# Effects of Crop Leaf Angle on LAI-Sensitive Narrow-Band Vegetation Indices Derived from Imaging Spectroscopy

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## Abstract

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_{705}), the normalized difference vegetation index (NDVI), and the soil-adjusted vegetation index (SAVI) were only affected for sparse canopies (LAI < 3) and MTA exceeding 60°. Generally, the effect of MTA on the vegetation indices increased as a function of decreasing LAI. The leaf chlorophyll content did not affect the relationship between BNDVI, MSAVI, NDVI, and LAI, while the green atmospherically resistant index (GARI), GNDVI, and MSR

_{705}were the most strongly affected indices. While the relationship between SR and LAI was somewhat affected by both MTA and the leaf chlorophyll content, the simple ratio (SR) displayed only slight saturation with LAI, regardless of MTA and the chlorophyll content. The best index found in the study for LAI estimation was BNDVI, although it performed robustly only for LAI > 3 and showed considerable nonlinearity. Thus, none of the studied indices were well suited for across-species LAI estimation: information on the leaf angle would be required for remote LAI measurement, especially at low LAI values. Nevertheless, narrowband indices can be used to monitor the LAI of crops with a constant leaf angle distribution.

## 1. Introduction

^{2}/m

^{2}are often quoted. The typical LAI values of field crops depend on the species and cultivar, but LAI also varies within species depending on the planting density and the phenological stage of the plant [4,5,6]. The determination of LAI, or its temporal course, allows an understanding of ongoing biophysical processes and the prediction of plant growth and, ultimately, crop productivity. Unfortunately, in situ measurement of LAI is time consuming and cannot be operationally applied to large areas.

## 2. Materials and Methods

#### 2.1. Field Plots

#### 2.2. Remote Sensing Data

#### 2.3. Model Simulations

^{−2}, LAI between 1 and 5, MTA between 15° and 70°, and the leaf water content between 0.001 and 0.020 cm. The leaf mesophyll structure parameter was fixed to 1.55, the average value of various crop species [34], and the leaf dry matter content to 0.005 g cm

^{−2}, a value suitable for the six studied species [35,36,37,38]. The leaf carotenoid content was linked to Cab with the ratio 1:5 based on LOPEX93 data [39]. The brown pigment content was set to 0, assuming that the leaves were green during the measurement. The fraction of diffuse radiation was calculated with the 6S atmosphere radiative transfer model [40] using the input data derived from the image itself and the nearby sun photometer measurements. The hot-spot size parameter had a negligible effect on the simulation due to the observation geometry (sufficiently far from backscatter, or the hot spot) and was set to a reasonable value for a vegetation canopy (0.01). The view and illumination geometry parameters in the model were set to coincide with airborne measurement conditions (solar zenith angle 49.4°, sensor zenith angle 9°, and azimuth angle 90°). The soil reflectance was taken from measurements. A detailed description of the PROSAIL inputs is given by Zou and Mõttus [12]. The PROSAIL spectral resolution was 1 nm, and it was resampled to correspond to the wavelengths measured by AISA using a Gaussian spectral response function.

#### 2.4. Vegetation Indices

#### 2.5. Statistical Methods and Data Analysis

_{k}) between LAI and the selected VIs from both simulated and field-measured data. Kendall’s τ

_{k}is a non-parametric measure of the strength of a monotonic relationship between paired data. The value of τ

_{k}lies between −1 and 1, with τ

_{k}= −1 indicating a perfect negative correlation between the paired data, τ

_{k}= 0 the lack of a relationship and τ

_{k}= 1 a perfect positive correlation. We chose τ

_{k}instead of the more standard Pearson’s correlation coefficient R (and the related coefficient of determination R

^{2}) because the field data did not satisfy the assumption of normality. Neither did we have to assume a linear relationship between the vegetation parameters and VIs. Despite similar ranges, the numerical value of τ

_{k}for a relationship between any two variables is generally different from R.

^{−2}. Next, we divided the simulations into groups based on MTA (15°, 30°, 50°, and 70°) and plotted the VIs calculated from the data against LAI. Similarly, we fixed MTA at 57° and varied Cab between three levels (25–30, 55–60, and 95–100 µg cm

^{−2}) to estimate the effect of Cab on the VI–LAI relationship. Due to the imbalance in the measured actual species-specific leaf angles caused by an uneven distribution of samples between species, we could not analyze the sensitivity of the VI–LAI relationship to MTA in the field-measured dataset.

## 3. Results

^{−2}(Table 3, Figure 4a,b). Oat had the highest Cab (93 µg cm

^{−2}) and turnip rape the lowest value (32 µg cm

^{−2}). There was a significant (p < 0.01) relationship between the field-measured LAI and Cab, with τ

_{k}= 0.35 (Figure 4a), and a weaker (τ

_{k}= 0.19), yet still significant, correlation between the photographic MTA and Cab (Figure 4b).

_{k}between 0.34 and 0.64. For the field-measured data (Figure 5), the rank correlation coefficients were all above 0.4, except for MSAVI, MSR

_{705}, and SAVI (τ

_{k}= 0.34–0.36), and with GARI and GNDVI performing best among the tested VIs (τ

_{k}= 0.50). In model simulations (Figure 6), GARI and GNDVI produced the lowest τ

_{k}of 0.38, with BNDVI being the most strongly correlated (τ

_{k}= 0.64). All the relationships for both empirical analysis and model simulations were significant (p < 0.01).

_{k}> 0.7 at all four MTA levels (Table 5). The relationships between VIs and LAI were most notably affected at MTA > 60°; at a lower MTA, the effect of leaf angle was less evident (Figure 7), especially for BNDVI, GARI, GNDVI, NDVI, and MSR

_{705}at LAI > 3 (Figure 7a,f,g). The effect of MTA on the VI–LAI relationship increased as a function of decreasing LAI for BNDVI, GNDVI, MSR

_{705}, NDVI, and SAVI; for the remaining indices, the trend was unclear. Across the whole studied LAI variation range, the VI–LAI relationships for MSAVI and SR were most strongly affected by MTA, as the point clouds corresponding to the distinct MTA levels are clearly separable in Figure 7d,h. On the other hand, SR was the least saturating VI with LAI, and the relationships were nearly linear for the whole LAI range at MTA 15–50° (Figure 7h).

_{705}, and, to a smaller extent, SR; Figure 8b,c,e,h), relationships with LAI were clearly affected by Cab, with the influence of Cab generally increasing as a function of LAI.

## 4. Discussion

_{k}was between 0.34 and 0.64 for all the selected VIs. However, the relationship was nonlinear [20,43], and some indices (e.g., NDVI) saturated at high LAI values [44].

_{k}was between 0.34 and 0.64), even though the selected indices were clearly sensitive to LAI. This is in agreement with other studies [26,45,46], which have found a wide range of coefficients of determination (0.05 < R

^{2}< 0.66) between VIs and LAI. It is known that differences between crop species affect the goodness of fit more than the vegetation indices used [47]. Evidently, the coefficients were affected by the large volume of simulated data and the range of species with different characteristics in the true data. Both datasets included sufficient structural and biochemical variation to blur the relationships between LAI and VIs. Estimating the LAI of heterogeneous vegetated areas (with subpixel heterogeneity) from remote sensing data is hence not as reliable as estimation of the LAI of homogeneous fields. This is demonstrated by Figure 7 and Table 5, where the correlations improved and correlation coefficients increased from the range of 0.38–0.64 to 0.72–0.93 when a structural parameter, MTA, was fixed. Other studies have also shown the relationship between VIs and LAI to vary across vegetation types (canopy architecture) and the correlations to improve when analyzing the relationship between VIs and LAI for each vegetation type separately [48,49]. The leaf angle distribution, and thus MTA, affects the spectral properties of a canopy [50] to a degree that confuses LAI estimation algorithms based on simple VIs [50].

_{k}= 0.50) performed slightly better than BNDVI (τ

_{k}= 0.48) in the field study and were insensitive to MTA (Figure 7b,c). Unfortunately, both indices were sensitive to Cab (Figure 8b,c). For example, at a medium LAI (LAI = 3), when Cab increased from low levels (25–30 µg cm

^{−2}) to high levels (95–100 µg cm

^{−2}), the indices increase by approximately 50% of their whole range of variation (Figure 8b,c), and hence did not show a strong correlation with LAI in the model-simulated data (τ

_{k}= 0.38). On the other hand, BNDVI (similarly to GNDVI) clearly saturated with LAI (Figure 7a,c), while GARI was more linear with LAI (Figure 7b). The slope of the GARI–LAI relationship, however, depended on Cab (Figure 8b). The slope varied from 0.94 to 0.19 when Cab increased from low (25–30 µg cm

^{−2}) to high levels (95–100 µg cm

^{−2}). SR displayed only slight saturation with LAI, regardless of MTA and the chlorophyll content. This index was largely insensitive to Cab (Figure 8h) and showed similar slopes (approximately 0.15) when plotted against LAI for MTA < 60°. Unfortunately, MTA created varying offsets in the LAI–SR relationship (Figure 7h). As a result, SR showed only an average performance, with τ

_{k}= 0.41 and 0.53 in the field-measured and model-simulated datasets, respectively. Nevertheless, it could be the index of choice for mapping areas with limited variations in structure, e.g., covered by the same crop species. Indeed, together with MSAVI, SR was among the indices independent of Cab and producing the most linear relationships with LAI (Figure 8). For reasons unknown to us, MSAVI and SAVI were the worst performers with field-measured data (Table 4) and hence cannot be recommended based on this study.

## 5. Conclusions

_{k}= 0.64 for empirical data). Nevertheless, the performance of all studied VIs in LAI estimation, including BNDVI, was affected by the leaf tilt angle, especially at LAI < 3. Most of the studied indices were suitable for monitoring the LAI of crops with a constant leaf angle distribution (Kendall’s tau τ

_{k}> 0.7 in the simulated dataset), with SR outperforming others in linearity and applicability to both measured and simulated data. In the future, more crop species with different leaf angle distributions, leaf pigment contents, contrasting canopy architectures, and different growth stages should be used to empirically validate the effects of leaf angle and Cab on LAI-sensitive indices, so that the results can be applied to a wider geographic region.

## Author Contributions

## Funding

## Conflicts of Interest

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**Figure 1.**Crop species: (

**A**) barley, (

**B**) faba bean, (

**C**) oat, (

**D**) wheat, (

**E**) lupin, and (

**F**) turnip rape.

**Figure 2.**A false-color infrared image of the University of Helsinki Viikki campus with the experimental sites Patoniitty and Porvoontie indicated (AISA Eagle II imagery, 25 July 2011).

**Figure 3.**Averaged canopy reflectances (spectral hemispherical-directional reflectance factors) of six crops species acquired from AISA imaging spectrometer data.

**Figure 4.**Correlation between field-measured LAI, the chlorophyll a and b content (Cab), and the leaf mean tilt angle (MTA): (

**a**) field-measured LAI and Cab; (

**b**) photographic MTA and Cab.

**Figure 5.**Correlation between LAI and the selected vegetation indices from imaging spectroscopy data: (

**a**) BNDVI, (

**b**) GARI, (

**c**) GNDVI, (

**d**) MSAVI, (

**e**) MSR

_{705}, (

**f**) NDVI, (

**g**) SAVI, (

**h**) SR. Kendall’s correlation coefficient τ

_{k}and the significance level p are given in each plot.

**Figure 6.**Correlation between LAI and the selected vegetation indices according to PROSAIL simulations: (

**a**) BNDVI, (

**b**) GARI, (

**c**) GNDVI, (

**d**) MSAVI, (

**e**) MSR

_{705}, (

**f**) NDVI, (

**g**) SAVI, (

**h**) SR. Kendall’s correlation coefficient τ

_{k}and the significance level p are given in each plot.

**Figure 7.**Correlation between vegetation indices and the leaf area index (LAI) for a fixed Cab (45–50 µg cm

^{−2}) and different leaf mean tilt angles (MTA = 15, 30, 50, 70°): (

**a**) BNDVI, (

**b**) GARI, (

**c**) GNDVI, (

**d**) MSAVI, (

**e**) MSR

_{705}, (

**f**) NDVI, (

**g**) SAVI, (

**h**) SR. Canopy reflectance simulated with PROSAIL.

**Figure 8.**Correlation between vegetation indices and the leaf area index (LAI) for a fixed MTA of 57° and different leaf chlorophyll contents (Cab = 25–30, 55–60, 95–100 µg cm

^{−2}): (

**a**) BNDVI, (

**b**) GARI, (

**c**) GNDVI, (

**d**) MSAVI, (

**e**) MSR

_{705}, (

**f**) NDVI, (

**g**) SAVI, (

**h**) SR. Canopy reflectance simulated with PROSAIL.

**Table 1.**Field plots measured in the study. Soil types: fertile luvic stagnosol and sandy clay loam (1), haplic gleysols and silty clay loam (2), sulfic cryaquepts (3), fertile luvic stagnosol and sandy medium clay loam (4) (WRB, 2007).

Species | Cultivars | No. of Plots | Soil Type |
---|---|---|---|

Oat | ‘Ivory’, ‘Mirella’ | 4 | 3 |

Turnip rape | ‘Apollo’ | 4 | 3 |

Barley | ‘Streif’, ‘Chill’, ‘Fairytale’ | 10 | 3, 4 |

Lupin | ‘HaagsBlaue’ | 4 | 3 |

Wheat | ‘Amaretto’ | 99 | 1, 2, 3 |

Faba bean | ‘Kontu’ | 40 | 1, 3 |

Total | 162 |

Vegetation Index | Equation | Central Wavelength Used in This Study | Reference |
---|---|---|---|

BNDVI | $\left({\mathrm{R}}_{800}-{\mathrm{R}}_{450}\right)/\left({\mathrm{R}}_{800}+{\mathrm{R}}_{450}\right)$ | ${\mathrm{R}}_{805}$, ${\mathrm{R}}_{452}$ | [21] |

GARI | ${\mathrm{R}}_{800}/{\mathrm{R}}_{530}-1$ | ${\mathrm{R}}_{805}$, ${\mathrm{R}}_{533}$ | [20] |

GNDVI | $\left({\mathrm{R}}_{800}-{\mathrm{R}}_{530}\right)/\left({\mathrm{R}}_{800}+{\mathrm{R}}_{530}\right)$ | ${\mathrm{R}}_{805}$, ${\mathrm{R}}_{533}$ | [22] |

MSAVI | $0.5\left[2{\mathrm{R}}_{800}+1-\sqrt{{\left(2{\mathrm{R}}_{800}+1\right)}^{2}-8\left({\mathrm{R}}_{800}-{\mathrm{R}}_{680}\right)}\right]$ | ${\mathrm{R}}_{805}$, ${\mathrm{R}}_{682}$ | [18] |

MSR_{705} | $\left({\mathrm{R}}_{750}/{\mathrm{R}}_{705}-1\right)/\sqrt{{\mathrm{R}}_{750}/{\mathrm{R}}_{705}+1}$ | ${\mathrm{R}}_{748}$, ${\mathrm{R}}_{701}$ | [3] |

NDVI | (${\mathrm{R}}_{800}-{\mathrm{R}}_{680})/\left({\mathrm{R}}_{800}+{\mathrm{R}}_{680}\right)$ | ${\mathrm{R}}_{805}$, ${\mathrm{R}}_{682}$ | [16] |

SAVI | $\left({\mathrm{R}}_{800}-{\mathrm{R}}_{680}\right)\left(1+0.5\right)/\left({\mathrm{R}}_{800}+{\mathrm{R}}_{680}+0.5\right)$ | ${\mathrm{R}}_{805}$, ${\mathrm{R}}_{682}$ | [17] |

SR | ${\mathrm{R}}_{800}/{\mathrm{R}}_{680}$ | ${\mathrm{R}}_{805}$, ${\mathrm{R}}_{682}$ | [19] |

**Table 3.**Key characteristics of field plots measured in the study. LAI: leaf area index, MTA: mean tilt angle, Cab: chlorophyll a and b content.

Species | Average LAI | MTA (°) | Average Cab (µg cm^{−2}) |
---|---|---|---|

Oat | 3.91 | 58 | 93 |

Turnip rape | 3.58 | 32 | 33 |

Barley | 3.74 | 46 | 56 |

Lupin | 3.46 | 18 | 61 |

Wheat | 2.96 | 64 | 53 |

Faba bean | 3.16 | 27 | 50 |

**Table 4.**Kendall’s rank correlation coefficient (τ

_{k}) between vegetation indices and LAI for model simulations and field-measured data. All correlations were statistically significant (p < 0.01).

Vegetation Index | Model Simulation | Field Measurements |
---|---|---|

BNDVI | 0.64 | 0.48 |

GARI | 0.38 | 0.50 |

GNDVI | 0.38 | 0.50 |

MSAVI | 0.38 | 0.34 |

MSR_{705} | 0.39 | 0.36 |

NDVI | 0.53 | 0.41 |

SAVI | 0.38 | 0.34 |

SR | 0.53 | 0.41 |

**Table 5.**Kendall’s rank correlation coefficient (τ

_{k}) between vegetation indices and LAI in PROSAIL-simulated data for different MTA values at a fixed Cab (45–50 µg cm

^{−2}). All correlations were statistically significant (p < 0.01).

Vegetation Index | MTA = 15° | MTA = 30° | MTA = 50° | MTA = 70° |
---|---|---|---|---|

BNDVI | 0.98 | 0.99 | 0.99 | 0.95 |

GARI | 0.72 | 0.80 | 0.88 | 0.93 |

GNDVI | 0.72 | 0.80 | 0.88 | 0.93 |

MSAVI | 0.98 | 0.98 | 0.98 | 0.94 |

MSR_{705} | 0.73 | 0.83 | 0.91 | 0.94 |

NDVI | 0.93 | 0.97 | 0.98 | 0.95 |

SAVI | 0.93 | 0.97 | 0.98 | 0.95 |

SR | 0.95 | 0.98 | 0.99 | 0.95 |

© 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Zou, X.; Haikarainen, I.; Haikarainen, I.P.; Mäkelä, P.; Mõttus, M.; Pellikka, P.
Effects of Crop Leaf Angle on LAI-Sensitive Narrow-Band Vegetation Indices Derived from Imaging Spectroscopy. *Appl. Sci.* **2018**, *8*, 1435.
https://doi.org/10.3390/app8091435

**AMA Style**

Zou X, Haikarainen I, Haikarainen IP, Mäkelä P, Mõttus M, Pellikka P.
Effects of Crop Leaf Angle on LAI-Sensitive Narrow-Band Vegetation Indices Derived from Imaging Spectroscopy. *Applied Sciences*. 2018; 8(9):1435.
https://doi.org/10.3390/app8091435

**Chicago/Turabian Style**

Zou, Xiaochen, Iina Haikarainen, Iikka P. Haikarainen, Pirjo Mäkelä, Matti Mõttus, and Petri Pellikka.
2018. "Effects of Crop Leaf Angle on LAI-Sensitive Narrow-Band Vegetation Indices Derived from Imaging Spectroscopy" *Applied Sciences* 8, no. 9: 1435.
https://doi.org/10.3390/app8091435