# Angular-Based Radiometric Slope Correction for Sentinel-1 on Google Earth Engine

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## Abstract

**:**

## 1. Introduction

## 2. Method

#### 2.1. Sentinel-1 Data Ingestion into Google Earth Engine

- Apply Orbit file
- Remove thermal noise
- Remove GRD border noise
- Radiometric calibration to ${\sigma}^{0}$
- Range-Doppler terrain correction

#### 2.2. Radiometric Slope Correction

#### 2.2.1. Radar Geometry

#### 2.2.2. Terrain Geometry

#### 2.2.3. Model Geometry

#### 2.2.4. Reference Models

#### 2.3. Layover and Shadow Mask

## 3. Case Study

#### 3.1. Study Area and Data

#### 3.2. Evaluation Scheme

## 4. Results

## 5. Discussion

#### 5.1. Earth Engine Module for Slope Correction

#### 5.2. Model Selection

#### 5.3. DEM Selection

#### 5.4. Layover & Shadow Mask

#### 5.5. Drawbacks and Future Perspective

## 6. Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Geometry of resolution cell in range direction adapted from [13]: for flat terrain (left triangle) and facing slope (right triangle). The angle of slope steepness in range direction is $\alpha $ (or ${\alpha}_{r}$); the incidence angle ${\theta}_{i}$ equals ${90}^{\xb0}-\theta $, the range resolution is $1/2c\tau $ (or half pulse length; where pulse length is the product of speed of light c and pulse duration $\tau $).

**Figure 2.**Simplified slant and ground range geometry in case of layover (

**a**) and shadow (

**b**). In case of layover, the backscatter of point B reaches the satellite before the backscatter of point A, which leads to a geometrical inversion in the slant range. This effect occurs when the angle $\alpha $ of the foreslope is steeper than the incidence angle. The red line depicts active layover areas that can be derived from the angular dependencies, whereas the blue lines indicate passive layover. In case of shadow, the backslope is steeper than the look angle ($90-{\theta}_{i}$). The red line is situated on the active shadow part, while the blue line represents passive shadow.

**Figure 4.**Sentinel-1 RGB color composite (R: ${\sigma}^{0}$-VV (dB), G: ${\sigma}^{0}$-VH (dB) B: VV/VH power ratio) over the Area of Interest before (

**a**) and after correction with Model 1 (

**b**) and Model 2 (

**c**), as well as the difference of Model 1–Model 2 for the VV polarised bands stretched between −5 and 5 dB (

**d**). Regions of active layover and shadow are overlaid in black and white (

**b**,

**c**) as well as in red and blue (

**d**).

**Figure 5.**VV backscatter ($\gamma $) for coniferous trees as a function of aspect (left column) and slope steepness in range (right column) for: top row (

**a**,

**b**): original scene corrected for ${\theta}_{i}$, middle row (

**c**,

**d**): after correction for isotropic opaque volume scattering (Model 1), bottom row (

**e**,

**f**): after correction for isotropic surface scattering (Model 2). The vertical lines in the left column indicate the back- and forward-scattering directions. The horizontal lines indicate the mean backscatter level. The numbers in the bottom left stand for amplitude (A), slope (s), mean ($\mu $) and standard deviation ($\sigma $) of $\gamma $ in dB.

**Figure 6.**Comparison of the effect of the buffer parameter for the layover and shadow masks. Overview of study area (

**a**) and zoom in (

**b**) for VV backscatter (${\gamma}^{0}$). Corrected VV backscatter (${\gamma}_{f}^{0}$) with layover and shadow masks with no buffer (

**c**), and added buffer size of 30, 50 and 100 metres, respectively, over the zoomed in area (

**d**–

**f**).

**Table 1.**Slope effect statistics for different land cover classes for the VV- and VH-polarisation. Mean backscatter ($\mu $), standard deviation of backscatter ($\sigma $), amplitude of backscatter as a function of slope aspect angle (A) and backscatter increase per degree slope steepness in range (s) for both models.

$\mathit{\mu}-\mathbf{VV}$ | $\mathit{\sigma}$-VV | s-VV | A-VV | $\mathit{\mu}$-VH | $\mathit{\sigma}$-VH | s-VH | A-VH | |
---|---|---|---|---|---|---|---|---|

Trees—broad-leaved | ||||||||

Original | −8.584 | 4.433 | 0.176 | 4.469 | −14.144 | 4.208 | 0.160 | 4.024 |

Model I | −7.900 | 3.276 | −0.013 | 1.398 | −13.460 | 3.250 | −0.029 | 1.308 |

Model II | −8.947 | 3.519 | 0.074 | 2.272 | −14.507 | 3.390 | 0.058 | 1.845 |

Tree—coniferous | ||||||||

Original | −7.332 | 4.679 | 0.181 | 5.232 | −12.973 | 4.426 | 0.168 | 4.824 |

Model I | −7.908 | 3.172 | −0.020 | 1.461 | −13.550 | 3.144 | −0.034 | 1.404 |

Model II | −8.630 | 3.393 | 0.057 | 2.283 | −14.272 | 3.252 | 0.044 | 1.892 |

Herbaceous permanent— | ||||||||

high productivity | ||||||||

Original | −10.225 | 3.889 | 0.167 | 2.970 | −16.107 | 3.635 | 0.138 | 2.463 |

Model I | −10.149 | 3.104 | −0.020 | 0.888 | −16.031 | 3.153 | −0.049 | 1.111 |

Model II | −10.636 | 3.199 | 0.060 | 1.337 | −16.518 | 3.115 | 0.030 | 0.958 |

Herbaceous periodically | ||||||||

Original | −8.753 | 3.310 | 0.152 | 1.022 | −15.354 | 3.223 | 0.130 | 0.814 |

Model I | −8.622 | 3.131 | −0.024 | 0.686 | −15.223 | 3.101 | −0.046 | 0.490 |

Model II | −8.785 | 3.187 | 0.065 | 0.632 | −15.386 | 3.107 | 0.043 | 0.306 |

Bushes and shrubs | ||||||||

Original | −8.313 | 5.793 | 0.196 | 6.252 | −13.944 | 5.238 | 0.171 | 5.442 |

Model I | −8.828 | 4.027 | −0.020 | 1.597 | −14.458 | 3.953 | −0.046 | 1.686 |

Model II | −9.905 | 4.280 | 0.067 | 2.734 | −15.536 | 3.975 | 0.042 | 1.995 |

Bare rock and scree | ||||||||

Original | −6.946 | 7.556 | 0.219 | 8.448 | −13.456 | 6.956 | 0.189 | 7.293 |

Model I | −6.825 | 5.760 | −0.013 | 2.005 | −13.334 | 5.684 | −0.043 | 1.761 |

Model II | −8.737 | 6.261 | 0.089 | 4.253 | −15.247 | 5.872 | 0.060 | 3.140 |

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**MDPI and ACS Style**

Vollrath, A.; Mullissa, A.; Reiche, J.
Angular-Based Radiometric Slope Correction for Sentinel-1 on Google Earth Engine. *Remote Sens.* **2020**, *12*, 1867.
https://doi.org/10.3390/rs12111867

**AMA Style**

Vollrath A, Mullissa A, Reiche J.
Angular-Based Radiometric Slope Correction for Sentinel-1 on Google Earth Engine. *Remote Sensing*. 2020; 12(11):1867.
https://doi.org/10.3390/rs12111867

**Chicago/Turabian Style**

Vollrath, Andreas, Adugna Mullissa, and Johannes Reiche.
2020. "Angular-Based Radiometric Slope Correction for Sentinel-1 on Google Earth Engine" *Remote Sensing* 12, no. 11: 1867.
https://doi.org/10.3390/rs12111867