# Adjustment of Sentinel-2 Multi-Spectral Instrument (MSI) Red-Edge Band Reflectance to Nadir BRDF Adjusted Reflectance (NBAR) and Quantification of Red-Edge Band BRDF Effects

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Data

#### 2.1. Sentinel-2A Data

#### 2.2. Fixed Global Annual MODIS Red and NIR BRDF Model Parameters

_{vol}(Ω,Ω’) and K

_{geo}(Ω,Ω’) are volumetric scattering and geometric-optical model kernels, respectively, which only depend on the sun-view geometry; and ${f}_{iso}\left(\lambda \right)$, ${f}_{vol}\left(\lambda \right)$, and ${f}_{geo}\left(\lambda \right)$ are the MODIS spectral BRDF model parameters.

#### 2.3. Spectral BRDF Parameters Derived from the POLDER BRDF Database

## 3. Methodology

#### 3.1. Sentinel-2 MSI Red-Edge Band NBAR Derivation

#### 3.2. Derivation of Sentinel-2 MSI Red-Edge Band BRDF Spectral Model Parameters by Linear Interpolation between the Red and NIR MODIS BRDF Spectral Model Parameters

#### 3.3. Quantification of Sentinel-2 MSI Red-Edge Directional Reflectance Effects and Reduction of Directional Reflectance Effects in MSI Red-Edge NBAR

## 4. Results

#### 4.1. Sentinel-2 MSI Red-Edge Band NBAR Derivation

#### 4.2. Quantification of Sentinel-2 MSI Red-Edge Band Bi-Directional Reflectance Effects

^{2}values (>0.7) for January than for April (>0.3) (Table 4). The B-F difference, i.e., the OLS slope term multiplied by the maximum observed view zenith range (23.86°), quantifies the average difference between surface reflectance in the forward and backward scatter directions at the MSI scan edges. The B-F differences for all three red-edge bands are about 0.07 to 0.08 (January) and 0.02 to 0.03 (April) (Table 4).

#### 4.3. Quantification of Sentinel-2A MSI Red-Edge Directional Reflectance Effect Reduction in the NBAR

^{2}values (<0.21), but are statistically significant (p < 0.0001) (Table 6). The NBAR B–F differences are small, ~0.02 for the January data and <0.007 for the April data.

## 5. Discussion

## 6. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 1.**Spectral response functions for the Sentinel-2 MSI (solid, [1]) and MODIS (dashed, [23]) red to NIR wavelength bands. The MSI red-edge bands 5 (705 nm), band 6 (740 nm), and band 7 (783 nm) are shown in black. The MSI bands (in order of increasing central wavelength) are band 4 (665 nm), band 5 (705 nm), band 6 (740 nm), band 7 (783 nm), band 8 (842 nm), and band8A (865 nm). The MODIS red (645 nm) and NIR (858 nm) bands are shown by the dashed lines.

**Figure 2.**Predicted reflectance (derived as 1) using the fixed global annual POLDER NIR 865 nm (blue), red-edge 765 nm (black), and red 670 nm (red) BRDF model parameters (Table 2) and using the interpolated POLDER red-edge 765 nm (orange) BRDF model parameters. Shown for MODIS or POLDER ± 60° view zenith angle range and for three fixed solar zenith angles (0°, 30°, 45°).

**Figure 3.**c-factors (derived as 2) using the fixed global annual POLDER NIR 865 nm (blue), red-edge 765 nm (black), and red 670 nm (red) BRDF model parameters (Table 2) and using the interpolated POLDER red-edge 765 nm (orange) BRDF model parameters. Shown for Sentinel-2 MSI ± 10.3° view zenith angle range and for three fixed solar zenith angles (0°, 30°, 45°). The orange and blue lines are almost identical and the blue lines are plotted over the orange lines.

**Figure 4.**Sentinel-2A MSI red-edge surface reflectance differences in the Southern Africa January swath image overlap zones plotted against view zenith for a total of 6,600,685 pairs of forward and back scatter surface reflectance values. The plot colors show the relative frequency of occurrence of similar difference values (with a log2 scale). The solid lines show ordinary least squares (OLS) linear regression fits of these data (see Table 4). Results shown for MSI bands 5 (705 nm), 6 (740 nm), and 7 (783 nm).

**Figure 6.**Sentinel-2A MSI red-edge surface NBAR differences in the Southern Africa January swath image overlap zones plotted against view zenith for a total of 6,600,685 pairs of forward and back scatter surface NBAR values. The plot colors show the relative frequency of occurrence of similar difference values (with a log2 scale). The solid lines show ordinary least squares (OLS) linear regression fits of these data (see Table 6). Results shown for MSI bands 5 (705 nm), 6 (740 nm), and 7 (783 nm).

**Table 1.**Fixed global annual MODIS spectral BRDF model parameters for the MODIS red and NIR bands (reproduced from Table 5 of [16]) used in this study.

MODIS Band (Center Wavelength) | ${\mathit{f}}_{\mathit{i}\mathit{s}\mathit{o}}\left(\mathit{\lambda}\right)$ | ${\mathit{f}}_{\mathit{g}\mathit{e}\mathit{o}}\left(\mathit{\lambda}\right)$ | ${\mathit{f}}_{\mathit{v}\mathit{o}\mathit{l}}\left(\mathit{\lambda}\right)$ |
---|---|---|---|

1 (red, 645 nm) | 0.1690 | 0.0227 | 0.0574 |

2 (NIR, 858 nm) | 0.3093 | 0.0330 | 0.1535 |

**Table 2.**Fixed global annual spectral BRDF model parameters for the six POLDER bands derived from the POLDER database [17]. The 765 nm band is a red-edge band.

POLDER Band | ${\mathit{f}}_{\mathit{i}\mathit{s}\mathit{o}}\left(\mathit{\lambda}\right)$ | ${\mathit{f}}_{\mathit{g}\mathit{e}\mathit{o}}\left(\mathit{\lambda}\right)$ | ${\mathit{f}}_{\mathit{v}\mathit{o}\mathit{l}}\left(\mathit{\lambda}\right)$ |
---|---|---|---|

490 nm | 0.0708 | 0.0120 | 0.0547 |

565 nm | 0.1039 | 0.0171 | 0.0680 |

670 nm | 0.1216 | 0.0193 | 0.0602 |

765 nm | 0.2598 | 0.0369 | 0.1531 |

865 nm | 0.2907 | 0.0410 | 0.1611 |

1020 nm | 0.3201 | 0.0471 | 0.1611 |

**Table 3.**Sentinel-2 MSI red-edge band BRDF spectral model parameters derived by linear interpolation between the red and NIR MODIS BRDF spectral model parameters (Table 1).

Sentinel-2 Red-Edge Band (Center Wavelength) | ${\mathit{f}}_{\mathit{i}\mathit{s}\mathit{o}}\left(\mathit{\lambda}\right)$ | ${\mathit{f}}_{\mathit{g}\mathit{e}\mathit{o}}\left(\mathit{\lambda}\right)$ | ${\mathit{f}}_{\mathit{v}\mathit{o}\mathit{l}}\left(\mathit{\lambda}\right)$ |
---|---|---|---|

5 (705 nm) | 0.2085 | 0.0256 | 0.0845 |

6 (740 nm) | 0.2316 | 0.0273 | 0.1003 |

7 (783 nm) | 0.2599 | 0.0294 | 0.1197 |

**Table 4.**Summary of the ordinary least squares (OLS) linear regressions of the surface reflectance differences illustrated in Figure 4 and Figure 5; OLS regression coefficient of determination (r

^{2}), the OLS regression F-test p-value, and the B-F difference. A total of 6,600,685 and 10,656,197 pairs of forward and back scatter surface reflectance values were considered in January and April, respectively.

Sentinel-2 Red-Edge Band | January | April | ||||
---|---|---|---|---|---|---|

OLS Equation | OLS ${\mathit{r}}^{2}$ (p-Value) | B-F Difference | OLS Equation | OLS ${\mathit{r}}^{2}$ (p-Value) | B-F Difference | |

705 nm | Δ = −0.0029 θ_{v} + 0.0018 | 0.7271 (<0.0001) | 0.0698 | Δ = −0.0010 θ_{v} + 0.0003 | 0.2877 (<0.0001) | 0.0226 |

740 nm | Δ = −0.0033 θ_{v} + 0.0048 | 0.7379 (<0.0001) | 0.0787 | Δ = −0.0015 θ_{v} + 0.0015 | 0.4014 (<0.0001) | 0.0352 |

783 nm | Δ = −0.0033 θ_{v} + 0.0051 | 0.7086 (<0.0001) | 0.0776 | Δ = −0.0014 θ_{v} + 0.0015 | 0.3311 (<0.0001) | 0.0323 |

**Table 5.**Mean absolute reflectance differences $(\overline{{\mathsf{\Delta}\rho}_{\lambda})}$ (Equation (5)) and mean absolute relative percentage differences ${\overline{({\mathsf{\Delta}\rho}_{\lambda}}}^{*})$ (Equation (6)) between the pairs of forward and backward scatter Sentinel-2A surface reflectance values illustrated in Figure 4 and Figure 5. A total of 6,600,685 and 10,656,197 pairs of forward and back scatter surface reflectance values were considered in January and April, respectively.

Sentinel-2 Red-Edge Band | January | April | ||
---|---|---|---|---|

$\overline{{\mathsf{\Delta}\mathsf{\rho}}_{\mathsf{\lambda}}}$ | ${\overline{{\mathsf{\Delta}\mathsf{\rho}}_{\mathsf{\lambda}}}}^{*}$ | $\overline{{\mathsf{\Delta}\mathsf{\rho}}_{\mathsf{\lambda}}}$ | ${\overline{{\mathsf{\Delta}\mathsf{\rho}}_{\mathsf{\lambda}}}}^{*}$ | |

705 nm | 0.0314 | 14.928 | 0.0133 | 10.487 |

740 nm | 0.0358 | 14.283 | 0.0186 | 9.699 |

783 nm | 0.0356 | 13.300 | 0.0182 | 9.378 |

**Table 6.**Summary of the ordinary least squares (OLS) linear regressions of the surface NBAR differences illustrated in Figure 6 and Figure 7; OLS regression coefficient of determination (r

^{2}), the OLS regression F-test p-value, and the B-F difference. A total of 6,600,685 and 10,656,197 pairs of forward and back scatter surface reflectance values were considered in January and April, respectively.

Sentinel-2 Red-Edge Band | January | April | ||||
---|---|---|---|---|---|---|

OLS Equation | OLS ${\mathit{r}}^{2}$ (p-Value) | B-F Difference | OLS Equation | OLS ${\mathit{r}}^{2}$ (p-Value) | B-F Difference | |

705 nm | Δ =−0.0009 θ_{v} + 0.0017 | 0.2059 (<0.0001) | 0.0217 | Δ =−0.0001 θ_{v} − 0.0003 | 0.0018 (<0.0001) | 0.0015 |

740 nm | Δ =−0.0010 θ_{v} + 0.0032 | 0.2061 (<0.0001) | 0.0237 | Δ =−0.0003 θ_{v} + 0.0015 | 0.0218 (<0.0001) | 0.0063 |

783 nm | Δ =−0.0008 θ_{v} + 0.0032 | 0.1300 (<0.0001) | 0.0191 | Δ =−0.0000 θ_{v} + 0.0016 | 0.0002 (<0.0001) | 0.0006 |

**Table 7.**Mean absolute reflectance differences $(\overline{{\mathsf{\Delta}\rho}_{\lambda})}$ (Equation (5)) and mean absolute relative percentage differences ${\overline{({\mathsf{\Delta}\rho}_{\lambda}}}^{*})$ (Equation (6)) between the pairs of forward and backward scatter Sentinel-2A surface NBAR values illustrated in Figure 6 and Figure 7. A total of 6,600,685 and 10,656,197 pairs of forward and back scatter surface NBAR values were considered in January and April, respectively.

Sentinel-2 Red-Edge Band | January | April | ||
---|---|---|---|---|

$\overline{{\mathsf{\Delta}\mathsf{\rho}}_{\mathsf{\lambda}}}$ | ${\overline{{\mathsf{\Delta}\mathsf{\rho}}_{\mathsf{\lambda}}}}^{*}$ | $\overline{{\mathsf{\Delta}\mathsf{\rho}}_{\mathsf{\lambda}}}$ | ${\overline{{\mathsf{\Delta}\mathsf{\rho}}_{\mathsf{\lambda}}}}^{*}$ | |

705 nm | 0.0150 | 7.480 | 0.0104 | 9.735 |

740 nm | 0.0163 | 6.646 | 0.0123 | 9.016 |

783 nm | 0.0157 | 5.973 | 0.0127 | 8.643 |

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**MDPI and ACS Style**

Roy, D.P.; Li, Z.; Zhang, H.K.
Adjustment of Sentinel-2 Multi-Spectral Instrument (MSI) Red-Edge Band Reflectance to Nadir BRDF Adjusted Reflectance (NBAR) and Quantification of Red-Edge Band BRDF Effects. *Remote Sens.* **2017**, *9*, 1325.
https://doi.org/10.3390/rs9121325

**AMA Style**

Roy DP, Li Z, Zhang HK.
Adjustment of Sentinel-2 Multi-Spectral Instrument (MSI) Red-Edge Band Reflectance to Nadir BRDF Adjusted Reflectance (NBAR) and Quantification of Red-Edge Band BRDF Effects. *Remote Sensing*. 2017; 9(12):1325.
https://doi.org/10.3390/rs9121325

**Chicago/Turabian Style**

Roy, David P., Zhongbin Li, and Hankui K. Zhang.
2017. "Adjustment of Sentinel-2 Multi-Spectral Instrument (MSI) Red-Edge Band Reflectance to Nadir BRDF Adjusted Reflectance (NBAR) and Quantification of Red-Edge Band BRDF Effects" *Remote Sensing* 9, no. 12: 1325.
https://doi.org/10.3390/rs9121325