# Surface Albedo Retrieval from 40-Years of Earth Observations through the EUMETSAT/LSA SAF and EU/C3S Programmes: The Versatile Algorithm of PYALUS

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## Abstract

**:**

## 1. Introduction

## 2. Algorithm Description

#### 2.1. Method Overview

- Step 1.
- Atmospheric Correction: In a first step, the reflectances measured by the sensor at the Top of the Atmosphere (TOA) are used to estimate the reflectances at the Top of the Canopy (TOC) by applying the Simplified Method for the Atmospheric Correction (called SMAC) [36] of satellite measurements in the solar spectrum. This atmospheric correction process is described in Section 2.2.
- Step 2.
- Harmonisation (optional): This second step aims to harmonise data that are spectrally heterogeneous because they have been acquired by different sensors. The spectral harmonisation step is an optional step that allows the calculation of spectral albedos at fixed wavelengths (corresponding to a chosen reference sensor) from different sensors having different spectral characteristics (only used in C3S). First, a reference sensor is chosen (i.e., the four bands of SPOT/VGT2). The TOC reflectances from each given sensor are then harmonised into reflectances that would have been observed by the reference sensor on each of its bands. This method is further detailed in Section 2.3.
- Step 3.
- BRDF Inversion: In the third step, the measured TOC reflectances are used to fit the coefficients of a semi-empirical kernel-based reflectance model. These coefficients allow to rebuild the complete angular dependency of the bi-directional reflectance distribution function (BRDF). More information is presented in Section 2.4.
- Step 4.
- Albedo Computation: This step is composed of two main processes. First, the spectral albedo values, which are associated to the instrument channels, are determined by angular integration of the bi-directional reflectance factors. Second, the narrow-to-broadband conversion of albedos is performed. More information on this last step is given in Section 2.5.

#### 2.2. Atmospheric Correction

- Gas content (mainly ozone and water vapour);
- Aerosol content and aerosol type;
- Molecular scattering mainly driven by the sea-level surface pressure and the surface elevation.

#### 2.3. Spectral Harmonisation

#### 2.4. BRDF Inversion

#### 2.4.1. BRDF Models

_{β}(θ

_{s}, θ

_{v}, φ). This latter is estimated in the spectral channel, β of the measuring sensor, and for all angular geometries, even for those far from the illumination and viewing geometries acquired by the sensor capabilities (that means for all sun θ

_{s}and view θ

_{v}angles comprised between 0 and 90°, and for all relative azimuth φ angles comprised between 0 and 180°). The surface directionality estimation consists in determining, by mathematical inversion, the coefficients of a semi-empirical kernel-based reflectance model, based on TOC reflectances (or in the case of prior harmonisation, the TOC reflectances harmonised to another reference sensor). The system to invert, composed by a linear combination of f

_{i}kernel functions, is defined as follows:

_{β}(θ

_{s}, θ

_{v}, φ) = k

_{β}

^{T}f(θ

_{s}, θ

_{v}, φ)

_{iβ}, and the kernel functions, f

_{i}, respectively (with i numbers of kernel functions).

#### 2.4.2. Least Square Solution

_{j}are quantified by means of weight factors w

_{j}, which are related to the inverse of the standard “1-sigma” uncertainty estimates σ[R

_{j}] (with j the index for the cloud-free observation of n elements). We introduce the scaled reflectance vector b with the elements b

_{j}= R

_{j}w

_{j}and the “design matrix” A with the elements A

_{ji}= f

_{ji}w

_{j}(see e.g., [38] with i being the index for the kernel function number i of usually three elements). The linear least squares solution to the inversion problem in Equation (2) can be found by solving the following “normal equations” for the parameters k.

^{T}A) k = A

^{T}b

_{k}= (A

^{T}A)

^{−1}

_{ii}of this matrix represent the variance σ

^{2}[k

_{i}] of the respective parameters k

_{i}. If the matrix A

^{T}A is not singular, the solution can be found by multiplying Equation (3) “from the left” by the covariance matrix C

_{k}.

#### 2.4.3. Addition of a Priori Constraints Using a Recursive Method

_{i}= k

_{ap}± σ

_{ap}[k

_{i}]

_{0}, k

_{1}and k

_{2}. In this case, adding the constraint of Equation (5) to the system of Equation (3) corresponds to extending the (n, m)-matrix A to the (n + m, m)-matrix

_{1}, …, b

_{n}, k

_{0ap}σ

_{ap}

^{−1}[k

_{0}], k

_{1ap}σ

_{ap}

^{−1}[k

_{1}], k

_{2ap}σ

_{ap}

^{−1}[k

_{2}]

^{T}. The linear least squares solution with a priori information is then obtained in the same way as above by solving the normal equations where both A and b are replaced respectively by A′ and b′. The use of an a priori information triggers the issue of the initialisation of the run at the first-time step. The next section presents the approach used to generate a meaningful a priori for the first run.

^{T}A + C

_{ap}

^{−1})k = A

^{T}b + C

_{ap}

^{−1}k

_{ap}

_{k}= (A

^{T}A + C

_{ap}

^{−1})

^{−1}

_{ap}= (k

_{0ap}, …, k

_{m−1ap})

^{T}and C

_{ap}the covariance matrix. For uncorrelated a priori information on the parameters, C

_{ap}= diag(σ

_{ap}

^{2}[k

_{0}], …, σ

_{ap}

^{2}[k

_{m−1}]) is diagonal. The determination of k

_{ap}and C

_{ap}is explained in [30], and also briefly in Section 2.4.4.

#### 2.4.4. Initialisation—Determination of the First a Priori Information

_{in}and Ck

_{in}) are used. These previous estimates are then used in the following way as a priori information for the linear model inversion specified in Equations (7) and (8):

- Step 1—Spin up run—Run is performed for one year. The BRDF estimates of the last day of the spin up period is later used in Step 2 as first guess (a priori BRDF in Equation (7)). After one year, the KF has lost memory of its initial state: the lack of initial BRDF model has no more impact on the output product. In most cases, a shorter period (around 3 months) is sufficient to initialize the KF depending on the cloudiness, but one year has been chosen to take into account the vegetation cycle.
- Step 2—Actual run—Using the latest model from step 1, consider it as the initial a priori BRDF model and generate the product for the full period with Kalman filtering enabled.

#### 2.4.5. Regularisation

_{0}= k

_{0reg}± σ

_{reg}[k

_{0}]

k

_{1}= k

_{1reg}± σ

_{reg}[k

_{1}]

k

_{2}= k

_{2reg}± σ

_{reg}[k

_{2}]

_{1}= 0.03 +/− 0.05). The goal is here only to avoid numerical instabilities and the standard deviations are sufficiently large to avoid a noticeable prejudice in the inversion result. Moreover, if the a priori information from a previous retrieval is available with an associated uncertainty not too important, this regularization has clearly no (or negligible) impact.

#### 2.5. Albedo Computation

#### 2.5.1. Angular Integration

_{β}.

#### 2.5.2. Narrow-to-Broadband Conversion

#### 2.6. Extra-Filters—Impact of Clouds, Cloud Shadows, and Eclipses

^{2}[R], see Section 2.4.2) by a factor 10. The same approach is adopted for the pixels that might be contaminated by cloud shadows, when positioned next to cloudy pixels and depending on the solar azimuth direction. Cloud shadow is estimated by using the sun geometry for expanding the cloud mask as described in LSA SAF albedo ATBDs (available on https://www.eumetsat.int/lsa-saf). In this way, those potentially affected observations are only significant in the inversion process if no “reliable” observations are available at all. Moreover, a solar eclipse calendar database is used to systematically remove the global file corrupted by a solar eclipse. Shadow of clouds and solar eclipse induce strong and rapid decreases of surface brightness which are not linked to intrinsic changes of land surface properties.

## 3. Data

#### 3.1. Input: Auxiliary Data

#### 3.1.1. Digital Elevation Model (DEM)

#### 3.1.2. Atmospheric Parameters

#### 3.1.3. SMAC Coefficients

#### 3.2. Radiance Inputs and Albedo Outputs

#### 3.2.1. NOAA-X/AVHRR

#### 3.2.2. SPOT/VGT

#### 3.2.3. Metop/AVHRR-3

#### 3.2.4. MSG/SEVIRI

#### 3.2.5. PROBA-V

## 4. Product Design

#### 4.1. EUMETSAT and C3S Albedos

#### 4.2. Albedo Characteristics: Spectral and Temporal

- Bi-hemispherical (‘white-sky’ or ‘WSA’) albedo products that are representative of diffuse conditions of illumination (typically cloudy sky conditions).
- Directional-hemispherical (‘black-sky’ or ‘BSA’) albedo products that are representative of direct conditions of illumination (typically clear sky conditions with pure atmosphere). As the surface is usually non-Lambertian and has directional properties, the value of surface albedo is given at a reference angle (solar position at the local noon).

- Spectral albedo for VGT-2 channels (B0, B2, B3 and MIR; Table 2);
- Broadband albedo for the visible (VIS) (0.4–0.7 µm), near-infrared (NIR) (0.7–4 µm) and the total shortwave (BB) (0.3–4 µm) spectral domains.

#### 4.3. Product Content

## 5. Discussion and Known Issues

#### 5.1. Differences between the LSA SAF and C3S Albedo Products

#### 5.1.1. Atmospheric Correction

#### 5.1.2. Spectral Harmonisation

#### 5.2. Known Issues and Limitations

#### 5.2.1. Residual of Clouds and Subpixel Clouds

#### 5.2.2. Treatment of Snow Target Pixels

#### 5.2.3. Calibration, Radiometry, and Orbit Drift

#### 5.2.4. Atmospheric Correction

#### 5.2.5. Review Process

## 6. Roadmap for Product Continuity

_{clim}and Ck

_{clim}resulting from this climatology will be added. This will improve the continuity robustness between the various generations of sensors. Moreover, a noticeable improvement of the atmospheric correction will be implemented considering the anisotropy of the surface for taking into account the multi-scattering effects. Finally, the long-term continuity will be prepared through the use of Sentinel-3 (S3) observations (after the end-of-life of PROBA-V).

## 7. Access to the Code Sources and Data Policy

## 8. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Appendix A. Spectral Harmonisation

**Figure A1.**Simulated surface reflectance values for various soil types. Only 100 simulated surface reflectances are shown but, in practice, 50,000 were generated.

- The Fraction of Vegetation Cover (FCover) corresponds to the fraction of ground covered by green vegetation. It is a dimensionless parameter that takes values between 0 and 1.
- The Leaf Area Index (LAI) is another dimensionless quantity (m
^{2}/m^{2}) that characterises plant canopies. It corresponds to the one-sided green leaf area per unit ground surface area.

Name | Characteristics |
---|---|

Fcover | Uniform distribution on (0,1) |

LAI | Normal distribution with mean = 4 × Fcover and standard deviation = 2, bounded within (0,10) |

Hotspot parameter | Randomized on a uniform distribution between 0 and (1 + LAI/8)/2 |

_{i}is the i-th data point and ${\widehat{y}}_{i}$is the model estimate for the i-th data point.

_{0}= 0.0005 and w

_{1}= 0.01 are the regularisation parameters and have been carefully chosen to alter the model without degrading its performance (in terms of R

^{2}).

**Table A2.**Coefficients (${\alpha}_{\to \beta}^{\left(AVHRRX\right)}$ in the first column and ${\alpha}_{\beta {}^{\prime}\to \beta}^{\left(AVHRRX\right)}$) of each linear model (Equation (1)) to predict the reflectance values ${R}_{\beta}^{\left(VGT2\right)}$ for the VGT-2 B0, B2, B3 and MIR bands from the reflectance values ${R}_{\beta {}^{\prime}}^{\left(AVHRRX\right)}$ for the NOAA-X/AVHRR bands. The standard deviation resulting from the regression is given in the last column. Only NOAA-7, 9, 11, 14, 16, 17 are considered. These coefficients are only valid for snow-free pixels. For pixels flagged with snow/ice, a different set of coefficients is used following the same approach based on snow ice spectra only (for more information see ATBD on https://cds.climate.copernicus.eu/).

β′_{(NOAA-7/AVHRR)}β_{(VGT2)} | ${\mathit{\alpha}}_{\to \mathit{\beta}}^{\left(\mathit{A}\mathit{V}\mathit{H}\mathit{R}\mathit{R}7\right)}$ | ${\mathit{\alpha}}_{\mathit{\beta}{}^{\prime}\to \mathit{\beta},}^{\left(\mathit{A}\mathit{V}\mathit{H}\mathit{R}\mathit{R}7\right)}$ $\mathit{\beta}{}^{\prime}=\mathbf{RED}$ | ${\mathit{\alpha}}_{\mathit{\beta}{}^{\prime}\to \mathit{\beta},}^{\left(\mathit{A}\mathit{V}\mathit{H}\mathit{R}\mathit{R}7\right)}$ $\mathit{\beta}{}^{\prime}=\mathbf{NIR}$ | ${\mathit{\alpha}}_{\mathit{\beta}{}^{\prime}\to \mathit{\beta},}^{\left(\mathit{A}\mathit{V}\mathit{H}\mathit{R}\mathit{R}7\right)}$ $\mathit{\beta}{}^{\prime}=\mathbf{MIR}$ | Sigma |

B0 | −0.0523 | 0.5813 | 0.0960 | 0.0309 | |

B2 | 0.0097 | 1.0150 | −0.0203 | 0.0146 | |

B3 | 0.0053 | −0.0746 | 1.0608 | 0.0162 | |

MIR | 0.0216 | 0.5062 | 0.0873 | 0.0639 | |

β′_{(NOAA-9/AVHRR)}β_{(VGT2)} | ${\mathit{\alpha}}_{\mathbf{\to}\mathit{\beta}}^{\left(\mathit{A}\mathit{V}\mathit{H}\mathit{R}\mathit{R}\mathbf{9}\right)}$ | ${\mathit{\alpha}}_{\mathit{\beta}{}^{\mathbf{\prime}}\mathbf{\to}\mathit{\beta}\mathbf{,}}^{\left(\mathit{A}\mathit{V}\mathit{H}\mathit{R}\mathit{R}\mathbf{9}\right)}$ $\mathit{\beta}{}^{\mathbf{\prime}}$ = RED | ${\mathit{\alpha}}_{\mathit{\beta}{}^{\mathbf{\prime}}\mathbf{\to}\mathit{\beta}\mathbf{,}}^{\left(\mathit{A}\mathit{V}\mathit{H}\mathit{R}\mathit{R}\mathbf{9}\right)}$ $\mathit{\beta}{}^{\mathbf{\prime}}$ = NIR | ${\mathit{\alpha}}_{\mathit{\beta}{}^{\mathbf{\prime}}\mathbf{\to}\mathit{\beta}\mathbf{,}}^{\left(\mathit{A}\mathit{V}\mathit{H}\mathit{R}\mathit{R}\mathbf{9}\right)}$ $\mathit{\beta}{}^{\mathbf{\prime}}$ = MIR | Sigma |

B0 | −0.0528 | 0.5820 | 0.0938 | 0.0311 | |

B2 | 0.0088 | 1.0192 | −0.0258 | 0.0147 | |

B3 | 0.0066 | −0.0802 | 1.0640 | 0.0162 | |

MIR | 0.2016 | 0.5101 | 0.0829 | 0.0638 | |

β′_{(NOAA-11/AVHRR)}β_{(VGT2)} | ${\mathit{\alpha}}_{\mathbf{\to}\mathit{\beta}}^{\left(\mathit{A}\mathit{V}\mathit{H}\mathit{R}\mathit{R}\mathbf{11}\right)}$ | ${\mathit{\alpha}}_{\mathit{\beta}{}^{\mathbf{\prime}}\mathbf{\to}\mathit{\beta}\mathbf{,}}^{\left(\mathit{A}\mathit{V}\mathit{H}\mathit{R}\mathit{R}\mathbf{11}\right)}$ $\mathit{\beta}{}^{\mathbf{\prime}}$ = RED | ${\mathit{\alpha}}_{\mathit{\beta}{}^{\mathbf{\prime}}\mathbf{\to}\mathit{\beta}\mathbf{,}}^{\left(\mathit{A}\mathit{V}\mathit{H}\mathit{R}\mathit{R}\mathbf{11}\right)}$ $\mathit{\beta}{}^{\mathbf{\prime}}$ = NIR | ${\mathit{\alpha}}_{\mathit{\beta}{}^{\mathbf{\prime}}\mathbf{\to}\mathit{\beta}\mathbf{,}}^{\left(\mathit{A}\mathit{V}\mathit{H}\mathit{R}\mathit{R}\mathbf{11}\right)}$ $\mathit{\beta}{}^{\mathbf{\prime}}$ = MIR | Sigma |

B0 | −0.0530 | 0.5807 | 0.0941 | 0.0312 | |

B2 | 0.0084 | 1.0181 | −0.0256 | 0.0146 | |

B3 | 0.0071 | −0.0802 | 1.0636 | 0.0162 | |

MIR | 0.2015 | 0.5103 | 0.0825 | 0.0638 | |

β′_{(NOAA-14/AVHRR)}β_{(VGT2)} | ${\mathit{\alpha}}_{\mathbf{\to}\mathit{\beta}}^{\left(\mathit{A}\mathit{V}\mathit{H}\mathit{R}\mathit{R}\mathbf{14}\right)}$ | ${\mathit{\alpha}}_{\mathit{\beta}{}^{\mathbf{\prime}}\mathbf{\to}\mathit{\beta}\mathbf{,}}^{\left(\mathit{A}\mathit{V}\mathit{H}\mathit{R}\mathit{R}\mathbf{14}\right)}$ $\mathit{\beta}{}^{\mathbf{\prime}}$ = RED | ${\mathit{\alpha}}_{\mathit{\beta}{}^{\mathbf{\prime}}\mathbf{\to}\mathit{\beta}\mathbf{,}}^{\left(\mathit{A}\mathit{V}\mathit{H}\mathit{R}\mathit{R}\mathbf{14}\right)}$ $\mathit{\beta}{}^{\mathbf{\prime}}$ = NIR | ${\mathit{\alpha}}_{\mathit{\beta}{}^{\mathbf{\prime}}\mathbf{\to}\mathit{\beta}\mathbf{,}}^{\left(\mathit{A}\mathit{V}\mathit{H}\mathit{R}\mathit{R}\mathbf{14}\right)}$ $\mathit{\beta}{}^{\mathbf{\prime}}$ = MIR | Sigma |

B0 | −0.0533 | 0.5706 | 0.1037 | 0.0312 | |

B2 | 0.0082 | 0.9953 | −0.0036 | 0.0141 | |

B3 | 0.0068 | −0.0382 | 1.0236 | 0.0155 | |

MIR | 0.2020 | 0.5036 | 0.0880 | 0.0638 | |

β′_{(NOAA-16/AVHRR)}β_{(VGT2)} | ${\mathit{\alpha}}_{\mathbf{\to}\mathit{\beta}}^{\left(\mathit{A}\mathit{V}\mathit{H}\mathit{R}\mathit{R}\mathbf{16}\right)}$ | ${\mathit{\alpha}}_{\mathit{\beta}{}^{\mathbf{\prime}}\mathbf{\to}\mathit{\beta}\mathbf{,}}^{\left(\mathit{A}\mathit{V}\mathit{H}\mathit{R}\mathit{R}\mathbf{16}\right)}$ $\mathit{\beta}{}^{\mathbf{\prime}}$ = RED | ${\mathit{\alpha}}_{\mathit{\beta}{}^{\mathbf{\prime}}\mathbf{\to}\mathit{\beta}\mathbf{,}}^{\left(\mathit{A}\mathit{V}\mathit{H}\mathit{R}\mathit{R}\mathbf{16}\right)}$ $\mathit{\beta}{}^{\mathbf{\prime}}$ = NIR | ${\mathit{\alpha}}_{\mathit{\beta}{}^{\mathbf{\prime}}\mathbf{\to}\mathit{\beta}\mathbf{,}}^{\left(\mathit{A}\mathit{V}\mathit{H}\mathit{R}\mathit{R}\mathbf{16}\right)}$ $\mathit{\beta}{}^{\mathbf{\prime}}$ = MIR | Sigma |

B0 | −0.0080 | 0.6869 | 0.1190 | −0.2241 | 0.0274 |

B2 | −0.0010 | 0.9766 | −0.0068 | 0.0441 | 0.0135 |

B3 | 0.0072 | −0.0287 | 1.0306 | −0.0160 | 0.0155 |

MIR | 0.0119 | 0.0413 | 0.0210 | 0.9326 | 0.0141 |

β′_{(NOAA-17/AVHRR)}β_{(VGT2)} | ${\mathit{\alpha}}_{\mathbf{\to}\mathit{\beta}}^{\left(\mathit{A}\mathit{V}\mathit{H}\mathit{R}\mathit{R}\mathbf{17}\right)}$ | ${\mathit{\alpha}}_{\mathit{\beta}{}^{\mathbf{\prime}}\mathbf{\to}\mathit{\beta}\mathbf{,}}^{\left(\mathit{A}\mathit{V}\mathit{H}\mathit{R}\mathit{R}\mathbf{17}\right)}$ $\mathit{\beta}{}^{\mathbf{\prime}}$ = RED | ${\mathit{\alpha}}_{\mathit{\beta}\mathbf{}{}^{\mathbf{\prime}}\mathbf{\to}\mathit{\beta}\mathbf{,}}^{\left(\mathit{A}\mathit{V}\mathit{H}\mathit{R}\mathit{R}\mathbf{17}\right)}$ $\mathit{\beta}{}^{\mathbf{\prime}}$ = NIR | ${\mathit{\alpha}}_{\mathit{\beta}\mathbf{}{}^{\mathbf{\prime}}\mathbf{\to}\mathit{\beta}\mathbf{,}}^{\left(\mathit{A}\mathit{V}\mathit{H}\mathit{R}\mathit{R}\mathbf{17}\right)}$ $\mathit{\beta}{}^{\mathbf{\prime}}$ = MIR | Sigma |

B0 | −0.0346 | 0.6920 | 0.1961 | −0.2742 | 0.0304 |

B2 | −0.0032 | 0.9317 | −0.0476 | 0.1430 | 0.0132 |

B3 | −0.0015 | −0.0749 | 1.0085 | 0.0793 | 0.0155 |

MIR | 0.0710 | −0.2946 | −0.5074 | 1.8174 | 0.0346 |

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**Figure 1.**Flow diagram of the surface albedo retrieval algorithm. The spectral harmonisation (step 2) is optional. The boxes at the right side are the inputs: i.e., aerosol optical depth (AOD), water vapour (WV), ozone (O3), digital elevation model (DEM) etc. The boxes in grey colour are the outputs of each module (box bordered by dashed lines).

**Figure 2.**Angular dependence of the geometric (

**a**) and volumetric (

**b**) scattering kernels of the RTLS (RossThick-LiSparse-Reciprocal) model. Both graphs correspond to the principal plane (i.e., conditions with a relative azimuth equal to 0° or 180°). Negative zenith angle values correspond to the back-scattering direction (relative azimuth angle = 0°) and positive zenith angle values to the forward scattering direction (180°).

**Figure 3.**Illumination (

**a**) and observation (

**b**) geometries corresponding to a geographical location of (47°47′ N, 10°37′ E) and an observation period between the days of year 150 and 170. The relative azimuth angle is identical for the two graphs. The convention was chosen such that the top of the graphs (=0°) corresponds to the back-scattering regime. The colours of the dots denote observations taken by different sensors as follows: Red: MSG/SEVIRI, Green: Metop/AVHRR, Blue: NOAA-16/AVHRR.

**Figure 5.**Spectral response on the (300 nm, 2500 nm) interval for NOAA-X/AVHRR and VGT-2 sensors. Only NOAA: (

**a**)—7, (

**b**)—9, (

**c**)—11, (

**d**)—14, (

**e**)—16, and (

**f**)—17 are considered, and (

**g**) VGT2 in C3S.

**Figure 6.**Total shortwave directional-hemispherical albedo (BB-DH) for 1 July 2005 based on NOAA-X/AVHRR (C3S-V1).

**Figure 7.**Total shortwave directional-hemispherical albedo (BB-DH) for 1 July 2005 based on SPOT/VGT (C3S-V1).

**Figure 8.**Total shortwave directional-hemispherical albedo (BB-DH) for 1 July 2015 based on Metop/AVHRR-3 (ETAL).

**Figure 9.**Total shortwave directional-hemispherical albedo (BB-DH) for 1 July 2015 based on MSG/SEVIRI (MDAL).

**Figure 10.**Total shortwave directional-hemispherical albedo (BB-DH) for 1 July 2015 based on PROBA-V (C3S-V0).

**Figure 11.**Flowchart of the satellite missions used for the retrieval of the surface albedo products using the Météo France algorithm presented in this paper.

**Table 1.**List of the operational albedo products developed by the Météo France research laboratory. LSA SAF (Satellite Application Facility on Land Surface Analysis) albedo (referred as LSA in the Table) are disseminated in NRT (near real-time) (3 h after the last observation at 00UTC). The timeliness will be reduced in 2021 to 1 h. C3S (Copernicus Climate Change Service) (referenced as C3S in the Table) are reprocessing. CGLS (Copernicus Global Land Service) product, which were under responsibility of Météo France and not still maintained, are in grey colour. PROBA-V product from CGLS was reused for the generation of C3S-V0 ICDR Interim Climate Data Record). In 2021, the C3S-V2 and LSA-107 and 108 will complete this portfolio.

Product | Sensor (Coverage) | Product ID (Type) | Production Frequency | Composite Window | Temporal Characteristic Time Scale | Spatial Scale | Composition Method | BRDF Model | Atmospheric Correction | Documentation and Data Link Accesses | Temporal Coverage | Product Continuity |
---|---|---|---|---|---|---|---|---|---|---|---|---|

Albedo (CDR) | NOAA-X/AVHRR (global) | C3S-V1 | 10-day | 20-day | 10-day | 1–4 km | recursive | Li-Sparse Reciprocal | Hygeos | C3S-V1 access | 1981–2015 | C3S-V2 |

Albedo (CDR) | SPOT/VGT (global) | C3S-V1 | 10-day | 20-day | 10-day | 1 km | recursive | Li-Sparse Reciprocal | Hygeos | C3S-V1 access | 1998–2014 | C3S-V2 |

Albedo (ICDR) | PROBA-V (global) | C3S-V0 | 10-day | 30-day | 20-day | 1 km | recursive | Roujean | VITO | C3S-V0 access | 2014+ | C3S-V2 |

Albedo (NRT) | SPOT/VGT (global) | VGP-P | 10-day | 30-day | 20-day | 1 km | recursive | Roujean | VITO | CGLS access | 1998–2014 | |

Albedo (NRT) | PROBA-V (global) | PROBA-V L2A | 10-day | 30-day | 20-day | 1 km | recursive | Roujean | VITO | CGLS access | 2014–2020 | |

Albedo (NRT) | MSG/SEVIRI (Africa, Europe, South America) | LSA-101 | 1-day | 1-day | 5-day | SEVIRI grid | recursive | Roujean | Météo France | LSA-101 access | 2005+ | LSA-107 (MTG/FCI) |

Albedo (NRT) | MSG/SEVIRI (Africa, Europe, South America) | LSA-102 | 10-day | 30-day | 30-day | SEVIRI grid | classic | Roujean | Météo France | LSA-102 access | 2009+ | LSA-108 (MTG/FCI) |

Albedo (CDR) | MSG/SEVIRI (Africa, Europe, South America) | LSA-150 | 10-day | 30-day | 30-day | SEVIRI grid | classic | Roujean | Météo France | LSA-150 access | 2005–2015 | |

Albedo (NRT) | Metop/AVHRR (global) | LSA-103 | 10-day | 20-day | 10-day | 1 km | recursive | Li-Sparse Reciprocal | Météo France | LSA-103 access | 2015+ | LSA-110, 111 (Metop-SG/METimage, 3MI) |

Band | VGT-2 (µm) |
---|---|

Blue (B0) | 0.439–0.476 (0.458) |

Red (B2) | 0.616–0.690 (0.653) |

NIR (B3) | 0.783–0.892 (0.838) |

SWIR (MIR) | 1.584–1.685 (1.635) |

**Table 3.**MSG/SEVIRI and Metop/AVHRR-3 spectral bands, full width at half maximum and centre wavelength in parentheses.

Band | SEVIRI (µm) | AVHRR-3 (µm) |
---|---|---|

Blue (B0) | - | 0.439–0.476 (0.458) |

Red (B2) | 0.56–0.71 (0.635) | 0.616–0.690 (0.653) |

NIR (B3) | 0.74–0.88 (0.81) | 0.783–0.892 (0.838) |

SWIR (MIR) | 1.50–1.78 (1.64) | 1.584–1.685 (1.635) |

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**MDPI and ACS Style**

Carrer, D.; Pinault, F.; Lellouch, G.; Trigo, I.F.; Benhadj, I.; Camacho, F.; Ceamanos, X.; Moparthy, S.; Munoz-Sabater, J.; Schüller, L.; Sánchez-Zapero, J. Surface Albedo Retrieval from 40-Years of Earth Observations through the EUMETSAT/LSA SAF and EU/C3S Programmes: The Versatile Algorithm of PYALUS. *Remote Sens.* **2021**, *13*, 372.
https://doi.org/10.3390/rs13030372

**AMA Style**

Carrer D, Pinault F, Lellouch G, Trigo IF, Benhadj I, Camacho F, Ceamanos X, Moparthy S, Munoz-Sabater J, Schüller L, Sánchez-Zapero J. Surface Albedo Retrieval from 40-Years of Earth Observations through the EUMETSAT/LSA SAF and EU/C3S Programmes: The Versatile Algorithm of PYALUS. *Remote Sensing*. 2021; 13(3):372.
https://doi.org/10.3390/rs13030372

**Chicago/Turabian Style**

Carrer, Dominique, Florian Pinault, Gabriel Lellouch, Isabel F. Trigo, Iskander Benhadj, Fernando Camacho, Xavier Ceamanos, Suman Moparthy, Joaquin Munoz-Sabater, Lothar Schüller, and Jorge Sánchez-Zapero. 2021. "Surface Albedo Retrieval from 40-Years of Earth Observations through the EUMETSAT/LSA SAF and EU/C3S Programmes: The Versatile Algorithm of PYALUS" *Remote Sensing* 13, no. 3: 372.
https://doi.org/10.3390/rs13030372