of solar zenith angle and cosine of view zenith angle, respectively, and $\varphi $ is relative azimuth angle.)

**Figure 5.**Spectral response under different input parameter values. (

**a**–

**d**) are the different reflectance changes of physicochemical parameters Cab, Cw, Cm and LAI, respectively. (

**e**,

**f**) are the difference reflectance changes of structure parameter N and geometry parameter ALA, respectively. (

**g**–

**i**) are the difference reflectance changes of parameters Car, Hspot and Psoil, respectively.

**Figure 6.**The DFS of crop parameters: (

**a**) the DFS of different wavelengths for all parameters and (

**b**) the DFS of five bands for each parameter.

**Figure 8.**Retrieval process demonstration: (

**a**) the illustration of the iterative process for reflectance based on the coupling model and (

**b**) the description of the convergence process for the cost function.

**Figure 9.**Validation of the Cab and LAI with the OE-iteration method: (

**a**) validation of the Cab with the OE-iteration method against the true value under different observation geometries and (

**b**) validation of the LAI with the OE-iteration method against the true value under different observation geometries. The blue solid line, dashed line, and orange solid line are the 1:1 line, error line, and fit line, respectively. The error lines of (

**a**,

**b**) are E = x ± 0.02x ± 0.08 and E = x ± 0.08x ± 0.08. The statistics of the linear fitting result, including slope, intercept, R

^{2}, and RMSE, are listed in the upper left corner of each scatter plot.

**Figure 10.**Validation of the Cab and LAI with the OE-iteration method: (

**a**) validation of the Cab with the OE-iteration method against the true value under different AODs and (

**b**) validation of the LAI with the OE-iteration method against the true value under different AODs. The blue solid line, dashed line, and orange solid line are the 1:1 line, error line, and fit line, respectively. The error lines of (

**a**,

**b**) are E = x ± 0.04x ± 0.08.and E = x ± 0.14x ± 0.08. The statistics of the linear fitting result, including slope, intercept, R

^{2}, and RMSE, are listed in the upper left corner of each scatter plot.

Parameter Types | Parameter Symbols | Parameter Description | Unit |
---|---|---|---|

Geometry | SZA | Solar zenith angle | Degrees (°) |

VZA | Viewing zenith angle | Degrees (°) | |

SAA | Solar azimuthal angle | Degrees (°) | |

VAA | Viewing azimuthal angle | Degrees (°) | |

Atmosphere | Atmospheric type | The meteorological and air density profile | -- |

Pressure | Surface pressure | hPa | |

Altitude | Surface altitude | m | |

Aerosol | AOD | Aerosol optical depth | -- |

Ri | Complex refractive index of aerosol | -- | |

Profile | The vertical profile of aerosol | -- | |

PSD | Aerosol particle size distribution | -- | |

Surface | Lambertian | Lambertian surface reflectance | -- |

BRDF | Surface bidirectional reflectance | -- | |

Spectra | Wavelength | Central wavelength of spectral channel | nm |

FWHM | Full width at half maximum of spectral channel | nm |

Model | Parameter Symbols | Parameter Description | Common Value | Search Range | Unit |
---|---|---|---|---|---|

PROSPECT | N | Leaf structure parameter | 1.3 | 1.2~2.8 | -- |

Cab | Chlorophyll a and b content | 50 | 20~70 | μg·cm^{−2} | |

Car | Carotenoids content | 8 | 6~12 | μg·cm^{−2} | |

Cw | Equivalent water thickness | 0.004 | 0.004~0.05 | cm | |

Cm | Leaf mass per unit leaf area | 0.012 | 0.003~0.027 | g·cm^{−2} | |

SAIL | LAI | Leaf area index | 1.4 | 1~7 | -- |

ALA | Average leaf angle | 15 | 0~90 | Degrees (°) | |

Hspot | Hot spot | 0.01 | 0.01~1.0 | -- | |

Psoil | Soil coefficient | 0.1 | 0.1~1.0 | -- |

Band | Center Wavelength/nm | Bandwidth |
---|---|---|

Band1-Blue | 450 | 16 |

Band2-Green | 560 | 16 |

Band3-Red | 650 | 16 |

Band4-RedEdge | 730 | 16 |

Band5-NIR | 840 | 26 |

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**MDPI and ACS Style**

Zheng, F.; Wang, X.; Ji, J.; Ma, H.; Cui, H.; Shi, Y.; Zhao, S.
Synchronous Retrieval of LAI and Cab from UAV Remote Sensing: Development of Optimal Estimation Inversion Framework. *Agronomy* **2023**, *13*, 1119.
https://doi.org/10.3390/agronomy13041119

**AMA Style**

Zheng F, Wang X, Ji J, Ma H, Cui H, Shi Y, Zhao S.
Synchronous Retrieval of LAI and Cab from UAV Remote Sensing: Development of Optimal Estimation Inversion Framework. *Agronomy*. 2023; 13(4):1119.
https://doi.org/10.3390/agronomy13041119

**Chicago/Turabian Style**

Zheng, Fengxun, Xiaofei Wang, Jiangtao Ji, Hao Ma, Hongwei Cui, Yi Shi, and Shaoshuai Zhao.
2023. "Synchronous Retrieval of LAI and Cab from UAV Remote Sensing: Development of Optimal Estimation Inversion Framework" *Agronomy* 13, no. 4: 1119.
https://doi.org/10.3390/agronomy13041119