# Deriving Vegetation Indices for 3D Canopy Chlorophyll Content Mapping Using Radiative Transfer Modelling

Ahmed Elsherif, Magdalena Smigaj, Rachel Gaulton, Jean-Philippe Gastellu-Etchegorry, Alexander Shenkin

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Ahmed Elsherif, Magdalena Smigaj, Rachel Gaulton, Jean-Philippe Gastellu-Etchegorry, Alexander Shenkin. Deriving Vegetation Indices for 3D Canopy Chlorophyll Content Mapping Using Radiative Transfer Modelling. Forests, 2024, 15 (11), pp.1878. 10.3390/f15111878. hal-04847209

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Article

# Deriving Vegetation Indices for 3D Canopy Chlorophyll Content Mapping Using Radiative Transfer Modelling

Ahmed Elsherif <fnref n="1" />,* , Magdalena Smigaj <fnref n="2" />, , Rachel Gaulton <fnref n="3" />, , Jean-Philippe Gastellu-Etchegorry <fnref n="4" />, and Alexander Shenkin <fnref n="5" />

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**Citation:** Elsherif, A.; Smigaj, M.; Gaulton, R.; Gastellu-Etchegorry, J.-P.; Shenkin, A. Deriving Vegetation Indices for 3D Canopy Chlorophyll Content Mapping Using Radiative Transfer Modelling. *Forests* 2024, *15*, 1878. https://doi.org/10.3390/f15111878

Academic Editor: Yunjun Yao

Received: 26 September 2024

Revised: 8 October 2024

Accepted: 22 October 2024

Published: 25 October 2024

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**Copyright:** © 2024 by the authors.
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This article is an open access article
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4.0/).

**Abstract:** Leaf chlorophyll content is a major indicator of plant health and productivity. Optical remote sensing estimation of chlorophyll limits its retrievals to two-dimensional (2D) estimates, not allowing examination of its distribution within the canopy, although it exhibits large variation across the vertical profile. Multispectral and hyperspectral Terrestrial Laser Scanning (TLS) instruments can produce three-dimensional (3D) chlorophyll estimates but are not widely available. Thus, in this study, 14 chlorophyll vegetation indices were developed using six wavelengths employed in commercial TLS instruments (532 nm, 670 nm, 808 nm, 785 nm, 1064 nm, and 1550 nm). For this, 200 simulations were carried out using the novel bidirectional mode in the Discrete Anisotropic Radiative Transfer (DART) model and a realistic forest stand. The results showed that the Green Normalized Difference Vegetation Index (GNDVI) of the 532 nm and either the 808 nm or the 785 nm wavelengths were highly correlated to the chlorophyll content (R<fnref n="2" /> = 0.74). The Chlorophyll Index (CI) and Green Simple Ratio (GSR) of the same wavelengths also displayed good correlation (R<fnref n="2" /> = 0.73). This study was a step towards canopy 3D chlorophyll retrieval using commercial TLS instruments, but methods to couple the data from the different instruments still need to be developed.

**Keywords:** forest health; terrestrial LiDAR; plant health monitoring; terrestrial laser scanning; the DART model; 3D RTM; remote sensing of vegetation

## 1. Introduction

Leaf chlorophyll content is the primary pigment driving photosynthesis, making remote retrieval of its concentrations valuable for monitoring plant physiological status and ecosystem processes. Reductions in chlorophyll content can be indicative of plant stress and an onset of chlorosis, which is commonly used for identifying vegetative decline [1]. Since chlorophyll molecules facilitate the exchange of matter and energy fluxes between the biosphere and the atmosphere, Canopy Chlorophyll Content (CCC) has proven invaluable in terrestrial biosphere models for quantification of carbon and water fluxes, primary productivity, and light use efficiency [2–4]. As such, CCC has been suggested as one of the Essential Biodiversity Variables (EBVs) for evaluating progress towards the Aichi Biodiversity Targets [5,6].

Remote sensing-based retrieval of total chlorophyll content (chlorophyll a + b) typically focuses on optical imagery following one of the two approaches: (i) directly relating ground measurements to optical remote sensing observations via Vegetation Indices (VIs)

<footnote n="1">¹ Faculty of Engineering, Tanta University, Tanta 31527, Egypt</footnote>

<footnote n="2">² Laboratory of Geo-Information Science and Remote Sensing, Wageningen University & Research, 6708 PB Wageningen, The Netherlands; magdalena.smigaj@wur.nl</footnote>

<footnote n="3">³ School of Natural and Environmental Sciences, Newcastle University, Newcastle NE1 7RU, UK; rachel.gaulton@newcastle.ac.uk</footnote>

<footnote n="4">⁴ CESBIO, CNES-CNRS-IRD-UT3, University of Toulouse, 31401 Toulouse CEDEX 09, France; jean-philippe.gastellu@iut-tlse3.fr</footnote>

<footnote n="5">5 School of Informatics, Computing, and Cyber Systems, Northern Arizona University, Flagstaff, AZ 86011, USA; alexander.shenkin@nau.edu</footnote>

<footnote>* Correspondence: ahmed.elsherif@f-eng.tanta.edu.eg</footnote>
or (ii) physical modelling of light propagation within the canopy using Radiative Transfer Models (RTMs). Over the years, a broad range of VIs have been developed to estimate chlorophyll content [7,8]. Among the most widely used are the Normalized Difference Vegetation Index (NDVI) [9], Green Normalized Difference Vegetation Index (GNDVI) [10], and Modified Chlorophyll Absorption Reflectance Index (MCARI) [11], the last of which incorporates a red edge band to minimize the influence of non-photosynthetic materials. Although VIs are easy to compute and deploy, physically-based approaches, which involve inverting RTMs, have been shown to be advantageous in heterogeneous sites where canopy structure plays a significant role in light penetration and scattering [12,13]. However, a significant drawback of RTMs is their complexity since they need many inputs for parameterization. They are also demanding in terms of computational time and required resources, an issue that has now been addressed in the state-of-the-art RTMs such as the LESS model [14] and the new bidirectional mode in the Discrete Anisotropic Radiative Transfer (DART) model [15].

Nevertheless, optical imagery-based chlorophyll content retrievals are limited to 2D estimates, preventing the examination of its distribution within the canopy. Most leaf biochemical traits, including chlorophyll content, exhibit significant variation across light and height gradients within the canopy [16–18]. Previous studies have found substantial differences across the canopy vertical profile with shaded leaves often having greater chlorophyll concentrations, likely as a strategy to increase PAR absorption efficiency [19,20]. Tree growth stage and species composition were also shown to affect the level of variation across the vertical gradient [19–21]. A 3D understanding of chlorophyll distribution within the canopy would allow more accurate modelling of carbon fluxes, energy balance, and primary productivity [22,23].

Multi- and hyperspectral Terrestrial Laser Scanning (TLS) have shown their potential in recent years for 3D chlorophyll mapping. Nevalainen et al. [24] accurately estimated the chlorophyll content in Scots pine (*Pinus sylvestris*) with a multispectral LiDAR ($R^2$ = 0.88). Li et al. [25] achieved similar results for various species using indices derived from a 32-channel LiDAR ($R^2$ = 0.83). Sun et al. [26], however, reported lower accuracy ($R^2$ = 0.55) when estimating rice (*Oryza sativa*) chlorophyll content with a similar instrument. Bi et al. [27] reported high correlation ($R^2$ = 0.96) between leaf chlorophyll content of red hot poker (*Kniphofia uvaria*) plants and reflectance from a 32-channel LiDAR instrument. Xu et al. [23] estimated leaf chlorophyll content of nine species using a hyperspectral LiDAR and a combination of the PROSPECT-5 [28] and the 4SAIL [29] RTMs with good accuracy ($R^2$ = 0.77). While the aforementioned studies, among others, have shown promising results, they relied on prototype instruments with limited availability.

An alternative approach to the use of multi- and hyperspectral TLS instruments involves coupling the data from multiple commercial TLS instruments after calibration of their backscattered intensity data. This method has been applied successfully in real forest environments for 3D canopy water content mapping [30,31], but its effectiveness for chlorophyll content estimation remains unexplored. The challenges in this approach include the limited number of wavelengths employed within commercial TLS instruments, and the high uncertainty regarding which combinations of these wavelengths would be most suitable for chlorophyll estimation. Therefore, an investigation of commercially available TLS systems' sensitivity to chlorophyll content, which is the aim of this study, is timely. Additionally, examining the sensitivity of such systems to other leaf traits, including Leaf Mass per Area (LMA), leaf internal structure, and leaf water content is also crucial since these traits significantly influence radiation's interaction with foliage [31–34].

In this study, a realistic 3D forest stand was reconstructed in the DART model; the novel bidirectional mode, known as the DART-Lux mode [15], was used to carry out simulations that aimed to (1) derive fourteen VIs for chlorophyll a + b estimation using wavelengths employed in commercial TLS instruments; (2) investigate the influence of leaf biochemical and biophysical traits on the developed indices' accuracy, including leaf internal structure, LMA, leaf water content, carotenoids, and brown pigments; and (3) test
the speed and efficiency of the DART-Lux mode and examine its ability to run hundreds of simulations on a mid-range machine using a complex scene.

## 2. Materials and Methods

### 2.1. 3D Forest Stand

The methods described in this section were adapted from Elsherif [35]. The forest scene used in this study was a 65 m × 55 m subset of the 3D model of a one-hectare forest stand in Wytham Woods, Oxford, UK, described in detail in Calders et al. [36]. Scans carried out using a RIEGL VZ-400 TLS instrument (RIEGL Laser Measurement Systems GmbH, Horn, Austria) in leaf-on and leaf-off conditions were used to reconstruct the one-hectare 3D model, as described thoroughly in Calders et al. [36], following three main steps: (1) tree segmentation, (2) modelling of tree structure, and (3) leaf insertion. The open-source software treeseg [37], available at https://github.com/apburt/treeseg/ was utilized for tree segmentation, whilst tree structure modelling was carried out by converting each extracted tree point cloud to a Quantitative Structure Model (QSM) using the approach described in Calders et al. [38]. A tree QSM is a geometrical model that describes the complete tree woody components in a hierarchical order [39]. To add leaves to each tree QSM, the Foliage and Needles Naïve Insertion (FaNNI) algorithm [40], hosted at https://github.com/InverseTampere/qsm-fanni-matlab was used, guided by the leaf-on point cloud to define the leaf shape, target leaf area, leaf area density distribution, leaf size distribution, and leaf orientation distribution. The one-hectare model is available online for download (https://bitbucket.org/tree_research/wytham_woods_3d_model/, accessed on 10 February 2019).

The subset used in this study contained 116 trees, including the understory trees, mainly from three species: sycamore maple (Acer pseudoplatanus L.), ash (Fraxinus excelsior), and hazel (Corylus avellana). The tree 3D models were not optimized for use in the DART model, as each tree QSM defined the woody components as a group of cylinders, with each cylinder defined by two vertices and a radius. Thus, the cylinders were reconstructed first in Matlab (version R2021a, The MathWorks Inc., Natick, MA, USA) using the free add-on 'cylinder between two points' function [41], then the cylinders for each tree were merged to build its woody material 3D model. The woody material 3D model and the leaf 3D model of each tree were then grouped to build the tree 3D model, which was ready to be imported into DART.

### 2.2. TLS Wavelengths

The 532 nm green wavelength, utilized in the Leica ScanStation C10 (Leica Geosystems, St. Gallen, Switzerland), and the 670 nm red wavelength, used in the Leica HDS 6100 (Leica Geosystems, St. Gallen, Switzerland), were the only two laser wavelengths identified that were previously linked to chlorophyll content estimation [42,43]. No commercial instruments operating in the red-edge region (690–740 nm) were identified. Most modern TLS instruments tend to utilize either the 1550 nm SWIR or the 1064 nm NIR wavelengths, as both wavelengths are more energy efficient and less scattered by atmospheric particles than shorter wavelengths; thus, good range measurement accuracy can be achieved even in challenging conditions such as fog or smoke [44]. Table 1 shows the wavelengths included in this study and their corresponding TLS instruments.

<table><caption>**Table 1.** The wavelengths included in this study and their corresponding TLS instruments.</caption><thead><tr><td>Wavelength</td><td>TLS Instruments</td></tr></thead><tbody><tr><td>532 nm (green)</td><td>Leica ScanStation C10</td></tr><tr><td>670 nm (red)</td><td>Leica HDS 6100</td></tr><tr><td>808 nm (NIR)</td><td>Leica ScanStation P20 <sup>1</sup></td></tr><tr><td>785 nm (NIR)</td><td>Z+F Imager 5006EX <sup>2</sup>, FARO LS880 HE80 <sup>3</sup></td></tr></tbody></table>
<table><caption>**Table 1. Cont.**</caption><thead><tr><th>Wavelength</th><th>TLS Instruments</th></tr></thead><tbody><tr><td>1064 nm (NIR)</td><td>Topcon GLS-2200 <sup>4</sup>, RIEGL VZ-6000 <sup>5</sup>, Teledyne Optech ILRIS-LR <sup>6</sup>, among others.</td></tr><tr><td>1550 nm (SWIR)</td><td>RIEGL VZ-400, FARO Focus3D X330 <sup>3</sup>, Leica RTC360 <sup>1</sup>, Leica P40 <sup>1</sup>, Leica P50 <sup>1</sup>, among others.</td></tr></tbody></table>

¹ Leica Geosystems, St. Gallen, Switzerland, ² ZF Group, Friedrichshafen, Germany, ³ FARO Technologies, Lake Mary, Florida, USA, ⁴ Topcon Positioning Systems, Tokyo, Japan, ⁵ RIEGL Laser Measurement Systems GmbH, Horn, Austria, and ⁶ Teledyne Optech Incorporated, Toronto, Ontario, Canada.

## 2.3. Chlorophyll Indices

The indices developed in this study were adapted from widely-used optical chlorophyll indices, including the Chlorophyll Index (CI) [45], the NDVI, the GNDVI, and the inverted Green Simple Ratio (GSR) [46]. As three NIR wavelengths were available, all possible NIR and green/red wavelength combinations were tested, resulting in three variations for each index. Furthermore, two additional indices were developed and tested by combining the 532 nm wavelength with the 1550 nm SWIR wavelength in a ratio index and a Normalized Difference Index (NDI). The total number of indices involved in this study was fourteen, as described in Table 2.

<table><caption>**Table 2.** The vegetation indices developed in this study adapted for the available TLS wavelengths.</caption><thead><tr><th>Index</th><th>Formula</th></tr></thead><tbody><tr><td>CI<sub>808</sub></td><td>(ρ<sub>808</sub>/ρ<sub>532</sub>) - 1</td></tr><tr><td>CI<sub>1064</sub></td><td>(ρ<sub>1064</sub>/ρ<sub>532</sub>) - 1</td></tr><tr><td>CI<sub>785</sub></td><td>(ρ<sub>785</sub>/ρ<sub>532</sub>) - 1</td></tr><tr><td>GNDVI<sub>808</sub></td><td>(ρ<sub>808</sub> - ρ<sub>532</sub>)/(ρ<sub>808</sub> + ρ<sub>532</sub>)</td></tr><tr><td>GNDVI<sub>1064</sub></td><td>(ρ<sub>1064</sub> - ρ<sub>532</sub>)/(ρ<sub>1064</sub> + ρ<sub>532</sub>)</td></tr><tr><td>GNDVI<sub>785</sub></td><td>(ρ<sub>785</sub> - ρ<sub>532</sub>)/(ρ<sub>785</sub> + ρ<sub>532</sub>)</td></tr><tr><td>GSR<sub>808</sub></td><td>(ρ<sub>532</sub>/ρ<sub>808</sub>)</td></tr><tr><td>GSR<sub>1064</sub></td><td>(ρ<sub>532</sub>/ρ<sub>1064</sub>)</td></tr><tr><td>GSR<sub>785</sub></td><td>(ρ<sub>532</sub>/ρ<sub>785</sub>)</td></tr><tr><td>NDVI<sub>808</sub></td><td>(ρ<sub>808</sub> - ρ<sub>670</sub>)/(ρ<sub>808</sub> + ρ<sub>670</sub>)</td></tr><tr><td>NDVI<sub>1064</sub></td><td>(ρ<sub>1064</sub> - ρ<sub>670</sub>)/(ρ<sub>1064</sub> + ρ<sub>670</sub>)</td></tr><tr><td>NDVI<sub>785</sub></td><td>(ρ<sub>785</sub> - ρ<sub>670</sub>)/(ρ<sub>785</sub> + ρ<sub>670</sub>)</td></tr><tr><td>Ratio<sub>1550</sub></td><td>(ρ<sub>1550</sub>/ρ<sub>532</sub>)</td></tr><tr><td>NDI<sub>1550</sub></td><td>(ρ<sub>1550</sub> - ρ<sub>532</sub>)/(ρ<sub>1550</sub> + ρ<sub>532</sub>)</td></tr></tbody></table>

ρ refers to leaf apparent reflectance.

It is worth mentioning that popular chlorophyll indices that could not be included in this study due to the absence of a red-edge wavelength were the red-edge NDVI, the MCARI, the red-edge CI, the Normalized Difference Red Edge index (NDRE), and the Leaf Chlorophyll Index (LCI). Furthermore, indices that utilized three or more wavelengths, such as the Chlorophyll Vegetation Index (CVI), were disregarded, as deploying three different TLS instruments in field and combining their data would be unfeasible.

## 2.4. The DART Model Background and Parameters

The DART model [47], developed in the Centre for the Study of the Biosphere from Space (CESBIO) since 1992, simulates the radiation scattering and absorption by the atmosphere and Earth landscape in the visible and infrared regions of the electromagnetic spectrum for any user-defined Earth-atmosphere system [48]. The legacy, standard DART mode, known as DART-FT, uses the discrete ordinates method. It computes radiation propagation and interactions in discrete directions through the scene by tracing iteratively radiation fluxes per cell (voxel). This process can be time consuming and computationally demanding for large, complex scenes [15].
This study used the state-of-the-art DART-Lux mode in the DART model, which has been developed to overcome the limitations of the standard DART-FT mode. DART-Lux is a novel Monte Carlo radiative transfer method utilizing the bidirectional path tracing algorithm of the LuxCoreRender (https://luxcorerender.org) to simulate the bidirectional reflectance factor (BRF) and spectral images rapidly and efficiently even in complex scenes [15]. The method was reported to be capable of reducing both the simulation time and memory requirements by a hundredfold whilst producing consistent results with the DART-FT mode, with a relative error of <1% [15].

To reconstruct the 3D forest scene in DART, the tree 3D models were imported and placed into the scene using their exact coordinates (Figure 1). As the purpose of this study was not to compare the DART model simulation results to actual satellite imagery, generic vegetation and wood spectral profiles from the DART database were used to define the optical properties of the understory and woody components. The spectral profiles are shown in Figures 2 and 3 and were kept constant throughout all the simulations. The leaf optical properties were defined and altered using the integrated PROSPECT model [28] based on the simulations described in Section 2.5. Table 3 displays the other values and settings used to parametrize the DART model. It is worth mentioning that to test the efficiency of the DART-Lux mode, a mid-range laptop with a dated 8-core RYZEN 7 CPU (Advanced Micro Devices, Inc., Santa Clara, CA, USA) and 16 GBs of RAM was used to run the simulations.

<table><caption>**Table 3.** The DART model parameters.</caption><thead><tr><td>Parameter</td><td>Value</td></tr></thead><tbody><tr><td>Spectral bands (nm)</td><td>532, 670, 785, 808, 1064, 1550</td></tr><tr><td>Maximal scattering order <sup>1</sup></td><td>100</td></tr><tr><td>Target sample density per pixel <sup>1</sup></td><td>50</td></tr><tr><td>Sun zenith angle</td><td>32</td></tr><tr><td>Sun azimuth angle</td><td>161</td></tr><tr><td>Atmospheric database</td><td>USSTD76, RURALV23</td></tr><tr><td>Atmospheric geometry</td><td>Manual, mid atmosphere layer 4 km, high atmosphere layer 80 km</td></tr></tbody></table>

<figure><img src="image_6.png" /><figcaption>**Figure 1.** The 3D forest scene reconstructed in the DART model.</figcaption></figure>

<footnote n="1">¹ Determined by increasing the value until no change in simulated reflectance was observed.</footnote>
<figure><img src="image_7.png" /><figcaption>**Figure 2.** The understory spectral profile (DART database); vertical lines represent the six TLS wavelengths of interest.</figcaption></figure>

<figure><img src="image_8.png" /><figcaption>**Figure 3.** Wood spectral profile (DART database); vertical lines represent the six TLS wavelengths of interest.</figcaption></figure>

## 2.5. Simulations

The total number of simulations carried out in this study was 200, divided into two sets of simulations, as described in the following sections.

### 2.5.1. First Set of Simulations

This set of simulations aimed to (1) examine the sensitivity of the six TLS wavelengths involved in this study and the developed VIs to the chlorophyll a + b content, referred to as Chl in the model and (2) investigate the influence of leaf internal structure, LMA, leaf Equivalent Water Thickness (EWT), leaf carotenoid content ($C_{ar}$), and leaf brown pigment content ($C_b$) on the developed VIs. These biochemical and biophysical traits have previously been reported to influence the interaction of radiation with foliage and thus the performance of VIs [32,49]. Leaf internal structure refers to the number, arrangement, and thickness of leaf mesophyll cell layers; it is defined in the model as the leaf structure parameter (N) [32]. LMA is defined as the leaf dry weight divided by its surface area [50], whilst EWT is the amount of water per unit leaf area [51].

Table 4 shows the values of the vegetation traits used in the first set of simulations [28,32]. To carry out the simulations, an average value of each trait was calculated and defined
in the PROSPECT model integrated into DART. Then, to investigate the influence of a certain vegetation trait on the developed VIs, the value of that trait was increased incrementally, as described in Table 4, and the DART model was run at each incremental step while maintaining the remaining leaf parameters unchanged. This resulted in a total of 117 simulations.

<table><caption>**Table 4.** Values of the vegetation traits used in the simulations.</caption><thead><tr><th>Vegetation Trait</th><th>Minimum</th><th>Maximum</th><th>Incremental Step</th></tr></thead><tbody><tr><td>Chl (µg cm<sup>-2</sup>)</td><td>5</td><td>100</td><td>5</td></tr><tr><td>N</td><td>1</td><td>3</td><td>0.1</td></tr><tr><td>LMA (g cm<sup>-2</sup>)</td><td>0.0017</td><td>0.0157</td><td>0.0005</td></tr><tr><td>EWT (g cm<sup>-2</sup>)</td><td>0.004</td><td>0.054</td><td>0.005</td></tr><tr><td>C<sub>ar</sub> (µg cm<sup>-2</sup>)</td><td>1</td><td>25</td><td>1</td></tr><tr><td>C<sub>b</sub></td><td>0</td><td>1</td><td>0.1</td></tr></tbody></table>

## 2.5.2. Second Set of Simulations

This group of simulations aimed to examine the correlation between the developed VIs and the chlorophyll a + b content using realistic combinations of leaf biochemical and biophysical traits. For this, subsets of leaf optical properties from two independent datasets were used: the Leaf Optical Properties Experiment (LOPEX) dataset [52] and the ANGERS dataset [53]. The LOPEX dataset included the collection of 320 leaf samples from 45 plant species acquired in 1993 in the region of Ispra, Italy, whilst the ANGERS dataset contained 276 leaf samples obtained in 2003 from 43 species from the area surrounding Angers, France. For each leaf sample, the datasets provide leaf optical properties (reflectance and transmittance) in addition to biochemical and biophysical measurements. Thus, the two datasets have been widely utilized in deriving and evaluating vegetation indices [28,54,55].

The subsets used in this study included 28 leaf samples from the LOPEX dataset and 55 samples from the ANGERS dataset. The samples were chosen so that they (1) covered a variety of species, (2) covered the whole range of chlorophyll concentrations, and (3) included as much variation as possible in leaf biochemical and biophysical properties. The utilized species included, among others, sycamore maple, filbert (*Corylus maxima* 'Purpurea'), black locust (*Robinia pseudoacacia* L.), European alder (*Alnus glutinosa* L.), and white poplar (*Populus alba* L.). To carry out the simulations, the biochemical and biophysical properties of each leaf sample were defined in the PROSPECT model, and then the DART model was run, resulting in 83 simulations.

## 2.6. Statistical Analysis

Each of the 200 simulations produced plot-level reflectance at the six modelled wavelengths, which was used to calculate the fourteen VIs described in Table 2. To evaluate the sensitivity of a VI to a certain vegetation trait, the Standard Deviation (SD) and the range were computed. However, as the indices had different numerical ranges, their SDs and ranges could not be directly compared. Thus, the Relative SD and Relative Percentage Difference (RPD) were calculated following Equations (1) and (2), respectively. All calculations were carried out in Microsoft Excel (Microsoft 365 Apps for enterprise, Microsoft Corporation, Redmond, WA, USA).

$$ \text{Relative SD (\%)} = (SD/\text{mean}) \times 100, \qquad (1) $$

$$ \text{RPD (\%)} = (\text{range}/\text{mean}) \times 100, \qquad (2) $$

# 3. Results

The speed of the DART-Lux mode was found to be phenomenal, as a simulation that needed approximately 20 min to run using the DART-FT mode only needed 3 min in the DART-Lux mode. Furthermore, by utilizing the sequencer tool, simulation time, following
a base simulation, was cut to <1 min as the tool only needed to run time-consuming steps, such as generating the 3D objects files, once. Memory usage during a simulation ranged between 1 and 1.2 GBs for the DART-Lux mode, in comparison to 9 GBs for the DART-FT mode. The following sections describe the results of the simulations.

### 3.1. Sensitivity of Tested Wavelengths to the Chlorophyll Content

As shown in Figure 4, the 532 nm wavelength showed the highest sensitivity to chlorophyll content as the reflectance dropped by 53.4% between the highest and lowest chlorophyll concentrations tested (Relative *SD* of 24.1%). Although the 670 nm wavelength exhibited the highest Relative *SD* (74.5%) amongst all tested wavelengths, it demonstrated high sensitivity to chlorophyll content only within the range of 5 to 35 µg cm⁻², with a reflectance drop of 73.7% before plateauing. Thus, a vegetation index employing the 670 nm wavelength would be suitable for estimating the chlorophyll content only within this range. The remaining tested wavelengths showed no sensitivity to chlorophyll content, with Relative *SD* values ranging between 0.08% and 0.54%.

<figure><img src="image_9.png" /><figcaption>**Figure 4.** Sensitivity of the tested wavelengths to the chlorophyll content.</figcaption></figure>

### 3.2. Sensitivity of Tested VIs to Chlorophyll Content

Figure 5 displays the relationships between the VIs and chlorophyll content, whilst Table 5 shows the statistical properties of these relationships. The results revealed that all indices were sensitive to chlorophyll content, but to varying degrees. The CIs displayed the highest sensitivity, with a Relative *SD* of 25% and *RPD* of 75%, followed by the GSRs (Relative *SD* of 23% and *RPD* of 72%). The Ratio$_{1550}$ and NDI$_{1550}$ had a Relative *SD* of 22%
and 16%, respectively, and RPD of 71% and 51%, respectively. The NDVIs and GNDVIs showed the least sensitivity to the chlorophyll content. The relationships between the indices and the chlorophyll concentration were linear for the CIs, GSRs, and the Ratio<sub>1550</sub>, but showed nonlinearity in the case of the GNDVIs and NDI<sub>1550</sub>. As for the NDVI group, the indices were saturated at a chlorophyll concentration of approximately 35 µg cm<sup>-2</sup>. Within each group of indices, the performance variations were minor.

<figure><img src="image_10.png" /><figcaption>**Figure 5.** Sensitivity of the tested VIs to the chlorophyll content.</figcaption></figure>

<table><caption>**Table 5.** Statistics of the relationships between the tested VIs and the chlorophyll content.</caption><thead><tr><th>Index</th><th>Relative SD (%)</th><th>RPD (%)</th><th>Index</th><th>Relative SD (%)</th><th>RPD (%)</th></tr></thead><tbody><tr><td>CI<sub>808</sub></td><td>24.68</td><td>78.64</td><td>GNDVI<sub>808</sub></td><td>4.51</td><td>14.72</td></tr><tr><td>CI<sub>1064</sub></td><td>24.70</td><td>79.42</td><td>GNDVI<sub>1064</sub></td><td>4.45</td><td>14.71</td></tr><tr><td>CI<sub>785</sub></td><td>24.79</td><td>79.67</td><td>GNDVI<sub>785</sub></td><td>4.61</td><td>15.22</td></tr><tr><td>GSR<sub>808</sub></td><td>22.47</td><td>71.58</td><td>NDVI<sub>808</sub></td><td>5.37</td><td>22.68</td></tr><tr><td>GSR<sub>1064</sub></td><td>22.53</td><td>72.44</td><td>NDVI<sub>1064</sub></td><td>5.34</td><td>22.52</td></tr><tr><td>GSR<sub>785</sub></td><td>22.54</td><td>72.42</td><td>NDVI<sub>785</sub></td><td>5.51</td><td>23.23</td></tr><tr><td>Ratio<sub>1550</sub></td><td>22.37</td><td>71.43</td><td>NDI<sub>1550</sub></td><td>15.81</td><td>51.20</td></tr></tbody></table>

### 3.3. Sensitivity of Tested VIs to EWT

The results shown in Figure 6 and Table 6 revealed that NDI<sub>1550</sub> and Ratio<sub>1550</sub> were highly influenced by EWT. NDI<sub>1550</sub> experienced a 99% drop in its value as EWT changed between its lowest and highest values, with a Relative SD of 76% and RPD of 230%, whilst
Ratio<sub>1550</sub> decreased by 81% (Relative *SD* of 60% and *RPD* of 192%). Indices that coupled the 532 nm wavelength with either the 808 nm or 785 nm wavelengths were insensitive to EWT. On the other hand, the CI<sub>1064</sub> and the GSR<sub>1064</sub> indices showed some sensitivity to EWT, with a Relative *SD* of 5% and 4%, respectively, and *RPD* of 14% and 13%, respectively.

<figure><img src="image_11.png" /><figcaption>**Figure 6.** Sensitivity of the tested VIs to EWT.</figcaption></figure>

<table><caption>**Table 6.** Statistics of the relationships between the tested VIs and the EWT.</caption><thead><tr><th>Index</th><th>Relative SD (%)</th><th>RPD (%)</th><th>Index</th><th>Relative SD (%)</th><th>RPD (%)</th></tr></thead><tbody><tr><td>CI<sub>808</sub></td><td>0.74</td><td>2.20</td><td>GNDVI<sub>808</sub></td><td>0.14</td><td>0.40</td></tr><tr><td>CI<sub>1064</sub></td><td>4.68</td><td>14.12</td><td>GNDVI<sub>1064</sub></td><td>0.86</td><td>2.58</td></tr><tr><td>CI<sub>785</sub></td><td>0.91</td><td>2.75</td><td>GNDVI<sub>785</sub></td><td>0.17</td><td>0.51</td></tr><tr><td>GSR<sub>808</sub></td><td>0.67</td><td>1.98</td><td>NDVI<sub>808</sub></td><td>0.04</td><td>0.11</td></tr><tr><td>GSR<sub>1064</sub></td><td>4.21</td><td>12.69</td><td>NDVI<sub>1064</sub></td><td>0.25</td><td>0.75</td></tr><tr><td>GSR<sub>785</sub></td><td>0.82</td><td>2.47</td><td>NDVI<sub>785</sub></td><td>0.05</td><td>0.14</td></tr><tr><td>Ratio<sub>1550</sub></td><td>59.84</td><td>192.25</td><td>NDI<sub>1550</sub></td><td>76.49</td><td>229.59</td></tr></tbody></table>

### 3.4. Sensitivity of Tested VIs to the Leaf Structure Parameter (N)

As shown in Figure 7 and Table 7, the ratio indices showed more sensitivity to changes in leaf structure parameter (N) than the normalized difference indices. The CI and GSR groups were most influenced by N variation with a Relative *SD* of approximately 26% and 23%, respectively, and *RPD* of approximately 88% and 78%, respectively. The Ratio<sub>1550</sub> and NDI<sub>1550</sub> followed, with a Relative *SD* of 11% and 9%, respectively, and *RPD* of 37% and
29%, respectively. Among all tested indices, the NDVIs successfully normalized the effects of leaf internal structure, whilst the GNDVI group minimized these effects to a certain extent, with an observed Relative *SD* of 5% and *RPD* of 17%.

<figure><img src="image_12.png" /><figcaption>**Figure 7.** Sensitivity of the tested VIs to leaf structure parameter (N).</figcaption></figure>

<table><caption>**Table 7.** Statistics of the relationships between the tested VIs and N.</caption><thead><tr><th>Index</th><th>Relative SD (%)</th><th>RPD (%)</th><th>Index</th><th>Relative SD (%)</th><th>RPD (%)</th></tr></thead><tbody><tr><td>CI<sub>808</sub></td><td>26.13</td><td>88.42</td><td>GNDVI<sub>808</sub></td><td>5.28</td><td>17.13</td></tr><tr><td>CI<sub>1064</sub></td><td>26.22</td><td>88.73</td><td>GNDVI<sub>1064</sub></td><td>5.20</td><td>16.88</td></tr><tr><td>CI<sub>785</sub></td><td>25.95</td><td>87.72</td><td>GNDVI<sub>785</sub></td><td>5.31</td><td>17.21</td></tr><tr><td>GSR<sub>808</sub></td><td>23.04</td><td>77.94</td><td>NDVI<sub>808</sub></td><td>0.60</td><td>1.82</td></tr><tr><td>GSR<sub>1064</sub></td><td>23.18</td><td>78.42</td><td>NDVI<sub>1064</sub></td><td>0.60</td><td>1.81</td></tr><tr><td>GSR<sub>785</sub></td><td>22.84</td><td>77.20</td><td>NDVI<sub>785</sub></td><td>0.60</td><td>1.83</td></tr><tr><td>Ratio<sub>1550</sub></td><td>11.28</td><td>36.62</td><td>NDI<sub>1550</sub></td><td>9.18</td><td>29.47</td></tr></tbody></table>

### 3.5. Sensitivity of Tested VIs to the LMA

The results displayed in Figure 8 and Table 8 showed similarities to the leaf structure parameter results, as N and LMA are known to be highly correlated [32]. The ratio indices were more influenced by LMA variation than the normalized difference indices, with the CI group (Relative *SD* of 13% and *RPD* of 42%) and the GSR group (Relative *SD* of 11% and *RPD* of 37%) being the most sensitive to such variation. The 1550 nm indices followed, whilst the GNDVI group of indices managed to minimize the LMA effects (Relative *SD*
of 3%, and RPD of 9%). The NDVI group was the least influenced by the LMA variation (Relative SD of 1%, and RPD of 3%).

<figure><img src="image_13.png" /><figcaption>**Figure 8.** Sensitivity of the tested VIs to LMA.</figcaption></figure>

<table><caption>**Table 8.** Statistics of the relationships between the tested VIs and LMA.</caption><thead><tr><th>Index</th><th>Relative SD (%)</th><th>RPD (%)</th><th>Index</th><th>Relative SD (%)</th><th>RPD (%)</th></tr></thead><tbody><tr><td>CI<sub>808</sub></td><td>12.61</td><td>42.12</td><td>GNDVI<sub>808</sub></td><td>2.64</td><td>8.71</td></tr><tr><td>CI<sub>1064</sub></td><td>12.63</td><td>42.34</td><td>GNDVI<sub>1064</sub></td><td>2.60</td><td>8.64</td></tr><tr><td>CI<sub>785</sub></td><td>12.33</td><td>41.29</td><td>GNDVI<sub>785</sub></td><td>2.61</td><td>8.66</td></tr><tr><td>GSR<sub>808</sub></td><td>11.11</td><td>37.09</td><td>NDVI<sub>808</sub></td><td>0.91</td><td>3.01</td></tr><tr><td>GSR<sub>1064</sub></td><td>11.15</td><td>37.38</td><td>NDVI<sub>1064</sub></td><td>0.90</td><td>2.98</td></tr><tr><td>GSR<sub>785</sub></td><td>10.85</td><td>36.31</td><td>NDVI<sub>785</sub></td><td>0.91</td><td>3.00</td></tr><tr><td>Ratio<sub>1550</sub></td><td>7.61</td><td>24.96</td><td>NDI<sub>1550</sub></td><td>6.43</td><td>21.03</td></tr></tbody></table>

### 3.6. Sensitivity of Tested VIs to the Variation in Carotenoids

Similar to the observed effects of N and LMA on the tested indices, the results revealed that carotenoid concentration variations had an impact on all tested indices, except the NDVI group that was insensitive to such effects. Additionally, the ratio indices were more sensitive to the carotenoid variation, with the CI group, followed by the GSR group, being the most affected (Relative SD of 38% and RPD of 122% for the CIs, and 34% and 109% for the GSRs). The Ratio<sub>1550</sub> and NDI<sub>1550</sub> were also severely influenced by the carotenoid concentration variations, whilst the GNDVI group of indices showed the least sensitivity (Relative SD of 9%, and RPD of 30%). Figure 9 and Table 9 summarize these results.
<figure><img src="image_14.png" /><figcaption>**Figure 9.** Sensitivity of the tested VIs to the carotenoids.</figcaption></figure>

<table><caption>**Table 9.** Statistics of the relationships between the tested VIs and the carotenoids.</caption><thead><tr><th>Index</th><th>Relative SD (%)</th><th>RPD (%)</th><th>Index</th><th>Relative SD (%)</th><th>RPD (%)</th></tr></thead><tbody><tr><td>CI<sub>808</sub></td><td>37.66</td><td>121.27</td><td>GNDVI<sub>808</sub></td><td>8.80</td><td>29.93</td></tr><tr><td>CI<sub>1064</sub></td><td>37.70</td><td>121.42</td><td>GNDVI<sub>1064</sub></td><td>8.64</td><td>29.32</td></tr><tr><td>CI<sub>785</sub></td><td>37.85</td><td>121.90</td><td>GNDVI<sub>785</sub></td><td>8.94</td><td>30.33</td></tr><tr><td>GSR<sub>808</sub></td><td>33.85</td><td>109.00</td><td>NDVI<sub>808</sub></td><td>0.03</td><td>0.12</td></tr><tr><td>GSR<sub>1064</sub></td><td>33.96</td><td>109.36</td><td>NDVI<sub>1064</sub></td><td>0.01</td><td>0.02</td></tr><tr><td>GSR<sub>785</sub></td><td>33.96</td><td>109.37</td><td>NDVI<sub>785</sub></td><td>0.01</td><td>0.02</td></tr><tr><td>Ratio<sub>1550</sub></td><td>33.81</td><td>109.20</td><td>NDI<sub>1550</sub></td><td>31.18</td><td>104.39</td></tr></tbody></table>

### 3.7. Sensitivity of Tested VIs to the Brown Pigments

The results revealed that indices involving the 1064 nm and 1550 nm wavelengths were more sensitive to changes in brown pigments concentration than the remaining indices. The NDVI group was an exception, as NDVI<sub>1064</sub> successfully normalized the brown pigments' effects. Among all tested indices, CI<sub>1064</sub>, Ratio<sub>1550</sub>, GSR<sub>1064</sub>, and NDI<sub>1550</sub> were the most influenced by the variation in brown pigments. On the other hand, the remaining indices showed low sensitivity. Figure 10 and Table 10 show these results.
<figure><img src="image_15.png" /><figcaption>**Figure 10.** Sensitivity of the tested VIs to the brown pigments.</figcaption></figure>

<table><caption>**Table 10.** Statistics of the relationships between the tested VIs and the brown pigments.</caption><thead><tr><th>Index</th><th>Relative SD (%)</th><th>RPD (%)</th><th>Index</th><th>Relative SD (%)</th><th>RPD (%)</th></tr></thead><tbody><tr><td>CI<sub>808</sub></td><td>2.20</td><td>6.21</td><td>GNDVI<sub>808</sub></td><td>0.39</td><td>1.09</td></tr><tr><td>CI<sub>1064</sub></td><td>17.82</td><td>53.61</td><td>GNDVI<sub>1064</sub></td><td>2.55</td><td>7.73</td></tr><tr><td>CI<sub>785</sub></td><td>1.42</td><td>4.50</td><td>GNDVI<sub>785</sub></td><td>0.26</td><td>0.83</td></tr><tr><td>GSR<sub>808</sub></td><td>1.98</td><td>5.61</td><td>NDVI<sub>808</sub></td><td>1.12</td><td>3.41</td></tr><tr><td>GSR<sub>1064</sub></td><td>16.53</td><td>49.73</td><td>NDVI<sub>1064</sub></td><td>0.01</td><td>0.02</td></tr><tr><td>GSR<sub>785</sub></td><td>1.27</td><td>4.03</td><td>NDVI<sub>785</sub></td><td>1.44</td><td>4.36</td></tr><tr><td>Ratio<sub>1550</sub></td><td>16.91</td><td>50.84</td><td>NDI<sub>1550</sub></td><td>9.18</td><td>27.78</td></tr></tbody></table>

### 3.8. The LOPEX and ANGERS Datasets Results

Figure 11 shows the relationships between the tested indices and chlorophyll content for the LOPEX dataset, whilst Figure 12 shows the same relationships for the ANGERS dataset. Figure 13 combines the two datasets. Table 11 shows the coefficient of determination ($R^2$) values of the relationships, the highest $R^2$ of each relationship after testing linear and nonlinear fitting. The results revealed that the Ratio$_{1550}$ and the NDI$_{1550}$ had moderate correlation with the chlorophyll content, with an $R^2$ of 0.46 and 0.52, respectively, in LOPEX, 0.56 and 0.53, respectively, in ANGERS, and 0.53 and 0.51, respectively, in the combined datasets. The NDVIs displayed low to average correlations with the chlorophyll content, with $R^2 < 0.50$ in the LOPEX, and around 0.50 in the ANGERS and the combined datasets. Also, the NDVIs demonstrated saturation around a chlorophyll content of 35 µg cm$^{-2}$. The
remaining indices showed stronger correlation with chlorophyll concentration, but the results varied between the two datasets. For the LOPEX dataset, the GNDVIs displayed higher correlation (R² between 0.70 and 0.74) than the CIs and GSRs (R² between 0.61 and 0.64), whilst the CI and GSR groups had slightly higher correlation than the GNDVI group in the ANGERS dataset (R² between 0.74 and 0.76 for the CIs and GSRs, and between 0.71 and 0.74 for the GNDVIs). However, when the two datasets were combined, the three groups of indices showed similar results. Overall, the GNDVIs showed the most consistent performance in the two datasets. Furthermore, in the three groups, the 1064 nm indices showed slightly lower correlation than the 808 nm and 785 nm indices.

<table><caption>**Table 11.** Coefficient of determination R² for the relationships between tested indices and chlorophyll content for LOPEX, ANGERS, and the two datasets combined.</caption><thead><tr><th>Index</th><th>LOPEX</th><th>ANGERS</th><th>Combined Datasets</th></tr></thead><tbody><tr><td>CI<sub>808</sub></td><td>0.64</td><td>0.75</td><td>0.73</td></tr><tr><td>CI<sub>1064</sub></td><td>0.61</td><td>0.74</td><td>0.72</td></tr><tr><td>CI<sub>785</sub></td><td>0.63</td><td>0.76</td><td>0.73</td></tr><tr><td>GNDVI<sub>808</sub></td><td>0.74</td><td>0.73</td><td>0.74</td></tr><tr><td>GNDVI<sub>1064</sub></td><td>0.70</td><td>0.71</td><td>0.72</td></tr><tr><td>GNDVI<sub>785</sub></td><td>0.72</td><td>0.74</td><td>0.74</td></tr><tr><td>GSR<sub>808</sub></td><td>0.64</td><td>0.75</td><td>0.73</td></tr><tr><td>GSR<sub>1064</sub></td><td>0.61</td><td>0.74</td><td>0.72</td></tr><tr><td>GSR<sub>785</sub></td><td>0.63</td><td>0.76</td><td>0.73</td></tr><tr><td>NDVI<sub>808</sub></td><td>0.46</td><td>0.51</td><td>0.52</td></tr><tr><td>NDVI<sub>1064</sub></td><td>0.42</td><td>0.49</td><td>0.50</td></tr><tr><td>NDVI<sub>785</sub></td><td>0.45</td><td>0.51</td><td>0.52</td></tr><tr><td>Ratio<sub>1550</sub></td><td>0.46</td><td>0.56</td><td>0.53</td></tr><tr><td>NDI<sub>1550</sub></td><td>0.52</td><td>0.53</td><td>0.51</td></tr></tbody></table>

<figure><img src="image_16.png" /><figcaption>**Figure 11.** Relationships between tested VIs and chlorophyll content for LOPEX dataset.</figcaption></figure>
The charts combining the results of the two datasets suggested that leaves with a structure parameter (N) > 2 (five leaves out of eighty-three leaves) seemed to deviate from the relationships and have their own trendline, as displayed in Figure 13. Thus, these leaves were excluded and the R² recalculated, revealing a significant increase in the correlation for all indices, as shown in Table 12. The GNDVI group of indices displayed the highest correlation to chlorophyll content (R² between 0.85 and 0.87), followed by the CIs and GSRs (R² between 0.81 and 0.83). In the three groups, even after excluding leaves with N > 2, the 1064 nm indices (GNDVI<sub>1064</sub>, CI<sub>1064</sub>, and GSR<sub>1064</sub>) displayed slightly lower correlation than the 808 nm and 785 nm indices. On the other hand, the correlation between the NDVIs, Ratio<sub>1550</sub>, and NDI<sub>1550</sub>, although improved after excluding leaves with N > 2, remained at a moderate level (R² between 0.58 and 0.60). The NDI<sub>1550</sub> showed the lowest observed correlation with an R² of 0.58, whilst GNDVI<sub>808</sub> and GNDVI<sub>785</sub> displayed the highest correlation with chlorophyll content (R² = 0.87). The relationships between the GNDVIs and the chlorophyll concentration were nonlinear before and after the exclusion of leaves with N > 2. As for the NDVI group, the indices showed nonlinearity, before saturating at a chlorophyll concentration of approximately 35 µg cm<sup>-2</sup>. The relationships between the remaining indices and the chlorophyll content were linear.

<figure><img src="image_17.png" /><figcaption>**Figure 12.** Relationships between tested VIs and chlorophyll content for ANGERS dataset.</figcaption></figure>
<figure><img src="image_18.png" /><figcaption>**Figure 13.** Relationships between tested VIs and chlorophyll content for LOPEX and ANGERS datasets combined; leaves with N > 2 are highlighted with purple boxes.</figcaption></figure>

<table><caption>**Table 12.** Coefficient of determination R² for the relationships between tested indices and chlorophyll content for LOPEX and ANGERS datasets combined, before and after excluding the five leaves with N > 2.</caption><thead><tr><th>Index</th><th>Before</th><th>After</th></tr></thead><tbody><tr><td>CI<sub>808</sub></td><td>0.73</td><td>0.83</td></tr><tr><td>CI<sub>1064</sub></td><td>0.72</td><td>0.81</td></tr><tr><td>CI<sub>785</sub></td><td>0.73</td><td>0.83</td></tr><tr><td>GNDVI<sub>808</sub></td><td>0.74</td><td>0.87</td></tr><tr><td>GNDVI<sub>1064</sub></td><td>0.72</td><td>0.85</td></tr><tr><td>GNDVI<sub>785</sub></td><td>0.74</td><td>0.87</td></tr><tr><td>GSR<sub>808</sub></td><td>0.73</td><td>0.83</td></tr><tr><td>GSR<sub>1064</sub></td><td>0.72</td><td>0.81</td></tr><tr><td>GSR<sub>785</sub></td><td>0.73</td><td>0.83</td></tr><tr><td>NDVI<sub>808</sub></td><td>0.52</td><td>0.60</td></tr><tr><td>NDVI<sub>1064</sub></td><td>0.50</td><td>0.59</td></tr><tr><td>NDVI<sub>785</sub></td><td>0.52</td><td>0.60</td></tr><tr><td>Ratio<sub>1550</sub></td><td>0.53</td><td>0.59</td></tr><tr><td>NDI<sub>1550</sub></td><td>0.51</td><td>0.58</td></tr></tbody></table>

## 4. Discussion

The speed of the DART-Lux mode in the DART model and its ability to run hundreds of simulations efficiently on mid-range machines, such as the one utilized in this study, using a
complex forest scene can allow wider utilization of 3D RTMs and realistic vegetation stands, derived from TLS data, for various applications. Furthermore, the model's efficiency can allow broader groups of researchers to experiment with 3D RTMs for different purposes. The model's efficiency was also highlighted by Regaieg et al. [56] for simulating solar-induced chlorophyll fluorescence (SIF) of large agriculture and forest scenes that DART-FT failed to simulate.

For the tested VIs, the results showed that the indices combining the 532 nm wavelength with the 1550 nm wavelength (Ratio<sub>1550</sub> and NDI<sub>1550</sub>) were not suitable for Chlorophyll content estimation despite their high sensitivity to the chlorophyll concentration (Section 3.2). This was a result of the indices being more sensitive to the change in leaf water content than to the change in chlorophyll content (Table 6). The 1550 nm wavelength has been previously utilized in EWT estimation because of its high sensitivity to the change in leaf water content [31,34,57]. Thus, in a site with high variation in leaf water content, the Ratio<sub>1550</sub> and NDI<sub>1550</sub> would be detecting the differences in EWT rather than the desired chlorophyll content variation. This was the main reason for the poor correlation between the indices and the chlorophyll content in the LOPEX and the ANGERS datasets, as the subsets of the two datasets used in this study exhibited high variation in EWT. EWT varied between 0.005 g cm<sup>-2</sup> and 0.036 g cm<sup>-2</sup> in the LOPEX dataset, and between 0.006 g cm<sup>-2</sup> and 0.034 g cm<sup>-2</sup> in the ANGERS dataset.

Although the NDVI has been widely adapted in measuring canopy greenness and chlorophyll content [58,59], the NDVI of the 670 nm and either the 808 nm, 785 nm, or 1064 nm wavelength displayed low to average correlation with the chlorophyll content when applied to the LOPEX and ANGERS datasets. This was despite the observed ability of the indices to normalize the leaf structural and LMA effects, and the indices being almost insensitive to EWT, carotenoids, and brown pigments. The reason for the poor correlation was the saturation of the 670 nm wavelength at around 35 µg cm⁻² chlorophyll concentration, and the saturation of the NDVIs as a result, whilst leaf samples in the subsets of the LOPEX and ANGERS datasets covered a broad range of chlorophyll content (8 to 89 µg cm⁻²). Saha et al. [43] also reported the average correlation between NDVI of two laser wavelengths (660 nm and 905 nm) and tomato fruit (Solanum lycopersicum) chlorophyll content (R² = 60%), whilst Gao et al. [7] reported the saturation of the NDVI at around 40 µg cm⁻² chlorophyll concentration. Thus, the NDVIs might be suitable for chlorophyll estimation in sites with species known to have lower chlorophyll concentration (<35 µg cm⁻²). However, the data in the LOPEX and ANGERS datasets suggested that this may be challenging, as leaves within individual species displayed high variability in chlorophyll content. For instance, the chlorophyll concentration for sycamore maple leaves varied between 5 and 107 µg cm⁻².

The GNDVI, CI, and GSR, which combined the 532 nm wavelength with either the 808 nm wavelength, 785 nm wavelength, or 1064 nm wavelength, can successfully lead to chlorophyll content estimation, even in a mixed species site, as shown by the LOPEX and ANGERS dataset results. The GNDVIs were the most consistent among the tested indices. Furthermore, indices employing the 808 nm or 785 nm wavelengths slightly outperformed those utilizing the 1064 nm wavelength, as the 1064 nm wavelength has been reported to have some sensitivity to the leaf water content [31].

Although the results of the simulations displayed in Section 3.4, Section 3.5, and Section 3.6 showed that leaf structure parameter (N), LMA, and carotenoids influenced the GNDVIs, CIs, and GSRs, with variations in N and carotenoids severely impacting the indices, the values used in the simulations covered the whole range of such vegetation traits [28], which was unlikely to occur in a real-life scenario. For instance, when the ANGERS dataset was analyzed, it was revealed that amongst the measured 276 leaf samples, only 12 leaves had an N > 2, two leaves had an N value less than 1.1, whilst 262 leaves from 40 species had an N value between 1.2 and 2. Similar observations were reported in Wytham Woods, where all species had an N varying between 1.1 and 2 [36]. Nevertheless, in case of the presence of species known for their thicker leaves in a mixed species site,
those species would require their own chlorophyll estimation relationship, as using a
general relationship would significantly underestimate their chlorophyll content. As for the
carotenoids, it was found that 70% of leaves in ANGERS dataset had carotenoids between
4 and 11 µg cm⁻², in comparison to the 1–25 µg cm⁻² range used in the simulations.

Although this study has paved the way for estimating chlorophyll content in 3D
in heterogeneous sites by introducing suitable indices and TLS instruments, RTMs have
been designed to simulate passive remote sensing products [23]. That is, experiments that
include collecting leaf samples and scanning them with the actual TLS instruments are
needed to investigate the impacts of the instrumental effects and the incidence angle of the
laser beam on the proposed chlorophyll indices. That said, some recent studies have shown
good agreement between the performance of spectral VIs and that of their corresponding
laser VIs for water content estimation [31] and for chlorophyll content estimation [43,60].

Additionally, approaches to combine the data from the two different TLS instruments to generate 3D chlorophyll estimates at the canopy and plot levels need to be developed. For this, the techniques successfully utilized to map forest canopy water content in 3D can be used as guidance [30,31]. And based on those studies, coupling the data from the Leica ScanStation C10 (532 nm) and the Leica ScanStation P20 (808 nm) in a GNDVI, CI, or GSR might be more feasible than coupling the data from the Leica ScanStation C10 and the instruments operating on the 785 nm or 1064 nm wavelengths, as the Leica ScanStation C10 and ScanStation P20 are from the same manufacturer and have a relatively similar design and laser beam exit locations, thus simplifying the process of aligning the point-clouds from the two scanners.

Despite the promising results reached in this study, some limitations may hinder the
retrieval of 3D chlorophyll distribution using commercial TLS instruments. The TLS scan-
ners found to be suitable for chlorophyll estimation are dated and no longer in production,
especially the Leica ScanStation C10 and ScanStation P20 instruments, making them harder
to find and utilize. Furthermore, the Leica ScanStation C10 point-cloud density is low
(acquisition rate of 50,000 points per second) in comparison to modern TLS instruments.
Occlusion is another limitation, especially in dense forests where the lower canopy lay-
ers will partly or fully block the laser beams, limiting the number of laser beam returns
acquired from the upper canopy layers. A possible solution to this issue is to utilize multi-
spectral airborne LiDAR instruments equipped with suitable wavelengths for chlorophyll
estimation. An example is the RIEGL VQ-1560i-DW scanner (RIEGL Laser Measurement
Systems GmbH, Horn, Austria), operating at 532 nm and 1064 nm wavelengths.

5. Conclusions

In this study, fourteen VIs were developed for 3D chlorophyll estimation using six
wavelengths utilized in commercial TLS instruments (532 nm, 670 nm, 785 nm, 808 nm,
1064 nm, and 1550 nm). The indices were based on popular optical chlorophyll VIs,
including the CI, the GSR, the NDVI, and the GNDVI. They were designed by carrying out
200 simulations using the novel DART-Lux mode in the DART model, a realistic mixed-
species 3D forest stand, and leaf biochemical and biophysical traits retrieved from the
LOPEX and ANGERS datasets. The results showed that coupling the 532 nm wavelength,
employed in the Leica ScanStation C10 instrument, with either the 808 nm wavelength (the
Leica ScanStation P20) or the 785 nm wavelength (the Z+F Imager 5006EX or the FARO
LS880 HE80) in a GNDVI showed a strong correlation to the chlorophyll content. The CIs
and GSRs of the same wavelengths also displayed promising results, but their performance
was inconsistent between the two datasets. Although the proposed VIs have the potential to
generate canopy 3D chlorophyll estimates, future experiments to investigate the influence
of the incidence angle of the laser beams on their performance, and to develop methods to
couple the data from multiple TLS instruments are still needed. If successfully achieved, the
retrieval of 3D chlorophyll estimates can allow the examination of its distribution within the
canopy across light and height gradients at high spatial and temporal resolutions, leading
to more accurate modelling of carbon fluxes, energy balance, and primary productivity.
Furthermore, the 3D estimates at plot level can be used in the calibration and validation of optical satellite chlorophyll estimation models by mapping the chlorophyll distribution in the upper canopy layers, which are known to dominate the satellite received signal.

**Author Contributions:** Conceptualization, A.E., R.G. and A.S.; methodology, A.E., R.G., J.-P.G.-E. and A.S.; software, J.-P.G.-E. and A.E.; validation, A.E. and J.-P.G.-E.; formal analysis, A.E. and J.-P.G.-E.; investigation, A.E., M.S., R.G. and A.S.; data curation, A.E. and M.S.; writing—original draft preparation, A.E. and M.S.; writing—review and editing, A.E., R.G., M.S., J.-P.G.-E. and A.S.; visualization, A.E. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Data Availability Statement:** All datasets needed to repeat the experiments described in this study are publicly available for download at https://drive.google.com/file/d/1VYBeUGyx_P9AhW-X12twZiWb5gyEcemi/view?usp=sharing.

**Conflicts of Interest:** The authors declare no conflicts of interest.

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