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Article

Simulation and Analysis of Bidirectional Reflection Factors of Southern Evergreen Fruit Trees Based on 3D Radiative Transfer Model

1
College of Agronomy, Hebei Agricultural University, Baoding 071001, China
2
Key Lab of Guangdong for Utilization of Remote Sensing and Geographical Information System, Guangdong Open Laboratory of Geospatial Information Technology and Application, Research Center of Guangdong Province for Engineering Technology Application of Remote Sensing Big Data, Guangzhou Institute of Geography, Guangdong Academy of Sciences, Guangzhou 510070, China
3
School of Civil Engineering and Geomatics, Shandong University of Technology, Zibo 255000, China
4
Faculty of Geographical Science, Beijing Normal University, Beijing 100875, China
5
Guangdong Provincial Key Laboratory of Applied Botany, Key Laboratory of Vegetation Restoration and Management of Degraded Ecosystems, South China Botanical Garden, Chinese Academy of Sciences, Guangzhou 510650, China
6
Guangdong Laboratory for Lingnan Modern Agriculture, College of Horticulture, South China Agricultural University, Guangzhou 510642, China
*
Author to whom correspondence should be addressed.
Horticulturae 2024, 10(8), 790; https://doi.org/10.3390/horticulturae10080790
Submission received: 11 June 2024 / Revised: 23 July 2024 / Accepted: 24 July 2024 / Published: 26 July 2024

Abstract

:
The canopy of perennial evergreen fruit trees in southern China has a unique Bidirectional Reflectance Factor (BRF) due to its complex multi-branch structure and density changes. This study aimed to address the lack of clarity regarding the changes in BRF of evergreen fruit trees in southern China. Litchi, a typical fruit tree in this region, was chosen as the subject for establishing a three-dimensional (3D) real structure model. The canopy BRF of litchi was simulated under different leaf components, illumination geometry, observed geometry, and leaf area index (LAI) using a 3D radiation transfer model. The corresponding changes in characteristics were subsequently analyzed. The findings indicate that the chlorophyll content and equivalent water thickness of leaves exert significant influences on canopy BRF, whereas the protein content exhibit relatively weak effects. Variation in illumination and observation geometry results in the displacement of hotspots, with the solar zenith angle and view zenith angle exerting significant influence on the BRF. As the LAI of the litchi orchard increases, the distribution of hotspots becomes more concentrated, and the differences in angle information are relatively smaller when observed from multiple angles. With the increase in LAI in litchi orchards, the BRF on the principal plane would be saturated, but observation at hotspots could alleviate this phenomenon. The above analysis provides a reference for quantitative inversion of vegetation parameters using remote sensing monitoring information of typical perennial evergreen fruit trees.

1. Introduction

The reflectance of vegetation canopy is non-Lambertian, and it is closely influenced by the ground, leaf optical properties, canopy structure, observed geometry, and illumination geometry [1]. Nicodemus et al. proposed the Bidirectional Reflectance Distribution Function (BRDF) to quantitatively characterize this property, reflecting spatial structural information of target reflectance spectra. This laid the theoretical foundation for implementing multi-angle remote sensing [2]. Considering the bidirectional reflection characteristics of vegetation will increase the difficulty and complexity of remote sensing models. Still, it is an inevitable process for developing remote sensing of vegetation from qualitative to quantitative [3].
Multi-angle observation is a crucial method for accurately acquiring canopy bidirectional reflection information. However, research based on ground-measured multi-angle data typically only applies to low vegetation and presents challenges when applied to tall trees. Although basic equipment can achieve forest canopy observation, it faces difficulties in observing the same area from multiple angles [4]. The development of unmanned aerial vehicle (UAV) hyperspectral multi-angle observation and a remote sensing mechanism model brings new opportunities for studying the bidirectional reflection characteristics of tall vegetation [5].
The remote sensing mechanism model is a crucial tool for analyzing the bidirectional reflection characteristics of vegetation. The traditional model, which substitutes a heterogeneous canopy with a horizontally uniform canopy, fails to consider the roles of non-leaf organs, the spatial distances between vegetation components, and the phenomena of non-random distribution [5]. It may cause significant deviations in the simulated canopy bidirectional reflectance [6]. Geometric optics models can describe the 3D structure of tree canopies, but they cannot characterize multiple scattering inside the canopy as the radiative transfer equation does [1]. Since the 3D radiative transfer model takes into account the multi-scale canopy structure, it is more suitable for the radiative transfer simulation of heterogeneous canopy with a large number of shadows and branching changes [7]. Zhao et al. used the multiple-layer canopy reflectance model (MRTM) to simulate the vertical distribution of spike characteristics and leaf characteristics of winter wheat canopy reflectance [8]. Malenovsky et al. successfully used DART to invert leaf chlorophyll content from imaging spectra [9]. Qi et al. developed a 3D radiation transmission model LESS (LargE-Scale remote sensing data and image Simulation framework) based on a ray tracing algorithm [10]. The model accurately reconstructs a 3D real scene structure using triangle meshes or turbid media, taking into full consideration the spectrum and structural characteristics of various vegetation components. This not only enables the expression of a real scene structure, but also efficient simulation of large scenes, with clear physical significance [11]. This provides a reliable tool for understanding the mechanisms of radiation interaction with tall vegetation canopies. It also enables multi-angle observations of tall vegetation canopies, meeting the demand for simulating complex scenes [12,13].
In the subtropical region of South China, perennial evergreen fruit trees are tall [14]. Among these, litchi is widely cultivated, with its yield and planting area ranking first in the world [15]. The litchi industry not only provides direct economic income for fruit farmers, but also stimulates the local economy through related industrial chains, such as processing, transportation, and sales [16]. Litchi tree canopies are mostly round-headed with numerous branches that grow vigorously and often intersect [17], resulting in a complex spatial structure and variable canopy density that significantly impacts light absorption and reflection. Currently, there is a lack of comprehensive studies on the BRF of these perennial evergreen fruit trees, which possess intricate spatial structures. However, the development of the precision fruit industry urgently needs to carry out relevant remote sensing monitoring applications based on clarifying the bidirectional reflection characteristics of its canopy. The development of the 3D radiative transfer model provides a powerful tool for in-depth analysis of the changes in the BRF. This study utilizes litchi trees as an example to analyze the effects of leaf parameters, structural parameters, illumination geometry, and observation geometry on the BRF of the litchi canopy, employing a 3D radiative transfer model. The aim is to provide theoretical references for the remote sensing monitoring of perennial evergreen fruit trees in southern China.

2. Materials and Methods

2.1. Field Data Collection

This study was conducted in the litchi orchard located on the eastern slope of Longhua Town, Huizhou City, Guangdong Province, China (23°3′–23°7′ N, 113°9′–115°5′ E). The canopy spectra of litchi trees were collected using an ASD FieldSpec3 spectrometer (Analytical Spectral Devices, Inc., Boulder, CO, USA). Data collection took place under clear, cloudless conditions between 10:00 and 14:00 Beijing Time in May 2018. Canopy spectra were obtained from 16 litchi trees. The measurements employed a 10° fiber optic lens, with the probe positioned 0.5 m above the canopy to ensure the tree crown filled the probe’s field of view. Each sampling point involved observations from four directions around the litchi tree, with 10 spectral curves collected per observation at intervals of 0.1 s. The average of the 40 spectral curves from the 4 directions was used as the canopy spectrum for the sample point. To eliminate noise and the strong absorption effects of water on the spectra, data in the ranges of 350–399 nm and 1801–1959 nm were excluded. The processed data were then denoised using the Savitzky–Golay (SG) to reduce noise interference. Additionally, the LAI-2200C Plant Canopy Analyzer (LI-COR, Inc., Lincoln, NE, USA) was used to measure the LAI of the litchi canopy. Multiple measurements were taken under the canopy around the litchi tree, and the average value was used as the LAI for the litchi canopy in this study.

2.2. Scenario Construction

The 3D model of litchi single wood used in this study was obtained from https://www.cgtrader.com/3d-models/plant/other/xfrogplants-litchi-litchi-chinensis, accessed on 20 June 2023. The component elements of the litchi tree were represented in triangle meshes to realistically depict the leaves and branches of the canopy. The crown size of a single litchi tree with strong growth, good management, and mature age in an orchard was adjusted in Blender (V2.83 https://www.blender.org/, accessed on 28 June 2023), resulting in a tree height of 3.95 m and a crown width of 5.21 m (Figure 1a). By adjusting the row and column spacing of litchi trees in the scene, a row structure was created to alter the LAI of the orchard (Figure 1b–e).

2.3. BRF Simulation Based on 3D Radiation Transfer Model

2.3.1. Radiation Transfer Model

This study employs the PROSPECT-PRO to simulate leaf reflectance and transmittance. This model separates the protein parameters from other carbon-based constituents such as cellulose, lignin, hemicellulose, starch, and sugars [18]. The simulations using PROSPECT-PRO were conducted in MATLAB (R2023b), generating corresponding leaf reflectance and transmittance by altering leaf parameters.
At the canopy scale, we used the 3D radiation transmission model LESS, which constructs a realistic 3D scene using triangular meshes. LESS implements forward photon tracing and backward path tracing algorithms based on the origin of the light to simulate photon propagation throughout the entire scene. By recording photon energy, it can simulate scene reflectance and accurately describe the spatial heterogeneity of the canopy [10]. The simulation of canopy reflectance is performed in the visual interface of LESS, which includes a scene display area and a parameter setting area. The parameter setting area encompasses several sub-regions such as sensors, observation geometry, incident light, optical properties, and terrain. We imported the leaf reflectance and transmittance simulated using PROSPECT-PRO into LESS and assigned them to leaf components. Additionally, we adjusted observation and illumination geometry and wavelength bands as needed within the interface. The reflectance of the soil in this study used ‘dark_soil_mollisol’ provided by LESS.
A local parameter sensitivity analysis was used in this study to examine the impact of each parameter on the spectral regions and identify the spectral region most sensitive to changes in input parameters [7]. A local sensitivity analysis of 10 parameters was performed, using LESS (LESS-2.1.4-2023-8-22) to evaluate the impact of each parameter on spectral reflectance. The value range, change step, and fixed value settings of each parameter are shown in Table 1. The range of leaf parameters for the model input was determined by previous studies [7,18,19,20].

2.3.2. Setting Geometric Parameters

The bidirectional reflection characteristics of the ground object are shown in Figure 2, where the AEC plane is the principal plane and the BED is the vertical principal plane. During the principal plane observation, the view zenith angle was measured at intervals of 10°, ranging from 60° (−60°) backward to 60° (+60°) forward. Set the solar zenith angle to 45° and the solar azimuth angle to 90° (due east direction). Observations of hot and dark spots were added (Figure 3). Consequently, each scene was observed from 15 different angles within the principal plane.

3. Results and Discussion

3.1. Evaluation of LESS

The evaluation of the model’s accuracy is a crucial prerequisite for the subsequent analysis [21]. The actual measured LAI of the litchi canopy is 3.73, and the canopy reflectance under the same LAI is simulated using LESS. By comparing the measured and simulated spectral data, we further assess the accuracy of LESS [22]. The root mean square error (RMSE) between the two spectra is 0.023, which is relatively small overall. Therefore, we conclude that the LESS simulation is suitable for modeling the canopy spectra of litchi orchards. Cheng et al. used LESS to estimate chlorophyll at the apple canopy scale, and the simulation accuracy of LESS was mainly around 0.02 [22]. The simulation accuracy of LESS was in the range of 0–0.21 in the study of the effect of apple orchard aggregation on chlorophyll inversion by Cheng et al. [23]. These studies collectively demonstrate that the data simulated using LESS can well-represent the measured spectra for relevant analyses (Figure 4).

3.2. Effects of Leaf Physicochemical Parameters on Canopy BRF

The influence of changes in physicochemical parameters of leaves on the canopy BRF is shown in Figure 5. Cab and Cw had strong influences on canopy BRF, which were the basis for remote sensing inversion of the above parameters [24,25]. The effect of the Cab on canopy BRF was mainly in visible light. The canopy BRF decreased with the increase in Cab value. When Cab was increased from 10 μg·cm−2 to 50 μg·cm−2, the BRF decreased rapidly, and when Cab value was greater than 50 μg·cm−2, the decline rate slowed down and gradually tended to saturation. Car mainly affected the band at 500–560 nm, where the canopy BRF decreased as the Car value increased, with the rate of decrease gradually diminishing and saturation becoming more pronounced. Cw and CBC predominantly influenced the near-infrared and short-wave infrared bands, with the BRF decreasing as their values increased. In the whole spectral range of 400–2500 nm, the increase in N led to the enhancement of the multiple scattering effect of vegetation, resulting in higher BRF. The change in Prot was mainly reflected at 1500–1850 nm and 2100–2350 nm, showing a decreasing trend with the increased content. The variation in protein content had no significant effect on the canopy BRF. A large number of studies have been conducted to invert nitrogen content based on the strong correlation between leaf nitrogen and chlorophyll content in vegetation [18]. Nitrogen in plants is one of the components of amino acids and proteins [26]. The application of protein absorption features in the inversion model can improve the accuracy of nitrogen inversion when nitrogen is not correlated with chlorophyll to a certain extent [27]. The vegetation canopy has a 3D spatial structure, and the non-uniform distribution of canopy agronomic parameters leads to the obvious heterogeneity of the canopy [6]. Therefore, the impact of internal leaf physiological and chemical parameter variations on canopy BRF should be considered in studies of canopy bidirectional reflectance characteristics.

3.3. Influence of the Illumination and Observed Geometry on Canopy BRF

The canopy BRF under varying illumination and observation geometry in the vertical sensor observation direction is depicted in Figure 6. It was evident that the entire spectral range from 400 nm to 2500 nm was affected by the illumination and observation geometry, with particularly pronounced changes in canopy reflection in the near-infrared band (Figure 6a,b). This can be attributed to higher transmittance of plant leaves in the near-infrared region. The near-infrared radiation transmitted to the lower canopy layer was reflected by lower layer leaves and transmitted through upper layer leaves, thereby enhancing the near-infrared reflectance of the canopy [28]. Figure 6 illustrates the variation in canopy BRF with view zenith angle. With the increase in view zenith angle, the BRF exhibited a consistent upward trend. As the view zenith angle increases, more components of the upper canopy layer become observable within the field of view, characterized by the highest reflectance of the upper layer, thereby resulting in an increase in canopy reflectance [29]. When the view zenith angle reached 45°, the sensor angle coincided with the sun angle. Consequently, vegetation shadow diminished gradually [12], resulting in maximal BRF values—findings that were congruent with the analysis of how illumination and observed geometry impact apple canopy reflectance [22]. Figure 6b shows that the BRF decreases as the solar zenith angle gradually increases. The primary factor is that an increase in the solar zenith angle results in a larger heated area, causing greater dispersion of light and heat, which in turn reduces the intensity of solar radiation [30]. When the solar zenith angle was 0°, it aligned with the sensor’s vertical observation angle, resulting in no influence from canopy shadow and the highest BRF value. Compared to the view zenith angle and the solar zenith angle, changes in the solar azimuth angle have a smaller impact on the BRF (Figure 5c), with a significant increase only at the hotspot. In field operations, when considering the solar angle, it is advisable to prioritize the calibration and optimization of the solar zenith angle, as it has a more significant impact on the BRF. Except for the hotspot, data collection can be conducted within a broader time without the need to wait for a specific solar azimuth angle.
This study selected three wavelengths: visible light at 670 nm, near-infrared at 800 nm, and a band sensitive to protein at 2250 nm (Figure 5). It set up 840 observation angles within the space of the entire upper hemisphere under 9 solar angles to analyze the impact of sun observation geometry changes in the canopy BRF in a scene with 300 litchi trees (Figure 1d). Monitoring signals can be optimized by simulating and analyzing remote sensing signals at different times and angles. The variation in BRF acquisition time (i.e., changes in solar angles) affects the canopy gap fraction [29], resulting in litchi canopy BRF with distinct characteristics at different times (Figure 6 and Figure 7). The size and distribution of BRF hotspot high-value and low-value regions were related to the band used. In the polar diagram at 670 nm, the distribution of the hotspot high region became more concentrated as the zenith angle increased, whereas at 800 nm and 2500 nm it became more diffuse with the increasing zenith angle. With an increase in solar zenith angle, there was a downward trend observed for maximum BRF at the hotspot for 670 nm, but an upward trend for both 800 nm and 2250 nm. The changing trend in visible and near-infrared bands was consistent with the results of the BRF of the Qinghai spruce canopy [30]. When the zenith angle was 10°, the low-value region of the 670 nm (Figure 7a) formed an approximate ring shape, but exhibited discontinuity in the planting row direction of the canopy. In the low-value region of 800 nm (Figure 7b), a ring-shaped distribution did not appear, but only manifested in the forward position. At 2250 nm (Figure 7c), most of its distribution was oriented forward, with a small and discontinuous area distributed backward. As the solar zenith angle increased, the hotspot area shifted to one side, and each band’s low-value area only appeared in the forward direction with a wider distribution range. Moreover, changes from high value to low value were only evident on one side. Therefore, when the solar zenith angle is small, there are richer variations in high and low values in both the forward and backward directions, allowing for the acquisition of richer multi-angle information. This makes it a relatively better time and angle for monitoring remote sensing. In addition, studies on the reflectance properties of maize canopies have shown that the size of the hotspot high-value region is also related to the vegetation type [31].
The BRF of backward observations in the principal plane direction exceeded that of most forward observations, with the highest value occurring at the hotspot (Figure 8). The hotspot effect was more pronounced in the visible band compared to the near-infrared band due to enhanced anisotropy of litchi chlorophyll in red light and increased multiple scattering effects of leaves in the near-infrared band, resulting in reduced vegetation anisotropy in this band [32]. As the view angle increased, the hotspot effect gradually diminished as a result of a greater number of ground objects within the field of view, consistent with findings by Zhen et al. [12]. When the view zenith angle is greater than 40°, an increase in the view zenith angle in the near-infrared band leads to a noticeable bowl-edge effect, characterized by elevated reflectance. The reason for this is that when the tree canopy spacing is close, the shadows often fall at the base of adjacent canopies. When observing the tree crowns from a low angle, only the sunlit tops of the crowns are visible, and the reflectance of the uppermost canopy layer is highest, resulting in a bowl-shaped BRF [33]. In addition, while dark spots appeared at VZA = −45° for BRF values in the near-infrared band, no such spots were evident in the visible band. The BRF in the vertical principal planes were distributed with 0° as the symmetry axis, and the changes in the observation angle had no significant effect on the BRF in different bands, which was similar to the results of the rice study [27]. It proves that canopy structure does not affect the symmetry of vertical principal planes. Consequently, multi-angle remote sensing offered more comprehensive remote sensing information through principal planes.
The sun and observation geometry primarily change the shape characteristics of BRF by influencing the observation range. Therefore, when using sensors for parameter inversion, it is crucial to fully consider the illumination and observed geometry, as they can strongly impact the reflectivity sensitivity of the canopy to target parameters [34]. Employing multiple observation configurations has the potential to enhance inversion accuracy compared to utilizing a single lowest point observation [35].

3.4. Influence of LAI on Canopy BRF

With the increase in LAI, the overall trend in canopy BRF decreased and gradually stabilized (Figure 9). In this study, LAI stabilized after reaching 3.80. Qi et al. also observed a similar stabilization of BRF in coniferous forests when LAI exceeded 3 (the reflectance stability of LAI is influenced by the increments defined in the study; in this research, each increment is defined as an additional 100 litchi trees in the scene) [10]. As red light (610–680 nm) is absorbed by green vegetation, an increase in LAI strengthens the canopy’s absorption capacity for red light, leading to a reduction in plant BRF. Conversely, the changing pattern of BRF in the near-infrared band (750–1000 nm) is the opposite, as vegetation exhibits a reflection peak, causing it to increase with higher LAI [28].
In the principal plane direction (Figure 10a–c), canopy BRF exhibited consistent behavior across different LAI values in each spectral band, with a noticeable hotspot effect. Additionally, the 800 nm and 2250 nm bands displayed distinct bowl-edge effects, while the 670 nm band only showed this effect at low LAI. Compared to Li et al., who utilized the Modified Geometry Optical Mutual Shadow (MGOMS) model to simulate forest BRF trends with LAI, the hotspot effect was more pronounced in the results of the 3D radiative transfer model simulation for litchi orchards [36]. This is because the two models differ in their approach to vegetation canopy structure construction. At both the 670 nm and 2250 nm bands (Figure 10a,c), canopy BRF decreased gradually as LAI increased. Conversely, at 800 nm (Figure 10b), BRF exhibited an opposite trend with increasing LAI. Specifically at 670 nm, when LAI ≥ 3.80, BRF is saturated in forward observation directions. However, near the hotspot direction, there was still a decreasing trend as LAI increased from 3.80 to 4.98. The saturation of BRF did not occur until LAI exceeded 4.98, suggesting that high LAI in litchi orchards near hotspots had a mitigating effect on saturation. At 800 nm, the BRF near hotspots showed no significant differences under different LAI due to the strong reflection characteristics of vegetation [37]. In the 2250 nm, higher LAI only resulted in noticeable BRF differences between 20° and 50° in backward observation. When LAI was at 1.29 and 2.53, there were significant variations in BRF among different observation directions in the principal plane, indicating that multi-angle remote sensing contained more ground object information than single-directional remote sensing. When LAI exceeds 3.80, the differences in BRF across different angles at the same LAI are small. This indicates that although multi-angle observations provide more information than single-angle measurements for orchards with high LAI, inherent limitations still exist.
On the vertical principal plane (Figure 10d–f), when LAI = 1.29, the canopy reflectance curve exhibited instability and significant variability in BRF at different angles. As LAI increased, the differences in BRF among all directions became negligible. Therefore, it is only under low LAI conditions that observations on the vertical principal plane can provide comprehensive multi-angle information.
The impact of varying LAI in the 670 nm band under three solar orientations on bidirectional reflection factors in litchi orchards is illustrated in Figure 11. The width of the hotspot area was associated with the crop planting density within the scene [38]. A higher LAI in the litchi orchard led to a more clustered hotspot area, resulting in relatively reduced multi-angle information provided. This is attributed to the soil being the driving factor for the variation in canopy BRF. With a high LAI, the soil background effect weakens and angle dependence decreases as vegetation coverage increases [39]. Dorigo utilized multi-angle measurements to describe medium-density cotton canopy structures more robustly and accurately [40]. Due to differences in cotton and litchi canopy structure, they respond differently to incident light, leading to varying sensitivity of medium-density and high-density canopies to multi-angle measurements. The scene was arranged in a ridge structure, and when LAI ≤ 3.80, BRF exhibited a concentric ellipse with a long axis along the planting row direction. LAI increased to 4.98 due to an increase in the number of litchi trees in the scene, gradually reducing the gaps between rows and columns, weakening the ridge structure effect. The polar map gradually transitions into concentric circles, which is consistent with the polar map of the canopy structure in the ridge and random arrangements, as studied by Cao et al. [41].
The LAI inversion method based on vegetation index is widely utilized in agricultural remote sensing applications [42,43]. However, the vegetation index has limitations due to saturation or lack of sensitivity in mid- to high-density canopies [44]. In remote sensing monitoring, some researchers have turned to utilizing the rich canopy structure information found in hotspots to infer LAI and other structural parameters [32]. Some other scholars opt to incorporate additional features into LAI inversion as a new approach to address the saturation issue [45]. This study discovered that multi-angle observations revealed a certain anti-saturation effect on orchards with high LAI near hotspots. Litchi is extensively cultivated in southern subtropical areas with robust photosynthetic capacity, year-round continuous growth, and high LAI [46,47]. When the LAI of litchi is excessively high, the canopy reflectance no longer effectively reflects changes in vegetation characteristics. At this time, utilizing hotspot observations can alleviate this phenomenon. In field observations, UAV is the best means for multi-angle observation of tall and dense litchi orchards. In recent years, UAV remote sensing imaging technology has developed rapidly, characterized by high flexibility and strong timeliness [48]. When using multispectral UAVs to survey orchards, it is necessary to calculate the sun’s position based on the time and location before the flight and plan the flight path and angles accordingly to obtain information on the principal plane. Additionally, determine the hotspot position based on the solar zenith angles to acquire observation data at the hotspot. In this way, the collected canopy reflectance data of the litchi orchard will be more valuable, avoiding reflectance saturation caused by excessively high LAI. Utilizing hotspot data greatly enhances the potential for improving the accuracy of LAI remote sensing inversion in high-yield litchi orchards in South China.
In addition, this study treats the canopy as a state of vegetation in an ideal situation. In reality, orchards under different management practices face problems of light and nutrient availability, as well as threats from pests or diseases and the corresponding conditions of different varieties. Therefore, subsequent research will be carried out in further depth in relation to specific scenarios.

4. Conclusions

In this study, a 3D radiation transfer model was employed in conjunction with an accurate 3D model of a single litchi tree to construct a detailed litchi orchard scene. This allowed for an in-depth analysis of the variation patterns and influencing factors of the canopy BRF. The physicochemical parameters of leaves were pivotal factors impacting the canopy BRF, each exerting varying degrees of influence. Therefore, identifying the impact of physical and chemical parameters is fundamental for retrieving remote sensing parameters. Additionally, spatial heterogeneity of parameters within different parts of the canopy should be taken into consideration. Illumination geometry and observation geometry also significantly affect changes in BRF. Compared to single-angle observation, multi-angle observation provides more comprehensive target information conducive to an extensive study on changes in canopy BRF. Variations in solar angle result in distinct characteristics of litchi canopy BRF at different times, leading to differences in multi-angle information obtained. When the solar zenith angle is small, richer information differences are observed which facilitates optimization of timing and angles for multi-angle observation. Principal plane observation yields relatively rich multi-angle information, particularly regarding hotspot direction. The in-depth research on the hotspot effect shows that when the LAI of a litchi orchard increases to around 4, the BRF on the main plane gradually begins to saturate. Observing within the range from −60° backward to 10° forward near the hotspot can mitigate this issue. When the LAI approaches 5, the BRF becomes almost completely saturated. The planting density of litchi orchards is a crucial factor influencing canopy BRF. As the orchard planting density, the hotspot peak area becomes more clustered, weakening the impact of angle change on canopy BRF.

Author Contributions

Conceptualization, D.L., L.H. and X.D.; methodology, D.L., L.H. and C.H.; formal analysis, C.H.; investigation, D.L. and C.H.; writing—original draft preparation, D.L.; writing—review and editing, D.L., S.C., J.Q., C.W., X.Z., B.Q., H.J., K.J. and Z.S.; project administration, D.L.; funding acquisition, D.L. All authors have read and agreed to the published version of the manuscript.

Funding

This work was supported by National Natural Science Foundation of China (No. 41301401); Guangzhou Science and Technology Project (No. 2024B03J1321); Special Fund for Rural Revitalization Strategy (Improving Agricultural Science and Technology Capacity) project (No. 2024TS-2-2).

Data Availability Statement

The raw data supporting the conclusions of this article will be made available by the authors on request.

Acknowledgments

We would like to thank the kind help of the editor and the reviewers for improving the manuscript.

Conflicts of Interest

The authors declare no conflicts of interest.

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Figure 1. Real 3D model of litchi tree and orchard scene construction. (a) Real 3D model of litchi tree. (b) ntrees = 100 LAI = 1.29. (c) ntrees = 200 LAI = 2.53. (d) ntrees = 300 LAI = 3.80. (e) ntrees = 400 LAI = 4.98.
Figure 1. Real 3D model of litchi tree and orchard scene construction. (a) Real 3D model of litchi tree. (b) ntrees = 100 LAI = 1.29. (c) ntrees = 200 LAI = 2.53. (d) ntrees = 300 LAI = 3.80. (e) ntrees = 400 LAI = 4.98.
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Figure 2. Schematic diagram of canopy BRF.
Figure 2. Schematic diagram of canopy BRF.
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Figure 3. Schematic diagram of principal plane observation.
Figure 3. Schematic diagram of principal plane observation.
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Figure 4. Comparison of simulated and measured BRF.
Figure 4. Comparison of simulated and measured BRF.
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Figure 5. Changes in canopy BRF under different leaf parameters in the vertical direction (a) canopy BRF with different Cab content. (b) canopy BRF with different Car content. (c) canopy BRF with different CBC content. (d) canopy BRF with different Cw content. (e) canopy BRF with different N. (f) canopy BRF with different Prot content. (SZA = 45°; SAA = 90°; VZA = 0°; VAA = 90°).
Figure 5. Changes in canopy BRF under different leaf parameters in the vertical direction (a) canopy BRF with different Cab content. (b) canopy BRF with different Car content. (c) canopy BRF with different CBC content. (d) canopy BRF with different Cw content. (e) canopy BRF with different N. (f) canopy BRF with different Prot content. (SZA = 45°; SAA = 90°; VZA = 0°; VAA = 90°).
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Figure 6. Effects of observation angle and solar angle changes on canopy BRF. (a) Canopy BRF with different VZA. (b) Canopy BRF with different SZA. (c) Canopy BRF with different SAA.
Figure 6. Effects of observation angle and solar angle changes on canopy BRF. (a) Canopy BRF with different VZA. (b) Canopy BRF with different SZA. (c) Canopy BRF with different SAA.
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Figure 7. BRF of 9 different solar angles at 670 nm, 800 nm, and 2250 nm bands when 300 litchi trees are placed in the scene. (a) 670 nm SZA:SAA = 10°:120°; 10°:180°; 10°:240°; 30°:120°; 30°:180°; 30°:240°; 60°:120°; 60°:180°; 60°:240°. (b) 800 nm SZA:SAA = 10°:120°; 10°:180°; 10°:240°; 30°:120°; 30°:180°; 30°:240°; 60°:120°; 60°:180°; 60°:240°. (c) 2250 nm SZA:SAA = 10°:120°; 10°:180°; 10°:240°; 30°:120°; 30°:180°; 30°:240°; 60°:120°; 60°:180°; 60°:240°.
Figure 7. BRF of 9 different solar angles at 670 nm, 800 nm, and 2250 nm bands when 300 litchi trees are placed in the scene. (a) 670 nm SZA:SAA = 10°:120°; 10°:180°; 10°:240°; 30°:120°; 30°:180°; 30°:240°; 60°:120°; 60°:180°; 60°:240°. (b) 800 nm SZA:SAA = 10°:120°; 10°:180°; 10°:240°; 30°:120°; 30°:180°; 30°:240°; 60°:120°; 60°:180°; 60°:240°. (c) 2250 nm SZA:SAA = 10°:120°; 10°:180°; 10°:240°; 30°:120°; 30°:180°; 30°:240°; 60°:120°; 60°:180°; 60°:240°.
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Figure 8. Variations of canopy BRF in the red and near-infrared bands with the VZA in the main plane. (a) 670 nm. (b) 800 nm. (LAI = 3.80).
Figure 8. Variations of canopy BRF in the red and near-infrared bands with the VZA in the main plane. (a) 670 nm. (b) 800 nm. (LAI = 3.80).
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Figure 9. Effects of different LAI on canopy BRF (SZA = 45°; SAA = 90°; VZA = 0°; VAA = 90°).
Figure 9. Effects of different LAI on canopy BRF (SZA = 45°; SAA = 90°; VZA = 0°; VAA = 90°).
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Figure 10. Variation of BRF in the principal plane and vertical principal plane at 670 nm, 800 nm, and 2250 nm with the view zenith angle under different LAI. (a) 670 nm-principal plane. (b) 800 nm-principal plane. (c) 2250 nm-principal plane. (d) 670 nm-vertical principal plane. (e) 800 nm-vertical principal plane. (f) 2250 nm-vertical principal plane. The gray shadow shows the anti-saturation characteristics near the hotspot.
Figure 10. Variation of BRF in the principal plane and vertical principal plane at 670 nm, 800 nm, and 2250 nm with the view zenith angle under different LAI. (a) 670 nm-principal plane. (b) 800 nm-principal plane. (c) 2250 nm-principal plane. (d) 670 nm-vertical principal plane. (e) 800 nm-vertical principal plane. (f) 2250 nm-vertical principal plane. The gray shadow shows the anti-saturation characteristics near the hotspot.
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Figure 11. BRF of different solar angles under different LAI. (a) SZA = 0°, SAA = 90°. (b) SZA = 45°, SAA = 180°. (c) SZA = 60°, SAA = 270°. (d) SZA = 0°, SAA = 90°. (e) SZA = 45°, SAA = 180°. (f) SZA = 60°, SAA = 270°. (g) SZA = 0°, SAA = 90°. (h) SZA = 45°, SAA = 180°. (i) SZA = 60°, SAA = 270°. (j) SZA = 0°, SAA = 90°. (k) SZA = 45°, SAA = 180°. (l) SZA = 60°, SAA = 270°.
Figure 11. BRF of different solar angles under different LAI. (a) SZA = 0°, SAA = 90°. (b) SZA = 45°, SAA = 180°. (c) SZA = 60°, SAA = 270°. (d) SZA = 0°, SAA = 90°. (e) SZA = 45°, SAA = 180°. (f) SZA = 60°, SAA = 270°. (g) SZA = 0°, SAA = 90°. (h) SZA = 45°, SAA = 180°. (i) SZA = 60°, SAA = 270°. (j) SZA = 0°, SAA = 90°. (k) SZA = 45°, SAA = 180°. (l) SZA = 60°, SAA = 270°.
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Table 1. Main parameter range of local sensitivity analysis.
Table 1. Main parameter range of local sensitivity analysis.
ItemParameter Symbol and UnitParameters RangeFixed ValueStep Length
Structure coefficientN1–2.51.50.5
Chlorophyll contentCab (μg/cm−2)10–1104020
Carotenoid contentCar (μg/cm−2)0–20105
Equivalent water thicknessCw (cm)0.002–0.0420.0150.01
Protein contentProt (g/cm−2)0–0.0030.0010.001
Carbon-based constituentsCBC (g/cm−2)0–0.010.0090.002
Leaf area indexLAI (m2/m2)1.29, 2.53, 3.80, 4.98 (100–400)3.80 (300)100
Solar zenith anglesSZA (°)0–704510
Solar azimuth anglesSAA (°)0–3609030
View zenith anglesVZA (°)0–70010
View azimuth anglesVAA (°)90
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Hong, C.; Li, D.; Han, L.; Du, X.; Chen, S.; Qi, J.; Wang, C.; Zhou, X.; Qin, B.; Jiang, H.; et al. Simulation and Analysis of Bidirectional Reflection Factors of Southern Evergreen Fruit Trees Based on 3D Radiative Transfer Model. Horticulturae 2024, 10, 790. https://doi.org/10.3390/horticulturae10080790

AMA Style

Hong C, Li D, Han L, Du X, Chen S, Qi J, Wang C, Zhou X, Qin B, Jiang H, et al. Simulation and Analysis of Bidirectional Reflection Factors of Southern Evergreen Fruit Trees Based on 3D Radiative Transfer Model. Horticulturae. 2024; 10(8):790. https://doi.org/10.3390/horticulturae10080790

Chicago/Turabian Style

Hong, Chaofan, Dan Li, Liusheng Han, Xiong Du, Shuisen Chen, Jianbo Qi, Chongyang Wang, Xia Zhou, Boxiong Qin, Hao Jiang, and et al. 2024. "Simulation and Analysis of Bidirectional Reflection Factors of Southern Evergreen Fruit Trees Based on 3D Radiative Transfer Model" Horticulturae 10, no. 8: 790. https://doi.org/10.3390/horticulturae10080790

APA Style

Hong, C., Li, D., Han, L., Du, X., Chen, S., Qi, J., Wang, C., Zhou, X., Qin, B., Jiang, H., Jia, K., & Su, Z. (2024). Simulation and Analysis of Bidirectional Reflection Factors of Southern Evergreen Fruit Trees Based on 3D Radiative Transfer Model. Horticulturae, 10(8), 790. https://doi.org/10.3390/horticulturae10080790

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