1. Introduction
Spectral reflectance is a crucial information source in optical remote sensing that is used to extract the status of, and changes in, biogeophysical parameters, land cover, and surface energy budgets. Numerous processing methods have been developed in an attempt to derive accurate, detailed information from remotely sensed spectral reflectance data; however, the ability to resolve specific features is limited, as the reflectance of a target differs depending on its position and the relative positions of the sun and the sensor (i.e., the sun–target–sensor geometry). Major causes of reflectance variation are shadow and terrain, which are closely related because terrain affects shadow coverage. Asner and Warner [
1] showed that shadow accounted for up to 30–50% of the variance in red and near-infrared (NIR) spectral reflectance data in the Amazon tropical forest. Vanonckelen et al. [
2] indicated that topographic correction of reflectance data improved the accuracy of land cover classification, especially in forest areas.
The ability to correct for the effects of shadow and terrain is still challenging and remains an essential topic in optical remote sensing of land. Various topographic correction methods using digital elevation models (DEMs) have been developed since the early 1980s. Teillet et al. [
3] investigated five kinds of topographic correction equations, including the well-known C-correction, using Landsat and airborne multispectral sensor data. Gu and Gillespie [
4] proposed a sun–canopy–sensor (SCS) method, which was advanced from the sun–terrain–sensor concept, by considering the verticality of forest stands regardless of the slope of the terrain. Soenen et al. [
5] improved the SCS method by adding a parameter, C, to address overcorrection issues, thus creating the SCS+C approach. Many studies have compared these correction methods [
6,
7,
8] and newly developed methods as path length correction [
9] and canopy surface model [
10]. Some other researchers have performed simultaneous correction for atmospheric and topographic effects [
11,
12,
13,
14]. Notably, the Sentinel-2 multispectral instrument (MSI) uses a simultaneous correction for its Level-2A product [
15,
16,
17].
The bidirectional reflectance distribution function (BRDF) is used to model anisotropic reflectance by shadow and terrain. In BDRF models, a casted shadow is often represented using geometric components involving cone [
18,
19], spheroid [
20,
21], cube [
22], or a combination of cone and cylinder [
23] configurations. In these models, the pixel reflectance of remotely sensed images is simulated for a given sun–target–sensor geometry based on the shape, size, distribution, and optical properties of the geometric object. Li and Strahler [
19] developed a geometric optical forest canopy model that treats the conifer canopy as a cone feature; they concluded that the geometric nature of the forest canopy is the major driving factor in directional reflectance. For example, the Moderate Resolution Imaging Spectroradiometer (MODIS) combines a geometric kernel derived from shadow casting theory with a volume scattering kernel for modeling [
24]. In BRDF models, directional variation in the anisotropic reflectance is considered an additional information source in the extraction of land surface properties, rather than an obstacle. The coefficients of the kernel-driven BRDF model of MODIS are used not only in the calculation of nadir reflectance but also in the extraction of albedo [
25] and other vegetation properties [
26,
27,
28].
Several radiative transfer modeling software platforms simulate shadow and BRDF by expressing the three-dimensional (3D) structure of the land surface using point clouds or voxels [
29,
30,
31,
32]. Discrete anisotropic radiative transfer (DART), for example, constructs complex landscapes virtually by combining voxels and facets to simulate spectral reflectance based on the optical properties of land features [
31]. Qi et al. [
32] proposed a large-scale remote-sensing data and image simulation framework (LESS); they compared LESS with other models and airborne observations of bidirectional reflectance data. These scene-based remote-sensing simulators facilitate feature resolution in land-surface remote-sensing data.
With the greater availability of data from light detection and ranging (LiDAR) systems, unmanned aerial vehicles (UAVs), and structure-from-motion (SfM) imagery over the past decade, 3D point clouds are now widely used to represent ground objects, as they are capable of characterizing the vertical information of land-surface objects. Thus, 3D point clouds have been employed extensively in ecological research and environmental management [
33,
34,
35,
36,
37]. Optical information such as color and laser return intensity can be added to individual points; this advantage simplifies the data structure and analysis scheme for 3D point cloud applications in the Earth and ecological sciences [
38].
Point clouds offer great flexibility in modeling the real structures of canopies and topography to account for shadow and topographic features in optical remote-sensing data. The purpose of this study was to use a 3D point cloud to develop an approach to correct for canopy shadow and topographic effects in satellite-observed reflectance imagery of mountainous forests. Unlike DEM-based correction, a point cloud was used to directly simulate the proportion of solar-illuminated area within a satellite image pixel (i.e., the sunlit fraction). The linear relationship between the simulated sunlit fraction and the observed spectral reflectance was analyzed. Evergreen conifer forest was the main target of the study due to its seasonally stable reflectance and structure combined with complex terrain for canopy self-shadowing analysis. Satellite data from the Sentinel-2 MSI were adopted due to their 10-m spatial and 5-day temporal resolutions.
The remainder of this paper is organized as follows.
Section 2 describes the study site and the data collected. Two correction methods, scene-based and pixel-based linear regression, are described in
Section 3 along with the calculation of the sunlit fraction using a 3D point cloud. In
Section 4, the corrected results are demonstrated and compared with those obtained using the SCS+C method and the Level-2A product of Sentinel-2. The advantages and improvements of this approach are discussed in
Section 5.
Section 6 presents a summary of our results and concluding remarks.
3. Methods
Shadow has a significant effect on remotely sensed radiance, so it is a first-order term with respect to controlling radiance [
42]. Our basic assumption in this study was that satellite-observed reflectance values have a linear relationship with the percentage of an area illuminated in a pixel (sunlit fraction). Two kinds of regression were adopted: scene-based and pixel-based. Scene-based regression uses the pixels in a single scene as a statistical linear regression sample; in pixel-based correction, time series reflectance with respect to individual pixels is used for linear regression analysis. Below, we discuss the use of a 3D point cloud to calculate the sunlit fraction, as well as scene-based and pixel-based correction. In addition, the DEM (SCS+C correction) and Sentinel-2 level-2A product are discussed, as these were included in a comparison analysis of the reflectance results.
3.1. Calculation of the Sunlit Fraction
The sunlit fraction (the percentage of solar-illuminated area within a Sentinel-2 pixel) at a particular observation time was simulated based on a ray-tracing scheme using the 3D point cloud. During this process, the point cloud was used to calculate the shadow area directly, without generating a canopy surface model. Thus, the influence of the point cloud noise was very small, even without the noise-reduction filtering of the SfM-generated point cloud. A conceptual diagram is shown in
Figure 2. We divided individual 10-m-resolution Sentinel-2 pixels into 400 (20 × 20) sub-pixels with 0.5-m resolution. Binary judgement of illumination/shade was carried out on a sub-pixel basis, as described below:
“Mean_Sun_Angle” was extracted from the MSI metafile to obtain the solar position (zenith and azimuth angles) at individual observation times.
The sensor position was assumed to be at nadir, as our research site is located almost at the center of the MSI observation swath.
A unique radius was assigned to each point in the 3D point cloud. Here, a “point” is regarded as a sphere for ray tracing. A 0.1-m radius was adopted after several trials.
In our approach, the line-of-sight vector started at the satellite position and was directed toward the center of individual sub-pixels, with 3D coordinates calculated for the first intersection of the vector and the sphere (i.e., a point in the 3D point cloud).
The vector was reflected from the intersection in the solar direction.
A sub-pixel was categorized as shaded or illuminated by determining whether the reflected vector intersected with another sphere.
In step 4, the intersection of the line-of-sight vector and point cloud was evaluated based on whether the distance between the line-of-sight vector and the center of the point cloud was smaller than the radius. Because the satellite was positioned at the nadir, the distance could be calculated from the horizontal coordinates (east, north). The same method was applied in step 6, after rotating the point cloud to orient the solar direction to the nadir. Finally, the sunlit fraction of the 10-m-resolution Sentinel-2 pixel was calculated by counting the number of illuminated sub-pixels among the 400 sub-pixels considered. Because the sub-pixels near the edge of the site did not contain any spheres, the pixels used in the analysis had to have at least one sphere within at least 360 sub-pixels (90%). It should be noted that the optical properties of the 3D point cloud, such as color or brightness, were not used for the sunlit fraction simulation.
Our research site is shaded by mountainous terrain in winter, as it is located on the northern slope of Mt Kuishi. We focused on canopy self-shadowing in this study; therefore, the terrain-induced shadow area was excluded from the regression by calculating the terrain shadow using the 10-m-resolution DEM provided by the Geospatial Information Authority (GSI) of Japan (
http://www.gsi.go.jp/index.html).
3.2. Scene-Based Correction
Scene-based correction uses the pixel data of a single scene as a statistical linear regression sample. The observed reflectance showed a linear relationship with the sunlit fraction (
Figure 3a). After linear regression, the reflectance of an individual pixel can be expressed as follows:
where
is the observed reflectance at the pixel position
in a Sentinel-2 image,
is the sunlit fraction at the same pixel position,
and
are the gain and offset, respectively, of the linear regression, and
is the regression residual. The regression residuals represent local variation in land cover reflectance (
Figure 3b). The regression residuals are preserved following the correction. Corrected reflectance is made by adding this regression residual to the extrapolated reflectance at a 1.0 sunlit fraction (
Figure 3c).
3.3. Pixel-Based Correction
In pixel-based correction, linear regression analysis of the sunlit fraction and reflectance was carried out pixel by pixel using multitemporal data. This method was used because Japanese cedar shows little seasonal variation in its reflectance, although the leaves change to brownish green for several weeks in early spring.
Figure 4a shows the time series of the sunlit fraction and reflectance for one pixel over the cedar canopy; the reflectance changes seasonally along the linear regression line. The regression model for individual pixels is given below:
where
is the observed reflectance at time
,
is the sunlit fraction at
,
and
are the respective gain and offset of the linear regression, and
is the regression residual at
.
Figure 4b shows the time series of the observed reflectance, along with the estimated reflectance values derived by the regression. Here, we assume that these regression residuals are related to the seasonal changes in the cedar trees. These regression residuals were used in the correction for canopy shadow, similar to the scene-based correction approach.
Figure 4c shows the corrected reflectance values obtained by adding individual regression residuals to the estimated reflectance values derived from regression coefficients and a sunlit fraction of 1.0.
The maximum sample size of the regression was 20; however, this number decreased if a particular pixel was shaded by terrain in winter. The analysis results showed that 42% of the analyzed pixels had the maximum number of samples, with 88% having more than 15 samples. The minimum sample size was 12.
3.4. Comparison with SCS+C Correction
SCS+C correction [
5] was adopted for comparison with existing topographic correction methods, although the topographic techniques used a DEM as opposed to a point cloud. SCS+C correction is based on scene-based linear regression of reflectance values with respect to the angle of incidence (i.e., the angle between the sun direction and the normal vector of the inclined surface). Following Soenen and Peddle [
5], the SCS+C correction can be expressed as
where
is the normalized reflectance,
is the uncorrected reflectance,
is the terrain slope,
is the solar zenith angle,
is the incidence angle. Parameter
is given by
where
and
are derived from linear regression of the uncorrected reflectance and the incidence angle, as follows:
In Equation (3), the denominator represents the variation in radiance from the inclined surface with respect to the angle between the surface normal and solar direction. Parameter C compensates indirect solar illumination, which contributes a small amount of brightness due to atmospheric scattering, even under a shadow. The cosine of the solar zenith angle () in the numerator functions to convert reflectance into radiance, eliminating the effects of the solar zenith angle in the calculation of top-of-atmosphere reflectance. The cosine of the slope angle () is adopted for the SCS correction to consider the increase in the area of instantaneous field of view (IFOV) of the sensor due to the slope surface. For the calculation of slope angle and incidence angle, we used the same DEM as that for the terrain–shadow calculation mentioned above.
3.5. Sentinel-2 MSI Level-2A Product
Topographic and atmospheric corrections were applied to the Level-2A product of Sentinel-2 MSI [
15,
16,
17]. We also used this product for corrected reflectance comparisons; however, based on the availability of Level-2A data (available after 12/15/2018 for our research site at the time of the analysis), 15 scenes among 20 observation dates (listed in
Table 1) were used for the comparison. These were downloaded from the Copernicus Open Access Hub and geometrically corrected to represent the same projection as the other data.
4. Results
4.1. Point Cloud and Sunlit Fraction
Figure 5 shows the 3D point cloud and digital surface model (DSM) generated by SfM. The 3D point cloud provides an oblique view of a 30 × 30-m
2 area (3 × 3 Sentinel-2 pixels). The canopy assumes a conical shape composed of needle leaf clumps of sub-meter size. The canopy height in the target plot has lower variation because all trees were planted in 1956 and 1957 [
40], and a dense canopy evenly covers the area, with the exception of several small gaps, as shown in the DSM.
The top images of
Figure 6 show six examples of the Sentinel-2/MSI top-of-the-atmosphere reflectance. In January and November, terrain-induced shadows (described in
Section 3.1) were cast onto some parts of the research area. These terrain-induced shadows in
Figure 6 are overlapped with white frames that were calculated using the DEM. In March, May, and September, north-facing slopes were darker than south-facing slopes, although the difference was less than that in winter. In July, the difference in reflectance between slope directions was much smaller due to the higher solar elevation. In contrast to the cedar canopy, the reflectance values of the logging road were high in band 8 (NIR) because it was fully covered by grass-type vegetation. Small gaps also showed higher NIR reflectance of low deciduous broad-leaved trees and understory vegetation. The bottom of
Figure 6 shows the sunlit fraction simulated by the 3D point cloud. The appearances of brightness were similar to the Sentinel-2 reflectance; that is, the contrast was higher in winter, and south-facing slopes were bright throughout the year. Because the terrain-induced shadow was not calculated, the brightness in the white frames differed from satellite reflectance; however, these areas were eliminated from the regression analysis.
4.2. Corrected Reflectance
Figure 7 shows examples of reflectance values corrected by the three correction methods (scene-based, pixel-based, and SCS+C), together with the uncorrected observed reflectance values. The corrected pixels are inside the white frame (reflectance in the area outside the frame corresponds to the observed reflectance). In scene-based correction, the reflectance values were significantly higher in winter (January and November) than in other seasons. In addition, differences due to variation in slope direction and canopy cover (evergreen cedar canopy versus other deciduous vegetation) were smaller, especially in November. In summer, the corrected scene was similar to the observed scene. In this correction, differences in reflectance values resulting from slope direction were reduced in summer, but remained in spring through autumn.
In pixel-based correction, scenes showed similar reflectance values throughout the year, and there was no apparent difference with respect to slope direction. Given that some pixels were shaded by terrain in winter, the reflectance values could be estimated by regression using another season. Additionally, the logging road and deciduous trees showed higher reflectance values than the cedar canopy in all three bands (green, red, and NIR).
In the SCS+C correction, gray pixels were not corrected because the solar incident angle on the sloped terrain was greater than 90 degrees. Scenes from May to September looked similar to those using scene-based correction; differences with respect to slope were corrected more than when using the scene-based method. However, winter scenes had a different appearance, with high local contrast due to the terrain slope calculated using the 10-m resolution DEM.
Figure 8 shows time series of the 10th, 50th, and 90th percentile points of observed and corrected reflectance values in bands 4 (red) and 8 (NIR). The observed reflectance values were higher in summer in both bands, although there was much less seasonal change in the red reflectance values. The gradual increase in red reflectance values from October is most likely due to the seasonal change in the cedar trees, as it is not synchronized with solar elevation; cedar leaves are brown from winter to early spring in this area due to low temperatures. In contrast, NIR reflectance during the same season was stable. The ranges between the 10th and 90th percentiles for bands 4 and 8 were larger in winter due to the significant contrast between illuminated and shaded pixels.
From
Figure 8, a summary of some of the key characteristics of the three correction schemes is given below:
Scene-based correction generated much higher reflectance values in winter than in summer.
Pixel-based correction resulted in stable reflectance values throughout the year.
The range of reflectance values was uniform throughout the year in scene-based and pixel-based corrections.
SCS+C correction generated data similar to the original data, i.e., having lower reflectance values and a wider range in winter.
4.3. Scene-Based Correction
As shown in
Figure 8, scene-based correction generated much higher reflectance values in winter. Notably, the corrected NIR-band reflectance in winter (0.4) was almost double that in summer (0.2).
Figure 9a shows all regression lines in the NIR band (band 8). Two scatter plots are shown in the figure, for December and July, corresponding to the highest (0.362) and lowest (−0.029) regression gains, respectively. The large change in reflectance values versus a unit sunlit fraction in winter (plotted by a circle) resulted in the higher regression gain. On the other hand, no clear change in reflectance values was evident in July; hence, a lower regression gain was recorded. This trend is the same as the results for July and October reported by Gu and Gillespie [
4], although they reflect the relationship between the DEM-based solar incidence angle and shortwave infrared reflectance. In addition to this higher gain, the lower range of the sunlit fraction in winter (about 0.0–0.4) required large extrapolation to the 1.0 sunlit fraction in this correction. Thus, corrected reflectance values were higher in winter.
Figure 9b shows the time series of regression gains for the three bands. The gains were synchronized with solar elevation, with the highest (lowest) gain at the winter (summer) solstice.
Figure 9c shows the linear relationship between the regression gains and the solar zenith angle. The gains in bands 3 and 8 showed sharp changes at both ends of the solar zenith angle. In band 4, restrained change was evident at both ends, implying that the accuracy of this correction method could be improved by considering reflection by a sunlit canopy.
4.4. Pixel-Based Correction
Figure 10 shows the gain and offset of pixel-based linear regression for the three Sentinel-2/MSI bands. The gains in bands 4 and 8 of the cedar canopy on the north-facing slope are larger than those of the south-facing slope; thus, the north-facing canopy had higher reflectance sensitivity to the sunlit fraction. On the other hand, the intercept of the south-facing slope was high; i.e., it showed high reflectance even for a zero sunlit fraction.
Figure 11 shows scatterplots for four sample pixels: pixels 1 and 2 are on the north-facing slope and pixels 3 and 4 are on the south-facing slope (pixel locations are shown in
Figure 5b). On the north-facing slope, the larger gain and smaller intercept were due to wide ranges of seasonal change in both the sunlit fraction and reflectance values. In contrast, the small gain and large intercepts for the south-facing slope are the result of the lower sensitivity of the reflectance to small changes in the sunlit fraction at higher values. Although the trends differed depending on the slope, almost the same reflectance values were observed for the highest sunlit fraction in summer, for example, about 0.20–0.25 reflectance in the case of band 8. This means that the decrease in reflectance during winter was restrained on the sunward slope due to canopy reflection.
Figure 12 shows the coefficient of determination and root mean square of the residual (RMSR) of the linear regression. The coefficient of determination (the proportion of the variance in reflectance that is predictable by the sunlit fraction) was higher for the north-facing slope; it was almost a value of 1 in band 8. This demonstrates the trend in the regression gain shown in top panels in
Figure 11. Dynamic seasonal changes in both the reflectance and sunlit fraction on the north-facing slope resulted in a higher coefficient of determination. On the other hand, the regression gain was almost zero for the south-facing slope, i.e., the reflectance was less predictable due to flat scatterplots. Although the coefficient of determination was lower (almost a value of 0 in bands 4 and 8), the regression residual was smaller on the south-facing slope. Thus, the relationships were linear (but flat) with respect to the sunlit fraction, with a similar magnitude of regression error.
Figure 13 shows the time series of observed and corrected NIR reflectance values of four sample pixels over the cedar canopy. There were large differences in the observed values between north-facing and south-facing slopes as the solar elevation declined during the winter. Because there is only a small seasonal change in cedar trees and all pixels are selected from the same plot, this difference was due mostly to the illumination conditions associated with canopy shadow and terrain. On the other hand, corrected reflectance values showed a significantly smaller seasonal change, although the reflectance displayed large variations among pixels. The reflectance values of north-facing pixels (pixels 1 and 2) increased in summer due to a larger regression gain, as shown in
Figure 11. In particular, the corrected reflectance values of point 1 were approximately 0.1 higher than those of the other three pixels, as the extrapolated reflectance values were higher for a 1.0 sunlit fraction. A significant change was not evident in south-facing pixels due to the small change in the reflectance versus the sunlit fraction. Seasonal change was considered in this correction using regression residuals; however, the change was very small (i.e., noise).
Although we focused on corrections for the conifer canopy, we also provide results for some deciduous vegetation types. Pixel-based regression assumes a small seasonal change in the cedar tree. Thus, the results are unrealistic for deciduous vegetation, such as the grass on the logging road or deciduous trees. In the case of the logging road, the trends in the regression gain and offset differed in the north–south and east–west directions (
Figure 10). This was due to the relative position of the sun. The north–south direction was less affected by shadows because there was no canopy on the south side; thus, the seasonal change was mainly due to the vegetation. However, the east–west direction had canopies on the south side that were likely responsible for the large seasonal change in reflectance. It should be noted that the RMSR was larger in both directions of the logging road and for other deciduous vegetation (
Figure 12); that is, the seasonal changes in the reflectance were not clearly linear with respect to the sunlit fraction.
Figure 14 shows a scatterplot of the logging road (pixel 5) and deciduous trees (pixel 6). Both plots show large residuals from the regression lines compared with that for the cedar canopy in
Figure 11; thus, the change here depends on both reflectance and shadow, further complicated by the seasonal changes in greenness and vegetation structure, respectively. Residuals were distributed below (above) the regression line in spring (autumn) because the vegetation activity was delayed in response to the annual solar cycle.
Figure 15 shows the time series of observed and corrected NIR reflectance values of the same two pixels as shown in
Figure 14. Although the reflectance values were increased by the large extrapolation from the lower sunlit fraction, seasonal change remained due to the larger regression residuals compared with those of the cedar canopy. However, the typical seasonal change in the reflectance of vegetation was nearly eliminated, as it was synchronized with the sunlit fraction.
4.5. SCS+C Correction
In SCS+C correction, the seasonal change in the corrected reflectance was similar to that for the observed reflectance (
Figure 8), except for an increase in the average reflectance and a decrease in the reflectance variation during the winter season. However, corrected images showed a much higher local contrast, even in the same cedar tree plot (
Figure 7).
Figure 16 shows scatterplots of the observed and corrected NIR (band 8) reflectance values in summer and winter; note that the horizontal axis is the local solar incidence angle, not the sunlit fraction.
In summer, C and in Equation (3) were larger (1.50 and 0.94, respectively), and and varied within a narrower range; therefore, the correction term varied only slightly around a value of 1. In winter, C and values were smaller (0.12 and 0.51, respectively), and varied more widely, resulting in a larger range for the correction term (0.7–4.5). The correction term in Equation (3) also increased exponentially as the incidence angle increased (i.e., as decreased). The rotation-like correction of the SCS+C method did not remove the shadow but rather normalized the terrain-induced variation in reflectance in the scene. Hence, the average reflectance in winter did not increase to the same level as that in summer.
4.6. Comparison with the Level-2A Product
Figure 17 shows seasonal profiles of the Level-1C (uncorrected) and Level-2A products of Sentinel-2 in the red and NIR bands, together with sample images, although some data for our research site were not available. After simultaneous corrections for the atmosphere and topography were applied in the Level-2A product, the seasonal profile was flattened in band 8. The image contrast was higher, particularly in winter (10th to 90th percentiles > 0.3), likely due to DEM-based topographic correction in winter. Atmospheric and topographic corrections under regular operation of a global satellite product can be quite challenging but are extremely valuable for users in terms of improving data quality.
6. Conclusions
In this study, we investigated the feasibility of using an SfM-derived 3D point cloud to correct shadow effects on reflectance in a conifer canopy. Scene-based correction resulted in overcorrection in winter due to a lower sunlit fraction and greater variation in observed reflectance values relative to the change in the sunlit fraction. In summer, corrected reflectance values were almost the same as the observed reflectance values due to weaker correlation with the sunlit fraction. Pixel-based correction was applied based on the assumption that seasonal changes in reflectance values are much smaller than the shadow effect. Corrected images and time series reflectance data showed small seasonal changes in the cedar canopy and lower variation due to slope direction. These results show the benefit of using the sunlit fraction of incident radiation in dealing with the reflection of incident radiation by the canopy and the propagation of reflected light deeper into the canopy layer.
A novel finding of this research is the favorable performance of shadow correction in flat terrain due to detailed canopy structure modeling using a point cloud. The proposed method corrected canopy self-shadowing even on flat ground, unlike conventional DEM-based correction.
Shadow-corrected reflectance is essential for accurate extraction of land cover types or bio-physical attributes of vegetation using optical remote sensing. This study provides a basis for future utilization of 3D point clouds for shadow correction, with specific issues highlighted here to be addressed as next steps in further developing this approach. Additionally, the application of our proposed method over wide areas using airborne LiDAR is a potential next step in future studies.