# A Method for Landsat and Sentinel 2 (HLS) BRDF Normalization

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Materials

#### 2.1.1. HLS Data

#### 2.1.2. MODIS Data

#### 2.1.3. Homogeneous Sites

#### 2.1.4. SURFRAD Data

#### 2.1.5. OzFlux Data

#### 2.2. Methods

#### 2.2.1. Current HLS BRDF Normalization

_{s}is the sun zenith angle, θ

_{v}is the view zenith angle, ϕ is the relative azimuth angle, F

_{1}is the volume scattering kernel, based on the Rossthick function derived by Roujean [18], and F

_{2}is the geometric kernel, based on the Li-sparse model [19] but considering the reciprocal form given by Lucht [20] and corrected for the Hot-Spot process proposed by Maignan [21]. ${\theta}_{s}^{out}$ is the sun zenith angle of the normalized data, which is set to constant value depending on the tile central latitude [1]. The BRDF coefficients of the model (k

_{0}, k

_{1}, and k

_{2}) are provided in [1,5].

#### 2.2.2. Proposed BRDF Normalization Method

_{1}and F

_{2}are fixed functions of the observation geometry, and k

_{0}, k

_{1}, and k

_{2}are free parameters. From this notation, we define V as k

_{1}/k

_{0}and R for k

_{2}/k

_{0}. In order to invert the MODIS BRDF parameters (V and R) we use the VJB method [12,13]. This method assumes that the difference between the successive observations in time is mainly attributed to directional effects while the variation of k

_{0}is supposed small. Additionally, it assumes that R and V are represented by a linear function of the NDVI.

_{x}, B

_{x}…, N

_{x}represent proportions of each the n classes within the x MODIS pixel. BRDF parameters for each class, which are unknowns in Equation (6), can be derived through matrix inversion. We only invert the k

_{1}and k

_{2}parameters since they describe the directional shape, while k

_{0}describes the reflectance magnitude. Considering the HLS surface reflectance and the classification image, we derive ${k}_{0}^{HLS}$ as shown in Equation (7).

_{0}, V

_{1}, R

_{0}, and R

_{1}in Equations (4) and (5) at HLS spatial resolution. Next, we apply a linear regression for the V and R parameters versus the NDVI to derive the V

_{0}, V

_{1}, R

_{0}, and R

_{1}parameters at HLS pixel level.

^{N}) at 45 degrees of solar zenith angle and nadir observation (Vermote et al., 2009):

#### 2.2.3. Temporal Evaluation of Homogeneous Sites

_{i}is the surface reflectance of day i.

#### 2.2.4. Spatial Evaluation of an Equatorial Region

#### 2.2.5. Albedo Validation

## 3. Results

#### 3.1. Temporal Evaluation of Homogeneous Sites

^{2}= 0.56) but mostly in the NIR band (r

^{2}= 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.

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

#### 3.3. Surface Albedo Validation

## 4. Discussion and Conclusions

_{0}, V

_{1}, R

_{0}, and R

_{1}) that is regularly updated to account for any land cover change. In this way, the effect of outliers and poor-quality pixels on the BRDF inversion is minimized, resulting in a more stable and robust BRDF model. We acknowledge that the assumption of a BRDF model being a function of the NDVI has limitations. For example, on sparse forests where the NDVI is not a good descriptor of canopy structure [24]. However, this simple model might be used for a rough correction of BRDF effects in reflectance time series. Although a full inversion of the BRDF model will give better results, some applications, such as real time processing, may want to trade accuracy for simplicity [25].

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Appendix A

## References

- Claverie, M.; Ju, J.; Masek, J.G.; Dungan, J.L.; Vermote, E.F.; Roger, J.-C.; Skakun, S.V.; Justice, C. The Harmonized Landsat and Sentinel-2 surface reflectance data set. Remote Sens. Environ.
**2018**, 219, 145–161. [Google Scholar] [CrossRef] - Vermote, E.; Justice, C.; Claverie, M.; Franch, B. Preliminary analysis of the performance of the Landsat 8/OLI land surface reflectance product. Remote Sens. Environ.
**2016**, 185, 46–56. [Google Scholar] [CrossRef] - Villaescusa-Nadal, J.L.; Franch, B.; Roger, J.; Vermote, E.F.; Skakun, S.; Justice, C. Spectral Adjustment Model’s Analysis and Application to Remote Sensing Data. IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens.
**2019**, 1–12. [Google Scholar] [CrossRef] - Gao, F.; He, T.; Masek, J.G.; Shuai, Y.; Schaaf, C.B.; Wang, Z. Angular Effects and Correction for Medium Resolution Sensors to Support Crop Monitoring. IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens.
**2014**, 7, 4480–4489. [Google Scholar] [CrossRef] - Roy, D.P.; Zhang, H.K.; Ju, J.; Gomez-Dans, J.L.; Lewis, P.E.; Schaaf, C.B.; Sun, Q.; Li, J.; Huang, H.; Kovalskyy, V. A general method to normalize Landsat reflectance data to nadir BRDF adjusted reflectance. Remote Sens. Environ.
**2016**, 176, 255–271. [Google Scholar] [CrossRef][Green Version] - Shuai, Y.; Masek, J.G.; Gao, F.; Schaaf, C.B. An algorithm for the retrieval of 30-m snow-free albedo from Landsat surface reflectance and MODIS BRDF. Remote Sens. Environ.
**2011**, 115, 2204–2216. [Google Scholar] [CrossRef] - Schaaf, C.B.; Gao, F.; Strahler, A.H.; Lucht, W.; Li, X.; Tsang, T.; Strugnell, N.C.; Zhang, X.; Jin, Y.; Muller, J.-P.; et al. First operational BRDF, albedo nadir reflectance products from MODIS. Remote Sens. Environ.
**2002**, 83, 135–148. [Google Scholar] [CrossRef][Green Version] - Shuai, Y.; Masek, J.G.; Gao, F.; Schaaf, C.B.; He, T. An approach for the long-term 30-m land surface snow-free albedo retrieval from historic Landsat surface reflectance and MODIS-based a priori anisotropy knowledge. Remote Sens. Environ.
**2014**, 152, 467–479. [Google Scholar] [CrossRef] - Flood, N.; Danaher, T.; Gill, T.; Gillingham, S. An Operational Scheme for Deriving Standardised Surface Reflectance from Landsat TM/ETM+ and SPOT HRG Imagery for Eastern Australia. Remote Sens.
**2013**, 5, 83–109. [Google Scholar] [CrossRef][Green Version] - Van doninck, J.; Tuomisto, H. Evaluation of directional normalization methods for Landsat TM/ETM+ over primary Amazonian lowland forests. Int. J. Appl. Earth Obs. Geoinf.
**2017**, 58, 249–263. [Google Scholar] [CrossRef] - Franch, B.; Vermote, E.F.; Claverie, M. Intercomparison of Landsat albedo retrieval techniques and evaluation against in situ measurements across the US SURFRAD network. Remote Sens. Environ.
**2014**, 152. [Google Scholar] [CrossRef] - Vermote, E.; Justice, C.O.; Breon, F.M. Towards a Generalized Approach for Correction of the BRDF Effect in MODIS Directional Reflectances. IEEE Trans. Geosci. Remote Sens.
**2009**, 47, 898–908. [Google Scholar] [CrossRef] - Franch, B.; Vermote, E.F.; Sobrino, J.A.; Julien, Y. Retrieval of Surface Albedo on a Daily Basis: Application to MODIS Data. IEEE Trans. Geosci. Remote Sens.
**2014**, 52, 7549–7558. [Google Scholar] [CrossRef] - Franch, B.; Vermote, E.; Skakun, S.; Roger, J.-C.; Santamaria-Artigas, A.; Villaescusa-Nadal, J.L.; Masek, J. Toward Landsat and Sentinel-2 BRDF Normalization and Albedo Estimation: A Case Study in the Peruvian Amazon Forest. Front. Earth Sci.
**2018**, 6, 185. [Google Scholar] [CrossRef] - Vihermaa, L.E.; Waldron, S.; Domingues, T.; Grace, J.; Cosio, E.G.; Limonchi, F.; Hopkinson, C.; Rocha, H.R.; Gloor, E. Fluvial carbon export from a lowland Amazonian rainforest in relation to atmospheric fluxes. J. Geophys. Res. Biogeosciences
**2016**, 121, 3001–3018. [Google Scholar] [CrossRef][Green Version] - Nagol, J.R.; Sexton, J.O.; Kim, D.-H.; Anand, A.; Morton, D.; Vermote, E.; Townshend, J.R. Bidirectional effects in Landsat reflectance estimates: Is there a problem to solve? ISPRS J. Photogramm. Remote Sens.
**2015**, 103, 129–135. [Google Scholar] [CrossRef] - Baldocchi, D.; Falge, E.; Gu, L.; Olson, R.; Hollinger, D.; Running, S.; Anthoni, P.; Bernhofer, C.; Davis, K.; Evans, R.; et al. FLUXNET: A new tool to study the temporal and spatial variability of ecosystem-scale carbon dioxide, water vapor, and energy flux densities. Bull. Am. Meteorol. Soc.
**2001**, 82, 2415–2434. [Google Scholar] [CrossRef] - Roujean, J.-L.; Leroy, M.; Deschamps, P.-Y. A bidirectional reflectance model of the Earth’s surface for the correction of remote sensing data. J. Geophys. Res. Atmos.
**1992**, 97, 20455–20468. [Google Scholar] [CrossRef] - Li, X.; Strahler, A.H. Geometric-optical bidirectional reflectance modeling of a conifer forest canopy. IEEE Trans. Geosci. Remote Sens.
**1986**, GE-24, 906–919. [Google Scholar] [CrossRef] - Lucht, W. Expected retrieval accuracies of bidirectional reflectance and albedo from EOS-MODIS and MISR angular sampling. J. Geophys. Res. Atmos.
**1998**, 103, 8763–8778. [Google Scholar] [CrossRef][Green Version] - Maignan, F.; Bréon, F.-M.; Lacaze, R. Bidirectional reflectance of Earth targets: Evaluation of analytical models using a large set of spaceborne measurements with emphasis on the Hot Spot. Remote Sens. Environ.
**2004**, 90, 210–220. [Google Scholar] [CrossRef] - Skakun, S.; Vermote, E.F.; Roger, J.-C.; Justice, C.O.; Masek, J.G. Validation of the LaSRC cloud detection algorithm for Landsat 8 images. IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens.
**2019**, 12. [Google Scholar] [CrossRef] - Liang, S. Narrowband to broadband conversions of land surface albedo I: Algorithms. Remote Sens. Environ.
**2001**, 76, 213–238. [Google Scholar] [CrossRef] - Stenberg, P.; Rautiainen, M.; Manninen, T.; Voipio, P.; Smolander, H. Reduced simple ratio better than NDVI for estimating LAI in Finnish pine and spruce stands. Silva Fennica
**2004**, 38, 431. [Google Scholar] [CrossRef] - Bréon, F.-M.; Vermote, E. Correction of MODIS surface reflectance time series for BRDF effects. Remote Sens. Environ.
**2012**, 125, 1–9. [Google Scholar] [CrossRef] - Muro, J.; Tuomisto, H.; Higgins, M.A.; Moulatlet, G.M.; Ruokolainen, K. Floristic composition and across-track reflectance gradient in Landsat images over Amazonian forests. ISPRS J. Photogramm. Remote Sens.
**2016**, 119, 361–372. [Google Scholar] [CrossRef][Green Version] - Higgins, M.A.; Asner, G.P.; Perez, E.; Elespuru, N.; Tuomisto, H.; Ruokolainen, K.; Alonso, A. Use of Landsat and SRTM data to detect broad-scale biodiversity patterns in Northwestern Amazonia. Remote Sens.
**2012**, 4, 2401–2418. [Google Scholar] [CrossRef] - Van doninck, J.; Tuomisto, H. A Landsat composite covering all Amazonia for applications in ecology and conservation. Remote Sens. Ecol. Conserv.
**2018**, 4, 197–210. [Google Scholar] [CrossRef][Green Version]

**Figure 1.**Harmonized Landsat/Sentinel-2 (HLS) image RGB composite on August 21th of 2016 in the Brazilian Amazon area. The seven dots next to the river show the location and size of the averaged area to analyze the transect covering different VZA (see Section 2.2.3).

**Figure 2.**Red band (

**a**) R and (

**b**) V parameters applying inverting Equation (6) over an HLS image (tile 11SQS) on June 20th of 2017 in Yuma, Arizona (US).

**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.

**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.

**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 8.**Broadband blue sky surface albedo validation of all the (

**a**) SURFRAD, (

**b**) OzFlux sites, and (

**c**) combining both sites considered from 2013 to 2017. (

**d**) The broadband directional surface reflectance comparison with surface albedo measurements.

**Table 1.**Geolocation and brief description of the US surface radiation budget observing network (SURFRAD) sites considered in this study.

Station Name | Network | Location Latitude, Longitude | Land cover Type | HLS Tile | Tower Height above Target |
---|---|---|---|---|---|

Desert Rock Station | SURFRAD | 36.6232N, 116.0196W | Sparse vegetation | 11SNA | 10 m |

Table Mountain | SURFRAD | 40.1256N, 105.2378W | Sandy with exposed rocks, sparse grasses and shrubs | 13TDE | 10 m |

Bondville | SURFRAD | 40.0516N, 88.3733W | Agriculture | 16TCK | 10 m |

Goodwin creek | SURFRAD | 34.2547N, 89.8729W | Pasture grass and sparsely distributed deciduous trees | 16SBD | 10 m |

Penn state university | SURFRAD | 40.7203N, 77.9310W | Agriculture Research field | 18TTL | 10 m |

Fort Peck | SURFRAD | 48.3078N, 105.1017W | Sparse vegetation | 13UDP | 10 m |

Sioux Falls | SURFRAD | 43.7340N, 96.62328W | Prairie grasses | 14TPP | 10 m |

Station Name | Network | Location Latitude, Longitude | Land cover Type | HLS Tile | Tower Height above Target |
---|---|---|---|---|---|

Calperum | OzFlux | 34.0027S, 140.5877E | Sand dunes with trees and shrubs | 54HVH | 20 m |

Cumberland Plain | OzFlux | 33.6152S, 150.7236E | Dry sclerophyll forest | 56HKH | 29 m (~6 m above canopy) |

Whroo | OzFlux | 36.6732S, 145.0294E | Eucalyptus forest | 55HCV | 36 m (~10 m above canopy) |

Wombat | OzFlux | 37.4222S, 144.0944E | Eucalyptus forest | 55HBU | 30 m (~5 m above canopy) |

Yanco | OzFlux | 34.9893S, 146.2907E | Grassland | 55HDB | 2 m |

CV (%) | RED | NIR | NDVI |
---|---|---|---|

Directional reflectance | 11.4 | 8.3 | 1.6 |

Current HLS BRDF normalization | 9.3 | 6.0 | 1.6 |

Proposed BRDF normalization | 7.6 | 4.5 | 1.6 |

CV (%) | RED | NIR | NDVI |
---|---|---|---|

Directional reflectance | 2.8 | 2.3 | 6.8 |

Current HLS BRDF normalization | 5.4 | 4.2 | 10.1 |

Proposed BRDF normalization | 3.3 | 2.5 | 8.2 |

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## Share and Cite

**MDPI and ACS Style**

Franch, B.; Vermote, E.; Skakun, S.; Roger, J.-C.; Masek, J.; Ju, J.; Villaescusa-Nadal, J.L.; Santamaria-Artigas, A. A Method for Landsat and Sentinel 2 (HLS) BRDF Normalization. *Remote Sens.* **2019**, *11*, 632.
https://doi.org/10.3390/rs11060632

**AMA Style**

Franch B, Vermote E, Skakun S, Roger J-C, Masek J, Ju J, Villaescusa-Nadal JL, Santamaria-Artigas A. A Method for Landsat and Sentinel 2 (HLS) BRDF Normalization. *Remote Sensing*. 2019; 11(6):632.
https://doi.org/10.3390/rs11060632

**Chicago/Turabian Style**

Franch, Belen, Eric Vermote, Sergii Skakun, Jean-Claude Roger, Jeffrey Masek, Junchang Ju, Jose Luis Villaescusa-Nadal, and Andres Santamaria-Artigas. 2019. "A Method for Landsat and Sentinel 2 (HLS) BRDF Normalization" *Remote Sensing* 11, no. 6: 632.
https://doi.org/10.3390/rs11060632