Beer-Lambert UV Attenuation by the Ozone Column: Quantifying the Stratospheric UV Shield
How to read this page
A Plain and a Clear version of this page have not been written yet. What follows is the document itself.
Precise — the source document
This is the document. Rendered from the repository at the commit above, with nothing rewritten for the web. A gate re-renders it on every deploy and fails the build if a single byte differs.
Scope
This document establishes one decomposed component of the "Ozone = Life" thesis: the UV shield. It quantifies how the atmospheric ozone (O₃) column attenuates biologically harmful ultraviolet radiation by physical absorption (Beer-Lambert law) in the Hartley band. It establishes attenuation physics only. It does not establish that ozone is alive, creates life, or proves any broad life thesis — see the fence below.
Equations (preserved exactly)
Beer-Lambert attenuation:
$$I(\lambda,z) = I_0(\lambda),e^{-\tau(\lambda,z)}$$
Optical depth from cross-section and column density:
$$\tau(\lambda) = \sum_i \sigma_i(\lambda), N_i$$
Dobson Unit to column number density:
$$N = \mathrm{DU} \times 2.69\times10^{16}\ \mathrm{molecules,cm^{-2}}$$
Variables and units
| Symbol | Meaning | Units |
|---|---|---|
| $I(\lambda,z)$ | spectral irradiance at depth $z$ | W m⁻² nm⁻¹ |
| $I_0(\lambda)$ | incident irradiance at top of column | W m⁻² nm⁻¹ |
| $\tau$ | optical depth | dimensionless |
| $\sigma_i(\lambda)$ | absorption cross-section of species $i$ | cm²/molecule |
| $N_i$ | vertical (or slant) column number density | molecules/cm² |
| DU | total ozone column | dimensionless (1 DU = 2.69×10¹⁶ cm⁻²) |
Worked example (vertical, Hartley peak ~255 nm)
Earth's mean total column ≈ 300 DU [B]. Convert: $N = 300 \times 2.69\times10^{16} = 8.07\times10^{18}\ \mathrm{cm^{-2}}$.
Hartley-peak cross-section $\sigma \approx 1.1\times10^{-17}\ \mathrm{cm^2}$ [B]:
$$\tau = (1.1\times10^{-17})(8.07\times10^{18}) = 88.8$$
$$I/I_0 = e^{-88.8} = 2.8\times10^{-39}$$
Surface UV-C at 255 nm is reduced to a bound of < 10⁻³⁸ — effectively zero. This figure is robust: at a band-edge cross-section $\sigma \approx 1\times10^{-18}\ \mathrm{cm^2}$, $\tau \approx 8$ (transmission ~3×10⁻⁴), and slant solar paths only increase $\tau$. The result is stated as a bound, not a pinned transmission value, because the monochromatic single-absorber idealization is not the full scattering radiative-transfer solution. (Using the verified peak $\sigma = 1.13\times10^{-17}$ raises $\tau$ to ~91, strengthening the conclusion.)
Dimensional check
Optical depth exponent: $[\mathrm{cm^2/molecule}]\times[\mathrm{molecules/cm^2}] = $ dimensionless → $e^{-\tau}$ dimensionless → $I$ inherits units of $I_0$. Consistent. DU conversion: $[\mathrm{DU}]\times[\mathrm{cm^{-2}/DU}] = \mathrm{cm^{-2}}$. Consistent.
Evidence class per claim
- Beer-Lambert exponential attenuation — A (established radiative-transfer physics; arithmetic).
- Hartley band peak ~255 nm, $\sigma \approx 1.1\times10^{-17}\ \mathrm{cm^2}$ — B (measured; magnitude verified to within uncertainty). Sourcing correction: the consensus value at 253.65 nm is 1.1329(35)×10⁻¹⁷ (Hodges et al. 2019, Metrologia); the 1.127×10⁻¹⁷ figure is the AMT 2015 single-lab determination — re-attribute accordingly. The companion 257.34 nm value is 11.07×10⁻¹⁸, not 11.26×10⁻¹⁸.
- 1 DU = 2.69×10¹⁶ molecules/cm², Earth column ~300 DU — B (NASA Ozone Watch).
- UV-C 100–280 / UV-B 280–315 / UV-A 315–400 nm — B (ICNIRP/CIE; re-source from primary).
- $\tau \approx 88.8$, transmission ~10⁻³⁹ — A (arithmetic from the above; stated as a bound).
- "Ozone provides UV attenuation" — supported-within-model. The shield is a consequence of pre-existing O₂ and is not an independent corroborator of biology.
Falsification conditions
This shield claim would be contradicted-by-test if: (1) measured O₃ Hartley cross-sections fell orders of magnitude below ~10⁻¹⁷ cm²; (2) measured surface solar UV-C at 255 nm under a ~300 DU column were non-negligible; or (3) DU-to-column conversion deviated from the Loschmidt-consistent 2.69×10¹⁶ cm⁻². None of these holds.
Outside this model
This domain establishes UV-attenuation physics only. It does not establish, and these are fenced out: ozone is alive (outside-model-scope); the shield "proves life" (UV protection is at most necessary-for-surface-life-as-we-know-it, never sufficient); Beer-Lambert is a "life force" (it is photon extinction; absorbed energy drives photodissociation $\mathrm{O_3} + h\nu \to \mathrm{O_2} + \mathrm{O}$, not any vital principle — metaphor-preserved at most); ozone makes water, replaces gravity, or that a simulation proves reality (all outside-model-scope). Allowed top statement: ozone provides strong, physically-quantified UV-C/UV-B attenuation via Beer-Lambert absorption in the Hartley band — supported-within-model. Forbidden: any leap from "shields UV" to "is life."
sha256 42e528d5bc0b5dd8 — of the original file, so what was ingested stays checkable.