# Retrieving Corn Canopy Leaf Area Index from Multitemporal Landsat Imagery and Terrestrial LiDAR Data

^{1}

^{2}

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## Abstract

**:**

^{2}/m

^{2}, with a strong and significant correlation (R

^{2}= 0.82, residual range = 0 to 0.6 m

^{2}/m

^{2}, p < 0.001). Comparatively, the accuracy of LAI retrieved results using default leaf angle distribution is lower, the RMSE of which is 0.56 with R

^{2}= 0.76 and residual range = 0 to 1.0 m

^{2}/m

^{2}, p < 0.001. This validation reveals that the introduction of inferred leaf angle distributions from TLS data points can improve the LAI retrieval accuracy using the PROSAIL model. Moreover, the comparations of LAI retrieval results on 10 July, 26 July, 19 August and 4 September with default and inferred corn leaf angle distribution functions are all compared with MODIS LAI products in the whole study area. This validation reveals that improvement exists in a wide spatial range and temporal range. All the comparisons demonstrate the potential of the modified PROSAIL model for retrieving corn canopy LAI from Landsat imagery by inferring leaf orientation from terrestrial laser scanning data.

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Study Area

#### 2.2. Data Collection

#### 2.2.1. TLS Data Acquisition and Pre-Processing

#### 2.2.2. Acquisition of Remote Sensing Images

_{19 August}> 0.6 and NDVI

_{4 September}> 0.55 are classified as the corn planted area by testing the NDVI difference of the corn planted area and the non-corn planted area in the whole study area.

#### 2.2.3. Field Data Collection

#### 2.3. LAI Retrieval

#### 2.3.1. PROSAIL Model and Sensitivity Analysis

_{ab}, C

_{ar}, C

_{w}, C

_{m}, LIDFa, LAI, hspot, tts, tto, psi, ρ

_{soil})

_{ab}), leaf carotenoid content (C

_{ab}), dry matter (C

_{m}), and equivalent water thickness (C

_{w}). Leaf chlorophyll (C

_{ab}) is measured with a SPAD-502 chlorophyll meter in this study. Equivalent water thickness (C

_{w}) is tied to the difference of fresh leaf weight and dry leaf weight (C

_{w}= (C

_{fresh leaf}− C

_{dry leaf})/LAI). Canopy structure is characterized by LAI, leaf angle distribution function (LIDFa) and the hot-spot parameter (hspot). LAI comes from the measured LAI value in field work using LAI-2200 Plant Canopy Analyzer. Leaf angle distribution function (LIDFa) comes from the calculated function using TLS points data of corn canopy in this study. The effect background soil (ρ

_{soil}) is descripted by the soil reflectance. The sun-view geometry is described by the solar zenith angle (tts), view zenith angle (tto), and the relative azimuth angle between sun and satellite sensor (psi).

_{ab}, C

_{ar}etc. are set as default values when we analyze the sensitivity of LAI input variable. If the simulated reflectance is obviously different using a range of LAI and default values of other variables (i.e., LIDFa, hspot, N, C

_{ab}, C

_{ar}etc.), we can conclude that LAI is a sensitive input parameter.

#### 2.3.2. Leaf Angle Distribution Function Inferred from the TLS Data

_{i}.

_{i}, there are k neighboring points which can organized as a point set P

_{i}(P

_{i}= p

_{i1}, p

_{i2}, p

_{i3}, p

_{i4},…, p

_{ik}). A surface T

_{i}can be constructed using the points set P

_{i}. $\overrightarrow{{n}_{i}}$ is the normal vector of surface T

_{i}, and ${\overline{p}}_{i}$ is the centroid of points set P

_{i}. And ${\overline{p}}_{i}$ is computed as:

_{i}using PCA method.

_{i}(P

_{i}= p

_{i1}, p

_{i2}, p

_{i3}, p

_{i4},…, p

_{ik}) is computed using PCA algorithm. Secondly, the eigenvalues (λ

_{1}, λ

_{2}, λ

_{3}) and eigenvectors ($\overrightarrow{{e}_{1}}$,$\overrightarrow{{e}_{2}}$,$\overrightarrow{{e}_{3}}$) of covariance matrix M are calculated. Lastly, exploring the eigenvectors of the critical eigenvalues, which is the normal vector for point p

_{i}. The covariance matrix M is computed as:

#### 2.3.3. LUT-Based LAI Retrieval Strategy Based on PROSAIL Model

- 1.
- LUT generation

_{soil}. Weiss et al. [41] found that an LUT based on 100,000 modeled spectra provides an optimal compromise between model accuracy and required computer-resources. Therefore, we combine the input variables using the following range/value and interval of input variables (see Table 3). The version of PROSPECT model used in this study is PROSPECT-5B [42], so the brown pigments (C

_{bp}) is fitted to 0 [43], which is not listed in Table 3.

- 2.
- Cost function

_{L}(λ) is the reflectance in band λ for the Landsat image, R

_{sim}(λ) is the simulated reflectance in band λ, and n is the number of wavelength bands. The retrieved LAI is found when the RMSE approaches 0.

## 3. Results and Analysis

#### 3.1. Sensitivity Analysis of PROSAIL for Simulating Corn Canopy Reflectance

_{w}, C

_{m}and hspot are changed and other inputs are fixed. This shows that C

_{w}, C

_{m}and hspot are sensitive within NIR band. Figure 5e,i,j show that the simulated reflectance is few different within all bands. This shows that C

_{ar}, psoil and skyl are insensitive inputs for the PROSAIL model.

#### 3.2. Inferred Leaf Angle Distribution Function from the TLS Scanner Data

#### 3.3. Retrieved Corn Canopy LAIs

^{2}/m

^{2}to 2.7 m

^{2}/m

^{2}. By 26 July (heading stage; Figure 7b), LAI had increased to 3.7. By late August (flowering stage; Figure 7c), LAI reached values of up to 7.2. By early September (grain filling stage; Figure 7d), LAI reached its seasonal maximum, with values reaching up to 7.8. The retrieved LAI maps therefore show a realistic progression of LAI throughout the growing season.

^{2}= 0.82, p < 0.001) and the retrieved LAI using default Campbell leaf angle function (R

^{2}= 0.76, p < 0.001). Both retrieved values did not differ significantly from in-situ values (t-test, p < 0.001). Moreover, we found a low RMSE value of 0.31 m

^{2}/m

^{2}for the retrieval using leaf angle function inferred from TLS scanner data, compared with the RMSE value of 0.56 m

^{2}/m

^{2}for the retrieval using the default Campbell leaf angle function. In addition, the difference between the retrieved LAI using inferred leaf angle function and in-situ value ranged from 0 to 0.6 m

^{2}/m

^{2}, and the difference between the retrieved using default Campbell leaf angle function and in-situ value ranged from 0 to 1.0 m

^{2}/m

^{2}. This comparation revealed that the use of leaf angle distribution inferred from TLS data worked better than the default value for this retrieval.

_{with inferred LAD}-LAI

_{with default LAD}. Figure 9b is the zoomed difference LAI map in the middle of the study area. We can see that the LAI result with inferred leaf angle distribution using TLS data is higher than the LAI result with default leaf angle function. The difference between LAI

_{with inferred LAD}and LAI

_{with default LAD}is ranging from 0 m

^{2}/m

^{2}to 1.5 m

^{2}/m

^{2}. This analysis shows that the use of leaf angle distribution inferred from TLS data increases the LAI retrieved result.

^{th}and 25

^{th}percentile, respectively. The comparison revealed that the LAI variation trend from 10 July to 4 September using inferred corn leaf angle distribution functions is more consistent with the MODIS LAI variation trend than the LAI variation trend using default leaf angle function. Both plots raised quickly from 10 July to 26 July when the corn grew quickly, and both plots raised slowly from 26 July to 4 September when the corn growth was slow. In addition, the curve of retrieved LAI using inferred corn leaf angle distribution functions is higher than the MODIS LAI curve and the curve of retrieved LAI using default leaf angle. Previous comparisons proposed that the MODIS LAI products underestimate the LAIs of corn crops [44] and other vegetation species [10,45,46,47,48]. Fortunately, our experiment shows that this underestimate can be alleviated for corn canopy LAI retrieval by considering the leaf angle difference in different phenological stages.

## 4. Discussion

_{ab}), dry matter (C

_{m}) etc. We are focusing on depicting the leaf angle change in this study. And we will expand the LAI retrieval improvement by bringing in other input variables in future work. The other validation is done in a wide spatial range (the whole study area) and multi-temporal (10 July, 26 July, 19 August and 4 September, 2014). Comparison results show that the spatial pattern and temporal trajectory of LAI retrieved results using inferred corn leaf angle distributions are closer to MODIS LAI products. This conclusion reveals that the LAI retrieval improvements can exist in a time series LAI retrieval and generalize to wider corn planted areas. Much research has indicated that the retrieved LAI using a remote sensing technique is underestimated [50,51,52,53,54], especially for MODIS LAI [10,44,45,46,47,48]. Therefore, the inferred leaf angle distribution improves the underestimation of LAI retrieval using remote sensing images.

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**Location of the study area (

**a**), the distribution of sampling quadrats in field work (

**b**), and sampling pattern used in the fieldwork (

**c**).

**Figure 2.**In-situ data collection activities conducted in each sampling plot: (

**a**) obtaining a 3D image of the plot using the TLS scanner, (

**b**) photographing the leaves for manual calculation of leaf angles, and (

**c**,

**d**) measuring LAI using the LI-COR LAI-2200C plant canopy analyzer.

**Figure 3.**Top view (

**a**) and side view (

**b**) of the laser scanning scheme for the corn canopy, and (

**c**) sample image of the scanning data for a corn canopy.

**Figure 4.**Overview of the LAI retrieval based on improving the leaf angle distribution function of the PROSAIL model.

**Figure 5.**Results of the sensitivity analysis for the 12 input parameters to which PROSAIL is sensitive.

**Figure 6.**The leaf angle probability density functions for the corn canopy on 10 July, 26 July, 19 August, and 4 September, 2014, respectively.

**Figure 7.**The LAI maps derived using the inferred leaf angle function from TLS scanner data on (

**a**) 10 July (stem elongation stage), (

**b**) 26 July (heading stage), (

**c**) 19 August (flowering state), and (

**d**) 4 September (grain-filling stage).

**Figure 8.**The relationships between the in-situ measured LAI and the retrieved LAIs using inferred and default leaf angle function. Values represent means ± SD based on the in-situ LAI measurements at each sample plot.

**Figure 9.**LAI bias (m

^{2}/m

^{2}) between the retrieved LAI with and without inferred leaf angle distribution function on 4 September 2014.

**Figure 10.**Comparation between the retrieved LAIs with default and inferred leaf angle distribution function on 10 July, 26 July, 19 August, 4 September, 2014, respectively.

Parameter | Range of Values |
---|---|

Scanning distance (m) | 0.6 to 330 |

Scanning speed (points/s) | 122,000 to 976,000 |

Ranging error (mm) | ±2 |

Resolution (pixels) | 7 × 107 |

Vertical field of view (°) | 300 |

Horizontal field of view (°) | 360 |

Laser class | Class 1 |

Wavelength (nm) | 1550 |

GPS | Integrated GPS receiver |

Date | Sensor | UTM Time | Sun Elevation Angle (°) | Sun Azimuth Angle (°) | Viewing Zenith Angle (°) | Viewing Azimuth Angle (°) |
---|---|---|---|---|---|---|

10 July | ETM+ | 02:51:27 | 64.77 | 124.82 | 0 | 90 |

26 July | ETM+ | 02:51:31 | 62.52 | 128.55 | 0 | 90 |

19 August | OLI | 02:53:59 | 58.03 | 138.33 | 0 | 90 |

4 September | OLI | 02:54:02 | 53.72 | 144.98 | 0 | 90 |

**Table 3.**Range and distribution of the input variables used to establish the synthetic corn canopy reflectance database in the lookup table.

Model Variables | Range or Value | Distribution | ||
---|---|---|---|---|

Canopy | LAI | Leaf area index (m^{2} m^{−2}) | 0.1 to 7.0 | Uniform |

LIDFa | Leaf angle distribution (º) | 0 to 90 | Gaussian | |

hspot | Hotspot parameter (m m^{−1}) | 0.1 | - | |

Leaf | N | Leaf structural parameter in PROSPECT | 1.518 | - |

C_{ab} | Chlorophyll a+b content in PROSPECT (μg cm^{−2}) | 0.1 to 60.0 | Uniform | |

C_{ar} | Carotenoid content in PROSPECT (μg cm^{−2}) | 8 | - | |

C_{w} | Equivalent water thickness in PROSPECT (cm) | 0.05 to 0.3 | Gaussian | |

C_{m} | Dry matter content in PROSPECT (g cm^{−2}) | 0.002 to 0.012 | Gaussian | |

Soil and sky | p_{soil} | Soil reflectance assumed to be Lambertian (1) or not (0) | 0–1 | Gaussian |

skyl | Ratio of diffuse to total incident radiation | Calculated by tts | - | |

Sun-sensor | tts | Solar zenith angle (°) | / | / |

tto | Viewing zenith angle (°) | / | / | |

psi | Relative azimuth angle (v) | / | / |

**Notes**: The boundary conditions for the corn canopy, leaves, and soil were selected to describe the characteristics of all growth conditions for the corn canopy in our study area. Sun and sensor viewing conditions corresponded to the measurement conditions when the satellite passed overhead. All possible combinations of all variables were calculated from the corn leaf and canopy input ranges.

Date | χ | Proportion of Leaf Angles (% of Total) | ||||||||
---|---|---|---|---|---|---|---|---|---|---|

0°–10° | 10°–20° | 20°–30° | 30°–40° | 40°–50° | 50°–60° | 60°–70° | 70°–80° | 80°–90° | ||

10 July | 1.223 | 7.83 | 11.33 | 14.2 | 16.1 | 16.68 | 15.05 | 10.63 | 5.68 | 2.5 |

26 July | 1.206 | 6.49 | 8.98 | 10.73 | 12.42 | 14.18 | 15.41 | 14.67 | 11.1 | 6.02 |

19 August | 1.214 | 7.1 | 10.11 | 11.3 | 11.89 | 13.4 | 14.79 | 14.02 | 10.85 | 6.54 |

4 September | 1.195 | 6.17 | 8.76 | 10.02 | 10.73 | 12.19 | 14.54 | 15.79 | 13.53 | 8.27 |

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## Share and Cite

**MDPI and ACS Style**

Su, W.; Huang, J.; Liu, D.; Zhang, M.
Retrieving Corn Canopy Leaf Area Index from Multitemporal Landsat Imagery and Terrestrial LiDAR Data. *Remote Sens.* **2019**, *11*, 572.
https://doi.org/10.3390/rs11050572

**AMA Style**

Su W, Huang J, Liu D, Zhang M.
Retrieving Corn Canopy Leaf Area Index from Multitemporal Landsat Imagery and Terrestrial LiDAR Data. *Remote Sensing*. 2019; 11(5):572.
https://doi.org/10.3390/rs11050572

**Chicago/Turabian Style**

Su, Wei, Jianxi Huang, Desheng Liu, and Mingzheng Zhang.
2019. "Retrieving Corn Canopy Leaf Area Index from Multitemporal Landsat Imagery and Terrestrial LiDAR Data" *Remote Sensing* 11, no. 5: 572.
https://doi.org/10.3390/rs11050572