Estimation of the total uncertainty of sky-radiance measurements in field experimental conditions: implications for the aerosol single-scattering albedo
Thierry Elias, Ana Maria Silva, and Mouhaydine Tlemcani
Thierry Elias, Ana Maria Silva, and Mouhaydine Tlemcani, "Estimation of the total uncertainty of sky-radiance measurements in field experimental conditions: implications for the aerosol single-scattering albedo," Appl. Opt. 41, 5059-5072 (2002)
We compare the spectral sky radiance measured by three ground-based optical radiometers during the second Aerosol Characterization Experiment (ACE-2) to estimate the total uncertainty of the radiance in field experimental conditions. The propagation of this uncertainty on the column-integrated aerosol single-scattering albedo ϖ0 at 868 nm is investigated. The radiance measurements are affected by a systematic gain uncertainty of less than 2% in the visible spectral region and within 6% in the near-IR region. Correcting the measured radiance by a systematic uncertainty reduces the dispersion of the ϖ0 from 0.07 to 0.03. Besides, the total relative uncertainty of the radiance measurements in field experimental conditions is within 4% at any wavelength. The corresponding uncertainty Δϖ0 is 4% for an aerosol optical thickness of 0.2.
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Dates and Locations When and Where Several Instruments Performed Measurements on the Same Day and at the Same Site
Date
Santa Cruz
La Laguna
Izaña
15 June
LOA-71; RefPol
20 June
LOA-71; NASA-02
21 June
LOA-71; RefPol; NASA-02
22 June
LOA-71; NASA-02
7 July
RefPol; LOA-71
NASA-02
8 July
RefPol; LOA-71
NASA-02
9 July
LOA-71
RefPol; NASA-02
13 July
RefPol; LOA-71
NASA-02
17 July
LOA-71
RefPol; NASA-02
Table 2
Equivalent Wavelengths λeq [Eq. (5)] of Each Interference Filter of RefPol and CIMEL Instruments and Relative Systematic Uncertainties ΔKcal/Kcal of Radiance Measurements
Parameters b0, b1, b2 of the Polynomial Regression {π[L(λ, Θ)]/ESun} = b0 + b1δaer(λ) + b2δaer(λ)2 Where Radiance (for Θ = 120°) and Aerosol Optical Thickness Are Measured Simultaneously for θSun ≃ 60° at the Same Location and at the Same Wavelengtha
The study was done at 673 and 868 nm; r2 is the correlation coefficient of the regression.
Ref. 7.
Table 4
As in Table 3 except That Θ = 60° and θSun ≃ 68 - 72°
Site
673 nm
868 nm
n
r2
b0
b1
b2
r2
b0
b1
b2
Cape Verde
100
0.971
1.36 × 10-2
1.16 × 10-1
-3.30 × 10-2
0.970
4.46 × 10-3
1.27 × 10-1
-3.66 × 10-2
Urban area
40
0.928
8.19 × 10-3
2.32 × 10-1
-2.55 × 10-1
0.958
4.30 × 10-3
2.00 × 10-1
-1.02 × 10-1
Izaña
80
0.985
1.09 × 10-2
1.37 × 10-1
-8.21 × 10-2
0.986
4.81 × 10-3
1.57 × 10-1
-7.33 × 10-2
Note: The corresponding polynomials at 868 nm are plotted in Fig.
1.
Table 5
Parameters of the Linear Regression between LOA-71 and NASA-02 Measurements at Four Wavelengths, LLOA-71′ = a1LNASA-02′ + a0
Wavelength (nm)
n
a1
a0
Δ (%)
Δmax (%)
440
21
0.92 ± 0.05
(4 ± 20) × 10-4
3.0
4.0
673
21
1.17 ± 0.08
(-4 ± 4) × 10-4
2.0
4.0
868
21
0.88 ± 0.07
(0.8 ± 1) × 10-4
5.0
10.0
1020
21
0.68 ± 0.09
(3 ± 0.8) × 10-4
7.0
16.0
Note: n is the number of measurement pairs, a1 is the slope, a0 is the intercept, Δ and Δmax represent the relative spread of the points around the regressed curve.
Table 6
As in Table 5 except for a Comparison between LOA-71 and RefPol Measurements at 868 nm, LLOA-71 = a1LRefPol′ + a0
Wavelength (nm)
n
a1
a0
Δ (%)
Δmax (%)
868
5
1.10 ± 0.04
(0.06 ± 4) × 10-4
5.0
6.0
Table 7
As in Table 5 except for a Comparison between NASA-02 and RefPol Measurements at Three Wavelengths, LNASA-02′ = a1LRefPol′ + a0
Wavelength (nm)
n
a1
a0
Δ (%)
Δmax (%)
440
12
0.99 ± 0.06
(2 ± 2) × 10-3
3.0
4.0
673
12
0.97 ± 0.05
(-3 ± 3) × 10-4
3.0
5.0
868
12
1.13 ± 0.04
(-1 ± 0.8) × 10-4
4.0
6.0
Table 8
Systematic Uncertainties of NASA-02 and RefPol Measurements, Measurement Dispersion of RefPol Measurements, and Total Uncertainty of the Measurement L̅ at Three Wavelengths
λ (nm)
Systematic Uncertainties
Measurement Dispersion ΔLRefPol′/LRefPol′ (%)
Total Uncertainty
RefPol
NASA-02
Gain (a1+1)/2
Offset (a0)/2
Gain (a1 + 1)/2a1
Offset a0/2a1
ΔL̅rel (%)
ΔL̅abso
440
0.995
1.00 × 10-3
1.010
-1.01 × 10-3
3.0
4.5
1.0 × 10-3
673
0.985
-1.50 × 10-4
1.020
1.55 × 10-4
3.0
4.0
1.5 × 10-4
868
1.065
-5.0 × 10-5
0.940
4.4 × 10-5
3.0
4.0
4.0 × 10-5
Note: The gains (a1 + 1)/2 and (a1 + 1)/2a1, measurement dispersion (ΔLRefPol′)/(LRefPol′), and Relative Total Uncertainty ΔL̅rel are dimensionless. Offsets a0/2 and a0/2a1 and the absolute total uncertainty ΔL̅abso are in radiance units (W m-2 sr-1 µm-1).
Tables (8)
Table 1
Dates and Locations When and Where Several Instruments Performed Measurements on the Same Day and at the Same Site
Date
Santa Cruz
La Laguna
Izaña
15 June
LOA-71; RefPol
20 June
LOA-71; NASA-02
21 June
LOA-71; RefPol; NASA-02
22 June
LOA-71; NASA-02
7 July
RefPol; LOA-71
NASA-02
8 July
RefPol; LOA-71
NASA-02
9 July
LOA-71
RefPol; NASA-02
13 July
RefPol; LOA-71
NASA-02
17 July
LOA-71
RefPol; NASA-02
Table 2
Equivalent Wavelengths λeq [Eq. (5)] of Each Interference Filter of RefPol and CIMEL Instruments and Relative Systematic Uncertainties ΔKcal/Kcal of Radiance Measurements
Parameters b0, b1, b2 of the Polynomial Regression {π[L(λ, Θ)]/ESun} = b0 + b1δaer(λ) + b2δaer(λ)2 Where Radiance (for Θ = 120°) and Aerosol Optical Thickness Are Measured Simultaneously for θSun ≃ 60° at the Same Location and at the Same Wavelengtha
The study was done at 673 and 868 nm; r2 is the correlation coefficient of the regression.
Ref. 7.
Table 4
As in Table 3 except That Θ = 60° and θSun ≃ 68 - 72°
Site
673 nm
868 nm
n
r2
b0
b1
b2
r2
b0
b1
b2
Cape Verde
100
0.971
1.36 × 10-2
1.16 × 10-1
-3.30 × 10-2
0.970
4.46 × 10-3
1.27 × 10-1
-3.66 × 10-2
Urban area
40
0.928
8.19 × 10-3
2.32 × 10-1
-2.55 × 10-1
0.958
4.30 × 10-3
2.00 × 10-1
-1.02 × 10-1
Izaña
80
0.985
1.09 × 10-2
1.37 × 10-1
-8.21 × 10-2
0.986
4.81 × 10-3
1.57 × 10-1
-7.33 × 10-2
Note: The corresponding polynomials at 868 nm are plotted in Fig.
1.
Table 5
Parameters of the Linear Regression between LOA-71 and NASA-02 Measurements at Four Wavelengths, LLOA-71′ = a1LNASA-02′ + a0
Wavelength (nm)
n
a1
a0
Δ (%)
Δmax (%)
440
21
0.92 ± 0.05
(4 ± 20) × 10-4
3.0
4.0
673
21
1.17 ± 0.08
(-4 ± 4) × 10-4
2.0
4.0
868
21
0.88 ± 0.07
(0.8 ± 1) × 10-4
5.0
10.0
1020
21
0.68 ± 0.09
(3 ± 0.8) × 10-4
7.0
16.0
Note: n is the number of measurement pairs, a1 is the slope, a0 is the intercept, Δ and Δmax represent the relative spread of the points around the regressed curve.
Table 6
As in Table 5 except for a Comparison between LOA-71 and RefPol Measurements at 868 nm, LLOA-71 = a1LRefPol′ + a0
Wavelength (nm)
n
a1
a0
Δ (%)
Δmax (%)
868
5
1.10 ± 0.04
(0.06 ± 4) × 10-4
5.0
6.0
Table 7
As in Table 5 except for a Comparison between NASA-02 and RefPol Measurements at Three Wavelengths, LNASA-02′ = a1LRefPol′ + a0
Wavelength (nm)
n
a1
a0
Δ (%)
Δmax (%)
440
12
0.99 ± 0.06
(2 ± 2) × 10-3
3.0
4.0
673
12
0.97 ± 0.05
(-3 ± 3) × 10-4
3.0
5.0
868
12
1.13 ± 0.04
(-1 ± 0.8) × 10-4
4.0
6.0
Table 8
Systematic Uncertainties of NASA-02 and RefPol Measurements, Measurement Dispersion of RefPol Measurements, and Total Uncertainty of the Measurement L̅ at Three Wavelengths
λ (nm)
Systematic Uncertainties
Measurement Dispersion ΔLRefPol′/LRefPol′ (%)
Total Uncertainty
RefPol
NASA-02
Gain (a1+1)/2
Offset (a0)/2
Gain (a1 + 1)/2a1
Offset a0/2a1
ΔL̅rel (%)
ΔL̅abso
440
0.995
1.00 × 10-3
1.010
-1.01 × 10-3
3.0
4.5
1.0 × 10-3
673
0.985
-1.50 × 10-4
1.020
1.55 × 10-4
3.0
4.0
1.5 × 10-4
868
1.065
-5.0 × 10-5
0.940
4.4 × 10-5
3.0
4.0
4.0 × 10-5
Note: The gains (a1 + 1)/2 and (a1 + 1)/2a1, measurement dispersion (ΔLRefPol′)/(LRefPol′), and Relative Total Uncertainty ΔL̅rel are dimensionless. Offsets a0/2 and a0/2a1 and the absolute total uncertainty ΔL̅abso are in radiance units (W m-2 sr-1 µm-1).