How CO₂ Satellites Measure Atmospheric Carbon Dioxide

Follow each step — from sunlight entering the atmosphere to the satellite computing XCO₂

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STRATOSPHERE TROPOSPHERE EARTH SURFACE tropopause ~12km O₃ O₃ N₂ O₂ CO₂ H₂O CO₂ aerosols aerosols SUN SATELLITE sensor ↓ UV VIS NIR SWIR MIR TIR 1.6 2.1 4.3 15µm ① ② ③ ④ ⑤ OVERVIEW — all key processes ① Solar beam (broadband, 0.25–4 µm) ② Rayleigh/Mie scatter back to space ③ Reflected solar (VIS+NIR) → satellite ④ Thermal IR emission (8–15 µm) ⑤ CO₂ absorption bands (1.6, 2.06, 15 µm) Broadband solar 0.25 – 4 µm Top of Atmosphere (TOA) 1361 W/m² solar constant Solar spectrum at TOA UV ~9% (<0.4 µm) VIS ~40% (0.4–0.7 µm) NIR/SWIR ~51% (0.7–4 µm) CO₂ absorption windows: 1.6 µm · 2.06 µm (NIR/SWIR used by satellites) Planck: B(λ,T)=(2hc²/λ⁵)·1/(e^(hc/λkT)−1) Sun T=5778K → peak λ=2898/5778≈0.50 µm Earth T=288K → peak λ=2898/288≈10 µm (TIR) CO₂ windows O₃ absorbs UV Hartley band UV lost (<0.31µm) → heats stratosphere VIS + NIR only Ozone Layer (stratosphere) O₃ absorbs UV < 0.31 µm completely Hartley band: 0.20–0.31 µm (strong) Huggins band: 0.31–0.36 µm (weak) Energy → heats the stratosphere Chappuis band 0.45–0.75µm (VIS, weak) Beam entering troposphere: VIS + NIR intact ~300 DU ozone column (Dobson Units) R Rayleigh Blue ↑ 0.45 µm ∝ 1/λ⁴ M Mie All λ ↑ white haze Rayleigh Scattering (whole column) • Molecules (N₂, O₂) scatter elastically • Intensity ∝ 1/λ⁴ → blue (0.45µm) scatters 5.5× more than red (0.70µm) • Scattered in ALL directions → blue sky Mie Scattering (boundary layer) • Aerosols, dust, cloud droplets (r > 0.1µm) • Wavelength-independent → white appearance • Forward-dominated scattering phase function ⚠ Aerosols = #1 error in CO₂ retrievals ~30% solar reflected by clouds/aerosols total OCO-2 rejects cloudy/hazy scenes (<0.3 AOD) CO₂ 1.6 µm 2.06 µm re-emit (random) H₂O 1.87µm 2.7µm attenuated Molecular Absorption (Beer-Lambert Law) I(λ) = I₀(λ) · exp(−σ(λ) · N · L) σ=cross-section, N=column density, L=path length CO₂ absorption bands (troposphere): 1.6 µm — weak NIR overtone 2.06 µm — stronger NIR overtone ← satellites use 4.3 µm — very strong MIR fundamental 15 µm — bending mode (TIR) H₂O bands: 1.37, 1.87, 2.7, 6.3 µm H₂O retrieved simultaneously to avoid bias More CO₂ → deeper dips → stronger satellite signal This downward traversal is pass 1-of-2 through the column pass 1↓ (CO₂ absorbs) Surface Albedo Ocean ~0.06 (very dark) Forest ~0.10–0.15 Desert ~0.30–0.40 ← good for OCO-2 Snow ~0.80–0.90 ← strongest signal High albedo → stronger CO₂ dip signal Dark ocean → too dim for SWIR retrieval CO₂ pass 2↑ absorbs again pass 2↑ (CO₂ absorbs again) Two-Way Path — Key Advantage Reflected solar passes through the CO₂ column TWICE (down + back up). τ_total = 2 × τ_one-way Dip depth is DOUBLED vs single pass. This is why SWIR passive remote sensing works for trace-gas column retrieval. OCO-2/GOSAT exploit this two-pass geometry. albedo: a = reflected / incident flux Thermal IR peak ~10 µm 288 K surface CO₂ abs 15µm re-emits all dir. emits up → satellite greenhouse ↓ back to surface Earth Thermal Emission (Blackbody) Surface T≈288K → peak ~10µm (Planck) Emitted day and night (no sun needed) CO₂ Greenhouse Effect (15µm band): 1. Surface emits TIR upward 2. CO₂ absorbs at 15µm in troposphere 3. CO₂ re-emits: some ↑ to space, some ↓ 4. Downward re-emission → warms surface Satellite (TIR mode): more CO₂→ emission from higher/colder level → less radiance at 15µm TIR vs SWIR Satellite Modes TIR (AIRS, IASI, CrIS): thermal emission → sensitive to mid/upper troposphere → works day AND night SWIR (OCO-2, GOSAT): reflected solar → sensitive full column (near-surface CO₂) → daytime only (needs sunlight) Combined: complementary vertical sensitivity CO₂ 2nd pass 1.6+2.06µm CO₂ 15µm VIS scattered Satellite receives mixed signal: ■ Reflected solar (1.6, 2.06 µm dips) ■ Thermal TIR (4.3, 15 µm) ■ Scattered VIS (0.4–0.7 µm) ■ O₂ A-band ref (0.76 µm) ■ Fluorescence (0.76, 0.77 µm, weak) Upwelling Radiance at Satellite L_obs(λ) = L_reflect(λ) + L_scatter(λ) + L_thermal(λ) + L_fluor(λ) At 1.6 & 2.06µm: reflected solar dips depth ∝ CO₂ column amount (2-way) At 15µm: emission bump from CO₂ layer shape reveals vertical CO₂ profile Spectrometer resolves individual spectral lines R~20,000 needed to see CO₂ line structure Different lines → different altitude sensitivities Measured Spectrum at Satellite Sensor Wavelength (µm) → Radiance → 0.76 1.6 2.06 continuum O₂ A 0.76µm CO₂ dip 1.6 µm CO₂ dip 2.06 µm depth ∝ XCO₂ XCO₂ Retrieval Pipeline ① Measure spectrum I_obs(λ) Spectrometer (R~20,000) disperses light onto detector array Records radiance at each wavelength simultaneously ② O₂ A-band reference (0.76 µm) O₂ = 20.95% of air (fixed, well-known) O₂ dip depth → path length + surface pressure Dividing CO₂/O₂ cancels viewing-angle geometry ③ Forward Radiative Transfer Model (RTM) Simulate I_mod(λ) for a trial state vector: x = [XCO₂, H₂O, T(z), aerosol, albedo, ...] HITRAN spectral database → σ(λ,T,p) for each gas ④ Optimal Estimation Inversion Iterate x until I_mod(λ) ≈ I_obs(λ) Cost fn: J = (x−xₐ)ᵀSₐ⁻¹(x−xₐ) + (y−F(x))ᵀSₑ⁻¹(y−F(x)) xₐ = prior, Sₐ = prior covariance, Sₑ = obs error ⑤ Output: XCO₂ (ppm) XCO₂ = ∫ x_CO₂(z)·p(z)dz / ∫ p(z)dz Pressure-weighted column average dry-air mole fraction e.g. 421.5 ± 0.5 ppm (OCO-2 target precision) Beer-Lambert: I(λ) = I₀(λ) · exp(−∫ n_CO₂(z) · σ(λ,T,p) · dz) σ(λ) known from HITRAN; n_CO₂(z) is what we retrieve → XCO₂ ← Deeper dips = more CO₂ in column ← O₂ dip normalises path length & pressure