# Using Copernicus Atmosphere Monitoring Service (CAMS) Products to Assess Illuminances at Ground Level under Cloudless Conditions

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## Abstract

**:**

## 1. Introduction

^{−2}) received at ground level and is expressed in (lm W

^{−1}).

_{6}363–408 nm, KB

_{7}408–452 nm, KB

_{8}452–518 nm, KB

_{9}518–540 nm, KB

_{10}540–550 nm, KB

_{11}550–567 nm, KB

_{12}567–605 nm, KB

_{13}605–625 nm, KB

_{14}625–667 nm, KB

_{15}667–684 nm, KB

_{16}684–704 nm, KB

_{17}704–743 nm and KB

_{18}743–791 nm.

## 2. Description of Measurements Used for the Validation

_{BN}is derived from the global and diffuse illuminances L

_{G}and L

_{D}measured on a horizontal surface as follows:

_{s}is the solar zenith angle, which is calculated with the SG2 algorithm [21].

## 3. Description of the Method

#### 3.1. Data Exploited by Libradtran

_{s}, aerosol optical properties that may be characterized by the Angström exponent, aerosol type and aerosol optical depth (AOD), total amount of water vapor (TWV) and ozone (TOC), ground albedo, vertical profiles of temperature, pressure, density, volume mixing ratio for gases as a function of altitude, and altitude of the ground above mean sea level. As previously mentioned, this study participates in the development of an operational method, and the sources of data to be input to libRadtran should be chosen to ease the estimation of illuminance at any location and any time. A convenient way to fulfill this operational constraint is the exploitation of the atmospheric products delivered by CAMS. The SoDa service (http://www.soda-pro.com/, accessed on 1 December 2020) provides an access to the CAMS aerosol optical properties together with TOC and TWV. ϴ

_{s}is calculated with the SG2 algorithm [21]. libRadtran offers several solar spectra; that of Gueymard [23] was selected for computing the solar spectral irradiance Io

_{Nλ}received at the top of atmosphere at normal incidence at any time, λ being the wavelength. Air Force Geophysics Laboratory (AFGL) vertical profiles are used and selected at any location using the map of Gschwind et al. [14]. The Shuttle Radar Topography Mission dataset is used to extract the ground altitude.

#### 3.2. Spectral Resampling Technique

_{G}and G

_{λ}be the global illuminance and the global spectral irradiance received on a horizontal surface at ground level, where λ is the wavelength (in nm). L

_{G}is given by:

^{−1}, and ${S}_{\lambda}$ is the standardized CIE action spectrum for human eye. In the same way, the direct illuminance at normal incidence L

_{BN}is given by:

_{Nλ}is the direct spectral irradiance at normal incidence.

_{λ}and KT

_{Bλ}be the spectral clearness index and the direct clearness index. They are given by:

_{KBi}and KT

_{B_KBi}in each of the 32 spectral bands. Altogether, the thirteen KBs, from KB

_{6}to KB

_{18}, do not precisely overlay the daylight spectral range 380–780 nm, since the KB

_{6}363–408 nm and KB

_{18}743–791 nm only partially cover the daylight spectral range.

_{j}for fine band, whose spectral clearness indices KT

_{FBj}and KT

_{B_FBj}are calculated from the integrated ones in the KB

_{i}by affine functions. This is the spectral disaggregation step. Then, a complete and detailed set of clearness indices at 1 nm of spectral resolution over the whole range 380–780 nm is obtained by a linear interpolation of these FB

_{j}clearness indices. The 1 nm clearness indices are converted into 1 nm irradiances G

_{λ}and B

_{Nλ}that are then weighted by the standardized CIE action spectrum for human eye for assessing the global illuminance L

_{G}on horizontal surface and the direct illuminance at normal incidence L

_{BN}.

_{G}and L

_{BN}can be computed as follows:

_{n}and the direct clearness index KT

_{B}

_{n}:

_{s}and the solar spectrum. For both the global and direct irradiances, this ensemble of runs provides two sets of clearness indices: the detailed indices at 1 nm resolution and the indices spectrally integrated over each KBi.

_{n}, respectively KT

_{Bn}, and KT

_{KBi}, respectively KT

_{B_KBi}, for the range 380–780 nm. A visual inspection of each 2D histogram clearly shows a straight line with a squared correlation coefficient greater than 0.99 in all cases. Therefore, affine functions were established between the clearness indices by a least-square fitting technique. There is a considerable number of affine functions, and for operational purposes, a limited set of 29 intervals of 1 nm in width, the fine bands FBj, was selected and then used in a linear interpolation process to obtain the clearness indices at each 1 nm without losing accuracy to compute the illuminance. The current approach is empirical with no guarantee that the selected set of FBj is the optimum. It could have been possible to use some mathematical optimization tools. For each FBj in a given KBi, two affine functions have been established:

_{FBj}, b

_{FBj}, c

_{FBj}, and d

_{FBj}are given in Table 2. These two sets of affine functions are obtained once for all. The operational method is as follows. For a given set of inputs, libRadtran with the Kato et al. [12] scheme is run to provide the set of thirteen KT

_{KBi}and KT

_{B}_

_{KBi}from which the set of 29 KT

_{FBj}and KT

_{B_FBj}is calculated using the affine functions. Then, KT

_{n}and KT

_{Bn}are estimated at each 1 nm between 380 and 780 nm using spectral linear interpolation of KT

_{FBj}and KT

_{B_FBj}. Then, this complete set of 1 nm clearness indices is converted into a set of spectral irradiances G

_{n}and B

_{Nn}, which in turn are multiplied by the standardized CIE action spectrum for human eye, yielding the illuminances L

_{G}and L

_{BN}.

^{−2}, AOD of 0.22 at 550 nm for a maritime tropical aerosol model with an Ångström exponent of 1.14, ground elevation of 0 m, and surface albedo of 0.07. The graph illustrates the spectral resampling technique starting from clearness indices calculated by the Kato et al. [12] scheme (in brown) up to those at the 1 nm band (in blue). The green line is the result of the detailed calculations made at 1 nm resolution with libRadtran; it is given here to show how the clearness indices resulting from the detailed calculations and from the interpolation (blue line) are very close. A visual inspection shows that in most cases, $K{T}_{FBj}$ and KT

_{KBi}, are approximately equal at the middle wavelength of the KB

_{i}range. Exceptions are for KB

_{12}, KB

_{14}, KB

_{16}, KB

_{17}, and KB

_{18}, where KT

_{n}exhibits a nonlinear behavior that cannot be accounted for with a single $K{T}_{FBj}$. That is the reason for selecting more than one FB

_{j}(magenta crosses). The linear interpolation of $K{T}_{FBj}$ (in blue line) provides a fairly accurate estimate of KT

_{n}. Overall, the graph illustrates the high capability of the spectral resampling technique to reproduce the spectral variation of the clearness index throughout the daylight spectral band.

## 4. Results and Discussion

^{2}) was also computed.

#### 4.1. Validation on Global Illuminance on Horizontal Surface

_{s}). The investigation has been done on deviations as well. Figure 3 shows the ratio (top) and deviation (bottom) as function of ϴ

_{s}, daylight albedo, TOC, TWV, and AOD for Golden. The dependence of the errors is graphically shown with the boxplot aiming to understand the distribution of errors and to measure the degree of dispersion and skewness of the errors for a specific interval based on a given CAMS input. The boxplot exhibits both upper and lower quartiles and the median. The results are displayed on the panels referring to one CAMS input. A boxplot is shown for a given range of values.

^{2}is very large, up to 0.98, meaning that 98% of the variability contained in the measurements is well captured by the method. The bias is still small and is 3 kx, i.e., +4% of the average of the measurements. The RMSE is small with a value of 5 klx (8%).

#### 4.2. Validation on Direct Illuminance at Normal Incidence

_{BN}is only carried out at Vaulx-en-Velin. Similarly to Figure 2, Figure 6 shows the 2D histogram between measurements of L

_{BN}and estimates for Vaulx-en-Velin while the statistics are reported in Table 4. R

^{2}is low, with a value of 0.53 denoting that the variability in L

_{BN}is only fairly well reflected by the estimates. This small coefficient of determination may be partly explained by the restrained range of variations of the direct illuminance at normal incidence in case of cloudless conditions, and the small values do not strictly imply weaknesses in the method. The bias is 7 klx, i.e., 9% of the average of the measurements. The RMSE and rRMSE are 12 klx and 15%, respectively.

#### 4.3. Error Analysis on Estimated Illuminances

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Illustration of the spectral resampling technique. The clearness indices obtained between 363 and 791 nm by two runs of libRadtran are shown in green and brown respectively for detailed calculations at 1 nm resolution and for the Kato et al. [12] scheme. The selected fine bands FB are shown by crosses in magenta. The linear interpolation provides the clearness indices every 1 nm drawn in blue.

**Figure 2.**Two-dimensional (2D) histogram between measurements and estimates of global illuminance on horizontal surface at Golden. The color bar depicts the number of points in the area of 1.5 klx × 1.5 klx. The two thin magenta lines delimit the area of relative errors of ±8% from the measurements.

**Figure 3.**Box plots of the ratio (

**top**) of the estimated (Esti) to the measured (Meas) global illuminance on horizontal surface and difference (

**bottom**) between estimated and measured global illuminance on horizontal surface with CAMS input data at Golden. The mean of the box is marked with a red dot. The 1st, 2nd, and 3rd quartiles are marked with a blue line. The notch in the box shows the 95% confidence interval around the median. The number of data for a given range are reported in pink number.

**Figure 4.**Diurnal variability of AOD at 550 nm from CAMS and measurements at Golden on 15 April 2017. SCI stands for selected cloudless instant.

**Figure 5.**Two-dimensional (2D) histogram between measurements and estimates of global illuminance at Vaulx-en-Velin. The color bar depicts the number of points in the area of 1.5 klx × 1.5 klx. The two thin magenta lines delimit the area of relative errors of ±5 % from the measurements.

**Figure 6.**Two-dimensional (2D) histogram between measurements and estimates of direct illuminance at normal incidence at Vaulx-en-Velin. The colorbar depicts the number of points in the area of 1.5 klx × 1.5 klx. The two thin magenta lines delimit the area of relative errors of ±5% from the measurements.

Station | Country | Lat. (°) | Long. (°) | Altitude a.s.l (m) | CAMS Mean Altitude (m) | Period |
---|---|---|---|---|---|---|

Vaulx-en-Velin | France | 45.78 | 4.92 | 170 | 634 | 1 January 2006 to 30 June 2020 |

Golden, CO | United States | 39.74 | −105.18 | 1829 | 2200 | 5 May 2005 to 31 December 2019 |

**Table 2.**KB

_{i}covering the daylight range and selected fine bands FB

_{j}, slopes and intercepts of the affine functions between the clearness indices in KB

_{i}and 1 nm FB

_{j}.

KB_{i} | Interval Δλ, nm | Fine Band FB_{j}, nm | Clearness Index | Direct Clearness Index | ||
---|---|---|---|---|---|---|

$\mathbf{Slope}\left({\mathit{a}}_{\mathit{F}\mathit{B}\mathit{j}}\right)$ | $\mathbf{Intercept}\left({\mathit{b}}_{\mathit{F}\mathit{B}\mathit{j}}\right)$ | $\mathbf{Slope}\left({\mathit{c}}_{\mathit{F}\mathit{B}\mathit{j}}\right)$ | $\mathbf{Intercept}\left({\mathit{d}}_{\mathit{F}\mathit{B}\mathit{j}}\right)$ | |||

6 | 363–408 | 385–386 | 1.0030 | −0.0032 | 0.9987 | −0.0023 |

7 | 408–452 | 430–431 | 0.9995 | 0.0013 | 1.0026 | −0.0004 |

8 | 452–518 | 484–485 | 0.9979 | 0.0000 | 1.0034 | 0.0005 |

9 | 518–540 | 528–529 | 1.0008 | −0.0013 | 0.9998 | −0.0005 |

10 | 540–550 | 545–546 | 1.0003 | −0.0003 | 1.0001 | 0.0003 |

11 | 550–567 | 558–559 | 0.9997 | 0.0012 | 1.0004 | 0.0004 |

569–570 | 1.0024 | −0.0100 | 0.9960 | −0.0119 | ||

12 | 567–605 | 586–587 | 0.9929 | 0.0267 | 1.0123 | 0.0064 |

589–590 | 0.9804 | −0.0434 | 0.9568 | −0.0109 | ||

602–603 | 1.0051 | 0.0212 | 1.0150 | 0.0167 | ||

13 | 605–625 | 615–616 | 0.9977 | 0.0033 | 1.0004 | 0.0009 |

625–626 | 1.0622 | −0.0551 | 1.0104 | −0.0174 | ||

14 | 625–667 | 644–645 | 0.9960 | 0.0154 | 1.0072 | 0.0029 |

656–657 | 0.9698 | 0.0205 | 0.9915 | 0.0068 | ||

15 | 667–684 | 675–676 | 0.9978 | 0.0036 | 1.0006 | 0.0007 |

685–686 | 0.9681 | 0.1036 | 1.0473 | 0.0212 | ||

16 | 684–704 | 687–688 | 1.0041 | −0.0531 | 0.9602 | −0.0130 |

694–695 | 1.0323 | −0.0642 | 0.9828 | −0.0153 | ||

715–716 | 0.9771 | 0.0596 | 1.0262 | 0.0121 | ||

719–720 | 1.1197 | −0.2733 | 0.899 | −0.0704 | ||

17 | 704–743 | 722–723 | 1.0457 | −0.0491 | 1.0049 | −0.0118 |

724–725 | 1.1046 | −0.1921 | 0.9484 | −0.0478 | ||

736–737 | 0.9663 | 0.0626 | 1.0156 | 0.0212 | ||

744–745 | 1.0401 | 0.0262 | 1.0629 | −0.0036 | ||

757–758 | 1.0169 | 0.0580 | 1.0622 | 0.0096 | ||

760–761 | 0.7613 | −0.3480 | 0.4914 | –0.0805 | ||

18 | 743–791 | 769–770 | 0.9975 | 0.0598 | 1.0459 | 0.0137 |

784–785 | 0.9688 | 0.1032 | 1.0492 | 0.0300 | ||

790–791 | 1.0135 | 0.0008 | 1.0158 | 0.0078 |

**Table 3.**Statistics from the validation of the method. Mean, bias, and RMSE are expressed in (klx). rBias and rRMSE are expressed relative to the mean of the measurements. Ndata is the number of cloudless instants.

Station | Ndata | Mean | Bias | RMSE | rBias (%) | rRMSE (%) | R^{2} |
---|---|---|---|---|---|---|---|

Golden | 1,295,585 | 67 | 1 | 6 | 1 | 9 | 0.95 |

Vaulx-en-Velin | 650,431 | 63 | 3 | 5 | 4 | 8 | 0.97 |

**Table 4.**Same as Table 3 but for direct illuminance at normal incidence.

Station | Ndata | Mean | Bias | RMSE | rBias (%) | rRMSE (%) | R^{2} |
---|---|---|---|---|---|---|---|

Vaulx-en-Velin | 650,431 | 76 | 7 | 12 | 9 | 15 | 0.53 |

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**MDPI and ACS Style**

Wandji Nyamsi, W.; Blanc, P.; Dumortier, D.; Mouangue, R.; Arola, A.; Wald, L. Using Copernicus Atmosphere Monitoring Service (CAMS) Products to Assess Illuminances at Ground Level under Cloudless Conditions. *Atmosphere* **2021**, *12*, 643.
https://doi.org/10.3390/atmos12050643

**AMA Style**

Wandji Nyamsi W, Blanc P, Dumortier D, Mouangue R, Arola A, Wald L. Using Copernicus Atmosphere Monitoring Service (CAMS) Products to Assess Illuminances at Ground Level under Cloudless Conditions. *Atmosphere*. 2021; 12(5):643.
https://doi.org/10.3390/atmos12050643

**Chicago/Turabian Style**

Wandji Nyamsi, William, Philippe Blanc, Dominique Dumortier, Ruben Mouangue, Antti Arola, and Lucien Wald. 2021. "Using Copernicus Atmosphere Monitoring Service (CAMS) Products to Assess Illuminances at Ground Level under Cloudless Conditions" *Atmosphere* 12, no. 5: 643.
https://doi.org/10.3390/atmos12050643