Effects of Atmospheric, Topographic, and BRDF Correction on Imaging Spectroscopy-Derived Data Products

Surface reflectance is an important data product in imaging spectroscopy for obtaining surface information. The complex retrieval of surface reflectance, however, critically relies on accurate knowledge of atmospheric absorption and scattering, and the compensation of these effects. Furthermore, illumination and observation geometry in combination with surface reflectance anisotropy determine dynamics in retrieved surface reflectance not related to surface absorption properties. To the best of authors' knowledge, no comprehensive assessment of the impact of atmospheric, topographic, and anisotropy effects on derived surface information is available so far. This study systematically evaluates the impact of these effects on reflectance, albedo, and vegetation products. Using three well-established processing schemes (ATCOR F., ATCOR R., and BREFCOR), high-resolution APEX imaging spectroscopy data, covering a large gradient of illumination and observation angles, are brought to several processing states, varyingly affected by mentioned effects. Pixel-wise differences of surface reflectance, albedo, and spectral indices of neighboring flight lines are quantitatively analyzed in their respective overlapping area. We found that compensation of atmospheric effects reveals actual anisotropy-related dynamics in surface reflectance and derived albedo, related to an increase in pixel-wise relative reflectance and albedo differences of more than 40%. Subsequent anisotropy compensation allows us to successfully reduce apparent relative reflectance and albedo differences by up to 20%. In contrast, spectral indices are less affected by atmospheric and anisotropy effects, showing relative differences of 3% to 10% in overlapping regions of flight lines. We recommend to base decisions on the use of appropriate processing schemes on individual use cases considering envisioned data products.

The extraction of surface information, such as various biogeophysical variables, is typically based on surface reflectance, a data product retrieved from measured at-sensor radiances via the so-called atmospheric compensation (or atmospheric correction).While empirical or semiempirical methods exist [23], this processing step usually employs physical atmospheric radiative transfer models to compensate for atmospheric absorption and scattering effects (e.g., caused by aerosols and water vapor) and to correct for surface irradiance variations.Resulting reflectance data are commonly described as hemisphericalconical reflectance factors (HCRF) [24].Reflectances and vegetation indices show significant sensitivities to the atmospheric compensation [25].In a study by [26], for example, it was found that the atmospheric compensation yields uncertainties in finally retrieved data products on the order of 2% to 5%.
Topography, especially in rugged mountainous terrain, additionally complicates reflectance retrievals, since the terrain orientation toward the sun changes with observation and illumination geometry and, thus, affects actual surface irradiance due to incidence angle-related irradiance variations, changes in diffuse sky irradiance, and changes in terrain irradiance.If not properly accounted for, topography effects lead to wavelength-dependent HCRF differences between pixels with similar surface properties but different orientation, and can alter the robustness of subsequently retrieved surface information [27], [28], [29].Topographic compensation (or topographic correction) methods account for such illumination dynamics.Common examples are the Statistical-Empirical method [30] or the Modified Minnaert method [27].Riaño et al. [31] provided a detailed overview of the most common approaches.Most of these topographic compensation methods were developed for space-based systems with spatial resolutions of 30 m or more, but can be adapted to high-spatial-resolution airborne systems with resolutions of few meters or less [32].While in most algorithms, the atmospheric and topographic compensation are sequential operations, i.e., a post hoc topographic compensation, recent approaches obtained promising results from a joint atmospheric and topographic compensation [33].Using such a joint approach, a recent study by [34] was even able to estimate topography directly from radiance data.
Natural surfaces usually show an angular dependence of the scattering of incident radiation, a characteristic called ground reflectance anisotropy.The reflectance behavior of surfaces, hence, also surface anisotropy, is typically described as a function of illumination and observation geometry by the bidirectional reflectance distribution function (BRDF) [24], [35].For vegetation, main contributors of reflectance anisotropy are volumetric and geometric-optical scattering.Both are determined by structural properties of the canopy (e.g., gap fraction, leaf orientation, leaf clumping) and change with vegetation type [36], [37], [38].Most current atmospheric and topographic compensation methods treat surfaces as Lambertian scatterers (perfectly hemispherical isotropic scattering) to solve the complex radiative transfer equations, and do not compensate for HCRF dynamics caused by anisotropy.Resulting HCRF products consequently show surface-and wavelength-specific variations of up to 20% in reflectance units [26], [39], [40].These variations become even more pronounced with larger field-of-view (FOV) sensors [41], and higher spatial resolution of the data [42], which leads to a larger contribution of small-scale anisotropy effects in pixels.Anisotropy-caused, wavelength-dependent variations in HCRF data and in their linear combinations [i.e., spectral indices like the normalized difference vegetation index (NDVI) or the photochemical reflectance index (PRI)], are optical effects resulting in visually perceptible differences in HCRF data and indices between neighboring flight lines.This leads to complications in the interpretation of mosaics of different flight lines [43] and of remote sensing-derived information for environmental research [44].Anisotropy effects should not be misinterpreted as retrieval artifacts, but rather understood as an intrinsic characteristic of natural surfaces, while approaches used to retrieve surface information (e.g., plant pigments, leaf area index) from HCRF data or spectral indices should account for reflectance anisotropy to avoid unwanted sensitivities in resulting data products [45].
Related complications in interpreting anisotropy-affected HCRF data and in retrieving unaffected surface information led to the development of an optional processing step, following the atmospheric and topographic compensation, to normalize for reflectance anisotropy, the so-called BRDF correction (BRDF compensation) or anisotropy correction (anisotropy compensation) [23].While several physical BRDF models have been developed and studied for various materials (e.g., [46], [47], [48]), most operational approaches work with semiempirical algorithms.These either normalize the data to an unambiguous bihemispherical reflectance (BHR) value (e.g., BREFCOR in [49]) or to nadir observation geometry (e.g., aNBAR in [40]).BREFCOR and similar approaches, such as RT-BRDF [42] or FlexBRDF [50], are all based on a description of the BRDF with semiempirical models, for example, Ross-Thick Li-Sparse (RTLS) kernels that are tuned to different surface cover types [51], either based on continuous index values [49], [50], or based on a preclassification of the land cover [52].These kernels represent different scattering types and allow us to model surface reflectance as a combination of isotropic, volumetric, and geometric scattering [53], and to convert HCRF data to BHR, i.e., angle-invariant spectral albedo [37].With some limitations, generally, anisotropy compensation schemes were found to efficiently reduce illumination and observation angle induced differences between neighboring flight lines [50], [54], [55].
Recently, several studies separately compared different atmospheric [25], topographic [32], or anisotropy [52] compensation schemes.To the best of the authors' knowledge, however, thus, far no study provided a systematic assessment of atmospheric, topographic, and anisotropy effects in high-resolution imaging spectroscopy data in order to identify their impact on derived surface information.Such insight, however, is essential to adequately account for the complex radiative transfer underlying remote sensing measurements.This is underpinned by various recent environmental studies mentioning that such knowledge would facilitate reliable information retrieval and, for instance, the correct interpretation of spectral diversity of grasslands [7], the upscaling of trait-based functional diversity using spectral indices as proxies [9], or the use of multitemporal data to derive the genetic structure of forests [56].This is of particular importance in ecologically valuable and highly vulnerable high-alpine areas with rugged topography and very sensitive responses to environmental changes [57], [58], necessitating reliable and high-quality data.
This study systematically investigates the impact of atmospheric, topographic, and anisotropy effects on reflectance, albedo, and vegetation products derived from high-resolution imaging spectroscopy data.We use Airborne Prism Experiment (APEX) imaging spectroscopy data [59] acquired over a high-alpine study site, reaching to elevations of well over 3000 m above sea level (ASL), to cover complex topography, thus, a large gradient of illumination and observation angles, and structurally different vegetation types.We use three wellestablished processing schemes [ATCOR F. (flat), ATCOR R. (rugged), and BREFCOR] to generate data products with increasing complexity of applied compensations.We compare the retrieved reflectance data products and vegetation indices [PRI, NDVI, normalized difference water index (NDWI)] in the overlapping regions of neighboring sequential flight lines, where differences in observation angle are large, but, owing to the  small temporal difference, other disturbing factors are minimal.Besides describing the influence of atmospheric, topographic, and anisotropy effects, we quantify the capacity of the investigated processing schemes to eliminate differences in flight line overlaps in reflectance, albedo, and spectral index values, and we discuss for which purposes different types of compensation are desirable.

A. Study Site
The study area (see Fig. 1) covers the Swiss National Park, which is located in a mountainous alpine region in the south-east of Switzerland, at the borders to Austria and Italy.The center of the study site is at approximately 46.66 • N, 10.19 • E. The elevation covers a range of roughly 1600 m to 3200 m ASL (mean: 2400 m ASL), the aspect shows two dominant maxima at 50 • (≈ north-east) and 230 • (≈ south-west), and 90% of the slopes lie within 10 • and 52 • (mean: 31 • ).Based on the European Space Agency WorldCover dataset [60], forests and grasslands each make up approximately 25% of the landscape, while another 25% are characterized by a mixture of sparse vegetation and bare soil/bare rocks, and the remaining 25% consist of moss, permanent snow/ice, water bodies, and built-up areas.Among the dominant tree species are Swiss pine (Pinus cembra), mountain pine (Pinus mugo), European larch (Larix decidua), and European spruce (Picea abies) [61].The alpine grasslands are dominated by grasses and forbs averaging around 9 cm to 15 cm in height [62], [63].Based on data from a nearby weather station in Buffalora, run by the Federal Office of Meteorology and Climatology (MeteoSwiss) [64], summers are typically dry with a low aerosol load and a clear atmosphere.

B. Imaging Spectroscopy Data
The imaging spectroscopy data were acquired with the APEX imaging spectrometer [59], which was mounted on a Cessna 208 Grand Caravan aircraft.APEX covers a theoretical wavelength region of 372 nm-2540 nm in 312 bands in default binning configuration.The full width at half max ranges from approximately 3.4 nm-14.4nm in the VNIR and from approximately 7.4 nm-12.3nm in the shortwave-infrared (SWIR).The instrument has 1000 spatial pixels and an FOV of 28.1 • , leading to an instantaneous FOV of 0.028 • or 0.489 mrad.At a flight altitude of approximately 4000 m above ground, data with a spatial resolution of 2 m can be acquired.
Five flight lines from APEX mission M0280 on July 16, 2019, which cover rugged, high-alpine areas, were selected for the analyses.Table I   Four overlaps result out of these five flight lines.They are characterized in Table II.The temporal difference between neighboring flight lines lies between 12 and 14 min.The average differences in solar zenith angle and solar azimuth angle are 1.8 • and 3.8 • .Due to the "lawnmower pattern," the average difference in heading is approximately 180 • .The flight lines have a lateral overlap of approximately 30% of the width of a flight line, i.e., approximately 600 m.
It must be noted that our experiment focuses on rugged topography and a solar direction almost perpendicular to the imaging direction.Obtained insights likely show the highest possible amounts of topographic and anisotropy effects.This is ideal for the investigation of the maximum contribution of these effects to imaging spectroscopy data.For less unfavorable imaging conditions, weaker contributions can be expected.

C. Data Processing
The raw data were processed to at-sensor-radiances in the APEX processing and archiving facility [66] based on laboratory measurements from spring 2019.The radiance data cover the wavelength range of 376 nm-2508 nm in 299 contiguous bands.Following radiometric processing, the radiance data were processed to reflectance values using three different processing schemes, and to at-sensor apparent reflectance.All topographic parameters used during the reflectance retrieval were derived from the swissALTI3D digital elevation model (DEM) with a spatial resolution of 2 m, produced by the Swiss Federal Office of Topography (swisstopo).Since the different methods of the processing schemes are a central part of this study, the different processing schemes are described in the methods section.As a last step, all reflectance datasets were geo-rectified with the parametric geo-rectification software PARGE [67], also using the swissALTI3D DEM.

III. METHODS
Three different datasets were used to investigate the differences in the overlapping area of the neighboring flight lines: 1) reflectance values in different wavelengths; 2) albedo; 3) three commonly used spectral indices.All of these datasets were derived from the four processing schemes described in Section III-B.The differences in the overlapping area were analyzed for three structurally different vegetation types.

A. Spectral Classification
For the determination of different land cover and vegetation types, a spectral classification of the flight lines was calculated using the SPECL algorithm [26], [68].SPECL is a simple hierarchical classifier built into the ATCOR software framework, successfully applied in previous studies [69], [70], [71].The advantages of SPECL are its simple, time-efficient and well-documented implementation, its reproducibility, and the lack of a need for ground measurements.SPECL works by comparing every pixel's spectrum to a set of wavelength-specific reflectance thresholds and assigning it to the closest matching class.A total of 16 different relatively generic classes are available, for instance, bright bare soil, dark bare soil, bright vegetation, dark vegetation, shadows, etc.For this study, dark, mid-bright, and bright vegetation, excluding shadows, were chosen.Table XI in the Appendix provides the total number of pixels per vegetation type and per flight line overlap.A visual inspection of the classification shows that dark vegetation is dominated by forests and single trees, mid-bright vegetation includes dense and moist grasslands and bushlands, and bright vegetation mostly consists of drier grasslands and moss/lichen areas.All reflectance datasets (from at-sensor apparent reflectance to BREFCOR) were evaluated as input to the SPECL classifier.Finally, the BREFCOR-based SPECL classification was used, since it showed the largest agreement of classified pixels in the overlapping area of the flight lines.For the study, only pixels with the same SPECL class in both flight lines were used.

B. Reflectance Calculation
Four reflectance data products were calculated considering an increasing level of complexity.As the most basic reflectance dataset, at-sensor apparent reflectance ρ * was calculated based on the at-sensor radiance data L, the distance between Earth and Sun in astronomical units d, the top-of-atmosphere solar irradiance data E toa , and the solar zenith angle θ s .The at-sensor apparent reflectance is a direct conversion from radiance values into reflectance values as Atmospheric, topographic, or anisotropy effects are not compensated in the at-sensor apparent reflectance data.
All further processing schemes involve an atmospheric compensation.Atmospheric compensation for accurate reflectance retrieval in complex terrain is a task, which can best be solved Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.
by physical inversion of radiative transfer-based modeling [23], [72].The ATCOR-4 model is a well-established standard to solve this problem [73].It uses the Moderate Resolution Atmospheric Transmission (MODTRAN) radiative transfer code [74] to model the atmospheric parameters describing upward and downward gaseous transmittance, aerosol scattering, and the corresponding direct and diffuse irradiance on the ground, as well as the spectrally and radiometrically calibrated data with accurate geometric information of both terrain and data acquisition.The ATCOR model is used with and without considering the terrain for the evaluation of the influence of processing steps on the reflectance products, as follows.
The flat terrain ATCOR processing ("ATCOR F.") does not consider topography, but assumes a constant altitude per flight line.It uses image-derived water vapor distribution, retrieved using the Atmospheric Precorrected Differential Absorption (APDA) algorithm [75] for correction of the variable water vapor transmittance.Aerosol distribution is assumed to be constant and is corrected with a visibility of 50 km.The variability of aerosol scattering with observation angle, due to the phase function differences, is also considered.The result of this processing is an apparent bidirectional bottom-of-atmosphere reflectance, which cannot be easily related to a theoretical quantity, i.e., the resulting reflectance values are still affected by anisotropy-induced variation and terrain influences, but are void of major atmospheric influences by subtraction of aerosol scattering influences and multiplicative correction of atmospheric transmittance.
Using per-pixel topographic information derived from a DEM (elevation, slope, and aspect), per-pixel solar geometry (azimuth, elevation), and per-pixel observation geometry (scan zenith, scan azimuth), the rugged terrain ATCOR processing ("ATCOR R.") takes terrain influence into account.By applying a Modified Minnaert topographic compensation combined with the calculation of the respective sky view factor and the backscattering from adjacent terrain [73], illumination-dependent influences are corrected.The outputs are close to a hemispherical-directional reflectance factor (HDRF), better named bottom-of-atmosphere directional reflectance, as it is an approximation of an HDRF.
The observation angle influence can further be reduced by the anisotropy effects compensation BREFCOR [49].This method uses the RTLS BRDF model for correction of the variability due to per-pixel scan zenith and azimuth angle, derived from the DEM and the aircraft's positional and attitudinal data.The model is calibrated by stratification such that various densities of vegetation and soils are corrected in a surface-specific parametrization of the BRDF model.The model calculates an approximation of the spectral albedo (BHR) from the HCRF outputs of ATCOR R., which theoretically is no longer depending on observation angle.The caveat of the model is that it cannot correct for terrain-dependent observation angles due to tilted geometries in sloped terrains in its current implementation, such that an approximation of flat reference planes is assumed for the BRDF models.
The four obtained reflectance datasets are corrected for different effects, which affect reflectance data.Table III provides an overview of these.At-sensor apparent reflectance, the most basic processing scheme, only considers the irradiance dynamics.ATCOR F. introduces the compensation for atmospheric effects described above.In addition, ATCOR R. includes a topographic compensation, which corrects for topography-induced brightness differences.BREFCOR furthermore introduces a compensation for anisotropy effects, which is, however, still limited to a flat reference plane.

C. Investigated Products
For the assessment of the atmospheric, topographic, and anisotropy effects, three different data products were investigated: reflectances, albedo, and spectral indices, all calculated based on the four different reflectance datasets.
Reflectances were analyzed in eight distinct wavelengths, i.e., 460 nm, 550 nm, 640 nm, 860 nm, 1080 nm, 1240 nm, 1650 nm, and 2250 nm.The selected wavelengths ideally represent various manifestations of scattering mechanisms and effects throughout the VSWIR region of the electromagnetic spectrum.
Spectrally integrated reflectance (apparent albedo) was considered as a relevant parameter, since it most accurately describes the brightness of a pixel.Among the processing levels, the anisotropy compensated BREFCOR reflectance value theoretically best approximates a BHR, i.e., the spectral albedo.A spectrally integrated albedo, i.e., a spectral integration of the reflectance values, however, is calculated for all processing levels to analyze brightness differences.The calculation is based on [73] and described in Appendix A.
Additionally, the following three spectral indices were selected for the analysis: the PRI (see [76]), the broadband NDVI (see [77]), and the NDWI (see [78]), with the PRI using wavelengths in the visible (VIS), the NDVI exploiting the VIS and near-infrared (NIR), and the NDWI using the NIR and SWIR.The selection of spectral indices is based on the fact that the reflectance anisotropy shows a clear wavelength-dependency [79], [80].Therefore, indices were selected to represent different regions of the electromagnetic spectrum to assess how this wavelength-dependency propagates into the anisotropy effects of the index values.Since the PRI uses the VIS spectral region, we expect the PRI to be most sensitive to anisotropy effects.We expect moderate sensitivity of the broadband NDVI to anisotropy effects, since it is partly based on the less affected spectral regions in the NIR.The NDWI is supposed to be least affected by anisotropy effects.The calculation of the spectral indices is described in Appendix B. The anisotropic behavior of further vegetation indices, not considered in this study, can be studied for instance in [44].
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D. Processing Workflow
The processing workflow is shown in Fig. 3.The workflow was run individually for reflectances, albedo, and indices.In a first step, two overlapping flight lines were each masked to their common overlap area.The flight lines were smoothed with a 3 × 3 convolution filter to account for the residual geometric inaccuracies of approximately 1.5 pixels after geo-rectification.Then, based on the SPECL classification, the same random pixel samples of a specific class (e.g., dark vegetation) were extracted from the same location in both flight lines in their overlapping area.We decided to use a random sampling strategy in order to avoid the risk of spatial autocorrelation.Due to relatively imbalanced class sizes (see Table XI in the Appendix), a relative sample size was used.Several sizes were tested with no significant impact on the results.Hence, a sample size of 5% of the pixels per class was chosen.Finally, the mean of a pixel-wise reflectance, albedo, or spectral index difference between the samples was calculated.In order to make the differences between data products comparable, we calculated the relative differences of investigated data products between flight lines, considering the mean for reflectance and albedo as reference, and the range of index mean plus and minus one standard deviation as reference for the three indices.

E. Simulations
In order to support and discuss our findings based on the airborne imaging spectroscopy data, we carried out simulations using the MODTRAN-6 (see [74]) and the SCOPE (see [81]) radiative transfer models.
For the assessment of the contribution of various radiance components to the signal obtained at the sensor, a MODTRAN simulation, based on a coniferous tree spectrum was run.For the simulation, a uniform background of the same spectrum was assumed.The simulation was calculated for the APEX spectral resolution with a flight altitude of 7 km and a ground altitude of 2 km.Standard atmospheric conditions were used.
Additionally, in order to get an estimate of the impact of illumination and observation geometry, and ground reflectance anisotropy on reflectance and index differences, vegetation spectra were simulated with the SCOPE radiative transfer model.The default leaf biochemical parameters provided by SCOPE were applied for the simulations.According to [82], a grass meadow can be assumed to be erectophile in the growing phase and to transition to a more spherical or uniform leaf angle distribution after a certain growth time.While erectophile canopies show strong anisotropy effects, other canopies show more isotropic behavior [83].Since the bright vegetation subsets analyzed in this study mostly correspond to grass meadow areas, they can likely be compared to erectophile or spherical/uniform, depending on the growth stage.Consequently, three different leaf angle distributions were used to simulate varying canopy structures (spherical, uniform, and erectophile).The solar geometries of flight lines 1 and 2 were used for the simulations (see Table I).SCOPE was run in the directional mode with 1-degree increments in observation azimuth and zenith angles in order to obtain reflectance spectra for various observation geometries.

A. Reflectance Differences
Fig. 4 shows the five flight lines as a true-color reflectance mosaic based on at-sensor apparent reflectance, ATCOR F., ATCOR R., and BREFCOR data.A visual inspection shows little differences between at-sensor apparent reflectance and ATCOR F. From ATCOR F. toward ATCOR R., a clear reduction of topography-induced brightness differences can be observed.From ATCOR R. toward BREFCOR, finally, brightness differences are further reduced, but the edges of the flight lines clearly remain visible.
Table IV provides a numerical analysis of the underlying effects leading to the observed brightness differences.Reflectance differences are shown for randomly sampled pixels in the overlapping areas of neighboring flight lines, averaged over three different vegetation types in four different overlaps.The relative reflectance differences are presented for eight different wavelengths, covering the whole VSWIR region of the electromagnetic spectrum and different scattering mechanisms (see also Section III-C): 460 nm, 550 nm, 640 nm, 860 nm, 1080 nm, 1240 nm, 1650 nm, and 2250 nm.
Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.In the processed datasets (ATCOR F., ATCOR R., BREF-COR), the NIR wavelengths (860 nm, 1080 nm, and 1240 nm) show the smallest relative reflectance differences (total average: 16.3%), and the VIS wavelengths (460 nm, 550 nm, and 640 nm) show the largest relative reflectance differences (total average: 37.2%) in flight line overlaps.The relative reflectance differences in the SWIR wavelengths (1650 nm, 2250 nm) are smaller again (total average: 24.8%) and, hence, lie between the VIS and NIR values.In the unprocessed at-sensor apparent reflectance data, the SWIR data show the largest relative reflectance differences (average: 24.9%), followed by the VIS wavelengths (average: 20.1%), and the NIR wavelengths (average: 18.4%).
In the NIR region, with the exception of 860 nm, at-sensor apparent reflectance shows the largest relative reflectance differences with values ranging from 17.8% to 19.7%.With values between 17.0% and 19.6%, the relative reflectance differences obtained from ATCOR F. and ATCOR R. are in the same order or only marginally smaller.In all three NIR wavelengths, BREFCOR finally shows relative reflectance differences between 11.9% and 13.7%, which is approximately −5% to −6% less than the other three processing schemes.
In the SWIR region, at-sensor apparent reflectance shows the largest relative reflectance differences at 1650 nm with a value of 24.8%.ATCOR F. and ATCOR R. again show relative reflectance differences very close to this.With a value of 21.1%, BREFCOR finally shows approximately −4% smaller relative reflectance differences than the other three processing schemes.At 2250 nm, the relative reflectance differences obtained from at-sensor apparent reflectance lie at 24.9%.Both ATCOR F. and ATCOR R. show approximately +1% to +2% larger relative reflectance differences.With a value of 24.8%, finally, BREFCOR shows the smallest relative reflectance differences, albeit only slightly smaller than at-sensor apparent reflectance.
Fig. 5 shows the relative reflectance differences in flight line overlaps as in Table IV, but broken down for the more specific vegetation types: dark, mid-bright, and bright vegetation.On average, the dark vegetation subset exhibits the largest relative reflectance differences, while the bright vegetation subset shows the smallest relative reflectance differences.
In the dark vegetation subset, the observed relative reflectance differences in the VIS wavelengths are roughly 1% to 15% larger than in the vegetation type averaged analysis.In the NIR and SWIR region, they are between 3% and 6% larger.There are several deviations from the results of the vegetation type averaged analysis.At-sensor apparent reflectance shows the smallest relative reflectance differences in all three VIS wavelengths, i.e., also at 550 nm.Furthermore, ATCOR F. instead of at-sensor apparent reflectance shows the largest relative reflectance differences at 1650 nm, although they are very close.In the VIS wavelengths, e.g., at 460 nm, the relative reflectance differences increase by approximately +53% and +57% from at-sensor apparent reflectance to ATCOR F. and ATCOR R. respectively.They decrease by roughly −18% from ATCOR R. to BREFCOR.In the NIR and SWIR wavelengths, there are only marginal differences between at-sensor apparent reflectance, ATCOR R., and ATCOR F. The decrease in relative reflectance differences from these three processing schemes to BREFCOR is in the order of −5%.
In the mid-bright vegetation subset, the observed relative reflectance differences are between 0.5% and 8.5% (VIS), respectively, 0.5% and 3.5% (NIR and SWIR) larger than in the vegetation type averaged analysis.The pattern of largest and smallest relative reflectance differences fully corresponds to the vegetation type averaged analysis.In the VIS wavelengths, e.g., at 460 nm, the increase in relative reflectance differences from at-sensor apparent reflectance to ATCOR F. and ATCOR R. is approximately +50% and +51%, respectively.The decrease in relative reflectance differences from ATCOR R. to BREFCOR is approximately −20%.In the NIR and SWIR wavelengths, there are again only marginal differences between at-sensor apparent reflectance, ATCOR R., and ATCOR F. The decrease in relative reflectance differences from these three processing schemes to BREFCOR is in the order of −5%.
In the bright vegetation subset, the relative reflectance differences are approximately 10% to 30% (VIS), respectively, 10% to 15% (NIR and SWIR) smaller than the relative reflectance differences in the dark vegetation subset, and 5% to 20% (VIS), respectively, 5% to 10% (NIR and SWIR) smaller than the relative reflectance differences in the vegetation type averaged analysis.Again, there are some deviations from the vegetation type averaged analysis.ATCOR F. instead of ATCOR R. shows the largest relative reflectance differences at 460 nm.Furthermore, at 2250 nm, BREFCOR instead of ATCOR F. shows the largest relative reflectance differences and at-sensor apparent reflectance instead of BREFCOR shows the smallest relative reflectance differences.In the VIS wavelengths, e.g., at 460 nm, the relative reflectance differences increase by approximately +25% and Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.

TABLE V RELATIVE ALBEDO DIFFERENCES IN %, AVERAGED OVER FOUR FLIGHT LINE OVERLAPS FOR DARK, MID-BRIGHT, AND BRIGHT VEGETATION
+24% from at-sensor apparent reflectance to ATCOR F. and ATCOR R., respectively.The decrease in relative reflectance differences amounts to roughly −13% from ATCOR R. to BREF-COR.In the NIR and SWIR wavelengths, there are only marginal differences between at-sensor apparent reflectance, ATCOR R., and ATCOR F. The decrease in relative reflectance differences from these three processing schemes to BREFCOR is in the order of −3%.

B. Albedo Differences
Mosaics with albedo values calculated based on at-sensor apparent reflectance, ATCOR F., ATCOR R., and BREFCOR are shown in Fig. 6.Similar to the reflectance mosaics in Fig. 4, after an increase from at-sensor apparent reflectance to ATCOR F. and to ATCOR R., a reduction of brightness differences is observable to BREFCOR, although the edges of the flight lines are still visible in all mosaics.
A numerical analysis of the underlying differences per vegetation type, averaged over the four different flight line overlaps, is provided in Table V and in the left part of Fig. 7.In all three vegetation subsets, BREFCOR shows the smallest relative albedo differences (dark vegetation: 20.3%, mid-bright vegetation: 15.4%, bright vegetation: 7.2%), while at-sensor apparent reflectance shows the second smallest relative albedo differences (dark vegetation: 21.7%, mid-bright vegetation: 20.1%, bright vegetation: 13.2%).ATCOR R. shows the largest relative albedo differences (dark vegetation: 28.5%, mid-bright vegetation: 24.1%,The relative albedo differences, hence, increase by roughly +1% to +6% from at-sensor apparent reflectance to ATCOR F. and ATCOR R., and decrease by approximately −8% to −9% from ATCOR F. and ATCOR R. to BREFCOR, ending up roughly 2% to 7% below the relative albedo differences obtained from at-sensor apparent reflectance.

C. Spectral Index Differences
Fig. 8 shows NDVI mosaics calculated based on at-sensor apparent reflectance, ATCOR F., ATCOR R., and BREFCOR data.While the edges of the flight lines are practically invisible in the at-sensor apparent reflectance mosaic, they are clearly increasingly well visible in ATCOR F. and ATCOR R. From ATCOR R. toward BREFCOR almost no further increase is visible.
Table VI provides a numerical analysis of the relative differences for three spectral indices between randomly sampled pixels in the overlapping area of neighboring flight lines, averaged over three different vegetation types in four different overlaps.
The smallest relative PRI differences are obtained from atsensor apparent reflectance with a value of 33.3%, while ATCOR R. shows the largest relative PRI differences with a value of 37.6%, which is approximately 4% more.The smallest relative NDVI differences are obtained from at-sensor apparent reflectance with a value of 25.2%, and the largest relative NDVI differences are obtained from BREFCOR with a value of 36.8%.This is an increase of approximately 12%.The smallest relative NDWI differences are obtained from ATCOR F. with a value of 38.2%, while BREFCOR shows the largest relative NDWI differences with a value of 41.3%, which is roughly 3% more.
With the PRI, the relative index differences increase by roughly +2% from at-sensor apparent reflectance to ATCOR F. and by another +2% from ATCOR F. to ATCOR R. From AT-COR R. to BREFCOR, they decrease by roughly −1.5% and end up approximately +3% above at-sensor apparent reflectance.The relative NDVI differences show a continuous increase from at-sensor apparent reflectance to BREFCOR, totaling to approximately +12%.With approximately +6%, the increase is largest from ATCOR R. to BREFCOR.The NDWI finally shows a decrease in relative index differences from at-sensor apparent reflectance to ATCOR F. (−1.5%), followed by a slight increase to ATCOR R. (+0.5%) and another increase to BREFCOR (+2.5%).
The analyses of specific vegetation subsets are shown in the second, third, and fourth plot of Fig. 7.For PRI, the largest relative differences are observed in the dark vegetation subset (average: 40.5%), while the largest NDVI and NDWI relative differences occur in the mid-bright vegetation subset (NDVI: average of 36.9%;NDWI: average of 45.7%).The smallest relative differences for all three indices again occur in the bright vegetation subset (PRI: 27.2%; NDVI: 23.3%; NDWI: 27.3%).
In general, the pattern of smallest and largest relative index differences is similar to the total average.In all three vegetation subsets, the smallest relative PRI and NDVI differences are obtained from the at-sensor apparent reflectance data and the smallest relative NDWI differences are obtained from ATCOR F. The largest relative NDVI and NDWI differences are obtained from BREFCOR.The largest relative PRI differences in the bright vegetation, however, are obtained from BREFCOR instead of ATCOR F.

D. Simulations
Abovementioned results indicate the existence of anisotropy effects in reflectance data and derived vegetation products across different processing schemes.Here, we present simulationbased insights on the origin of observed effects to facilitate the interpretation and evaluation of shown observational results.
Fig. 9 shows the results of the MODTRAN-6 [74] simulation run for the analysis of the impact of adjacency radiance on the signal obtained at the sensor.In Fig. 9(a), the main radiance components of the total at-sensor radiance are visualized.At short wavelengths, the signal from the pixel, i.e., the direct ground reflected radiance, only accounts for about 30% of the spectrum.The multiple scattered radiance is at an approximately similar level below 500 nm.As visible in Fig. 9(b), up to 40% of the total signal is, thus, driven by the adjacency radiance.For the analysis of the impact of illumination/observation geometry and ground reflectance anisotropy on reflectance and index differences, the SCOPE [81] simulated reflectance spectra at three positions in the overlapping area of flight lines 1 and 2 were extracted.The north-western edge of the overlap was acquired in flight line 1 with a scan zenith angle (SCZA) of approximately 4 • and in flight line 2 with an SCZA of approximately 14 • .The center of the overlap was acquired with an SCZA of about 9 • in both flight lines.The south-eastern edge of the overlap was acquired in flight line 1 with an SCZA of approximately 14 • and in flight line 2 with an SCZA of approximately 4 • .All three positions were acquired with a scan azimuth angle (SCAA) of 150 • from flight line 1 and with an SCAA of 330 • from flight line 2. Exemplary results are shown in Fig. 10 with a BRDF plot and two extracted vegetation spectra.For all three positions (i.e., north-west, center, and south-east), relative reflectance and spectral index differences were calculated in the same way as in the main analysis of this article.The calculated relative reflectance differences (see Tables VII-IX) are larger in the VIS wavelengths and decrease toward the NIR and SWIR wavelengths.The largest differences were obtained from the erectophile leaf angle distribution, followed by the spherical and the uniform.At 460 nm, for example, a relative   reflectance difference between 15.6% and 23.1% resulted from an erectophile leaf angle distribution, between 8.8% and 9.3% resulted from a spherical leaf angle distribution, while a uniform leaf angle distribution led to relative reflectance differences between 5.3% and 5.4%.The spectral indices (see Table X) show a similar behavior with the erectophile leaf angle distribution leading to the largest differences and the uniform leaf angle distribution leading to the smallest differences.While the NDWI does not show a very strong variability with leaf angle distribution and position within the overlap, the PRI and the NDVI are highly variable.The relative PRI differences, for example, vary between 5.0% and 54.4% for an erectophile leaf angle distribution, between 3.7% and 7.4% for a spherical leaf angle distribution, and between 3.3% and 4.4% for a uniform leaf angle distribution.
V. DISCUSSION

A. Reflectance and Albedo Differences
The presented reflectance and albedo differences in flight line overlaps can be explained by a combination of atmospheric disturbances, topography effects, and reflectance anisotropy.Interestingly, differences in the least processed at-sensor apparent reflectance data are, particularly for the VIS spectral region, smaller compared to differences in reflectance data after atmospheric (ATCOR F.) and topographic (ATCOR R.) compensation.Differences in anisotropy compensated reflectance data (BREFCOR) between flight lines, finally, decrease compared to atmospherically and topographically compensated reflectance data, and are often even smaller than differences in at-sensor apparent reflectance.
The increasing reflectance differences after atmospheric compensation can be explained by the large influence of atmospheric scattering effects in at-sensor apparent reflectance data.In fact, this most simple processing only accounts for irradiance dynamics but does not compensate radiation components that add to the target reflected radiance (i.e., atmospheric path radiance and adjacency radiance).In pixels representing dark objects, such as forest or water, such additive radiance components can account for a substantial part of the signal [84], [85].The MODTRAN-6 [74] simulation (cf., Fig. 9) confirms a large contribution of additive path radiance for dark coniferous forests in our test area of up to 40%, i.e., that the measured signal contains the information of the surrounding pixels by multiple scattering.Consequently, the target signal is masked by the surrounding pixels' signature.This masking of the underlying dark vegetation signature by atmospheric path radiance and adjacency radiance, as described in, e.g., [86] or [87], possibly determines the small reflectance differences in flight line overlaps.For shaded pixels, the portion Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply. of the adjacency radiance will be even higher, as the direct ground reflectance decreases while adjacent signals scattered directly to the sensor remain constant.
Compensating for atmospheric effects allows minimizing the contribution of this adjacency radiance and reveals the true underlying vegetation signature with pronounced anisotropy dependencies, i.e., increased reflectance and albedo differences compared to the at-sensor apparent reflectance case.It is interesting to note that particularly shorter wavelengths are more strongly affected by an increasing reflectance and albedo difference in the flight line overlaps.Differences in the vegetation type averaged analysis increase by roughly 42.5% at 460 nm from at-sensor apparent reflectance to atmospherically compensated reflectance, while the increase is only 10.0% at 550 nm, and further decreases to 8.5% at 640 nm.The increase in difference is larger over darker vegetation (i.e., 53% at 460 nm) compared to brighter vegetation (i.e., 25% at 460 nm).This behavior is expected since anisotropy effects are known to be wavelengthdependent with increasing contributions toward shorter wavelengths [39], [41].
The topographic compensation additionally accounts for topography-caused irradiance variations and optimizes atmospheric transfer functions.As a result, the observation angle effect on the vegetation signal becomes even better visible as shown by a slight increase in reflectance difference compared to the only atmospherically compensated data.The effect is most pronounced in the VIS wavelengths, while for longer wavelengths, an opposite behavior is observed, with differences generally decreasing from atmospherically toward atmospherically and topographically compensated data.This could imply that the observed increase in differences after topographic compensation, related to the better atmospheric compensation and the clearer observation angle-affected vegetation signal, might in the VIS wavelengths in fact be even larger, but is obscured by the topographic compensation-induced decrease in differences.The impact of the discussed effects is barely visible in the albedo differences, where atmospheric compensation and combined atmospheric and topographic compensation led to basically the same results.Likely, this is because both shorter and longer wavelengths with a contrary response to the interplay of the two mentioned effects (further exposure of the vegetation signal versus improvements due to topographic compensation) contribute to albedo.Finally, all topographic parameters derived from a DEM are subject to potential errors or inaccuracies in the elevation data, which can significantly influence the topographic compensation.As [28] have shown, this is especially important for low spatial resolution, global DEMs.Although a high spatial resolution (2 m) DEM was used for this study, DEM-induced errors are nonetheless well possible.
BREFCOR adds an anisotropy compensation to the ATCORderived HCRF data.Consistently, in almost all reflectance and albedo analyses, reducing anisotropy effects clearly leads to a decrease in reflectance or albedo difference in overlapping parts of flight lines compared to atmospherically and topographically compensated data.Similar to previously discussed effects, the influence of anisotropy also seems to be stronger in the shorter wavelengths and in dark to mid-bright vegetation.Overall, the anisotropy compensation achieves up to ca. 20% smaller relative reflectance differences and 9% smaller relative albedo differences compared to atmospherically and topographically compensated data, where the observation angle-related reflectance differences are maximal.
The simulations calculated with the SCOPE radiative transfer model [81] confirm that ground reflectance anisotropy indeed can lead to significant reflectance differences.The simulated reflectance and index differences depend on the wavelength, the position in the flight lines' overlap, and the leaf angle distribution.In the bright vegetation subset, the atmospherically and topographically compensated data, assumed to be mostly cleared of effects other than ground reflectance anisotropy, showed relative reflectance differences between 40.7% (460 nm) and 10.3% (1080 nm).Comparing these observed values to the SCOPE-simulated relative reflectance differences shows that, depending on the leaf angle distribution, up to approximately half of these observed ground reflectance differences can be explained by anisotropy [e.g., up to 23.1% at 460 nm assuming an erectophile canopy (see Table IX) or up to 9.3% assuming a spherical canopy (see Table VIII)].After BREFCOR, which intends to remove anisotropy-induced reflectance differences, indeed relative reflectance differences in the order of ATCOR R. minus the SCOPE-simulated relative reflectance differences are obtained.This would imply that the BREFCOR anisotropy compensation successfully largely removes anisotropy-related reflectance differences.
Remaining differences observed after a complete processing including BREFCOR anisotropy compensation might be related to both processing-internal, but also external factors.Processing-related, residual differences might be related to the assumption of flat reference planes in the current BREF-COR implementation, i.e., a separate consideration of topography and anisotropy.Furthermore, the semiempirical anisotropy compensation approach, based on RTLS kernels, which were fitted to several generalized surface types, might not be able to fully represent and, hence, compensate surface anisotropy.Here, physical approaches, as suggested by [46] or [47], which inherently account for topography and BRDF simultaneously, might show further improvements.An alternative strategy is to move the retrieval of surface information to the at-sensor level, as, for example, described in [88].This approach models the interaction of light with the atmosphere and the surface via coupled radiative transfer models, allows us to better represent the sequence of physical processes and enables to address topography and anisotropy together.
In addition, other, more external factors, not considered in this analysis, such as sensor nonuniformities, micro relief-induced illumination effects, etc., might contribute to observed differences.

B. Spectral Index Differences
Our analysis indicates substantial spectral index differences in the overlapping regions of flight lines.A SCOPE simulation (see Table X) shows that, depending on the leaf angle distribution, large spectral index differences can be attributed to anisotropy.This is in agreement with past studies [41], [44], which also found a significant influence of anisotropy on spectral indices.The differences in investigated index values differ, however, compared to observed differences in reflectance and albedo.While with a range of 4.3% and 3.1%, the PRI and the NDWI show little variation in index differences of overlapping flight line regions across processing options (see Table VI), NDVI, with a range of 11.6%, shows greater sensitivity to processing.The smallest relative index differences are predominately obtained from the at-sensor apparent reflectance data.After reducing atmospheric (with ATCOR F.) and topographic (with ATCOR R.) effects, anisotropy effects in the indices are better visible.Contrary to the reflectance and albedo data, after the anisotropy compensation with BREFCOR (which does not account for terrain structure), a further increase in index differences is visible, especially for the NDVI (i.e., 11% larger differences than after atmospheric compensation) and the NDWI (up to 6% larger than after atmospheric compensation).
Since the applied spectral indices are linear combinations of reflectance products, the observed index differences can be explained by the same effects as the reflectance and albedo differences.The atmospheric and topographic compensation revealed the observation angle effects influencing the vegetation signal obtained at the sensor.The BREFCOR anisotropy compensation does not generally reduce index differences in flight line overlaps compared to the atmospheric and topographic compensations, although a reduction of ground reflectance anisotropy was achieved for single wavelengths used to calculate these indices (e.g., 860 nm and 1240 nm).This may be due to wavelength-specific performance differences of the anisotropy compensation.
In fact, when looking at the anisotropy compensated reflectance data, a different compensation of the red wavelength region can be observed (cf.Table IV and Fig. 5), compared to the neighboring green and NIR wavelengths.The reduction in reflectance differences at 640 nm after the application of an anisotropy compensation is relatively smaller compared to the neighboring wavelengths.At 550 nm, for instance, the differences decrease from 31.5% to 18.7%, while at 640 nm they only decrease from 31.4% to 26.3%.This variation in correction may be related to the generally very low red reflectance above vegetation and the lower relative anisotropy at this wavelength, which could lead to a less reliable calibration of the BRDF model in this wavelength region.This behavior was also observed by other studies [50], [52], [89].Furthermore, our simulations (cf.Table X) show that the NDVI is very sensitive to anisotropy due to the difference in BRDF between the red and the NIR spectral bands.As a consequence, the larger NDVI differences after BREFCOR are to be attributed to an insufficient anisotropy compensation in the respective bands for this sample dataset.There is, however, currently ongoing research on better aerosol compensation in lower wavelengths, by analysis of cast shadow signatures.This might lead to a better parametrization of the BRDF model and to an improved compensation in these wavelength regions.

C. Limitations
Our study is limited in some aspects related to the selection and the characteristics of data and study site, and related to research design and methodology.
Data-wise, first, the imaging spectroscopy data used in this study are from one specific study site with rugged, high-alpine topography and coniferous forests and alpine meadows as main features.As a consequence, we are only able to investigate limited surface types, i.e., mostly vegetation in a certain phenological stage.This limits the gradient of anisotropic variety and behavior.Furthermore, only one atmospheric state with specific water vapor and aerosol loads could be analyzed.
Second, used data are quasi mono-temporal.Hence, our study can only analyze a limited, but still relatively difficult, combination of illumination and acquisition geometries with flights almost perpendicular to the solar principal plane, leading to an extreme case of anisotropy.Other illumination and observation geometries, such as flights in the solar direction, or other landscapes with less pronounced topography and, e.g., less or different vegetation might show other manifestations of the analyzed atmospheric, topographic, and anisotropic effects.Furthermore, our flight lines were flown at relatively high altitudes.Lower flights with smaller pixel sizes and potentially less path scattered radiance or space-based observations, with larger pixels and potentially higher path scattered radiance, could give further interesting insights.
Consequently, future studies with a larger temporal and spatial diversity due to more diverse study sites and acquisition/illumination geometries could provide further insight into the phenomena discussed here, and test the generality of our conclusions.
In addition to these limitations related to data and study site, there are also several methodology-related limitations, not considered in this study.Regarding the research design, our study is limited by the lack of ground truth data, which could be helpful in linking remote observations from, e.g., airplanes to phenomena on the ground and to assess the robustness of findings.Since we Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.
could not install a goniometer system in parallel to our airborne data acquisitions, we employed a modeling approach consisting of the atmospheric radiative transfer model MODTRAN and the canopy model SCOPE to evaluate a theoretical baseline for the expected anisotropy effects.
Furthermore, the employed processing methods are limited in some aspects.For the atmospheric correction, for example, typically, a well-established set of processing parameters, e.g., aerosol concentration, is used.Here, a sensitivity analysis with varying concentrations could provide quantitative information on the relationship of processing parameters with outputs.Then, inaccuracies in elevation data might have an influence on both the atmospheric and the topographic correction.Furthermore, the current implementation of the BREFCOR algorithm, which assumes flat reference planes and is, hence, topography-unaware, is limiting the anisotropy compensation.Finally, semiempirical anisotropy compensation methods, such as BREFCOR, might be limited by the circumstance that their models are restricted to a set number of surface types, hence, always involving a certain degree of generalization.

VI. CONCLUSION
When estimating the reflectance properties of surfaces from a remote airborne sensor, it is necessary to account for several effects.These are mainly effects of atmospheric absorption and scattering of light, which change with different atmospheric thickness due to topography, and anisotropic reflectance of light, which changes with viewing angle.We compared the results obtained from different processing schemes for reflectance values in several wavelengths, albedo, and commonly used vegetation indices, using airborne imaging spectroscopy data taken in overlapping flight lines above rugged high-alpine terrain with different vegetation types.
We found that the least processed reflectance data showed only relatively small reflectance, albedo, and spectral index differences in the overlapping area of neighboring flight lines.Based on MODTRAN simulations, we identified atmospheric effects, i.e., path scattered and adjacency radiance, masking the surface signature, as the most probable explanation for the observed low differences.We show that the actual surface signature only becomes visible after atmospheric and topographic compensation, resulting in a significant increase of the differences between neighboring flight lines, which are largely attributed to anisotropy effects.A subsequent anisotropy compensation can effectively reduce the differences.Hence, we conclude that the impact of atmospheric, topographic, and anisotropy effects in several data products is substantial and that in some cases, more comprehensive processing schemes even pronounce anisotropy effects, and thus, differences in the overlapping regions of flight lines.This is in part due to compensating for the scattering effects, and in part due to the general methodological limitation that the best available anisotropy compensation schemes cannot yet account for rugged terrain.
We recommend in all cases to apply proper atmospheric and topographic compensation to minimize the risk that sensitivities of reflectance and vegetation indices, particularly over dark objects, are dominated by adjacent and path scattered radiance rather than by the respective surface properties.Concerning anisotropy compensation, we recommend basing the decision on the actual purpose.If the aim is to depict a physically realistic image, showing the light reflected by the surface along a flight line, anisotropy is part of that and should not be removed.Furthermore, if reflectance data are required for physical-based information retrievals (e.g., model inversion-based estimates of vegetation pigments), and applied models inherently can consider anisotropy, anisotropy compensation should be avoided.Since vegetation indices have shown very diverse sensitivities to anisotropy, also for studies based on such indices, an anisotropy compensation might not be needed in all cases.Given the unexpectedly different behavior of vegetation indices compared to reflectance values, often showing larger differences between flight lines after anisotropy compensation, this recommendation comes, however, with a caveat and a suggestion to further investigate the influence of anisotropy compensation on spectral indices.For all other applications of reflectance data, like mosaicking, mineral mapping, or the retrieval of plant traits, we generally recommend applying an anisotropy compensation like BREFCOR, since such data have shown lowest differences between flight lines.
Methodology-wise, future work should focus on further optimizations of anisotropy compensation schemes (e.g., BREF-COR with the step to a full rugged terrain implementation), since this is likely to yield further improvements, especially for the mosaicking of reflectance and albedo datasets.Furthermore, the implementation of physical anisotropy compensation methods into operational surface reflectance retrieval workflows could be addressed.Application-wise, further analyses of the role of anisotropy compensation for spectral indices, and the study of more diverse landscapes and acquisition/illumination geometries could provide interesting insights.

APPENDIX A CALCULATION OF ALBEDO
Albedo is calculated based on [73] for all processing levels as an average of the spectral reflectance outputs, weighted by the irradiance function with i = band index, n = number of bands, ρ i = reflectance in band i, and E0 i = solar irradiance in band i.The albedo was calculated with 13 bands, which were already used for the reflectance and index analyses.

APPENDIX B CALCULATION OF VEGETATION INDICES
The PRI [76] was calculated as with two wavelengths in the green region of 531 nm for G1 and 571 nm for G2, respectively.The PRI quantifies the degree of Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.
epoxidation of xantophylls and consequently is a measure of the efficiency of photosynthetic light use.
The NDVI [77] was calculated as NDVI = ρ NIR − ρ red ρ NIR + ρ red (4) with wavelengths of 843 nm for NIR and 671 nm for red, respectively.The NDVI is the most commonly used vegetation index and is a general measure of vegetation health.Finally, the NDWI [78] was calculated as NDWI = ρ NIR − ρ SWIR ρ NIR + ρ SWIR (5) with wavelengths of 861 nm for NIR and 1241 nm for SWIR, respectively.The NDWI is sensitive to liquid water content in vegetation.

Fig. 1 .
Fig. 1.Overview of the study site, visualized as false-color infrared reflectance mosaic based on BREFCOR processed data (R = 860 nm, G = 640 nm, B = 550 nm).Background: Swisstopo DHM25 DEM.The flight lines are marked by dashed outlines and the letters A, B, C, D, and E. Coordinates are in the Swiss CH1903+ system (EPSG: 2056) in meter easting/northing, oriented south (bottom) to north (top).The inset map with latitude and longitude coordinates (EPSG: 4326) in degrees shows the location of the main map within Switzerland.

Fig. 2 .
Fig. 2. Schematic visualization of the five flight lines (FLn) and the solar azimuth at the along-track center of the FLn.Coordinates are in the Swiss CH1903+ system (EPSG: 2056) in meter easting/northing, oriented south (bottom) to north (top).

Fig. 5 .
Fig. 5. Relative reflectance differences in four different processing schemes and for three different vegetation types.APP = at-sensor apparent reflectance, ATF = ATCOR F., ATR = ATCOR R., and BCR = BREFCOR.In the box plots, the boxes cover the first quartile (Q1, 25%) until the third quartile (Q3, 75%).The solid line within the box plot shows the median, while the dotted line shows the mean.The whiskers can extend to the fifth and 95th percentile of the data.

Fig. 7 .
Fig.7.Relative albedo and index differences in four different processing schemes and for three different vegetation types.APP = at-sensor apparent reflectance, ATF = ATCOR F., ATR = ATCOR R., and BCR = BREFCOR.In the box plots, the boxes cover the first quartile (Q1, 25%) until the third quartile (Q3, 75%).The solid line within the box plot shows the median, while the dotted line shows the mean.The whiskers can extend to the fifth and 95th percentile of the data.

Fig. 10 .
Fig. 10.Exemplary outputs of a SCOPE [81] model simulation assuming a spherical leaf angle distribution.(a) Polar plot showing the BRDF for 860 nm with a SZA of 39.8°.The white dots mark 4 • , 9 • , and 14 • SCZA perpendicular to the headings of 60 • and 240 • in flight lines (FLn) 1 and 2. (b) Spectra extracted from the north-west edge of the overlap, with an SCZA of 4 • , an SCAA of 150 • , and a SZA of 39.8 • in flight line 1, respectively, an SCZA of 14 • , an SCAA of 330 • , and an SZA of 37.9 • in flight line 2.
XI NUMBER OF PIXELS PER VEGETATION CLASS IN THE OVERLAPPING AREA OF FLIGHT LINES A-B, B-C, C-D, AND D-E

TABLE I OVERVIEW
OF THE FIVE FLIGHT LINES (FLN) USED FOR THE ANALYSES provides an overview of some key characteristics of the five flight lines.The flight lines were acquired between 08:48 and 09:46 UTC, equaling 10:48 and 11:46 local time.This led to solar zenith angles (SZA) between 39.8 • and 32.8 • and solar azimuth angles between 116.3 • and 131.6 • .Fig. 2 schematically shows the orientation of the flight lines and the solar geometry.As the solar azimuth angle is almost perpendicular to the flight direction, the relative zenith

TABLE III EFFECTS
CONSIDERED (+) AND NOT CONSIDERED (−) BY THE FOUR PROCESSING SCHEMES

TABLE IV RELATIVE
REFLECTANCE DIFFERENCES IN %, AVERAGED OVER FOUR FLIGHT LINE OVERLAPS AND OVER THREE VEGETATION SUBSETS (DARK, MID-BRIGHT, AND BRIGHT VEGETATION)

TABLE VI RELATIVE
INDEX DIFFERENCES IN %, AVERAGED OVER FOUR FLIGHT LINE OVERLAPS AND OVER THREE VEGETATION SUBSETS (DARK, MID-BRIGHT, BRIGHT VEGETATION) FOR THREE SPECTRAL INDICES: PRI, NDVI, AND NDWI

TABLE VII RELATIVE
REFLECTANCE DIFFERENCE IN % BETWEEN TWO SIMULATED VEGETATION SPECTRA IN THE OVERLAPPING AREA OF FLIGHT LINE 1 AND 2, ASSUMING A UNIFORM LEAF ANGLE DISTRIBUTION

TABLE VIII RELATIVE
REFLECTANCE DIFFERENCE IN % BETWEEN TWO SIMULATED VEGETATION SPECTRA IN THE OVERLAPPING AREA OF FLIGHT LINE 1 AND 2, ASSUMING A SPHERICAL LEAF ANGLE DISTRIBUTION

TABLE IX RELATIVE
REFLECTANCE DIFFERENCE IN % BETWEEN TWO SIMULATED VEGETATION SPECTRA IN THE OVERLAPPING AREA OF FLIGHT LINE 1 AND 2, ASSUMING AN ERECTOPHILE LEAF ANGLE DISTRIBUTION

TABLE X RELATIVE
INDEX DIFFERENCE IN % BETWEEN TWO SIMULATED VEGETATION SPECTRA IN THE OVERLAPPING AREA OF FLIGHT LINE 1 AND 2 FOR A UNIFORM, SPHERICAL, AND ERECTOPHILE LEAF ANGLE DISTRIBUTION