Level 1 processing algorithms of MicroCarb microsatellite

DEGREE PROJECT IN COMPUTER SCIENCE AND ENGINEERING, SECOND CYCLE, 30 CREDITS

STOCKHOLM, SWEDEN 2020

Level 1 processing

algorithms of MicroCarb

microsatellite

Performance assessment of ISRF in-flight

estimation through new algorithms

... 2 ... 3 Table of Figures ... 5 ... 6 ... 7 ... 8 ... 10 ... 10 ... 11 ... 12 ... 14 ... 17 ... 17 ... 17 ... 18 i. Variable dictionary ... 18

ii. Constant dictionary ... 21

... 23 ... 24 ... 25 ... 26 ... 26 ... 28 ... 29 i. Single ISRF ... 30

ii. All ISRF ... 32

iii. Assessing the influence of stretch ... 34

... 35 ... 38 ... 38 ... 39 ... 40 i. Constant ISRF ... 40

ii. Variable ISRF ... 41

... 43 ... 45 ... 45 ... 45 ... 45 ... 46

Table of Figures

Figure 2: Illustration of keystone effect. Source: [14] ... 9

Figure 3: Spectra on MicroCarb’s NGP detector of 1024 x 128 pixels without distortion (left) and with smile + keystone effect (right). Source: [14] ... 9

Figure 4.a.: Evolution of mean GHG concentration as a function of 4 RCP (left). Source: [1] (modified). ... 10

Figure 5: Evolution of the global carbon balance over the years 1958-2006. Source: [8] ... 10

Figure 6: Research and Development Roadmap from IWGGMS-16 (June 2020) [13] ... 11

Figure 7: Overview of the 4 CNES centres and its annual budget ... 11

Figure 8: CNES 2020 budget. Source: [15] ... 12

Figure 9: Organigram of the Atmospheric Sounding office (DSO/SI/SA). Source: [16] ... 12

Figure 10: Overview of MicroCarb's payload structure. Source: [8] ... 13

Figure 11: Overview of MicroCarb's "push-broom". Source: [8]... 13

Figure 12: Measured spectrum of band 4 after a convolution + sampling between an “infinite” resolution spectrum 𝑆𝑡ℎ and 1024 ISRF at 1024 different 𝜆𝑐 (only one is shown for visualization purposes). Red dots indicate the O2 absorption lines. ... 14

Figure 13: Domino-like cascade effect of the radiance of the scene (Sentinel-2 imagery) on the distortion of Multi-Reading (MR) ISRF and Field Of View (FOV) ISRF. Source: [17] ... 15

Figure 14: Optimal Matching Pursuit (OMP) algorithm’s outlines ... 18

Figure 15: Error chart (top left), shape of the first 6 singular vectors (top right), entropy chart (bottom left), coefficient chart (bottom right). Set of test ISRF = ISRF database = MR ISRF from FOV 1. ... 19

Figure 16: Error chart (left), entropy chart (right). Set of test ISRF = ISRF database = MR ISRF from FOV 1 + 2 + 3. ... 20

Figure 17: Error chart (top left), shape of the first 6 singular vectors (top right), entropy chart (bottom left), true first ISRF and its corresponding estimation. Set of test ISRF = MR ISRF. ISRF database = ISRF IN + ISRF NU + ISRF S2. ... 21

Figure 18: Spectral shift due to "smile" between ISRF from pixel n°1 and ISRF from pixel n°100 (left), shape change of the FOV ISRF depending on the summation rules (right) ... 22

Figure 19: Error chart using ISRF from case 31 in the set of test ISRF (left), error chart using ISRF from case 23 in the set of test ISRF (right) ... 22

Figure 20: Singular values as a function of their index nk (top left), first 6 singular vectors (top right), error chart (bottom left), all the 15th singular vectors (bottom right). Set of test ISRF = MR ISRF from case 20, ISRF database = calibration pixel ISRF ... 23

Figure 21: Index of uniformity 𝑖𝑢 as a function of uniformity error 𝜀𝑢. The black curve represents the linear regression. ... 24

Figure 23: 5 ISRF max-normalized from CNES (left) and ADS (right) ... 26

Figure 24: Comparison of stretch law parameters 𝛼 & 𝛽 and the error 𝜖 using CNES (left) and ADS (right) simulated ISRF. ... 27

Figure 25: Outlines of the complementary operation of the single spectrum-based retrieval algorithm (left) and the multi spectrum-based algorithm (right) ... 28

Figure 26: Measured atmospheric (left) and solar (right) spectrum on band B4. ... 30

Figure 27: Log10 of the approximation error depending on the cardinality K and the number of measurements. These graphs were computed using the single spectrum-based retrieval algorithm with 𝑆𝑡ℎ = 𝑆𝑎𝑡𝑚𝑜𝑠𝑝ℎ𝑒𝑟𝑒 and constant ISRF n°250 (left column) and variable ISRF (right column). SNR varies from +∞ dB (top) to 40 dB (bottom). ... 31

Figure 28: Log10 of the approximation error depending on the ISRF’s pixel number and cardinality of approximation K. These graphs were computed using the single spectrum-based retrieval algorithm with 𝑆𝑡ℎ = 𝑆𝑎𝑡𝑚𝑜𝑠𝑝ℎ𝑒𝑟𝑒 (left column) and 𝑆𝑡ℎ = 𝑆𝑆𝑢𝑛 (right column) with a gaussian noise of 55 dB. The size of the rolling window varies from 25 pixels (top) to 80 pixels (bottom). The mean error for each cardinality is given in brackets. ... 33

Figure 29: Log10 of the approximation error depending on the ISRF’s pixel number and cardinality of approximation K. These 2 graphs were computed using the single spectrum-based retrieval algorithm with 𝑆𝑡ℎ = 𝑆𝑎𝑡𝑚𝑜𝑠𝑝ℎ𝑒𝑟𝑒 with a gaussian noise of 55 dB and a rolling window of 80 pixels. The mean error for each cardinality is given in brackets. They show results using a priori exact stretch modeling (left) and affine stretch modeling (right). ... 34

Figure 30: 𝛤𝑡ℎ for 5 ISRF (i.e., at 5 different wavelengths) ... 36

Figure 31: Log10 error chart for 5 ISRF as a function of cardinality K ... 37

Figure 32: 5 estimated ISRF from multi spectrum-based retrieval algorithm with K=25. ... 37

Figure 33: Illustration of the cross-validation solar test using EM27 and MicroCarb's spectrometer. ... 38

Figure 34: 𝑆𝑚𝑒𝑎𝑠, 𝑀𝑖𝑐𝑟𝑜𝐶𝑎𝑟𝑏 ∗ 𝐼𝑆𝑅𝐹𝐸𝑀27 and 𝑆𝑚𝑒𝑎𝑠, 𝐸𝑀27 ∗ 𝐼𝑆𝑅𝐹𝑀𝑖𝑐𝑟𝑜𝐶𝑎𝑟𝑏 on band 4 (left) and their relative error as a function of wavelength (right) when EM27’s spectral resolution is 0.5 cm-1 _{... 39}

Figure 35: Log10 error chart using the single spectrum-based retrieval algorithm with constant ISRF n°24 and 𝑆𝑡ℎ = 𝑆𝑚𝑒𝑎𝑠, 𝐸𝑀27 = 𝑆∞ ∗ 𝐼𝑆𝑅𝐹𝐸𝑀27 & 𝑆𝑚𝑒𝑎𝑠 = 𝑆𝑚𝑒𝑎𝑠, 𝑀𝑖𝑐𝑟𝑜𝑐𝑎𝑟𝑏 ∗ 𝐼𝑆𝑅𝐹𝐸𝑀27 ... 40

Figure 36: Log10 error chart using the single spectrum-based retrieval algorithm with a variable ISRF and a rolling window of 30 observations ... 41

Figure 37: Main 4 acquisition modes of MicroCarb ("City" mode is not shown but is quite similar to "Target" mode). Source: [12] ... 45

Figure 38: Relative error as a function of wavelength when EM27's spectral resolution is 0.01 cm-1 _{... 45}

Figure 39: Log10 error chart using the single spectrum-based retrieval algorithm with: constant ISRFn°24 (left) and a variable ISRF (right). ... 45

Figure 40: Log10 of the approximation error depending on the cardinality K and the number of measurements. These graphs were computed using the single spectrum-based retrieval algorithm with 𝑆𝑡ℎ = 𝑆𝑆𝑢𝑛 and constant ISRF n°250 (left column) and variable ISRF (right column). SNR varies from +∞ dB (top) to 40 dB (bottom). ... 46

Table 1: Outlines of the single spectrum-based algorithm ... 29

Table 2: Outlines of the multi spectrum-based algorithm ... 35

𝑇𝑖≈ 1.3

𝑺𝒕𝒉

𝑺𝒎𝒆𝒂𝒔

Figure 2: Illustration of keystone effect. Source: [14]

Figure 4.a.: Evolution of mean GHG concentration as a function of 4 RCP (left). Source: [1] (modified).

Figure 4.b.: Evolution of global average surface temperature and its uncertainties as a function of 4 RCP (right). Source: [1].

3 _{A random error of 1 ppm and a regional bias of 0.1 ppm. Above all, it is the reduction of the regional bias compared to}

OCO2 which provides better accuracy.

Figure 7: Overview of the 4 CNES centres and its annual budget

𝑋𝐶𝑂₂ 𝑁𝐶𝑂₂ 𝑧 𝑋𝐶𝑂₂= ∫ 𝑁𝐶𝑂2(𝑧)𝑑𝑧 ∞ 0 ∫ 𝑁𝑑𝑟𝑦 𝑎𝑖𝑟(𝑧)𝑑𝑧 ∞ 0 → 𝑋𝐶𝑂₂ = 0.20935 ∫ 𝑁𝐶𝑂2(𝑧)𝑑𝑧 ∞ 0 ∫ 𝑁𝑂2(𝑧)𝑑𝑧 ∞ 0 (0) 𝑇𝑖 = 1.3 𝛌𝐜

Figure 10: Overview of MicroCarb's payload structure. Source: [8]

𝑆𝑚𝑒𝑎𝑠 𝑆𝑡ℎ 𝑆𝑚𝑒𝑎𝑠(𝑡, 𝜆𝑐) =𝑆𝑡ℎ(𝑡, 𝜆𝑐) ∗ 𝐼𝑆𝑅𝐹𝑀𝑖𝑐𝑟𝑜𝐶𝑎𝑟𝑏(𝑡, 𝜆𝑐) (1.1) 𝑡 𝜆𝑐 𝐼𝑆𝑅𝐹𝑀𝑖𝑐𝑟𝑜𝐶𝑎𝑟𝑏 (1) 𝐼𝑆𝑅𝐹µ𝐶𝑎𝑟𝑏(𝑡, 𝜆𝑐) 𝑆𝑡ℎ(𝑡, 𝜆𝑐) 𝜀 = ∫ |𝐼𝑆𝑅𝐹(𝜆𝑐, 𝜆) − 𝐼𝑆𝑅𝐹̂ (𝜆𝑐, 𝜆)|𝑑𝜆 𝜆𝑚𝑎𝑥 𝜆𝑚𝑖𝑛 (1.2) [𝜆𝑚𝑖𝑛; 𝜆𝑚𝑎𝑥] 𝜀𝑇 < 1% 𝜀𝑂 < 0.5% 𝜀𝑂 < 0.1%

Figure 12: Measured spectrum of band 4 after a convolution + sampling between an “infinite” resolution spectrum 𝑆𝑡ℎ and 1024 ISRF at 1024

different 𝜆𝑐 (only one is shown for visualization purposes). Red dots indicate the O2 absorption lines.

𝑁 = 14 𝑅𝑛(𝑥) 𝑛𝑡ℎ 𝑅𝑛(𝑥) ≈ 𝑅𝑙𝑖𝑛𝑒𝑎𝑟𝑛(𝑥) = 𝑎𝑛 𝑅𝑢𝑛𝑖𝑓𝑜𝑟𝑚(𝑥) + 𝑏𝑛 𝑅𝑔𝑟𝑎𝑑𝑖𝑒𝑛𝑡(𝑥) (1.3) 𝑎𝑛 𝑏𝑛 𝐼𝑆𝑅𝐹𝑀𝑅(𝑅(𝑥), 𝜆𝑐) = ∑(𝑎𝑛 𝐼𝑆𝑅𝐹𝑔𝑟𝑜𝑢𝑛𝑑(𝑅𝑢𝑛𝑖𝑓𝑜𝑟𝑚(𝑥), 𝜆𝑐) + 𝑏𝑛 𝐼𝑆𝑅𝐹𝑔𝑟𝑜𝑢𝑛𝑑(𝑅𝑔𝑟𝑎𝑑𝑖𝑒𝑛𝑡(𝑥), 𝜆𝑐) 𝑁 6 _(1.4) ∑ (𝑎𝑁 𝑛+ 𝑏𝑛) = 1

Figure 13: Domino-like cascade effect of the radiance of the scene (Sentinel-2 imagery) on the distortion of Multi-Reading (MR) ISRF and Field Of View (FOV) ISRF. Source: [17]

𝑆𝑡ℎ

𝑎𝑘 𝐾 𝜀

𝑘 𝐾

log10(𝜀) 𝐾 𝜀 ≤ 10−3 _{𝐾 = 2} 𝐾 = 2 𝑎𝑘 • 𝜆𝑐 • 𝑛𝑝𝑡𝑠 • 𝑛𝐹𝑂𝑉 • 𝐾𝑜𝑝𝑡 • 𝑛_𝑈𝑆𝑉 IS RF # IS RF #

Figure 15: Error chart (top left), shape of the first 6 singular vectors (top right), entropy chart (bottom left), coefficient chart (bottom right). Set of test ISRF = ISRF database = MR ISRF from FOV 1.

{ 𝑽𝒘𝒊𝒕𝒉𝒐𝒖𝒕 𝑶𝑴𝑷= 𝜆𝑐× 𝑛𝑝𝑡𝑠 × 𝑛𝐹𝑂𝑉= 1024 × 300 × 3 = 𝟗𝟐𝟏𝟔𝟎𝟎 𝑣𝑎𝑙𝑢𝑒𝑠 𝑽𝑶𝑴𝑷, 𝑭𝑶𝑽/𝑭𝑶𝑽= 𝑛𝐹𝑂𝑉× (𝜆𝑐× 𝐾𝑜𝑝𝑡+ 𝑛𝑈𝑆𝑉× 𝑛𝑝𝑡𝑠) = 3 × (1024 × 2 + 3 × 300) = 𝟖𝟖𝟒𝟒 𝑣𝑎𝑙𝑢𝑒𝑠 𝜀 ≤ 10−3 𝑽𝑶𝑴𝑷, 𝟑𝑭𝑶𝑽= 𝜆 × 𝐾𝑜𝑝𝑡+ 𝑛𝑈𝑆𝑉× 𝑛𝑝𝑡𝑠= 4096 × 3 + 6 × 300 = 𝟏𝟒𝟎𝟖𝟖 𝑣𝑎𝑙𝑢𝑒𝑠 ~ 𝟏. 𝟔 × 𝑽𝑶𝑴𝑷, 𝑭𝑶𝑽/𝑭𝑶𝑽 W a ve le n g th

Figure 16: Error chart (left), entropy chart (right). Set of test ISRF = ISRF database = MR ISRF from FOV 1 + 2 + 3.

Log

10

(

𝜀 = 10−3

Figure 17: Error chart (top left), shape of the first 6 singular vectors (top right), entropy chart (bottom left), true first ISRF and its corresponding estimation. Set of test ISRF = MR ISRF. ISRF database = ISRF IN + ISRF NU + ISRF S2.

𝜆𝑐

𝜆𝑐 𝜆𝑐

𝜆𝑐

➢ ➢

Figure 18: Spectral shift due to "smile" between ISRF from pixel n°1 and ISRF from pixel n°100 (left), shape change of the FOV ISRF depending on the summation rules (right)

Figure 19: Error chart using ISRF from case 31 in the set of test ISRF (left), error chart using ISRF from case 23 in the set of test ISRF (right)

𝜀𝑚 𝜀𝑚 = 2.2204 × 10−16 ~10−14 𝑛𝑘 ≥ 6 𝑛𝑘 = 4 𝐾 ≥ 6 𝐾 ≥ 6 𝐾 ≥ 6 10−14 A m p litu d e Number of points

Figure 20: Singular values as a function of their index nk (top left), first 6 singular vectors (top right), error chart (bottom left), all the 15th singular vectors (bottom right). Set of test ISRF = MR ISRF from case 20, ISRF database = calibration pixel ISRF

Log

10

(

𝑖𝑢= |𝑅_𝑒𝑛𝑑−𝑅𝑠𝑡𝑎𝑟𝑡| 𝑚𝑒𝑎𝑛(𝑅) 𝜀𝑢= ∫ |𝐼𝑆𝑅𝐹𝑢𝑛𝑖𝑓𝑜𝑟𝑚(𝜆𝑐, 𝜆) − 𝐼𝑆𝑅𝐹(𝜆𝑐, 𝜆)|𝑑𝜆 𝜆𝑚𝑎𝑥 𝜆𝑚𝑖𝑛 𝜀 𝜀𝑢 𝑖𝑢

Figure 21: Index of uniformity 𝑖𝑢 as a function of uniformity error 𝜀𝑢. The black curve

represents the linear regression.

𝐼𝑆𝑅𝐹𝑝𝑖𝑥𝑒𝑙 𝐼𝑆𝑅𝐹𝑀𝑅

➢

➢

➢

𝜆𝑐

𝐼𝑆𝑅𝐹𝑠𝑡𝑟𝑒𝑡𝑐ℎ(𝜆) = 𝐼𝑆𝑅𝐹(𝛼 + 𝛽𝜆 + 𝛾𝜆2+ 𝛿𝜆3) (3.1.1)

(𝛼, 𝛽, 𝛾, 𝛿) β α 𝐼𝑆𝑅𝐹𝑠𝑡𝑟𝑒𝑡𝑐ℎ(𝜆) = 𝐼𝑆𝑅𝐹 ( 𝜆 𝛼) 𝛽 (3.1.2) 𝜖 ε

𝑆mes(𝜆𝑐) ≅ ∫ 𝑆𝑡ℎ(𝜆) ⋅ 𝐼𝑆𝑅𝐹(𝜆𝑐, 𝜆)𝑑𝜆 𝜆𝑚𝑎𝑥 𝜆_𝑚𝑖𝑛 (3.2.1) 𝐼𝑆𝑅𝐹 𝑆th

- 𝑆𝑡ℎ - 𝜙𝑘 - 𝑆𝑡ℎ 𝑆𝑚𝑒𝑎𝑠(𝜆𝑐) ≈ ∑𝐿𝑙=1𝑆𝑡ℎ(𝜆∗𝑙)𝐼(𝜆 − 𝜆𝑙∗) Ψ𝑘 𝑎𝑘 ε 𝜆𝑐 𝑆𝑡ℎ 𝑆meas(𝜆𝑐) ≈ ∑𝑎𝑘Ψ𝑘(𝜆𝑐) 𝐾 𝑘=1 = ∑ 𝑎𝑘∫ 𝑆𝑡ℎ(𝜆) ⋅ Φ𝑘(𝜆𝑐, 𝜆)𝑑𝜆 𝜆𝑚𝑎𝑥 𝜆_𝑚𝑖𝑛 𝐾 𝑘=1 = ∫ 𝑆𝑡ℎ(𝜆) ⋅ ∑ 𝑎𝑘 𝐾 𝑘=1 Φ𝑘 (𝜆𝑐, 𝜆) ⏟ 𝐼𝑆𝑅𝐹_{𝑒𝑠𝑡𝑖𝑚𝑎𝑡𝑒𝑑} 𝑑𝜆 𝜆𝑚𝑎𝑥 𝜆_𝑚𝑖𝑛 (3.3) 𝑆meas(𝜆𝑐) ≈ ∑𝑎𝑘Ψ𝑘(𝜆𝑐) 𝐾 𝑘=1 = ∑ 𝑎𝑘∫ 𝑆𝑡ℎ(𝜆) ⋅ Φ𝑘(𝜆𝑐, 𝜆)𝑑𝜆 𝜆𝑚𝑎𝑥 𝜆_𝑚𝑖𝑛 𝐾 𝑘=1 = ∫ 𝑆𝑡ℎ(𝜆) ⋅ ∑ 𝑎𝑘 𝐾 𝑘=1 Φ𝑘(𝜆𝑐, 𝜆) ⏟ 𝐼𝑆𝑅𝐹_{𝑒𝑠𝑡𝑖𝑚𝑎𝑡𝑒𝑑} 𝑑𝜆 𝜆𝑚𝑎𝑥 𝜆_𝑚𝑖𝑛 (3.3) 𝑆meas(𝜆𝑐) ≈ ∑𝑎𝑘Ψ𝑘(𝜆𝑐) 𝐾 𝑘=1 = ∑ 𝑎𝑘∫ 𝑆𝑡ℎ(𝜆) ⋅ Φ𝑘(𝜆𝑐, 𝜆)𝑑𝜆 𝜆𝑚𝑎𝑥 𝜆_𝑚𝑖𝑛 𝐾 𝑘=1 = ∫ 𝑆𝑡ℎ(𝜆) ⋅ ∑ 𝑎𝑘 𝐾 𝑘=1 Φ𝑘(𝜆𝑐, 𝜆) ⏟ 𝐼𝑆𝑅𝐹_{𝑒𝑠𝑡𝑖𝑚𝑎𝑡𝑒𝑑} 𝑑𝜆 𝜆𝑚𝑎𝑥 𝜆_𝑚𝑖𝑛 (3.3)

- - - - +∞ - 𝑆𝑚𝑒𝑎𝑠 𝑆𝑡ℎ 𝜆𝑐 𝜆𝑐 - 𝑆𝑚𝑒𝑎𝑠 𝑆𝑡ℎ 𝜆𝑐 𝜆𝑐 𝑆𝑚𝑒𝑎𝑠 𝑆𝑡ℎ= 𝑆𝑎𝑡𝑚𝑜𝑠𝑝ℎ𝑒𝑟𝑒 - 𝑆𝑚𝑒𝑎𝑠 - 𝑆𝑚𝑒𝑎𝑠 W /m²/ s r/ µ m W /m² /c m -1

Figure 26: Measured atmospheric (left) and solar (right) spectrum on band B4.

Figure 27: Log10 of the approximation error depending on the cardinality K and the number of measurements. These graphs were computed

using the single spectrum-based retrieval algorithm with 𝑆𝑡ℎ= 𝑆𝑎𝑡𝑚𝑜𝑠𝑝ℎ𝑒𝑟𝑒 and constant ISRF n°250 (left column) and variable ISRF (right

Figure 28: Log10 of the approximation error depending on the ISRF’s pixel number and cardinality of approximation K. These

graphs were computed using the single spectrum-based retrieval algorithm with 𝑆𝑡ℎ= 𝑆𝑎𝑡𝑚𝑜𝑠𝑝ℎ𝑒𝑟𝑒 (left column) and 𝑆𝑡ℎ=

𝑆𝑆𝑢𝑛 (right column) with a gaussian noise of 55 dB. The size of the rolling window varies from 25 pixels (top) to 80 pixels

(bottom). The mean error for each cardinality is given in brackets.

𝑆𝑡ℎ= 𝑆𝑆𝑢𝑛 𝑆𝑡ℎ= 𝑆𝑎𝑡𝑚𝑜𝑠𝑝ℎ𝑒𝑟𝑒 𝑆𝑆𝑢𝑛= 𝑆𝑡ℎ 10−3. 𝛼 𝛽

Figure 29: Log10 of the approximation error depending on the ISRF’s pixel number and cardinality of approximation K. These 2 graphs

were computed using the single spectrum-based retrieval algorithm with 𝑆𝑡ℎ= 𝑆𝑎𝑡𝑚𝑜𝑠𝑝ℎ𝑒𝑟𝑒 with a gaussian noise of 55 dB and a rolling

window of 80 pixels. The mean error for each cardinality is given in brackets. They show results using a priori exact stretch modeling (left) and affine stretch modeling (right).

Γ𝑡ℎ - - Γ𝑡ℎ 𝑃𝑠𝑢𝑟𝑓 𝑆𝑍𝐴 𝛼 𝑆𝑡ℎ 𝑃𝑠𝑢𝑟𝑓 = 850 𝑆𝑡ℎ 𝑃𝑠𝑢𝑟𝑓 = 1000 𝑆𝑡ℎ 𝛼 = 0.05 𝑆𝑡ℎ 𝛼 = 0.25 𝑆𝑡ℎ 𝛼 = 0.55 𝑆𝑡ℎ 𝑆𝑍𝐴

Figure 30: 𝛤𝑡ℎ for 5 ISRF (i.e., at 5 different wavelengths)

𝑎𝑘

Γ𝑚𝑒𝑎𝑠 Γ𝑡ℎ

Γ𝑡ℎ

Figure 31: Log10 error chart for 5 ISRF as a function of cardinality K

Figure 32: 5 estimated ISRF from multi spectrum-based retrieval algorithm with K=25.

A

mpli

tu

d

𝑆𝑚𝑒𝑎𝑠,𝐸𝑀27 𝑆𝑚𝑒𝑎𝑠,𝑀𝑖𝑐𝑟𝑜𝐶𝑎𝑟𝑏 𝐼𝑆𝑅𝐹𝐸𝑀27 𝐼𝑆𝑅𝐹𝑀𝑖𝑐𝑟𝑜𝐶𝑎𝑟𝑏

(4)

𝑆𝑚𝑒𝑎𝑠,𝑀𝑖𝑐𝑟𝑜𝐶𝑎𝑟𝑏∗ 𝐼𝑆𝑅𝐹𝐸𝑀27 𝑆𝑚𝑒𝑎𝑠,𝐸𝑀27∗ 𝐼𝑆𝑅𝐹𝑀𝑖𝑐𝑟𝑜𝐶𝑎𝑟𝑏 𝑆∞

𝑆𝑚𝑒𝑎𝑠,𝑀𝑖𝑐𝑟𝑜𝐶𝑎𝑟𝑏∗ 𝐼𝑆𝑅𝐹𝐸𝑀27 𝑆𝑚𝑒𝑎𝑠,𝐸𝑀27∗ 𝐼𝑆𝑅𝐹𝑀𝑖𝑐𝑟𝑜𝐶𝑎𝑟𝑏

⁻

Figure 34: 𝑆𝑚𝑒𝑎𝑠,𝑀𝑖𝑐𝑟𝑜𝐶𝑎𝑟𝑏∗ 𝐼𝑆𝑅𝐹𝐸𝑀27 and 𝑆𝑚𝑒𝑎𝑠,𝐸𝑀27∗ 𝐼𝑆𝑅𝐹𝑀𝑖𝑐𝑟𝑜𝐶𝑎𝑟𝑏 on band 4 (left) and their relative error as a function of wavelength (right)

when EM27’s spectral resolution is 0.5 cm-1

Table 3: Mean relative spectrum computational error as a function of EM27's spectral resolution

𝑆𝑡ℎ= 𝑆𝑚𝑒𝑎𝑠,𝐸𝑀27 𝐼𝑆𝑅𝐹𝑀𝑖𝑐𝑟𝑜𝐶𝑎𝑟𝑏 𝐼𝑆𝑅𝐹𝑀𝑖𝑐𝑟𝑜𝐶𝑎𝑟𝑏 𝑆𝑚𝑒𝑎𝑠 = 𝑆𝑚𝑒𝑎𝑠,𝑀𝑖𝑐𝑟𝑜𝐶𝑎𝑟𝑏∗ 𝐼𝑆𝑅𝐹𝐸𝑀27 (4) 𝐼𝑆𝑅𝐹𝑀𝑖𝑐𝑟𝑜𝐶𝑎𝑟𝑏 𝑆𝑡ℎ= 𝑆𝑚𝑒𝑎𝑠,𝐸𝑀27= 𝑆∞∗ 𝐼𝑆𝑅𝐹𝐸𝑀27 𝑆𝑚𝑒𝑎𝑠= 𝑆𝑚𝑒𝑎𝑠,𝑀𝑖𝑐𝑟𝑜𝑐𝑎𝑟𝑏∗ 𝐼𝑆𝑅𝐹𝐸𝑀27= 𝑆∞∗ 𝐼𝑆𝑅𝐹𝑀𝑖𝑐𝑟𝑜𝐶𝑎𝑟𝑏∗ 𝐼𝑆𝑅𝐹𝐸𝑀27 𝑎𝑘 𝜀 ≈ 10−2= 1% 𝜀 ≈ 10−1_{= 10%}

𝜆𝑐 𝑆𝑚𝑒𝑎𝑠 = 𝑆𝑚𝑒𝑎𝑠,𝑀𝑖𝑐𝑟𝑜𝑐𝑎𝑟𝑏∗ 𝐼𝑆𝑅𝐹𝐸𝑀27

Figure 36: Log10 error chart using the single spectrum-based retrieval algorithm with a variable ISRF and a rolling window of 30 observations

Log

10

(

𝜀 =

-

-

[1] IPCC, "AR5 Synthesis Report: Climate Change 2014," 2014.

[2] C. Le Quéré, R. B. Jackson, M. W. Jones and et al., "Temporary reduction in daily global CO2 emissions during the COVID-19 forced confinement," Nature Climate Change, p. 10, 2020.

[3] W. Steffen, J. Rockström, K. Richardson, T. M. Lenton, C. Folke, D. Liverman, C. P. Summerhayes and et al., "Trajectories of the Earth System in the Antropocene," Proceedings of the National Acadamy of Sciences of the United States of America (PNAS), Cambridge, Massachusetts, 2018.

[4] ESA - Earth and Mission Science Division, "Copernicus CO2 Monitoring Mission Requirements Document," Noordwijk (The Netherlands), 2019.

[5] C. Pittet and B. Vidal, "MicroCarb Science Algorithm Theoritical Basis Document - Level 1A/B," Toulouse, 2019.

[6] J.-Y. Tourneret, A. Basarab and H. Wendt, "Nouveaux algorithmes pour l'estimation en vol des ISRF," Toulouse, 2019.

[7] C. Pittet, D. Jouglet and C. Pierangelo, "Estimation en vol des ISRF pour MicroCarb - Evaluation de l'algorithme Multi-Reading," Toulouse, 2019.

[8] D. Jouglet, "La mission MicroCarb et la physique de la mesure associée," Toulouse, 2019.

[9] C. Pittet and C. Pierangelo, "Spécification Technique de Besoins - Nouveaux algorithmes pour l'estimation en vol des ISRF," Toulouse, 2019.

[10] IPCC, "Global Warming of 1.5°C," 2018.

[11] M. Castelnau, E. Cansot, C. Buil, V. Pascal, V. Crombez, S. Lopez, L. Georges and M. Dubreuil, "Modelization and validation of the diffraction effects in the Microcarb instrument for accurately computing the instrumental spectral response function," Society of Photo-Optical Instrumentation Engineers, 2019. [12] Jet Propulsion Laboratory - NASA, "OCO-2 - Measurement Approach," [Online]. Available:

https://ocov2.jpl.nasa.gov/measurement-approach/. [Accessed 20 August 2020].

[13] "Programme of IWGGMS-16," 16th International Workshop on Greenhouse Gas Measurements from Space,

2-5 June 2020. [Online]. Available:

https://www.eventsforce.net/eumetsat/frontend/reg/tAgendaWebsite.csp?pageID=3329&ef_sel_menu= 76&eventID=9&language=1. [Accessed 25 August 2020].

[14] C. Pittet and B. Vidal, "MicroCarb Science - Algorithm Theoritical Basis Document - Level 1A/B," CNES, Toulouse, 2019.

[15] B. Darolles, "General Presentation of CNES," CNES, Paris, 2020.

[16] C. Pierangelo, "Présentation du service DSO/SI/SA "Sondage de l'Atmopshère"," CNES, Toulouse, 2020. [17] C. Pittet, V. Crombez, D. Jouglet, L. Georges, E. Cansot and A. Albert-Aguilar, "In-flight estimation of

Figure 37: Main 4 acquisition modes of MicroCarb ("City" mode is not shown but is quite similar to "Target" mode). Source: [12]

For more detailed information about Nadir, Glint and Target modes, please refer to [12].

Figure 38: Relative error as a function of wavelength when EM27's spectral resolution is 0.01 cm-1

Figure 39: Log10 error chart using the single spectrum -based retrieval algorithm with: constant ISRFn°24 (left) and a variable ISRF (right).

Log

10

(

Appendix 4

Figure 40: Log10 of the approximation error depending on the cardinality K and the number of measurements. These graphs were

computed using the single spectrum-based retrieval algorithm with 𝑆𝑡ℎ= 𝑆𝑆𝑢𝑛 and constant ISRF n°250 (left column) and variable ISRF