# A Method for Estimating the Cloud Adjacency Effect on the Ground Surface Reflectance Reconstruction from Passive Satellite Observations through Gaps in Cloud Fields

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## Abstract

**:**

## 1. Introduction

- The reflectance for a cloudless area ${r}_{surf,clear}$(${\lambda}_{1}$) was determined at the smallest wavelength (${\lambda}_{1}=0.466$ $\mathsf{\mu}$m) under the assumption that only molecular scattering occurs beyond the cloudiness.
- The parameters a and b that relate the reflectance of areas strongly affected by cloudiness at the wavelengths ${\lambda}_{1}$ = 466 nm and ${\lambda}_{2}$ = 855 nm (${r}_{surf,cloud}\left({\lambda}_{2}\right)=a{r}_{surf,cloud}\left({\lambda}_{1}\right)+b$) were determined from measurements in the 20 × 20 pixel window.
- The reflectance of the area shadowed by cloudiness at the wavelength ${\lambda}_{2}$ was corrected for the average adjacency effect at the wavelength ${\lambda}_{2}$ obtained by multiplication of the average adjacency effect at the wavelength ${\lambda}_{1}$ to the constant a, i.e.,$${r}_{surf,clear}\left({\lambda}_{2}\right)={r}_{surf,cloud}\left({\lambda}_{2}\right)+a\Delta r\left({\lambda}_{1}\right),$$

## 2. Problem Formulation and Solution Method

- (1)
- From the MODIS data, the cloudiness mask (MOD06L2 data), the AOD of cloudless areas (MOD04L2), the upper cloud boundaries (MOD06L2), the AOD of cloudiness (MOD06L2), the solar zenith angles ${\theta}_{sun}$, and the satellite zenith angle ${\theta}_{d}$ and the azimuth angle $\phi $ of the receiving system (MOD03L2) are determined.
- (2)
- The AOD value averaged over clear sky pixels is determined.
- (3)
- Among the LOWTRAN-7 cloudless models, the model is selected with the AOD value closest to that of the MODIS channel.
- (4)
- From the MOD09L2 data, the average reflectance $\overline{{r}_{surf}}$ of cloudless areas is determined.
- (5)
- From the AOD of cloudiness and the altitude of the upper cloud boundary ${h}_{max}$, the cloud extinction coefficient is determined. The cloud medium is considered homogeneous. The quantum survival probability and the normalized cloud scattering phase function are selected from the LOWTRAN-7 models.
- (6)
- The molecular scattering coefficient is selected from the mid-latitude summer LOWTRAN-7 models.
- (7)
- The radiation intensities ${I}_{sum,cloud}\left(R\right)$ received by the satellite system and averaged over an ensemble of realizations of the cloud field for the examined optical and geometrical conditions, the preset average reflectance $\overline{{r}_{surf}}$, are calculated by the Monte Carlo method depending on the gap radii R.
- (8)
- The cloud adjacency effect on the reconstructed ground surface reflectance is estimated based on the expression for the total radiation intensity received by the satellite system in the cloudless case for the homogeneous ground surface (in the independent pixel approximation):$${I}_{sum,clear}={I}_{sun,clear}+\frac{{r}_{surf}{E}_{0,clear}}{1-{r}_{surf}{\gamma}_{1,clear}}{\tilde{I}}_{surf,clear},$$From Formula (2), we obtain the expression for the reflectance ${r}_{surf}$:$${r}_{surf}=\frac{Q\u2044{E}_{0,clear}}{1+{\gamma}_{1,clear}Q\u2044{E}_{0,clear}}$$$$Q=\frac{{I}_{sum,clear}-{I}_{sun,clear}}{{\tilde{I}}_{surf,clear}}.$$If we neglect the cloud adjacency effect at the point on the ground surface corresponding to the projection of the center in the gap of the cloudy field, we obtain the approximate value of the reflectance ${\tilde{r}}_{surf}$:$${\tilde{r}}_{surf}\left(R\right)=\frac{\tilde{Q}\u2044{E}_{0,clear}}{1+{\gamma}_{1,clear},\tilde{Q}\u2044{E}_{0,clear}}$$$$\tilde{Q}=\frac{{I}_{sum,cloud}\left(R\right)-{I}_{sun,clear}}{{\tilde{I}}_{surf,clear}},$$${I}_{sum,cloud}\left(R\right)$ is the total radiation received for satellite observations of the point on the ground surface located in the center of the deterministic gap with radius R.Then, the gap radius ${R}_{*}$ for which the neglect of the cloud adjacency effect introduces the reflectance reconstruction error $\Delta {r}_{surf}$ less than 0.005 is defined as the least radius $R={R}_{*}$ for which the condition$$\Delta {r}_{surf}=\mid {r}_{surf}-{\tilde{r}}_{surf}\left({R}_{*}\right)\mid \le \delta =0.005$$
- (9)
- Proceeding from the radii ${R}_{*}$, the mask of pixels is constructed for which the cloud adjacency effect is significant.

## 3. Testing of the Algorithm

## 4. Interpolation Formula for Estimating ${\mathit{R}}_{*}$

- 5 MODIS channels ($\lambda $ = 0.41, 0.47, 0.55, 0.68, and 0.86 $\mathsf{\mu}$m);
- Cloud layer thicknesses $\Delta h$ = 0.5, 1.5, 4, and 6 km;
- Cloud cover indices ${\delta}_{cl}$ = 0.05, 0.15, 0.3, and 0.5;
- Solar zenith angles ${\theta}_{sun}$ = 0, 30, 45, and 60${}^{\circ}$;
- Zenith angles of the receiving system ${\theta}_{d}$ = 0, 30, 45, and 60${}^{\circ}$;
- Azimuthal angle $\phi ={0}^{\circ}$;
- Ground surface reflectances ${r}_{surf}$ = 0, 0.1, 0.3, 0.5, and 1;
- Midlatitude summer model;
- Aerosol optical depth of the cloudless atmosphere ${\tau}_{0.55}$ = 0, 0.09, 0.3, and 0.89;
- Cloud extinction coefficients ${\sigma}_{cl}$ = 10, 20, 30, and 40 km${}^{-1}$.

## 5. Approbation Method

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 3.**Radiation intensity ${I}_{sum,cloud}$ as a function of the reflectance ${r}_{surf}$. (

**a**) $\lambda $ = 0.55 $\mathsf{\mu}$m, ${\theta}_{sun}={0}^{\circ}$, ${\theta}_{d}={0}^{\circ}$; (

**b**) $\lambda $ = 0.55 $\mathsf{\mu}$m, ${\theta}_{sun}={0}^{\circ}$, ${\theta}_{d}={45}^{\circ}$. Here, curve 1 is for the equidistant paraboloids (Figure 2), and curve 2 is for averaging over an ensemble of random paraboloid realizations.

**Figure 4.**Results of comparison of the calculated ${R}_{*}$ values and interpolated using Formula (12): (

**a**) ${\tau}_{0.55}$ = 0.09, $\Delta h$ = 1.5 km, ${\theta}_{sun}$ = ${\theta}_{d}$ = 45${}^{\circ}$, $\phi $ = 0${}^{\circ}$, ${\sigma}_{cl}$ = 20 km${}^{-1}$, and ${r}_{surf}$ = 0.1; (

**b**) ${\tau}_{0.55}$ = 0.09, ${\delta}_{cl}$ = 0.3, $\Delta h$ = 1.5 km, ${\theta}_{sun}$ = ${\theta}_{d}$ = 45${}^{\circ}$, $\phi $ = 0${}^{\circ}$, and ${\sigma}_{cl}$ = 20 km${}^{-1}.$

**Figure 5.**Dependence of the absolute error in determining the ground surface reflectance $\Delta {r}_{surf}$ on the gap radius R: (

**a**) fragment 1 and (

**b**) fragment 2.

**Figure 6.**Mask illustrating the adjacency effect on the reconstructed reflectance of cloudless areas: (

**a**) fragment 1, calculation; (

**b**) fragment 1, interpolation; (

**c**) fragment 2, calculation; and (

**d**) fragment 2, interpolation. Designations: 1 is for pixels shadowed by clouds and 2 is for cloudless pixels with significant $\Delta {r}_{surf}$ values caused by the cloud adjacency effect.

**Table 1.**Boundaries of the examined image fragments and average optical and geometrical conditions according to the MODIS data.

Parameter | Fragment 1 | Fragment 2 |
---|---|---|

Coordinates | 53.4–56.4 N, 109–115 E | 49.0–51.0 N, 121–123 E |

Cloud cover index ${\delta}_{cl}$ | 0.15 | 0.087 |

Average altitude of the upper boundary of cloudiness ${h}_{max}$, km | 4.1 | 2.6 |

Average optical thickness of cloudiness ${\tau}_{cl}$ | 30 | 15 |

Average AOD of cloudless areas | 1.25 | 0.43 |

Average reflectance ${\overline{r}}_{surf}$ from the MODIS data | 0.071 | 0.046 |

Average solar zenith angle ${\theta}_{sun}$, deg | 34 | 27 |

Average satellite zenith angle ${\theta}_{d}$, deg | 28 | 34 |

Average azimuthal angle $\phi $, deg | 152 | 166 |

Image Fragment | Calculation, km | Interpolation, km | Difference, km |
---|---|---|---|

1 | 17 | 15 | 2 |

2 | 3.5 | 2 | 1.5 |

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**MDPI and ACS Style**

Tarasenkov, M.V.; Zonov, M.N.; Engel, M.V.; Belov, V.V.
A Method for Estimating the Cloud Adjacency Effect on the Ground Surface Reflectance Reconstruction from Passive Satellite Observations through Gaps in Cloud Fields. *Atmosphere* **2021**, *12*, 1512.
https://doi.org/10.3390/atmos12111512

**AMA Style**

Tarasenkov MV, Zonov MN, Engel MV, Belov VV.
A Method for Estimating the Cloud Adjacency Effect on the Ground Surface Reflectance Reconstruction from Passive Satellite Observations through Gaps in Cloud Fields. *Atmosphere*. 2021; 12(11):1512.
https://doi.org/10.3390/atmos12111512

**Chicago/Turabian Style**

Tarasenkov, Mikhail V., Matvei N. Zonov, Marina V. Engel, and Vladimir V. Belov.
2021. "A Method for Estimating the Cloud Adjacency Effect on the Ground Surface Reflectance Reconstruction from Passive Satellite Observations through Gaps in Cloud Fields" *Atmosphere* 12, no. 11: 1512.
https://doi.org/10.3390/atmos12111512