**3. Results**

#### *3.1. Temporal Evaluation of Homogeneous Sites*

First, focusing on the Peruvian Amazon forest, Figure 3 shows the directional (red), BRDF-normalized using Roy [5] (green), and BRDF-normalized using the proposed BRDF normalization (black) surface reflectance versus solar zenith angle for each day of the year (DOY) considered in the time series (2013–2017). Note that we have represented differently Landsat 8 (dots) and Sentinel 2 (triangle) data. Results are shown for (a) the red band, (b) the near infrared (NIR) band, (c) the Normalized Difference Vegetation Index (NDVI), and (d) the SZA for each observation. Given the high frequency of cloud cover in this area, a total of 23 scenes were used in this analysis through the entire period 2013–2017.

All parameters show good consistency for both satellites' products. The directional surface reflectance (red) shows a clear dependency with the SZA in the RED (r2 = 0.56) but mostly in the NIR band (r2 = 0.82), showing higher values for low solar angles and lower values for higher angles. This effect is not fully corrected with the current BRDF-normalization of the HLS product (green), which after the correction still shows a dependency on the SZA in both bands. However, it is corrected on the BRDF-normalized RED reflectance and minimized in the NIR reflectance by decreasing the correlation coefficient and providing a slope closer to zero when using the proposed algorithm (black), which normalize all observations to SZA = 45◦ and nadir observation. The NDVI barely shows any dependency on the SZA for any product. Figure 4 shows a subset of the NIR band directional (left) and BRDF-normalized using the proposed algorithm (right) surface reflectance of the HLS image that is mostly affected by the SZA effect according to Figure 3. The directional reflectance image shows higher values than the BRDF-normalized one over the scene.

**Figure 3.** *Cont.*

**Figure 3.** Peruvian Amazon pixel Landsat 8 (dots) and Sentinel 2 (triangles) surface reflectance in the (**a**) RED, (**b**) Near infrared (NIR) and (**c**) Normalized Difference Vegetation Index (NDVI), with no normalization (red color), HLS BRDF normalization (green color) and the proposed BRDF-normalization (black color) from 2013 to 2017 versus the Solar Zenith Angle (SZA). The error bars displayed represent the uncertainty of the Landsat 8 surface reflectance product [2], assuming the same error for Sentinel 2. Adapted from Franch [14].

**Figure 4.** NIR band (**a**) directional and (**b**) BRDF-normalized surface reflectance of an HLS subset centered on the Peruvian Amazon tower on December 12th of 2015.

Similar to Figure 3, Figure 5 shows the directional (red), BRDF-normalized using Roy [5] (green), and BRDF-normalized using the proposed BRDF normalization (black) surface reflectance versus

the SZA in the desert site in Yuma (Arizona, US). The SZA of this site shows a greater variation during the year (from 20 to 60 degrees) compared to the previous site (from 20 to 45 degrees). Despite this, the directional reflectance barely shows any dependency with the SZA. However, the HLS BRDF-normalized data shows a high dependency (green) with higher values for high SZA and lower values for low SZA. This is not the case when applying the proposed algorithm (black), that shows more stable surface reflectance values.

**Figure 5.** Arizona desert pixel Landsat 8 (dots) and Sentinel 2 (triangles) surface reflectance in the (**a**) RED, (**b**) NIR, and (**c**) NDVI with no normalization (red), HLS BRDF normalization (green), and the proposed BRDF-normalization (black) from 2013 to 2017 versus the SZA. The error bars displayed represent the uncertainty of the Landsat 8 surface reflectance product [2], assuming the same error for Sentinel 2.

Tables 3 and 4 show the coefficient of variation of the two homogeneous sites considered. The forest shows a high CV in the red (11%) and the NIR (8%) directional surface reflectance. The CV reduction in both red and NIR bands is around 2% when applying the current HLS correction and 4% when applying the proposed algorithm. However, the NDVI CV remains low and constant for all surface reflectances. The desert's CV, on the other hand, is much lower and does not show any significant change for any band or the NDVI when applying the proposed algorithm, but it does show an increase when applying the current BRDF correction of about 2% to 3%.


**Table 3.** Coefficient of variation (CV) of the Peruvian Amazon pixel.

**Table 4.** Coefficient of variation (CV) of a desert site in Arizona (USA).


#### *3.2. Spatial Evaluation of an Equatorial Region*

Figure 6 shows the HLS NIR surface reflectance image. The directional reflectance (Figure 6a) shows higher values along the western part (compared to the eastern) where the VZA is larger (Figure 6c). Note that the solar azimuth angle image shows nearly constant values of 63 degrees. This means that the western part is observed in the backscattering direction, which explains the higher values observed. The current HLS correction (Figure 6b) reduces this angular effect. However, the west area still shows higher values. Finally, when applying the proposed normalization (Figure 6c) this illumination effect is minimized.

**Figure 6.** *Cont.*

**Figure 6.** HLS NIR surface reflectance: (**a**) directional, (**b**) using the current BRDF normalization and (**c**) using the proposed normalization. (**d**) The view zenith angle of each pixel. Image on August 21th of 2016 in the Brazilian Amazon area.

Figure 7 shows the transect surface reflectance versus the view zenith angle. Though there is variability through the different samples, we have added a trendline to show the angular dependency of each dataset. The directional reflectance shows the highest values and the largest slope with a *p*-value of 0.02, and it is followed by the current HLS BRDF normalization with a *p*-value of 0.08. The proposed method shows the lowest and more stable values with a slope closer to zero and a *p*-value of 0.31, meaning that there is no significant relationship between the corrected reflectance and the VZA. Additionally, the similar intercepts of the linear regressions show that the three datasets converge to a similar value at zero degrees observation. The analysis of the red band and NDVI (Appendix A) show similar conclusions but the directional effect is lower.

**Figure 7.** HLS NIR surface reflectance transect values versus the view zenith angle (VZA).
