# Experiment of Canopy Leaf Area Density Estimation Method Based on Ultrasonic Echo Signal

^{1}

^{2}

^{3}

^{*}

^{†}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Laboratory-Simulated Canopy Experimental Setup

^{2}. The simulated canopy had 2, 3, 4, or 5 planar leaf layers in the experiments, each layer had many simulated leaves, which were fixed on the nylon wires, and the nylon wires were arranged up and down in the steel profile frame. The nylon wires are moveable in the simulated canopy, which is convenient for adjusting the simulated canopy thickness and leaf area density, similar to the experimental setup used in reference [21]. The leaves on the nylon wires are basically evenly arranged along the wires according to the number of leaves. The temperatures ranged from 20 to 25 °C, and the humidity ranged from 38 to 50%.

#### 2.2. Canopy Leaf Area Density Estimation Equations

#### 2.3. Experiment to Establish Canopy Leaf Area Density Model

#### 2.3.1. Orthogonal Regression Experiment Design

#### 2.3.2. Detection Points Arrangement

#### 2.4. Laboratory-Simulated Canopy Verification

#### 2.5. Outdoor Tree Canopy Verification

_{i}is the total number of leaves in the effective volume. According to the definitions, there were 30 leaves collected from the upper, middle, and lower locations of the tree canopy, respectively. Commercial image analysis code IPP (Image Pro Plus, Meyer instruments, Inc., Houston, TX, USA) was used to measure the leaf area after leaf scanning. The average leaf area $\text{}\overline{\mathrm{S}}\text{}$ was about $1.55\times {10}^{-3}$ ${\mathrm{m}}^{2}$, and the canopy leaf area density of the selected detection points ranged from 1.80 to 5.88 ${\mathrm{m}}^{2}{\mathrm{m}}^{-3}$.

## 3. Results

#### 3.1. Mathematical Model Analysis

_{1}× X

_{2}is 0.2745, which indicates that X

_{1}× X

_{2}is not significant in the mathematical model equation and could be ignored in the model equation.

_{1}× X

_{2}from the mathematical model equation, the new analysis of variance of the canopy leaf-density model based on ${\mathrm{V}}_{\mathrm{c}}$ is shown in Table 6, the F value of the model is 34.01, and the p-value is 0.0003, which indicate that the mathematical model of canopy leaf area density is very significant. The F value of the lack of fit is 12.85, and the p-value is 0.0735, which indicate that the lack of fit of the canopy density model is not significant, and the mathematical model could be used in canopy leaf area density prediction. Based on the above analysis, the model equation is expressed with Equation (11).

^{2}= 0.96) than the results in reference [23] (R

^{2}= 0.944), the agreement between the predicted and the observed ${\mathrm{V}}_{\mathrm{c}}$ showed potential for parameter and canopy leaf-area density prediction.

#### 3.2. Laboratory-Simulated Canopy Verification Results

#### 3.3. Outdoor Tree Canopy Verification Results

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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Code | Factors | |
---|---|---|

${\mathbf{x}}_{1}$ | ${\mathbf{x}}_{2}$ | |

−r | 0.5 | 0.54 |

−1 | 0.55 | 0.79 |

0 | 0.9 | 2.95 |

1 | 1.25 | 5.09 |

r | 1.3 | 5.4 |

Number | ${\mathbf{Z}}_{1}$ | ${\mathbf{Z}}_{2}$ | ${\mathbf{x}}_{1}\text{}\left(\mathbf{m}\right)$ | ${\mathbf{x}}_{2}$$\text{}\left({\mathbf{m}}^{2}{\mathbf{m}}^{-3}\right)$ |
---|---|---|---|---|

1 | 0 | 0 | 0.9 | 2.95 |

2 | −r | 0 | 0.5 | 2.95 |

3 | 0 | r | 0.9 | 5.4 |

4 | 1 | 1 | 1.25 | 5.09 |

5 | 1 | −1 | 1.25 | 0.79 |

6 | 0 | 0 | 0.9 | 2.95 |

7 | 0 | −r | 0.9 | 0.54 |

8 | 0 | 0 | 0.9 | 2.95 |

9 | r | 0 | 1.3 | 2.95 |

10 | −1 | −1 | 0.55 | 0.79 |

11 | −1 | 1 | 0.55 | 5.09 |

${\mathbf{X}}_{1}(\mathbf{m})$ | ${\mathbf{X}}_{2}({\mathbf{m}}^{2}{\mathbf{m}}^{-3})$ | ${\mathbf{V}}_{\mathbf{a}}\left(\mathbf{v}\right)$ | ${\mathbf{V}}_{\mathbf{b}}\left(\mathbf{v}\right)$ | ${\mathbf{V}}_{\mathbf{c}}\left(\mathbf{v}\right)$ |
---|---|---|---|---|

0.90 | 2.95 | 1.95 | 4.51 | 1.83 |

0.50 | 2.95 | 2.14 | 5.41 | 1.96 |

0.90 | 5.40 | 1.94 | 5.05 | 1.81 |

1.25 | 5.09 | 1.90 | 4.11 | 1.79 |

1.25 | 0.79 | 1.70 | 2.47 | 1.65 |

0.90 | 2.95 | 1.94 | 4.53 | 1.84 |

0.90 | 0.54 | 1.59 | 1.97 | 1.57 |

0.90 | 2.95 | 1.96 | 4.52 | 1.82 |

1.30 | 2.95 | 1.86 | 3.74 | 1.76 |

0.55 | 0.79 | 1.82 | 3.62 | 1.71 |

0.55 | 5.09 | 2.11 | 5.25 | 1.92 |

${\mathbf{V}}_{\mathbf{a}}\left(\mathbf{v}\right)$ | ${\mathbf{V}}_{\mathbf{b}}\left(\mathbf{v}\right)$ | ${\mathbf{V}}_{\mathbf{c}}\left(\mathbf{v}\right)$ | |
---|---|---|---|

p value | 0.0005 | 0.0023 | 0.0003 |

${\mathrm{R}}^{2}$ | 0.97 | 0.95 | 0.93 |

Lack of Fit p value | 0.0461 | 0.0005 | 0.0722 |

Source | Sum of Squares | df | Mean Square | F Value | p Value |
---|---|---|---|---|---|

Model | 0.12 | 4 | 0.024 | 29.80 | 0.0010 |

X_{1} | 0.026 | 1 | 0.026 | 32.24 | 0.0024 |

X_{2} | 0.060 | 1 | 0.06 | 73.26 | 0.0004 |

X_{1} × X_{2} | $1.235\times {10}^{-3}$ | 1 | $1.235\times {10}^{-3}$ | 1.50 | 0.2745 |

${\mathrm{X}}_{1}^{2}$ | $4.085\times {10}^{-3}$ | 1 | $4.085\times {10}^{-3}$ | 4.98 | 0.0461 |

${\mathrm{X}}_{2}^{2}$ | 0.032 | 1 | 0.032 | 39.33 | 0.0015 |

Residual | $5.340\times {10}^{-3}$ | 6 | $8.210\times {10}^{-4}$ | ||

Lack of Fit | $5.140\times {10}^{-3}$ | 4 | $1.300\times {10}^{-3}$ | 13.01 | 0.0722 |

Pure Error | $2.000\times {10}^{-4}$ | 2 | $1.000\times {10}^{-4}$ | ||

Cor Total | 0.13 | 10 |

Source | Sum of Squares | df | Mean Square | F Value | p Value |
---|---|---|---|---|---|

Model | 0.12 | 4 | 0.030 | 34.01 | 0.0003 |

X_{1} | 0.026 | 1 | 0.026 | 29.77 | 0.0016 |

X_{2} | 0.060 | 1 | 0.060 | 67.57 | 0.0002 |

${\mathrm{X}}_{1}^{2}$ | $4.085\times {10}^{-3}$ | 1 | $4.085\times {10}^{-3}$ | 4.59 | 0.0449 |

${\mathrm{X}}_{2}^{2}$ | 0.032 | 1 | 0.032 | 36.28 | 0.0009 |

Residual | $5.340\times {10}^{-3}$ | 6 | $8.900\times {10}^{-4}$ | ||

Lack of Fit | $5.140\times {10}^{-3}$ | 4 | $1.285\times {10}^{-3}$ | 12.85 | 0.0735 |

Pure Error | $2.000\times {10}^{-4}$ | 2 | $1.000\times {10}^{-4}$ | ||

Cor Total | 0.13 | 10 |

Detection Distance (m) | $\mathbf{Canopy}\text{}\mathbf{Leaf}\text{}\mathbf{Area}\text{}\mathbf{Density}\text{}\left({\mathbf{m}}^{2}{\mathbf{m}}^{-3}\right)$ | $\mathbf{Predicted}\text{}{\mathbf{V}}_{\mathbf{c}}$ (V) | $\mathbf{Observed}\text{}{\mathbf{V}}_{\mathbf{c}}$ (V) | Relative Error |
---|---|---|---|---|

0.8 | 0.98 | 1.67 | 1.60 | 4.37% |

1.0 | 0.98 | 1.64 | 1.51 | 8.61% |

1.2 | 0.98 | 1.62 | 1.53 | 5.88% |

0.8 | 2.95 | 1.85 | 1.77 | 4.52% |

1.0 | 2.95 | 1.81 | 1.87 | −3.21% |

1.2 | 2.95 | 1.79 | 1.87 | −4.28% |

0.8 | 4.92 | 1.85 | 1.77 | 4.52% |

1.0 | 4.92 | 1.82 | 1.70 | 7.06% |

1.2 | 4.92 | 1.80 | 1.70 | 5.88% |

Detection Point | Detection Distance (m) | $\mathbf{Canopy}\text{}\mathbf{Leaf}\text{}\mathbf{Area}\text{}\mathbf{Density}\text{}\left({\mathbf{m}}^{2}{\mathbf{m}}^{-3}\right)$ | $\mathbf{Predicted}\text{}{\mathbf{V}}_{\mathbf{c}}$ (V) | $\mathbf{Observed}\text{}{\mathbf{V}}_{\mathbf{c}}$ (V) | Relative Error |
---|---|---|---|---|---|

1 | 1.05 | 2.11 | 1.75 | 1.73 | 1.36 |

2 | 0.88 | 2.05 | 1.77 | 1.76 | 0.73 |

3 | 0.90 | 2.63 | 1.81 | 1.65 | 9.32 |

4 | 1.06 | 3.27 | 1.82 | 1.83 | −0.79 |

5 | 1.04 | 1.80 | 1.72 | 2.02 | −14.71 |

6 | 1.02 | 5.60 | 1.78 | 1.84 | −3.27 |

7 | 1.11 | 4.71 | 1.81 | 1.91 | −5.25 |

8 | 1.11 | 5.28 | 1.79 | 1.82 | −1.91 |

9 | 1.10 | 5.88 | 1.75 | 1.76 | −0.56 |

10 | 1.11 | 5.41 | 1.78 | 1.92 | −7.03 |

11 | 1.02 | 4.82 | 1.82 | 1.93 | −6.04 |

12 | 1.04 | 5.38 | 1.79 | 1.82 | −1.46 |

13 | 1.08 | 4.71 | 1.82 | 1.99 | −8.56 |

14 | 1.07 | 4.82 | 1.81 | 1.86 | −2.36 |

15 | 1.11 | 5.40 | 1.78 | 1.82 | −2.06 |

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**MDPI and ACS Style**

Ou, M.; Hu, T.; Hu, M.; Yang, S.; Jia, W.; Wang, M.; Jiang, L.; Wang, X.; Dong, X.
Experiment of Canopy Leaf Area Density Estimation Method Based on Ultrasonic Echo Signal. *Agriculture* **2022**, *12*, 1569.
https://doi.org/10.3390/agriculture12101569

**AMA Style**

Ou M, Hu T, Hu M, Yang S, Jia W, Wang M, Jiang L, Wang X, Dong X.
Experiment of Canopy Leaf Area Density Estimation Method Based on Ultrasonic Echo Signal. *Agriculture*. 2022; 12(10):1569.
https://doi.org/10.3390/agriculture12101569

**Chicago/Turabian Style**

Ou, Mingxiong, Tianhang Hu, Mingshuo Hu, Shuai Yang, Weidong Jia, Ming Wang, Li Jiang, Xiaowen Wang, and Xiang Dong.
2022. "Experiment of Canopy Leaf Area Density Estimation Method Based on Ultrasonic Echo Signal" *Agriculture* 12, no. 10: 1569.
https://doi.org/10.3390/agriculture12101569