Topographic Effects on Optical Remote Sensing: Simulations by PLC Model

Optical remote sensing offers a convenient method to monitor changes in mountain vegetation at regional and global scales, thanks to its synoptic coverage and frequent temporal sampling capabilities provided by satellite observations. However, local topography substantially affects remotely sensed observations and subsequently impacts the accuracy of biophysical parameter retrieval [e.g., leaf area index (LAI)], hindering the application of remote sensing over mountainous areas. However, the quantification of topographic effects based on remote sensing imagery is limited by the variability of conditions in a study area. Additionally, it is also not conducive to investigate the topographic effects on hyperspectral observations. Therefore, this article employed computer simulation model, i.e., path length correction model, to controllably simulate the topographic effects on hyperspectral reflectance, and 12 vegetation indices (VIs) and LAI retrieval. The results showed that topographic effects varied with the spectral band and were modulated by various factors, such as slope, aspect, and sun position. The topographic effects on VIs exhibited divergence, in which the topographic effects on normalized difference vegetation index and difference vegetation index were smallest and largest, respectively. The topography effects on LAI retrieval were related to terrain configuration and canopy density under specific solar zenith angle. The relative error of LAI retrieval could exceed 100% under extreme conditions. This article will facilitate understanding of topographic effects on hyperspectral remote sensing over mountainous regions.

and carbon cycles, thanks to their rich water and terrestrial carbon storing capacity [3], [4], [5].The explosive development of optical remote sensing technology has facilitated accurately monitoring land surface variables over mountainous areas.However, remote sensing observations are susceptible to topographyinduced radiometric distortion [6], [7], [8], [9].The rugged terrain has two primary impacts on the optical remote sensing [10]: 1) terrain affects the incident conditions of canopy by redistributing incoming irradiance [8]; and 2) terrain modulates the canopy structural, illumination, and viewing geometry, and significantly impacts canopy bidirectional reflectance effects [7], [11].Those effects result in a change in the total radiance received by the satellite, and subsequently contaminate the accuracy of parameters retrieval over mountainous areas.
Vegetation indices (VIs) are straightforward mathematical transformations of spectral bands, meticulously designed to enhance the detection of vegetation properties.These indices can be directly computed, avoiding the introduction of biases or the need to make assumptions about land-cover classes, soil background types, and atmospheric conditions [12].The normalized difference vegetation index (NDVI) is extensively used across a variety of regional and global scale studies [13], [14], [15] among the various VIs.Nevertheless, numerous confounding factors, such as soil background and saturation effects, exert a significant influence on its values and pose obstacles to its practical applications [16].Therefore, several improvements have been implemented to reduce the impact of intervening atmospheric conditions and soil background, aiming to isolate vegetation contributions more effectively, including the enhanced vegetation index (EVI) [12], the soil adjusted vegetation index (SAVI) [17], two-band enhanced vegetation index (EVI2) [18], and the near-infrared reflectance of vegetation (NIRv) [19].However, VIs are also significantly affected by terrain [20] over rugged mountainous areas.Chen et al. [20] and Matsushita et al. [21] investigated the topographic effects on these VIs and revealed that NDVI is slightly sensitive to topographic effects, while SAVI, EVI, and NIRv are notably influenced by the terrain.However, these studies have been implemented for a specific imagery, and the impact of different terrain configurations on VIs has not been systematically evaluated.Furthermore, the topographic effects on recently developed novel VIs, such as the normalized difference greenness index (NDGI) [22] and kernel normalized difference vegetation index (kNDVI) [23], remain unclear.
Apart from the topographic effects, optical remote sensing is typically affected by atmospheric effects, field of view effects, etc.Therefore, obtaining quantitative comparative results that exclusively focus on topographic effects can be challenging.Computer simulations provide an efficient alternative method for validation activities [24].They offer a highly controlled environment for conducting validation, and allow for explicit specification of the topographic factors that can influence remote sensing observations/VIs, such as slope and aspect.Furthermore, through the dedicatedly designed scenarios, computer simulation can encompass a variety of conditions that exist in the real world, thereby increasing the representativeness of the quantization results [25].
The primary objective of this article is to investigate the topographic effects on optical remote sensing based on path length correction (PLC) model [26].Specific objectives are to evaluate the effects of slope and aspect on reflectance/VIs and explore the seasonal variations of topographic effects on reflectance/VIs.Moreover, we further explored the extent to which topography affects the inversion of leaf area index (LAI), and is the inputs of PLC model.
The rest of this article is organized as follows.In Section II, simulating reflectance/VIs of inclined terrains based on the PLC model is presented.The results and discussion, respectively, are described in Sections III and IV.Finally, Section V concludes this article.

A. PLC Models
In this article, we employed PLC model to investigate the topographic effects on optical remote sensing.Yin et al. [26] highlighted that the variation in path length induced by terrain plays a critical role in causing topographic effects.The performance of PLC model for inclined surface was thoroughly verified based on Monte Carlo simulation and remote sensing images.In this context, we provided a concise introduction to the modeling of single-order scattering from leaves and soil background, which are essential components of the PLC method.For information about the multiple scattering component, please refer to [26].
The single-order scattering of direct radiation from the canopy (ρ 1 ) is expressed as the sum of single-order scattering of vegetation (ρ c 1 ) and soil background (ρ s 1 ) where and where r 1 and r 2 are unit vectors in the solar direction and viewing direction, respectively; and Γ(r 1 , r 2 ) is the leaf scattering phase function, which quantifies the probability of the intercepted energy from solar direction in the viewing direction.μ 1 and μ 2 are the cosine of the polar angles of r 1 and r 2 directions, respectively; and ρ s (r 1 , r 2 ) is the soil bidirectional reflectance factor.Q 0 (r 1 , r 2 , −1) is the bidirectional gap probability underneath the canopy.Q (r 1 , r 2 , z) is the bidirectional gap probability between r 1 and r 2 when the relative optical height of z, which can be represented as follows: where p(r 1 , z) and p(r 2 , z) represent the directional gap probabilities within the canopy at height z in the directions r 1 and r 2 , respectively.C HS (γ, z) is the hotspot correction function used to reproduce the sharp reflectance increase close to the backscattering direction, which is controlled by the size of the hotspot γ [27].
Based on Beer's law [28], the directional gap probability can be derived as follows: where L z is the accumulated LAI from a relative optical height of z to the top of the canopy; and G(r, z) is the leaf projection function defined as the area of a unit LAI projected along the direction of z. d(r, z) is the photon path length, a crucial variable that affects radiation transfer, which represents the geometrical distance between relative optical height of z and the top of the canopy along the solar/viewing direction.On the inclined terrain, the photon path length is significantly affected by the terrain and can be expressed as [29] where α and β, respectively, are the slope and aspect of the inclined terrain.θ and ϕ are the solar/view zenith and azimuth angles, respectively.

B. Simulated Reflectance of Inclined Terrains Based on PLC Model
The generation of the canopy reflectance over inclined surfaces is the prerequisite for evaluating the topographic effects.We generated canopy reflectance in the 400-2500 nm wavelength based on the PLC model described in subsection A. The PROSPECT-5B model [30] embedded in PLC model was used to simulate the leaf optical properties.This model considers leaf reflectance and transmittance as functions of various leaf characteristics, including leaf chlorophyll content, carotenoid content, equivalent water thickness, dry matter content, brown pigment content, and leaf structure parameter.The soil background characteristics were characterized by a representative set of spectra multiplied by a brightness parameter ranging from 0 to 1 [31].The recommended values for these parameters are listed in Table I.The slope ranged from 0°to 70°, encompassing horizontal, gentle, moderate, and steep surfaces, which essentially covers most of the slopes found on Earth's surface.The aspect was varied from 0°to 360°to cover all possible directions.To capture the multiangle observation of reflectance, the view zenith angle was adjusted from 0°to 80°, while the view azimuth angle ranged from 0°to 360°.The solar zenith angles (SZAs) were set between 15°and 65°, with a fixed solar azimuth angle of 0°.The recommended values of the remaining parameters input by the model, i.e., canopy parameters (LAI, average leaf inclination, and hotspot size parameter) and atmospheric condition (diffuse sky radiation) can be found in Table I.

C. Vegetation Indices
VIs have been increasingly employed for vegetation dynamics monitoring and biophysical and biochemical parameters retrieval due to their ability to mathematically combine or transform reflectance from multispectral channels (using ratios, differences, and/or derivatives) [12], [32].After a comprehensive literature review, in this article, 12 VIs were employed to evaluate the topographic effects on VIs (see Table II for detailed descriptions, formulae, and references), based on their reported popularity and performance in remote sensing applications, particularly for assessing vegetation properties [32], [33], [34].

D. Quantifying the Topographic Effects
The commonly used topographic effects evaluation criteria, i.e., linear correlation analysis between the cosine of local solar incident angle [cos(i)] and the reflectances/VIs [40], was employed in this article.The magnitude of topographic effects on reflectances/VIs can be quantified using the determination coefficient of a linear relationship (referred to R 2 TC hereafter).The cos(i) is calculated as where θ s and ϕ s , respectively, are the solar zenith and azimuth angles.The larger R 2 TC values, the stronger the topographic effects, and vice versa.

E. Analysis of Effects of Topography on LAI Inversion
LAI is a crucial vegetation structural variable in vegetation monitoring, agriculture, ecology, carbon cycle, and climate [41].As an input parameter in PLC model, we explored the extent to which topography (i.e., slope and aspect) affects the inversion of LAI for a given SZA.First, an empirical relationship between EVI of the horizontal surface for slope of 0°and aspect of 0°under for a given SZA and LAI was established.Subsequently, the EVI values derived from inclined reflectance

A. Analysis of Topographic Effects on Reflectance
Fig. 1 showed the angular distributions of the reflectance over different inclined surfaces.For brevity, we only show results for the bands centered at 665 nm [Fig.1(a)] and 842 nm [Fig.1(b)], which are widely used for vegetation monitoring.The results showed that reflectance over a horizontal surface exhibited azimuthal symmetry, except in the hotspot direction (the viewing direction, i.e., 30°in this simulation, is consistent with the solar direction), and decreased/increased with increasing view zenith angle for 665/842 nm band.The presence of a slope distorts Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.the angular distribution of reflectance, making inclined surfaces unobservable from all view directions within the hemisphere.Specifically, in the sunny-slope direction, where the aspect is 90°and the view azimuth angle ranges from 0°to 180°, the reflectance value increased.Conversely, the reflectance value decreases in the shady-slope direction, with the view azimuth angle ranging from 180°to 360°.
Regarding the effects of aspect on reflectance, Fig. 2 exhibited the angular distributions of reflectance over inclined surfaces with aspects of 0°, 90°, 180°, and 270°, which represent the slope surface facing North, East, South, and West, respectively, for slope of 20°.A comparison of the reflectance for different aspects revealed complete symmetry at 90°and 270°, while noticeable differences were evident at 0°and 180°.The variations in aspect lead to changes in the local slope angles and the local solar-viewing geometries, resulting in the distortion of the angular distribution of reflectance.
The topographic effects on 400-2500 nm wavelengths reflectance with slope were shown in Fig. 3.The results indicated that the determination coefficient (R 2 TC ) between the reflectance in all wavelengths and cos(i) increase with increasing slope [Fig.3(a)].Closer inspection revealed that the R 2 TC of different wavelengths is not constant.Overall, larger values of R 2  TC are observed between the 700 and 1400 nm wavelengths (R 2 TC up to 0.6 when SZA is 60°), while lower values occur around 650, 1900, and 1700 nm wavelengths.
To explore the seasonal variations in the magnitude of topographic effects on reflectance, the SZA was set ranging from 15°to 65°with the step of 3°.Fig. 4 showed the topographic TC of fitted regression lines between the reflectance and cos(i) with slope when the solar zenith angle is 30°.Other parameters used for reflectance simulation were summarized in Table I.
effects on 400-2500 nm wavelengths reflectance with SZA.The results indicated that the magnitude of topographic effects on reflectance is not constant, depending on solar incident conditions, which increase with increasing SZA.Closer inspection revealed that the R 2 TC of different wavelengths is not constant either.Overall, the R 2 TC is slightly larger in the range of 700-1400 nm wavelengths.

B. Analysis of Topographic Effects on VIs
The topographic effects on VIs at different slopes were shown in Fig. 5.The results indicated that, overall, the R 2 TC between the VIs and cos(i) increase with increasing slope.However, there are significant differences observed among the different VIs.For SR, DVI, MSR, EVI, EVI2, NIRv, and kNDVI, the R 2 TC Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.TC of fitted regression lines between the VIs and cos(i) as function of slope.Other parameters used for reflectance simulation were summarized in Table I. maintained a relatively large value and obviously increased with an increasing slope, reaching the maximum value at the slope of 60°(DVI > MSR > SR > NIRv = kNDVI > EVI > EVI2).In contrast, the R 2 TC of NDVI, GRVI, SAVI, PRI, and NDGI was small, exhibiting a slight increase with increasing slope (NDVI < PRI < NDGI < SAVI < GRVI).Among those VIs, DVI and NDVI presented the largest and smallest topographic effects, respectively.We further analyzed the variations of Vis across different aspect angles with slope (Fig. 9).The results revealed obvious variations in the effects of aspect on different Vis, primarily on the sunny aspect (0°) and shady aspect (180°).When slope was small, the variations of each VI with aspect were slight.As the slope increased, the difference in VIs between the shady aspect and the sunny aspect become larger: SR, GRVI, PRI, MSR, and NDGI decreased with increasing slope on the sunny aspect and increased with increasing slope on the shady aspect, while SAVI, DVI, EVI, EVI2, NIRv, and kNDVI exhibited the opposite trend.In contrast, the difference in NDVI TC of fitted regression lines between the VIs and cos(i) as function of solar zenith angle.Other parameters used for reflectance simulation were summarized in Table I.
between the shady and sunny aspects remains nearly constant regardless of the slope.
Fig. 6 presents the topographic effects on VIs for different SZAs.The results indicated that, overall, the R 2 TC increases with increasing SZA.However, there are significant differences observed among the different VIs.For all SZAs, the relatively large R 2 TC values were observed for SR, DVI, and kNDVI.For MSR, EVI, EVI2, and NIRv, the R 2 TC increased with an increasing SZA, reaching the maximum value at the SZA of 65°.By contrast, R 2 TC of NDVI, GRVI, SAVI, PRI, and NDGI were at small values and hardly change with the increase of SZA.We also analyzed the variations of VIs across different aspect angles with SZA (Fig. 10).The results indicated that the distribution of SR, GRVI, PRI, and MSR on aspects is highly influenced by SZA, followed by kNDVI, while NDVI, SAVI, DVI, EVI, EVI2, NIRv, and NDGI were minimally affected.

C. LAI Inversion Errors Over Inclined Terrains
The relative errors between the simulated horizontal-and inclined-case scenes in a slope-aspect space were shown in Fig. 7. Notably, relative error exhibited different features for different canopy densities.The effects of topography on LAI inversion for sparse canopies were found to be minimal, whereas as the canopy density increased, the inversion errors also increased.The results also indicated that the smaller errors were attributed to areas with smaller slope and the errors increased with an increase in the slope.In the aspect domain, positive relative errors occurred when the terrain faced the sun (aspect angle = 0°), while negative relative errors appeared facing away from the sun (aspect angle = 180°).The inversion error was larger on sunny aspects compared to shady aspects.Moreover, the inversion error was also influenced by the SZA, with larger Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.Fig. 7. Distribution of the relative error of leaf area index (LAI) between the inclined surface and horizontal surface (slope = 0°and aspect = 0°) in the slope-aspect space with solar zenith angle (SZA).In the simulations, hotspot size was set to 0.1 and the leaf inclination distribution function was specified as spherical (average leaf angle of 57.3°).The solar azimuth, view zenith, and azimuth zenith angles were all set to 0°.
SZAs resulting in greater inversion errors.Overall, the inversion error was larger for denser canopies, larger slope angles, and larger SZAs.For example, the inversion error exceeds 100% for slope angle of 70°, LAI of 7 m 2 /m 2 , and SZA of 35°.

IV. DISCUSSION
This article investigated the topographic effects on remote sensing observations over inclined terrain.The analysis of topographic effects was accomplished through PLC model simulations.We first analyzed the effects of topography on reflectance for the bands from 400 to 2500 nm.The results revealed the topographic effects were modulated by various factors.The slope and aspect alter the canopy structure [26], [42], distorting the radiative transfer process of photons within the canopy.They also change the local solar/view geometries, which distorted the angular distribution of the reflectance (Figs. 1 and 2).As the slope increased, the difference of reflectance between sunny and shady aspects becomes more obvious.From Fig. 4, it also can be observed that the topographic effects are SZA-dependent, with stronger topographic effect observed when larger SZAs which increased the relative amount of surface shadows [43].However, the topographic effects slightly decreased under large SZAs.This could be due to the fact that PLC model does not consider the effects of terrain-reflected radiance [26].The radiation received by an inclined surface is more complex, including solar direct radiance, sky diffuse radiance, and adjacent terrain reflected radiance [6].The proportion of sky-diffuse and terrain-reflected radiance becomes dominant when SZA is slant [44].Therefore, the topographic effects on reflectance may be slightly underestimated at lager SZA.In addition, topographic effects were wavelength-dependent (Figs. 3 and 4).R 2 TC value was larger in the 700-1400 nm bands, while smaller in other bands.This may be due to the varying impact of sky diffuse reflection on different wavelengths [45].Moreover, compared to other bands, the 700-1400 nm bands reflectance penetrated deeper into the canopy and dominated by multiscattering within the canopy.Therefore, any changes in canopy structure caused by terrain variations can significantly influence the 700-1400 nm bands reflectance.
Topography significantly affects hyperspectral reflectances and then impacts the VIs.In this article, we analyzed variations of topographic effects on 12 popular VIs with slope, aspect, and SZA.The results shown the topographic effects on VIs exhibited divergent performances.Among the selected VIs, NDVI is insensitive to topography, consistent with existing studies [20], [21], [46], [47].Because of the normalized difference formula, NDVI not only eliminates the influence of the solar angle's variation, clouds, and clouds shadow [36], but also mitigates a large proportion of topographic effects over mountainous areas.GRVI, PRI, and NDGI, which share the same mathematical formulation as NDVI, exhibited slight sensitivity to topography.However, a caveat is that it is crucial to exercise caution when using those VIs in rugged mountainous areas characterized by large slopes and SZAs.To mitigate the influence of soil background on NDVI, several soil-adjusted VIs have been proposed  I. [48], [49], [50] based on the soil line concept [17].However, there have been report suggesting that soil adjustment factor may increase the sensitivity of these indices to topographic variations [21].Therefore, we explored topographic effects on SAVI under soil adjustment factor (0 to 1 with a step of 0.1), as shown Fig. 8. Surprisingly, the topographic effects of SAVI were not only influenced by slope and SZA, but were also regulated by the soil adjustment factor: the topographic effects on SAVI are the weakest when soil adjustment factor is equal to 0.1.With the increase of soil adjustment factor, the magnitude of topographic effects also increases.In addition, well-known issues of NDVI with nonlinear relations and saturation effects at high biomass regions have been reported [12], [51], [52].Several attempts have been proposed to address and correct these limitations, such as EVI, EVI2, and NIRv as the product of multiply NDVI with NIR and kNDVI based on the theory of kernel methods.Despite these attempts to increase the sensitivity of NDVI to vegetation biophysical and biochemical parameters which facilitate the monitoring the terrestrial carbon dynamics [23], [53], [54], [55], [56].However, our findings indicated that these efforts often decrease their applicability in mountainous regions, particularly kNDVI.The sensitivity of EVI, EVI2, and NIRv to topographic effects may be attributed to their sensitivity to BRDF effects [21], [32].However, the mechanism of topographic effects on kNDVI is not clear, and this remains a direction for future article.
VIs are extensively employed to estimate crucial biophysical climate variables, for instance, LAI [57].The EVI has been regarded as a modified NDVI, offering enhanced sensitivity to areas with high biomass and improved vegetation monitoring capabilities.It is widely used for LAI retrieval.In this article, we focused on exploring the impact of topography on LAI inversion over inclined terrain based on the EVI.The terrain characteristics strongly influence the spatial variations of EVI derived from reflectance of terrain-induced distortion (see Fig. 9), with EVI values being stretched on the sunny slopes and compressed on the shaded slopes.Consequently, this asymmetric effect leads to significant and unrealistic spatial discrepancies in LAI estimation over inclined surfaces (see Fig. 7), with overestimations on sunny slopes and underestimations on shaded slopes.Furthermore, the topographic effects on LAI inversion were found to be related to canopy density: the larger canopy density led to greater inversion errors, consistent with existing study [58].The leaf inclination angle distribution (LIDF) varies across different vegetation types and plays a crucial role in determining the canopy reflectance [59], [60].Due to the terrain, LAI estimates for different LIDF are generally lower [58].However, the variation trends do not change with the terrain characteristics [60].Therefore, only the most commonly used LIDF, i.e., spherical [61], was selected to explore the effects of topography on LAI inversion in this article.
In conclusion, topography significantly distorts remote sensing reflectance, subsequently affecting VIs, and ultimately impacts LAI retrieval over mountainous areas.Therefore, it is essential to mitigate or even eliminate the topographic effects on reflectance/VIs for accurately conducting downstream applications.Over the past four decades, numerous topographic correction methods for reflectance have emerged [40], for example, statistical-empirical [62], C-correction [62], PLC [7], and Sun-Canopy-Sensor + C-correction [63].Those methods achieved a best performance in mitigating topographic effects for most situations [40], [64], [65].The commonly used method to eliminate topographic effects on VIs is to first obtain the topography-free reflectance and then calculate the VIs [46].However, this may limit its applicability to large scale for operational implementation.Liao et al. [66] made a modification to the EVI by replacing the constant soil adjustment factor with a variable that is related to cos(i) and Chen et al. [67] integrated the terrain normalization conversion factors derived from the PLC into the NIRv, effectively extending the feasibility of these two VIs to mountainous areas.These pioneering studies provide valuable insights for the development of topographyindependent VIs in the future.
The main limitation of this article is the lack of groundbased measurement data for a more comprehensive assessment of the simulation results.This is mainly due to sparse distribution of field measurements and the lack of standardized measurement methods for sloped terrain [29], [68], [69].To provide relatively reliable validation results, we have employed a common validation strategy widely used in most research [58], [70].This strategy entails using values from the equivalent horizontal surface as the "truth value."In addition, the sky view factor, apart from slope and aspect, is another critical topographic factor.It is defined as the relative proportion of the solid angle of the sky visible from a pixel, unobstructed Fig. 9. Mean VIs values of different slopes across aspect angles when the solar zenith angle is 30°.The polar angle and radius represent different aspects and the magnitude of the VI, respectively.In the simulations, leaf area index and hotspot size were set to 3 m 2 /m 2 and 0.1, respectively, and the leaf inclination distribution function was specified as spherical (average leaf angle of 57.3°).The solar azimuth, view zenith, and azimuth zenith angles were all set to 0°. by the surrounding topography, and ranges between 0 and 1 [71].A small sky view factor indicates a large influence of surrounding reflected irradiance, and vice versa.However, it is worth noting that the PLC model lies in neglecting the nonlocal terrain effects, e.g., the surrounding-reflected irradiance.In future articles, there is potential for the PLC model to be integrated into existing radiative transfer simulation frameworks designed for rugged terrain.One such framework, proposed by Mousivand et al. [25], is based on the four-stream radiative transfer theory.This integration could provide a more comprehensive understanding of topographic effects on optical remote sensing.

V. CONCLUSION
In this article, we investigated the topographic effect on optical remote sensing and quantified this effect on LAI retrieval through PLC model simulations of mountain surface reflectance for across bands ranging from 400 to 2500 nm.The results showed that slope and aspect distorted the angular distribution of the reflectance.As slope increases, the topographic effects become more obvious; the topographic effect is greater on the sunny aspects compared to the shady aspects.In addition, topographic effects are SZA-and wavelength-dependent.The topographic effects on hyperspectral reflectance subsequently affects VIs.We analyzed the variations of topographic effects on 12 VIs.The results indicated the topographic effects on the band-ratio format VIs were usually smaller, particularly for NDVI, while a heavily influence on SR, MSR, EVI, EVI2, NIRv, and kNDVI.Surprisingly, the topographic effects of SAVI were also regulated by the soil adjustment factor.By comparing the differences relative error between LAI derived from inclined and equivalent horizontal under identical canopy parameters found that the significant increase in inversion error with higher values of slope, SZA, and canopy density, and could exceed 100% when the slope was 70°, SZA was 35°, and LAI was 7 m 2 /m 2 .These findings shed light on the effects of topography on remote sensing observations and LAI inversion over mountainous areas, contributing to a better understanding of this aspect in the field of remote sensing.APPENDIX See Figs. 9 and 10.
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Fig. 1 .
Fig. 1.Angular distributions of (a) 665 and (b) 842 nm band reflectance for a canopy with leaf area index of 1.0 m 2 /m 2 , hotspot size of 0.1, sun zenith angle of 30°, and sun azimuth angle of 0°with slopes increased from 0°to 70°with a step of 10°.In the simulations, the leaf inclination distribution function was specified as spherical (average leaf angle of 57.3°).

Fig. 2 .
Fig. 2. Angular distributions of (a) 665 and (b) 842 nm band reflectance for a canopy with leaf area index of 1.0 m 2 /m 2 , hotspot size of 0.1, sun zenith angle of 30°, and sun azimuth angle of 0°with a slope of 20°and aspects of 0°, 90°, 180°, and 270°.In the simulations, the leaf inclination distribution function was specified as spherical (average leaf angle of 57.3°).

Fig. 3 .
Fig. 3. Variation of the topographic effects represented by R 2TC of fitted regression lines between the reflectance and cos(i) with slope when the solar zenith angle is 30°.Other parameters used for reflectance simulation were summarized in TableI.

Fig. 4 .
Fig. 4. Seasonal variation of the topographic effects represented by R 2 TC of fitted regression lines between the reflectance and cos(i) with solar zenith angle when slope is 20°.Other parameters used for reflectance simulation were summarized in TableI.

Fig. 5 .
Fig. 5. Variation of the topographic effects represented by R 2TC of fitted regression lines between the VIs and cos(i) as function of slope.Other parameters used for reflectance simulation were summarized in TableI.

Fig. 6 .
Fig. 6.Variation of the topographic effects represented by R 2TC of fitted regression lines between the VIs and cos(i) as function of solar zenith angle.Other parameters used for reflectance simulation were summarized in TableI.

Fig. 8 .
Fig. 8. Variation of the determination coefficient (R 2 TC ) between the SAVI under difference soil adjustment factors and the cosine of the local solar incidence angle [cos(i)] as function of (a) slope and (b) solar zenith angle.Other parameters used for reflectance simulation were summarized in TableI.

Fig. 10 .
Fig. 10.Mean VIs values of different slopes across aspect angles when the slope is 20°.The polar angle and radius represent different aspects and the magnitude of the VI, respectively.The other parameters settings were the same as those in Fig. 9.

TABLE I SPECIFICATIONS
OF INPUT PARAMETERS UTILIZED IN THIS ARTICLE FOR SIMULATING THE SLOPING REFLECTANCE

TABLE II DEFINITIONS
OF THE VEGETATION INDICES TESTED IN THIS ARTICLE