Evaluation of the SAIL Radiative Transfer Model for Simulating Canopy Reflectance of Row Crop Canopies

Abstract

The widely used SAIL (Scattering by Arbitrarily Inclined Leaves) radiative transfer model (RTM) is designed for canopies that can be considered as homogeneous turbid media and thus should be inadequate for row canopies. However, numerous studies have employed the SAIL model for row crops (e.g., wheat and maize) to simulate canopy reflectance or retrieve vegetation properties with satisfactory accuracy. One crucial reason may be that under certain conditions, a row crop canopy can be considered as a turbid medium, fulfilling the assumption of the SAIL model. Yet, a comprehensive analysis about the performance of SAIL in row canopies under various conditions is currently absent. In this study, we employed field datasets of wheat canopies and synthetic datasets of wheat and maize canopies to explore the impacts of the vegetation cover fraction (fCover), solar angle and soil background on the performance of SAIL in row crops. In the numerical experiments, the LESS 3D RTM was used as a reference to evaluate the performance of SAIL for various scenarios. The results show that the fCover is the most significant factor, and the row canopy with a high fCover has a low soil background influence. For a non-black soil background, both the field measurement and simulation datasets showed that the SAIL model accuracy initially decreased, and then increased with an increasing fCover, with the most significant errors occurring when the fCover was between about 0.4 and 0.7. As for the solar angles, the accuracy of synthetic wheat canopy will be higher with a larger SZA (solar zenith angle), but that of a synthetic maize canopy is little affected by the SZA. The accuracy of the SAA (solar azimuth angle) in an across-row direction is always higher than that in an along-row direction. Additionally, when the SZA ranges from 65° to 75° and the fCover of wheat canopies are greater than 0.6, SAIL can simulate the canopy reflectance with satisfactory accuracy (rRMSE < 10%); the same accuracy can be achieved in maize canopies as long as the fCover is greater than 0.8. These findings provide insight into the applicability of SAIL in row crops and support the use of SAIL in row canopies under certain conditions (with rRMSE < 10%).

1. Introduction

Remote sensing plays a crucial role in efficiently monitoring the statuses of vegetation canopies. Radiative transfer models (RTMs) establish links between remotely sensed signals and the biophysical and biochemical characteristics of vegetation, while accounting for supplementary factors such as the sun-observer geometry and soil background. Among numerous vegetation canopy RTMs, the SAIL (Scattering by Arbitrarily Inclined Leaves) model is the most widely employed model in remote sensing applications [1,2]. However, the SAIL model is built on the assumption that a vegetation canopy can be considered as a turbid medium [1]. Due to this assumption, the applicability of SAIL for row crops has been doubted. Nevertheless, a number of studies have found that the SAIL model could effectively simulate the canopy reflectance and retrieve the vegetation properties of row crops with reasonable accuracy [3,4,5,6,7]. A reasonable assumption may be that under certain conditions, row canopies can be considered as turbid media, and by extension, the SAIL model is applicable. However, a comprehensive analysis about the accuracy of SAIL in row crops under various conditions is still missing.

Row canopies exhibit distinct behavior compared to turbid media. In the SAIL model, the extinction of incident direct solar radiation is described with Beer’s law. However, in row crop canopies, the extinction does not necessarily follow this law due to canopy heterogeneity. This difference is attributed to many factors, including the vegetation cover fraction (fCover) [8,9,10], solar angle [11,12,13] and soil background [14,15,16,17]. Therefore, studies have suggested that RTMs designed for homogeneous turbid media are inadequate for fragmented row crop canopies [18,19].

Efforts to extend the SAIL model for row crop canopies have been made. For instance, Zhao et al. [12] enhanced the SAIL model based on a novel mathematical treatment and achieved a more accurate simulation of a row canopy’s directional reflectance. The performance of this model was validated through both field-measured wheat datasets and a 3D computer simulation. Zhou et al. [20] introduced the 4SAIL-RowCrop model for row-planted rice and wheat, which agreed with the results of the field measurements. Furthermore, Ma et al. [21] developed an enhanced four-stream RTM based on the SAIL model, taking into account the transfer of radiation between rows and addressing the large viewing zenith angle problems. These models improved the accuracy in simulating the canopy reflectance, yet they required more parameters and had higher complexity. This increased complexity leads to a higher uncertainty in the inversion process and necessitates the inclusion of more parameters in applications [22,23,24].

Contrary to studies suggesting that the SAIL model should not be applied in row canopies, a number of studies have used the SAIL model to simulate the canopy reflectance and retrieve vegetation properties in row canopies with reasonable accuracy. For example, Moulin et al. [9] accurately simulated the reflectance of winter wheat based on the SAIL model. Vohland et al. [3] and Kimm et al. [4] used the PROSAIL model to retrieve the leaf area index (LAI) of summer barley and corn, respectively. Nie et al. [5] compared various LAI inversion methods, including statistical regression, machine learning regression and PROSAIL-D, and found that PROSAIL-D performed the best. Additionally, Wan et al. [25] found that PROSAIL performed better than the empirical models in estimating the rice LAI and biomass using UAV images.

Building upon these studies, we hypothesized that the fCover, solar angle and soil background constitute the primary factors affecting the accuracy of SAIL in row canopies. The fCover is defined as the vertical projection area of aboveground vegetation elements per unit of horizontal ground surface area [26]. The lower fCover of row canopies, which is an important characteristic compared to homogeneous turbid media, results from leaves gathering within the rows, which exposes more bare soil [18]. The solar angle comprises the solar azimuth angle (SAA) and the solar zenith angle (SZA), both of which markedly influence the spectral reflectance of row canopies by changing the canopy shadowing [27]. The soil background reflectance constitutes a crucial component of canopy reflectance, and numerous studies have reported its significant impact on the canopy reflectance when the fCover is low [16,28,29,30].

The aim of this study is to assess the accuracy of applying the SAIL model to row canopies. We hypothesized that as the fCover increases, row canopies progressively exhibit characteristics akin to turbid media. When the fCover surpasses a specific threshold, row canopies can be considered as turbid media, allowing the SAIL model to simulate their reflectance with negligible error. The specific objectives of our study were (1) to explore the influences of the fCover, solar angle and soil background on the accuracy of SAIL in row canopies and (2) to determine the conditions within which the SAIL model can simulate the row canopy reflectance with negligible error. To achieve these objectives, we employed field datasets of wheat canopies with various fCover and synthetic datasets of wheat and maize canopies based on the Large-scale Remote Sensing Data and Image Simulation Framework (LESS) to investigate the effects of the fCover, solar angle and soil background on the accuracy of SAIL in row canopies.

2. Materials and Methods

2.1. Study Site

The study site was located in the Agricultural Meteorology National Observation and Research Station, Gucheng, Baoding city in the Hebei Province of China (39.08°N, 115.40°E), in the north part of the North China Plain, where the main crops are winter wheat and summer maize (Figure 1). Soil type at the site is sandy loam. The average altitude of the field is 15.2 m above mean sea level, with a mean annual temperature of 12.1 °C and an annual precipitation of 479.6 mm. The total precipitation over the growing season for winter wheat (October to May of the following year) accounts for about 20% of the annual precipitation. In the site, winter wheat (Triticum aestivum L.) was planted in seven plots in a row structure. Each plot had a size of 2 m × 4 m, with a wheat row spacing of 25 cm, and the wheat planted in October 2022 was about 50 cm in height at the time of the field measurement. The wheat planting densities of the plots ranged from approximately 80 × 10⁴ plants ha⁻¹ to 300 × 10⁴ plants ha⁻¹, which resulted in various LAI and fCover values, and the plots were labeled from (a) to (g) according to the order of increasing fCover to distinguish.

2.2. Field Measurements

The field campaign was conducted on 29 April 2023. We collected spectral measurements of the wheat canopies, leaves and soil backgrounds, as well as the canopy LAI. All spectral measurements, including the canopy reflectance, soil reflectance, leaf reflectance and transmittance, were conducted using a QEPro instrument (Ocean Optics Inc., Dunedin, FL, USA). The spectrometer has a spectral resolution of about 0.375 nm, covering a range of 485 to 850 nm, with a total of 1036 channels.

Canopy reflectance was measured using the QEPro instrument, which was fixed on a platform approximately two meters above the ground. The probe’s position was in the middle of the plot, measured downward at the nadir direction with a 25° field of view. Each plot was measured twice to obtain the representative average measurement. Figure 2 depicts the QEPro instrument for canopy spectra over the plots. The row canopy reflectance can be expressed as follows [31]:

$$R=f\left(C_1\right)\rho \left(C_1\right)I\left(C_1\right)+f\left(C_S\right)\rho \left(C_S\right)I\left(C_S\right)+f\left(U_1\right)\rho \left(U_1\right)I\left(U_1\right)+f\left(U_S\right)\rho \left(U_S\right)I\left(U_S\right)$$

(1)

where $R$ represents the canopy reflectance. $C_1$, $C_s$, $U_1$ and $U_s$ represent the four components of row canopies, i.e., the sunlit canopy, shaded canopy, sunlit background and shaded background, respectively. $f$, $\rho$ and $I$ represent the areal fraction, reflectance and characteristic irradiance of each component. Leaf spectra were measured in situ on the wheat using a FluoWat leaf clip combined with QEPro (for details of FluoWat, refer to [32]). For each plot, we randomly selected six leaf samples from different wheat plants to measure the leaf reflectance and transmittance. Before and after each measurement, a reference white panel was measured to avoid the influence of short-term changes in solar irradiance. The leaf and canopy spectra of wheat canopies, as well as the average spectrum and standard deviation, are shown in Figure 3. Soil reflectance was measured with the fiber of QEPro, and the previous and later reference white panel were also measured. All spectral measurements were conducted between 9 a.m. and 3 p.m. local time.

The canopy LAI was measured using an optical method with the AccuPAR LP-80 instrument (Decagon Devices, Inc., Pullman, WA, USA). To obtain more representative LAI measurements, we conducted two measurements at 9 a.m. and 3 p.m., with three sampling points evenly selected in each measurement. During the measurements, the detector probe of the instrument was kept across the rows. The details about the LAI and fCover of field wheat canopies are shown in

Table 1. The LAI and fCover of field wheat canopies.

Wheat Plot	LAI	fCover
(a)	0.57	0.38
(b)	1.00	0.50
(c)	1.25	0.54
(d)	0.89	0.54
(e)	1.35	0.65
(f)	1.98	0.66
(g)	1.89	0.70

.

2.3. Synthetic Wheat and Maize Canopies with LESS Model

In addition to the wheat canopies acquired from the field datasets, we generated synthetic wheat and maize canopies with a wide range of fCover values. A total of 56 synthetic north–south row-planted canopies with different fCover values for the wheat and maize were produced, with each plot having a size of 10 m × 10 m. The 3D model of individual wheat was generated using 3D modeling software (Blender, version 3.6.4), with a bounding box size of 0.48 m × 0.54 m × 0.78 m, as shown in Figure 4a,b (the file is available from the corresponding author upon request). The 3D model of the maize plant we used was originated from http://lessrt.org/3dscenes/ (accessed on 17 July 2023), which had a bounding box size of 1.11 m × 1.16 m × 2.44 m, as shown in Figure 4c,d. For the synthetic wheat and maize canopies, the fCover was set from 0.046 to 0.979 and from 0.051 to 0.993, respectively, by adjusting the configuration of the rows, denoted as ($x$, $y$), where $x$ represents the row number of synthetic maize canopies, and $y$ represents the number of wheat or maize crops planted per row. The LAI ranged from 0.08 to 17.21 and from 0.048 to 10.579, respectively. Details can be seen in

Table 2. The LAI and fCover of synthetic wheat and maize canopies.

Configuration of Row (Wheat|Maize)	LAI (Wheat|Maize)	fCover (Wheat|Maize)	Configuration of Row (Wheat|Maize)	LAI (Wheat|Maize)	fCover (Wheat|Maize)
(4,4)|(2,2)	0.08|0.05	0.046|0.051	(20,20)|(10,10)	1.94|1.19	0.292|0.425
(4,12)|(2,6)	0.23|0.14	0.066|0.083	(16,30)|(8,15)	2.32|1.42	0.334|0.464
(8,8)|(4,4)	0.31|0.19	0.077|0.099	(12,60)|(6,30)	3.46|2.13	0.369|0.491
(4,20)|(2,10)	0.39|0.24	0.087|0.114	(16,40)|(8,20)	3.09|1.89	0.398|0.534
(4,30)|(2,15)	0.58|0.35	0.110|0.144	(20,30)|(10,15)	2.90|1.77	0.408|0.565
(12,12)|(6,6)	0.70|0.43	0.128|0.178	(16,60)|(8,30)	4.62|2.84	0.478|0.635
(8,20)|(4,10)	0.77|0.48	0.138|0.193	(20,40)|(10,20)	3.86|2.36	0.489|0.652
(12,16)|(6,8)	0.93|0.57	0.159|0.226	(30,30)|(15,15)	4.35|2.64	0.576|0.733
(8,30)|(4,15)	1.16|0.71	0.185|0.249	(20,60)|(10,30)	5.77|3.55	0.589|0.772
(8,40)|(4,20)	1.55|0.86	0.217|0.265	(30,40)|(15,20)	5.79|3.51	0.688|0.829
(12,20)|(6,10)	1.16|0.71	0.189|0.271	(40,40)|(20,20)	7.71|4.69	0.808|0.904
(16,20)|(8,10)	1.55|0.95	0.241|0.350	(30,50)|(15,30)	7.23|5.28	0.761|0.926
(12,30)|(6,15)	1.74|1.06	0.259|0.354	(40,60)|(20,30)	11.51|7.04	0.916|0.969
(12,40)|(6,20)	2.32|1.42	0.306|0.412	(60,60)|(30,30)	17.21|10.58	0.979|0.993

. Figure 5 shows the relationship between the LAI and fCover of field wheat and synthetic wheat and maize.

Besides the fCover, we set up various soil backgrounds and solar angles to evaluate their impacts on the accuracy of the SAIL model in row canopies. For each canopy, both black soil (i.e., soil reflectance is zero) and non-black soil background (the default soil type of the LESS model, which had an average reflectance of 0.4, and the reflectance was isotropic; the spectral reflectance is shown in Figure 6) scenarios were analyzed. The SZA was set as 9 angles from 15° to 75° (including 15°, 30°, 45°, 50°, 55°, 60°, 65°, 70° and 75°). The SAAs were set as 90° and 180°, respectively (i.e., the SAA across and along the row), corresponding to the smallest and largest reflectance errors, respectively [12,33,34]. The schematic representation of the settings for the fCover, soil background and solar angles is shown in Figure 7a,b, Figure 7c,d and Figure 7e,f, respectively.

2.4. SAIL and LESS Model

SAIL is a canopy RTM that simulates the interaction between radiation and vegetation canopies. The SAIL model is based on the principles of light scattering from arbitrary inclined leaves within the canopy. It considers factors such as the leaf angle distribution (LAD), canopy LAI, solar and viewing angles and leaf optical properties to compute the canopy reflectance under given conditions. The leaf optical properties are often derived from leaf RTMs, such as PROSPECT [35], and the coupled model is called PROSAIL [36]. PROSPECT simulates leaf optical properties (i.e., reflectance and transmittance) in the range of 400 to 2500 nm. The input parameters include chlorophyll content, structural parameters and equivalent water thickness. Nevertheless, once the leaf optical properties (i.e., leaf reflectance and transmittance) and the soil reflectance are provided, the SAIL model only requires additional canopy structural parameters (i.e., LAI and LAD) and the sun–observer geometry. 4SAIL [37] was used for this study; this version includes a hotspot effect and optimizes numerical calculations, and the code can be found at http://teledetection.ipgp.jussieu.fr/prosail/ (accessed on 21 May 2023). Additionally, since the leaf reflectance and transmittance of wheat canopies were measured in the field, and those of synthetic canopies in LESS were also available, the leaf RTMs (i.e., the PROSPECT model) were not required in this study.

The LESS model is a three-dimensional RTM based on ray tracing [38]. It can simulate large-scale remote sensing data and images. LESS not only facilitates the adjustment of environmental factors such as terrain, soil background and illumination but also provides the capability to create or import three-dimensional vegetation structures with customizable optical properties. This feature enables the LESS model to simulate complex scenarios while maintaining a high level of accuracy. In our experiment, the LESS model (version 2.1.4-2023-08-19) was used to generate synthetic wheat and maize canopies with various fCover, soil backgrounds and solar angles and to simulate this canopy reflectance as the reference spectra for row canopies. We then inputted the relevant parameters into SAIL to obtain simulations of canopies with turbid media.

2.5. Calculating fCover

In order to explore the impact of fCover on the accuracy of SAIL in row canopies, we estimated the fCover of field wheat canopies using nadir-viewed RGB images. The conventional image thresholding segmentation approach was employed for fCover calculation. This approach relies on vegetation indices to distinguish between the soil background and vegetation in the images. Five nadir-view RGB images were photographed for each plot, at a height of approximately 1.5 m above the ground. The Normalized Green-Red Difference Index (NGRDI) was chosen to calculate fCover. NGRDI has shown excellent performance in estimating the fCover from RGB images [39] and only requires the red and green bands:

$$\mathrm{N}\mathrm{G}\mathrm{R}\mathrm{D}\mathrm{I}=(G-R)/(G+R)$$

(2)

where $G$ represents the green band, and $R$ represents the red band.

After visual inspection using ENVI 5.6, we set the threshold for NGRDI to 0.04. This means that pixels with NGRDI greater than 0.04 were identified as wheat, while the remaining pixels were identified as soil background. Therefore, the fCover can be calculated as the ratio of the ‘wheat pixels’ count to the total pixel count.

For the synthetic wheat and maize canopies generated in LESS, we calculated their fCover based on the relationship between fCover and the gap fraction at nadir direction, which can be expressed as follows:

$$\mathrm{f}\mathrm{C}\mathrm{o}\mathrm{v}\mathrm{e}\mathrm{r}=1-P$$

(3)

where $P$ represents the gap fraction at nadir direction, which was produced directly in LESS.

2.6. Calculating Average Leaf Angle

2.6.1. Estimating Average Leaf Angle of Field Wheat Canopies

The leaf inclination distribution function (LIDF) is an important parameter of SAIL that describes the spatial distribution of vegetation leaves and can be represented by parameters LIDFa and LIDFb [40,41]. LIDFa controls the average leaf inclination, while LIDFb affects the shape of the distribution but does not impact the average leaf inclination. Instead of measuring the LIDF of wheat canopies, we used the average leaf angle (ALA) as a substitute and estimated the ALA for all canopies. The relationship between LIDF and ALA can be expressed as follows [42]:

$$\mathrm{A}\mathrm{L}\mathrm{A}=45°-\frac{360°}{{\pi }^2}\mathrm{L}\mathrm{I}\mathrm{D}\mathrm{F}\mathrm{a}$$

(4)

Since all plots were sown with wheat at the same time, we assumed that the ALAs for all plots were similar. According to previous studies [43,44], we found that the LAD of wheat exhibited a planophile pattern (40° < ALA < 60°), with ALA at 53.5°. Therefore, we set 53.5° as the ALA for all canopies.

2.6.2. Calculating Average Leaf Angle of Synthetic Wheat and Maize Canopies in LESS Model

The ALA of the synthetic wheat and maize canopies was calculated using the point cloud data of each plant. Since the wheat canopies were composed of the same individual plant, the ALA was identical for all wheat canopies, as was the case for the synthetic maize canopies. The normal vectors of each point were calculated, and only the normal vectors with upward components were retained to obtain the orientations of the wheat and maize leaves, as shown in Figure 4b,c. The ALA was then computed from all normal vectors of an individual wheat and maize plant, resulting in an ALA of 70.46° for wheat and an ALA of 55.36° for maize. The ALA value was used as the input of the SAIL model.

2.7. Simulating Canopy Reflectance

After calculating the ALA of the real wheat and synthetic wheat and maize canopies in Section 2.6, we obtained all input parameters of SAIL. The key input parameters are shown in

Table 3. The key input parameters of SAIL. In the field experiment, the plausible range of ALA was included to account for its potential uncertainty.

Parameter	Interpretation	Field (Wheat)	Synthetic (Wheat and Maize)
$\rho$	Leaf reflectance	Average measurement	Default (Mean reflectance = 0.22)
$\tau$	Leaf transmittance	Average measurement	Default (Mean reflectance = 0.25)
ALA	Average leaf angle	53.5° (range from 40° to 60° for potential uncertainty)	Wheat: 70.46° Maize: 55.36°
LAI	Leaf area index	Average measurement	Calculated
$R_{soil}$	Soil reflectance	Measurement	Default (Mean reflectance = 0.4)
$tts$	Solar zenith angle	Calculated from latitude, longitude and date time	15°, 30°, 45°, 50°, 55°, 60°, 65°, 70°, 75°
$tto$	Observe zenith angle	0°	0°
$psi$	The azimuth angle between sun and observed direction	Arbitrary	Arbitrary
$H_{spot}$	Hotspot parameter	0.01	0.01

. For the field wheat canopies, the solar zenith angle ($tts$) was calculated based on location of the site (i.e., latitude and longitude), date and time. The canopy reflectance was mesured at nadir, so the observation zenith angle ($tto$) was 0°, while the relative azimuth angle ($psi$) was considered arbitrary in the SAIL model. The leaf reflectance ($\rho$), leaf transmittance ($\tau$) and LAI were all set as the mean of the field measurements. However, when simulating reflectance with SAIL, we took into account potential uncertainties in the ALA. As a result, the ALA was set to range from 40° to 60°, which is consistent with the values obtained from existing research [44].

For the synthetic wheat and maize canopies, the leaf reflectance, transmittance and soil reflectance were all set to the default in LESS, as shown in Figure 6. The spectral data in LESS ranged from 400 to 2500 nm, with a 1 nm spectral resolution. The LAI of wheat and maize canopies was calculated using LESS. The SZA was set to 15°, 30°, 45°, 50°, 55°, 60°, 65°, 70° and 75°, the observation zenith angle was fixed as 0° and the relative azimuth angle could also be arbitrary.

2.8. Evaluating the Accuracy of SAIL in Modeling the Spectra of Row Canopies

We evaluated the SAIL model by comparing its simulated canopy reflectance with the measured wheat canopy reflectance and the simulated synthetic wheat and maize canopy reflectance using LESS, respectively. The relative root mean square error (rRMSE) was chosen as the evaluation index. It was calculated as follows:

$$\mathrm{r}\mathrm{R}\mathrm{M}\mathrm{S}\mathrm{E}=\left(\sqrt{\frac{\sum _{i=1}^N{(R_s-R_m)}^2}{N}}\right)/\left(\frac{{\sum }_{i=1}^N{R}_m}{N}\right)$$

(5)

where $R_s$ and $R_m$ represent the SAIL simulated canopy reflectance and the reference canopy reflectance (for field wheat canopies, $R_m$ is the measured canopy reflectance, but for the synthetic wheat and maize canopies, $R_m$ is the simulated canopy reflectance using LESS model), respectively, and $N$ represents the number of channels.

3. Results

3.1. Evaluation with the Field-Measured Wheat Canopies

Figure 8 shows the in situ-measured wheat canopy reflectance and a series of simulated wheat canopy reflectance values using the SAIL model. The simulated reflectance was considered the potential uncertainty of the ALA, which was denoted within the buffer region. According to Figure 8a–g, overall, the shapes of the modeled and measured spectral reflectance were similar. The modeled spectral reflectance of all canopies was slightly larger than the measured reflectance. In the visible region, the reflectance of the wheat canopies remains consistently low, exhibiting a small variation within the range of about 0.03 to 0.07 among the canopies. In the near-infrared region, the reflectance is higher, exhibiting a significant divergence and spanning from 0.2 to 0.37 among the canopies. The ALA significantly impacts the reflectance in the near-infrared region but shows little impact on the visible bands.

Figure 9 illustrates the relationship between the rRMSE and fCover and between the rRMSE and LAI of the field wheat canopies. The rRMSE first increases and then decreases with the increase in the fCover (Figure 9a). Similarly, the rRMSE first increases and then decreases with the increasing LAI (Figure 9b). The fCover ranged from 0.38 to 0.7, while the LAI ranged from 0.57 to 1.98, and the rRMSE ranged from 5% to 35%.

3.2. Evaluation Using the Synthetic Wheat and Maize Canopies

In synthetic wheat and maize canopies with a non-black soil background, the effects of the fCover and solar angle on the accuracy of SAIL in row canopies are shown in Figure 10 (synthetic wheat), Figure 11 (synthetic maize) and

Table 4. The mean rRMSE of synthetic wheat and maize canopies under non-black soil background and its difference between two SAAs.

SZA (°)	SAA (°)	Synthetic Wheat		Synthetic Maize
		Mean rRMSE (%)	Difference (%)	Mean rRMSE (%)	Difference (%)
15	90	24.1	1.9	10.3	3.4
	180	26		13.8
30	90	22.5	5.3	7.5	7
	180	27.9		14.5
45	90	21.3	9.2	8.3	7.8
	180	30.5		16.1
50	90	20.9	10.5	8.8	8.1
	180	31.3		16.9
55	90	20.4	11.9	9.5	8.2
	180	32.4		17.8
60	90	19.8	13.4	10.2	8.4
	180	33.2		18.7
65	90	19.2	15.1	10.8	9.0
	180	34.3		19.9
70	90	18.5	16.9	11.7	9.7
	180	35.4		21.4
75	90	18	18.7	13.1	10.2
	180	36.7		23.4

. Firstly, the rRMSE always initially rises and subsequently declines with the increasing fCover, regardless of the SZA and SAA (see Figure 10 and Figure 11). The SAIL model had lower accuracy when the wheat and maize canopies had medium coverage (about 0.2 < fCover < 0.5), with the maximum rRMSE reaching about 60% for wheat and 40% for maize. In contrast, when the wheat and maize canopies had very low or high coverage (0.1 > fCover or 0.8 < fCover), the SAIL model had high accuracy, with an rRMSE of < 20% for wheat and an rRMSE of < 10% for maize.

In addition, the rRMSE of the SAA in the across-row direction was always lower than that of the SAA in the along-row direction under various SZAs and fCover conditions. The mean rRMSE difference between the different SAAs gradually expanded with the increasing SZA (from 1.9% to 18.7% for wheat and from 3.4% to 10.2% for maize in Table 4). This indicated that SAIL had better accuracy when the SAA was across the row than along the row, and the larger the SZA, the greater the rRMSE difference between two SAAs would be.

Figure 12 is the mean rRMSE of synthetic wheat and maize canopies with 0.1 intervals of the fCover under non-black soil backgrounds and various solar angles. When the fCover was less than about 0.5, the rRMSE increased with the increase in the SZA, and when the fCover was greater than 0.5, the rRMSE of wheat decreased with the increasing SZA, while that of maize was little affected by the SZA. When the fCover was less than 0.1, both wheat and maize had high accuracy, and it gradually increased with the decrease in the SZA. From Table 4 and Figure 12, considering all the solar angles, the wheat canopies had higher rRMSE values, which indicated that SAIL seems to have better accuracy in maize canopies rather than in wheat canopies.

In synthetic wheat maize canopies with a black soil background, the effects of the fCover and solar angle on the accuracy of SAIL in row canopies are shown in Figure 13 (synthetic wheat), Figure 14 (synthetic maize) and

Table 5. The mean rRMSE of synthetic wheat and maize canopies under non-black soil background and its difference between two SAAs.

SZA (°)	SAA (°)	Synthetic Wheat		Synthetic Maize
		Mean rRMSE (%)	Difference (%)	Mean rRMSE (%)	Difference (%)
15	90	106.8	2.8	25.5	1.6
	180	109.6		27
30	90	109.8	11.7	24.6	9.2
	180	121.5		33.8
45	90	96.9	29.1	24.2	14
	180	126.0		38.2
50	90	91.4	36.6	26.5	15.4
	180	128.0		41.9
55	90	85.0	44.1	28.5	17.5
	180	129.1		45.9
60	90	78.3	52.3	31.3	19.5
	180	130.6		50.8
65	90	71.8	59	33.7	22.7
	180	130.9		56.4
70	90	64.5	66.9	35	27.1
	180	131.3		62.1
75	90	56.1	76.2	37	29.4
	180	132.2		66.4

. Unlike the case of non-black soil, the rRMSE continued to decrease with the increasing fCover regardless of wheat or maize, indicating that the SAIL model had higher accuracy in row canopies with higher fCover under the black soil background. The minimum rRMSE was smaller than 20% for wheat and 10% for maize, and the maximum rRMSE of SAIL could be as large as about 150% to 400% for wheat and 60% to 200% for maize. As for the SAA, the rRMSE values in the across-row direction were also always lower than those of the along-row direction, and the mean rRMSE differences between different SAAs were also gradually increasing with the increasing SZA (from 2.8% to 76.2% for wheat and from 1.6% to 29.4% for maize in Table 5), which was similar to the case of non-black soil, indicating that the SAIL model had higher accuracy when the SAA across the row, regardless of the soil background.

Figure 15 shows the mean rRMSE values of synthetic wheat and maize canopies with 0.1 intervals of the fCover under black soil backgrounds and various solar angles. Similar to Figure 12, the rRMSE increased with the increasing SZA when the fCover was less than about 0.5, and decreased with the increasing SZA when the fCover was greater than about 0.5. The influence of the SZA on maize canopies with high fCover values was still little. In addition, the wheat canopies also had a higher rRMSE than the maize canopies.

4. Discussion

4.1. Analysis of the Impact Factors on the Accuracy of SAIL in Modeling Row Crop Canopy Reflectance

In Figure 10 and Figure 11, the latter part of the curves (after the peak) aligns with our expectation, as we hypothesized that as the fCover increases, the row canopies gradually approximate the turbid media, thereby enhancing the simulation accuracy. However, a contradiction arose when the fCover was relatively low (before the peak, the fCover was about <0.4) and the rRMSE increased alongside the fCover, challenging our hypothesis. This phenomenon may arise due to the influence of the soil background, and it was confirmed by the results in Figure 13 and Figure 14 that the rRMSE consistently decreases with the increasing fCover, as expected when we changed to black soil to eliminate the effect of the background. This indicates that our hypothesis is reasonable. This conclusion aligns with a previous study that the influence of the soil background on the canopy reflectance would approach a maximum level at a low fCover, and it would significantly affect the accuracy of the inversion parameters. But when the fCover is high, the influence of the soil background on parameter inversion reduces greatly [30,45].

The upward trend of the rRMSE with the increasing fCover at a low fCover in Figure 10 and Figure 11 could be attributed to the influence of sunlit soil [11]. Although the presence of canopy heterogeneity introduced significant errors at a low fCover, due to the low LAI of the synthetic wheat and maize layer, the errors introduced by the unreasonable assumptions of SAIL was comparatively negligible when compared with the sunlit soil reflectance, i.e., the $f\left(U_1\right)\rho \left(U_1\right)I\left(U_1\right)\gg f\left(C_1\right)\rho \left(C_1\right)I\left(C_1\right)$ of Equation (1). As a result, the rRMSE remained at a low level under a low fCover. As the fCover gradually increased, the error induced by canopy heterogeneity diminished. However, the increase in the fCover reduced the areal fraction and characteristic irradiance of sunlit soil (i.e., $f\left(U_1\right)$ and $I\left(U_1\right)$) and increased the areal fraction and characteristic irradiance of sunlit canopy (i.e., $f\left(C_1\right)$ and $I\left(C_1\right)$). This led to the increasing rRMSE with the higher fCover. Upon reaching a balance among these influences, the rRMSE reached its peak. Subsequently, with a further increase in the fCover, the rRMSE began to decrease, and this decline could be primarily attributed to the escalating homogeneity of row canopies.

In our investigation of the impact of the solar angle on the accuracy of SAIL in row canopies, we found that the SAIL model always has better accuracy in the across-row direction compared to the along-row direction in Figure 10, Figure 11, Figure 13 and Figure 14. This corresponds to the previous studies that found that for the along-row or near along-row SAAs, more soil was illuminated through the void spaces between rows [12,33,34]. Compared to the canopy illuminated from the along-row direction of the SAA, the canopy illuminated from the across-row direction of the SAA more closely resembles turbid media due to the row structure. Figure 16 displays the synthetic maize canopy with a row configuration of (10,30) illuminated from the across-row and along-row directions of the SAA. In the canopy illuminated from the direction in (a) in Figure 16, the directional canopy gap is smaller and more uniformly distributed, making it more akin to turbid media compared to the canopy illuminated from the direction in (b).

The SZA mainly affects the magnitude of the rRMSE values, and this effect is influenced by the fCover. When the fCover was low (<0.5), the rRMSE tended to increase with the increase in the SZA (Figure 12 and Figure 15). When the fCover became larger (>0.5), the trend of wheat was the opposite (Figure 12a–c and Figure 15a–c), and the rRMSE decreased with the increasing SZA, but in this fCover range, the rRMSE of the maize canopies was little affected by the SZA (Figure 12b–d and Figure 15b–d). This could be attributed to the interplay between the SZA and the row canopy structure: at a low fCover, the portion of sunlit soil was larger than that of sunlit canopy, and the top of the canopy reflectance was mainly contributed by the soil reflectance. But for a large fCover, at a higher SZA, a larger portion of sunlit soil would be shaded by homogeneous turbid media compared to row canopies due to the row structure, i.e., the $f\left(U_1\right)$ of the turbid media decreased more. Li et al. [16] came to a similar conclusion. They found that, compared with the spectral measurements around 12:00 at noon (i.e., the SZA is low), the measurements at about 15:00 in the afternoon (i.e., the SZA is high) could improve the estimation of the leaf chlorophyll content, mainly due to the decrease in the observed sunlit soil fraction in off-noon times between the rows.

The difference between wheat and maize in Figure 12 and Figure 15 could be attributed to the plant structure difference, i.e., within-crown clumping [46], especially for small foliage plants (e.g., wheat), while for broadleaf plants (e.g., maize), the within-crown clumping tended to be small [47]. The difference between the relationship of the LAI and the fCover of synthetic wheat and maize also reflected the structure difference (Figure 5).

In the filed wheat canopies, the trend of the rRMSE with the increasing fCover was similar to that of synthetic wheat canopies (comparing Figure 9 with Figure 10), and the rRMSE value difference could be attributed to the following: (1) The solar angle of the wheat canopy was changing. The solar angle remained constant for the synthetic wheat canopies, whereas for the filed wheat canopies, a temporal shift during the measurements resulted in a changing solar angle throughout the measurement process. The SZA varied between 26° and 44°, and the azimuth angle spanned from 113° to 239° (wheat was row-planted in an east–west orientation). Based on the earlier analysis, we determined that the SAA and SZA would significantly influence the rRMSE. (2) The ranges of the wavelength were different. The wavelength of the synthetic wheat canopies ranged from 400 to 2500 nm, while that of the filed wheat canopies ranged from 485 to 850 nm. Due to the difference of the leaf optical properties in 400 to 2500 nm and 485 to 850 nm, there may be a great difference in the reflectance accuracy between wheat and maize canopies.

4.2. The Conditions of Row Canopies Close to Homogeneous Turbid Media

One of our objectives was to determine the conditions within which the SAIL model can accurately simulate the row canopy reflectance. In order to draw a more practical conclusion, the soil background was restricted to non-black soil, and in order to minimize the influence of the soil background, a larger fCover range was selected. Thus, according to Figure 12 and Figure 15, we suggested that when the fCover ranged from 0.6 to 1, and when the SZA ranged from 65° to 75° for wheat, SAIL could simulate the row canopy reflectance with satisfactory accuracy (rRMSE < 10%); the same simulation accuracy can be achieved in maize canopies as long as fCover is greater than 0.8. This range holds true for different SAAs, but for a higher accuracy, an SAA in the across-row direction is recommended, because there is always a high accuracy under this SAA.

It is worth noting that, when the fCover was less than 0.1, the SZA ranged from 15° to 50° in Figure 12, and SAIL also had a high accuracy (rRMSE < 10%). However, because the fCover range was significantly affected by the soil background (Figure 15), it was excluded.

5. Conclusions

In this study, we aimed to evaluate the accuracy of SAIL in modeling the canopy reflectance of row crop canopies. Specifically, both the field datasets of the wheat canopies and the synthetic datasets of the wheat and maize canopies were adopted to investigate the impacts of the vegetation cover fraction (fCover), soil background and solar angle on the performance of SAIL. The reference spectra were acquired from in situ spectra measurements in the field and the LESS 3D RTM simulated spectra, respectively.

The results demonstrate that the fCover has the most influential impact, and the influence of the soil background will decrease with the increasing fCover. With a non-black (normal) soil background, both the field measurement and simulation datasets show that the accuracy of SAIL first decreases and then increases with the increasing fCover, and the largest errors will occur when the row crops have medium coverage (0.4 < fCover < 0.7). As for the solar angles, at a high fCover, a higher SZA will lead to higher accuracy in the wheat canopies, but the SZA has little influence on the accuracy of the maize canopies. The accuracy of the SAA in the across-row direction is always higher than that in the along-row direction. In addition, we found that when the SZA ranged from 65° to 75° and when the fCover was greater than 0.6 for wheat, SAIL had satisfactory accuracy (rRMSE < 10%); the same accuracy could be achieved for maize as long as the fCover was greater than 0.8. This study provides a reference for the application of SAIL in row canopies and supports the application of SAIL in high fCover row canopies.