Constraints on the Early Terrestrial Surface UV Environment Relevant to Prebiotic Chemistry

2.1. Previous work

Recognizing the relevance of UV fluence to life (though mostly in the context of a stressor), previous workers have placed constraints on the surface UV environment of early Earth. In this section, we present a review of some recent work on this topic and discuss how our work differs from it.

Cockell (2002) calculated the UV flux received at the surface of Earth at 3.5 Ga using a monolayer delta-Eddington approach to radiative transfer, assuming a solar zenith angle SZA = 0° (i.e., the Sun directly overhead) ² , for an atmosphere composed of 0.7 bar N₂ and 40 mbar and 1 bar of CO₂, as well as an atmosphere with a sulfur haze. Cockell (2002) found the surface UV flux to be spectrally characterized by a cutoff at >190 nm imposed by CO₂. The author further found the surface UV flux for non-hazy primordial atmospheres to be far higher than that of the modern day due to a lack of UV-shielding oxygen and ozone, with hazes potentially able to provide far higher attenuation.

Cnossen et al. (2007) calculated the UV flux received at the surface of Earth at 4–3.5 Ga at SZA = 0°. To calculate atmospheric radiative transfer, they partitioned the atmosphere into layers. They computed absorption using the Beer-Lambert law. To account for scattering, they calculated the flux scattered in each layer and assumed half of it proceeds up and half proceeds down. They iterated this process to the surface and explored the effect of atmospheric composition on surface flux, assuming an N₂-CO₂-dominated atmosphere with levels of CO₂ varying from 0.02 to 1 bar, levels of CH₄ spanning 1 order of magnitude, and levels of O₃ spanning 5 orders of magnitude. Cnossen et al. (2007) found that atmospheric attenuation prevented flux at wavelengths shorter than 200 nm from reaching the surface in all the case studies they considered. In all cases, they found the surface flux to be far higher than that of modern Earth, again due to lack of UV-shielding oxic molecules. They further found that the surface flux was insensitive to variation in CH₄ and O₃ concentration at the levels they considered and that the wavelength cutoff from CO₂ rendered the surface flux insensitive to H₂O level. Cnossen et al. (2007) also used observations of a flare on an analogue to the young Sun, κ Ceti, to estimate the impact of solar variability on the surface UV environment; they found the effect to be minor due to strong atmospheric attenuation.

Rugheimer et al. (2015) used a coupled climate-photochemistry model to compute radiative transfer through, among others, an atmosphere corresponding to that of Earth at 3.9 Ga. Their model assumes an atmospheric pressure of 1 bar. It assumes atmospheric mixing ratios of 0.9, 0.1, and 1.65 × 10⁻⁶ for N₂, CO₂, and CH₄, respectively, coupled with modern abiotic outgassing rates of gases such as SO₂ and H₂S, and iterates to photochemical convergence. They reported the resulting actinic fluxes (spherically integrated radiances) at the bottom of the atmosphere. Rugheimer et al. (2015) reiterated the findings of previous workers that, overall, far more UV flux reached the surface of the primitive Earth compared to that of the modern day, with a cutoff at 200 nm due to shielding from CO₂ and H₂O.

Our work builds on these previous efforts. Like Rugheimer et al. (2015), we employed a two-stream multilayer approximation to radiative transfer, which consequently accounts for multiple scattering. Proper treatment of scattering is crucial in studies of the anoxic primitive Earth because of the uncovering of an optically thick, yet scattering-dominated, regime due to the absence of oxic shielding. For example, for a 0.9 bar N₂/0.1 bar CO₂ atmosphere of the kind considered by Rugheimer et al. (2015), the N₂ column density is 1.88 × 10²⁵ cm², and the CO₂ column density is 2.09 × 10²⁴ cm². At 210 nm, the Rayleigh scattering cross section due to N₂ is 2.9 × 10⁻²⁵ cm⁻², and the Rayleigh scattering cross section due to CO₂ is 6.8 × 10⁻²⁵ cm⁻², corresponding to a scattering optical depth of τ = 6.8 > 1. This optically thick scattering regime is shielded on Earth by strong O₂/O₃ absorption but is revealed under anoxic prebiotic conditions. In this regime, scattering interactions and reflection from the surface become common, and self-consistent calculation of the upward and downward scattered fluence becomes important. We argue that, consequently, the radiative transfer formalism of Cnossen et al. (2007) is inappropriate, because it implicitly neglects multiple scattering; it also ignores coupling between the upward and downward streams and implicitly assumes an albedo of zero. Such an approximation may be reasonable on modern Earth, where the scattering regime is confined to the optically thin region of the atmosphere by O₂ and O₃, meaning there are few scattering events and limited backscatter of reflected radiation. However, it is inappropriate for the anoxic prebiotic Earth where much of the prebiotically critical 200–300 nm regime is both scattering and optically thick, especially when treating cases with high albedo (e.g., snowfields).

Like Cnossen et al. (2007) and Cockell (2002), we explored multiple atmospheric compositions. However, we treated variations in the abundance of each gas independently in order to isolate each gas's effect individually, and explored a broader range of gases and abundances. We also explored the effects of albedo and zenith angle, which these earlier works did not.

Finally, Cnossen et al. (2007) and Cockell (2002) reported the surface flux. However, as pointed out by Madronich (1987), the flux “describes the flow of radiant energy through the atmosphere, while the [intensity] concerns the probability of an encounter between a photon and a molecule.” The distinction is often academic from a laboratory perspective, since in such studies the zenith angle of the source is often 0, meaning that the flux and spherically integrated radiance ³ are identical. However, the flux can deviate significantly from the radiance in a planetary context (see, e.g., Madronich, 1987). Rugheimer et al. (2015) reported the actinic flux (i.e., the integral over the unit sphere of the radiance field; see Madronich, 1987) at the bottom of atmosphere (BOA). This quantity, however, includes the upward diffuse reflection from the planet, which a molecule lying on the surface would not be exposed to. We instead report what we term the surface radiance, which is the integral of the radiance field at the planet surface, integrated over the hemisphere defined by positive elevation (i.e., that part of the sky not blocked by the planet surface). Figure 1 demonstrates the difference between the surface flux, the BOA actinic flux, and the surface radiance for the model atmosphere of Rugheimer et al. (2015), with a surface albedo corresponding to fresh snow and SZA = 60°.

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FIG. 1.

Top-of-atmosphere solar flux, surface flux, BOA actinic flux (reported by Rugheimer et al., 2015), and surface radiance for a planet with an atmosphere corresponding to that calculated by Rugheimer et al. (2015) for the 3.9 Ga Earth, with an albedo corresponding to fresh snow and a solar zenith angle of 60°. In this example, these quantities can vary by up to a factor of 3.6, despite being for identical physical conditions and having the same units. In this paper, we report the surface radiance.

2.2. Constraints on the composition of the atmosphere at 3.9 Ga

In this section, we briefly summarize available constraints on the terrestrial atmosphere at ∼3.9 Ga. A more detailed discussion is available in our earlier paper (Ranjan and Sasselov, 2016, Appendix B).

Measurements of oxygen isotopes in zircons suggest the existence of a terrestrial hydrosphere by 4.4 Ga, usually interpreted as evidence that liquid water was stable at Earth's surface (Mojzsis et al., 2001; Wilde et al., 2001; Catling and Kasting, 2007). Since the Sun was 30% less luminous in this era (the “faint young Sun paradox”), an enhanced greenhouse effect, for example, through higher levels of CO₂, is usually invoked (Kasting, 1993, 2014; Wordsworth and Pierrehumbert, 2013). The initial nebular atmosphere is thought to have been lost soon after planet formation, and the subsequent atmosphere is thought to have been dominated by volcanic outgassing from high-temperature magmas. Measurements of ancient volcanic rocks suggest that the redox state of Earth's mantle and, hence, the gas speciation from magma melts have not changed since 4.3 Ga (Delano, 2001; Trail et al., 2011), which suggests that an outgassed atmosphere would be dominated by CO₂, H₂O, and SO₂, with H₂S also being delivered. Measurements of N₂/Ar fluid inclusions in 3.5 Ga quartz crystals (Marty et al., 2013) have been used to demonstrate that N₂ was also a major atmospheric constituent, established at levels of 0.5–1.1 bar by 3.5 Ga (comparable to the present day). SO₂ and H₂S are not expected to have persisted at high levels in the atmosphere due to their tendency to photolyze and/or oxidize; however, it has been suggested that, during epochs of high volcanism, volcanogenic reductants could exhaust the surface oxidant supply, permitting transient buildup of gases vulnerable to oxidation, for example, SO₂, to the 1–100 ppm level (Kaltenegger and Sasselov, 2010). O₂ and its by-product O₃ are thought to have been rare due to strong sinks from volcanogenic reductants coupled with a lack of the biogenic oxygen source. This low-oxygen hypothesis is reinforced by measurements of mass-independent fractional of sulfur in rocks from >2.45 Ga (Farquhar et al., 2000), which suggests atmospheric UV throughput was high and oxygen/ozone content was low in the atmosphere prior to 2.45 Ga (Farquhar et al., 2001; Pavlov and Kasting, 2002), and by measurements of Fe and U-Th-Pb isotopes from a 3.46 Ga chert, which are consistent with an anoxic ocean (Li et al., 2013).

In summary, available geological constraints are suggestive of an atmosphere at 3.9 Ga with N₂ levels roughly comparable to that of the modern day, with sufficient concentration of greenhouse gases (e.g., CO₂) to support surface liquid water. O₂ (and hence O₃) levels are thought to have been low. If the young Earth were warm, water vapor would have been an important atmospheric constituent. During epochs of high volcanism, reducing volcanogenic gases (e.g., SO₂) may also have been important constituents of the atmosphere.

4.1. Tests of model physical consistency: the absorption and scattering limits

We describe here tests of the physical consistency of our model in the limits of pure absorption and pure scattering. We use the atmospheric model (composition and T/P profile) of Rugheimer et al. (2015) described in Section 4.2 and evaluate radiative transfer through this atmosphere in these two limiting cases. This atmospheric model includes an optically thick regime (τ > 1) from 130 to 332.5 nm and an optically thin regime (τ < 1) from 332.5 to 855 nm. For each of these limiting cases, we evaluate radiative transfer corresponding to a range of albedos and solar zenith angles. We evaluate uniform albedos of 0, 0.20, and 1, corresponding to the extrema of possible albedo values and the albedo assumed by Rugheimer et al. (2015). We evaluate solar zenith angles of 0°, 60°, and 85°, corresponding to extremal values of the possible solar zenith angle along with the value corresponding to the Rugheimer et al. (2015) findings. We choose 85° as our limit instead of 90° since the plane-parallel approximation breaks down when the Sun is sufficiently close to the horizon.

4.1.1. Pure absorption limit

As noted by Toon et al. (1989), in the limit of a purely absorbing atmosphere, the diffuse flux should vanish, and the surface flux should reduce to the direct flux. In exploring the pure absorption limit, we cannot set ω ₀ = 0 as under Gaussian quadrature γ ₂ = 0 for ω ₀ = 0, leading to a singularity when evaluating Γ under the Toon et al. (1989) formalism. We tried values for ω ₀ ranging from 10⁻³ to 10⁻¹⁰ for the A = 0.20, θ ₀ = 60° case. For all values of ω ₀, we found the diffuse surface flux to be highly suppressed relative to the direct TOA flux. For ω ₀ = 10⁻⁵, the diffuse flux was suppressed relative to the TOA flux by ≳6 orders of magnitude in each wavelength bin. The diffuse flux is also strongly suppressed relative to the direct surface flux, except at short wavelengths (λ < 198 nm) where extinction is so strong that that the diffuse layer blackbody flux dominates over the direct solar flux.

We evaluate the surface flux for ω ₀ = 10⁻⁵ for a range of A and θ ₀. Figure 2 presents the results. In all cases, the diffuse flux is highly suppressed relative to the TOA flux across all optical depths. Toon et al. (1989) reported that, while the pure absorption limit is satisfied by two-stream approximations with Gaussian closure for A = 0, for A > 0 exponential instabilities may lead to anomalous behavior. We do not observe this phenomenon in our model. We conclude that our implementation of the two-stream algorithm passes the absorption limit test.

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FIG. 2.

Direct, diffuse, and TOA fluxes (left-hand column) and diffuse flux at the surface normalized by TOA flux (right-hand column) for different solar zenith angles and surface albedos, for an atmosphere corresponding to the Rugheimer et al. (2015) 3.9 Ga Earth model with ω ₀ = 10⁻⁵. The diffuse flux vanishes in this limit, as expected.

4.1.2. Pure scattering limit

In the limit of a purely scattering atmosphere (ω ₀ = 1), F _net should be a constant throughout the atmosphere at all wavelengths since radiation is neither absorbed nor emitted by the atmospheric layers (Liou, 1973; Toon et al., 1989). In exploring this limit, we cannot set ω ₀ = 1: separate solutions are required for the fully conservative case (see, e.g., Liou, 1973). However, in practice we can set ω ₀ arbitrarily close to 1 (Toon et al., 1989) and ensure that the net flux is constant throughout the atmosphere or at least that its variations are small compared to the incident flux. We computed F _net at layer boundaries in the atmosphere for the A = 0.20, θ ₀ = 60° case, for values for ω ₀ ranging from 1–10⁻³ to 1–10⁻¹². For each wavelength bin, we computed the maximum deviation from the median net flux in the atmospheric column and normalized this deviation to the incident flux. For ω ₀ = 1–10⁻³, the variation of F _net from the median value ranged from 6 × 10⁻² at short wavelengths to 7 × 10⁻⁵ at long wavelengths. The increase in deviation toward shorter wavelengths is expected because of the higher opacity at shorter wavelengths. Increasing ω ₀ decreased the variation in F _net. For ω ₀ = 1–10⁻⁷, the fractional deviation of F _net from the columnar median varied from 6 × 10⁻⁴ to 7 × 10⁻⁹; and for ω ₀ = 1–10⁻¹², the deviation of F _net varied from 2 × 10⁻⁶ to 7 × 10⁻¹⁴.

We compute the maximum deviation of F _net at the layer boundaries from the columnar median as a function of wavelength for ω ₀ = 1–10⁻¹² for a range of A and θ ₀. Figure 3 presents the results. At optically thin wavelengths, larger albedos and zenith angles lead to higher deviations; we attribute this to higher levels of flux scattered into the more computationally difficult diffuse stream. At optically thick wavelengths, the magnitude of the deviations is insensitive to the planetary albedo. We attribute this to the extinction of incoming flux higher in the atmosphere, meaning that surface properties have less impact on the flux profile. In the optically thick regime, smaller zenith angles lead to higher deviations. For all values of θ ₀ and A considered here, the columnar deviation from uniformity is <3 × 10⁻⁶ of incoming fluence across all wavelengths for ω ₀ = 1–10⁻¹², and the deviation decreases as ω ₀ approaches 1 as expected.

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FIG. 3.

The maximum deviation of F _net from its median value in a given atmospheric column as a function of wavelength for an atmosphere corresponding to the Rugheimer et al. (2015) 3.9 Ga Earth model, with ω ₀ = 1–10⁻¹² and a variety of surface albedos and solar zenith angles. In the scattering limit, F _net approaches a constant value, with the variation in F _net decreasing as ω ₀ approaches 1.

4.2. Reproduction of results of Rugheimer et al. (2015)

In this section, we describe our efforts to recover the results of Rugheimer et al. (2015) with our code. Rugheimer et al. (2015) presented a model for the total BOA actinic flux on the 3.9 Ga Earth orbiting the 3.9 Ga Sun ⁷ from 130 to 855 nm. They couple a 1-D climate model (Kasting and Ackerman, 1986; Pavlov et al., 2000; Haqq-Misra et al., 2008) and a 1-D photochemistry model (Pavlov and Kasting, 2002; Segura et al., 2005, 2007) and iterate to convergence. They assume an overall atmospheric pressure of 1 bar and atmospheric mixing ratios of 0.9, 0.1, and 1.65 × 10⁻⁶ for N₂, CO₂, and CH₄, respectively. For all other gases, their model assumes outgassing rates corresponding to modern terrestrial nonbiogenic fluxes.

When computing layer-by-layer radiative transfer, Rugheimer et al. (2015) included absorption due to O₃, O₂, CO₂, and H₂O, and Mie scattering due to sulfate aerosols. Rayleigh scattering is computed via an N₂-O₂ scattering law (Kasting, 1982) that is scaled to include the effect of enhanced CO₂ scattering. Rugheimer et al. (2015) partitioned their atmosphere into 64 one-kilometer layers and assumed a solar zenith angle of 60°. As with our model, they computed the solar UV radiative transfer using a Toon et al. (1989) two-stream approximation with Gaussian quadrature closure. The surface albedo A = 0.20 is tuned to yield a surface temperature of 288 K in the modern Earth/Sun system to approximate the effect of clouds (Rugheimer et al., 2015).

We obtained the metadata ⁸ for an updated version of the 3.9 Ga Earth model of Rugheimer et al. (2015), courtesy of the authors. We used this metadata to run our radiative transfer model on the Rugheimer et al. (2015) atmospheric model. Figure 4 summarizes the results. The top row compares the incident flux at TOA (black) with the Rugheimer et al. (2015) results (red) and our model computations (blue, orange). The Rugheimer et al. (2015) results are not visible due to the close correspondence between our models. The bottom row gives the difference between our model and the Rugheimer et al. (2015) results, normalized to the TOA flux.

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FIG. 4.

Comparison of the BOA actinic fluxes obtained with our radiative transfer model for the updated 3.9 Ga Earth atmosphere of Rugheimer et al. (2015) versus that computed by the authors. The top shows the computed actinic fluxes and TOA flux, while the bottom shows the fractional difference between our models, normalized by the TOA flux. The difference between our results and those of Rugheimer et al. (2015) is driven by the use of different cross-section compilations; if we use the same cross sections as Rugheimer et al. (2015) (orange curves), we agree with Rugheimer et al. (2015) to better than 0.45% of the TOA flux.

Our model reproduces the Rugheimer et al. (2015) results to within 34% of the TOA flux. Much of the difference between our model and the Rugheimer et al. (2015) model can be accounted for by differences in the absorption cross sections we use. Our cross section lists are more complete than those of Rugheimer et al. (2015); for example, our H₂O cross section tabulation includes absorption at wavelengths longer than 208.3 nm, whereas that of Rugheimer et al. (2015) does not. Further, we include absorption due to SO₂ and CH₄, compute explicitly Rayleigh scattering on a gas-by-gas basis, and include blackbody emission from atmospheric layers and the planetary surface, whereas Rugheimer et al. (2015) did not (though this last is not a significant factor given the paucity of planetary radiation at UV wavelengths).

If we run our model using the Rugheimer et al. (2015) cross sections and scattering formalism and include only absorption due to O₂, O₃, CO₂, and H₂O, we arrive at the orange curve. This curve matches the Rugheimer et al. (2015) results to within 0.45% of the TOA flux. Our model, both with and without the Rugheimer et al. (2015) absorption, scattering, and emission formalism, can reproduce the scientific conclusions of Rugheimer et al. (2015) such as the 204 nm irradiance cutoff due to atmospheric CO₂. We conclude that our model is capable of reproducing the results of Rugheimer et al. (2015).

4.3. Comparison to modern Earth surficial measurements

We describe here comparisons of our radiative transfer model calculations to surface measurements of UV reported in the literature.

4.3.1. Reproduction of Antarctic diffuse spectral radiance measurements

Wuttke and Seckmeyer (2006) reported measurements of the diffuse spectral radiance (observed in the zenith direction) in Antarctica. We compare our model to their measurements of the diffuse radiance collected under low-cloud conditions (since our model does not include scattering processes due to clouds). The measurement site was flat and uniformly covered by snow, and the solar zenith angle during the measurements was 51.2°. When running our model, we assume the same solar zenith angle and take the albedo of the site to match freshly fallen snow. We run our model at a spectral resolution that matches the Wuttke and Seckmeyer (2006) measurements, that is, from 280 to 500 nm at 0.25 nm resolution and from 501 to 1050 nm at 1 nm resolution. We run our model from 0 to 60 km of altitude, at 600 m resolution (i.e., 100 layers evenly spaced in altitude) and assume a surface pressure of 1 bar. We assume composition and T/P profiles that match that of Rugheimer et al. (2013) for modern Earth. To reproduce the Wuttke and Seckmeyer (2006) measurements, we are obliged to reduce the water abundance by a factor of 10 relative to the Rugheimer et al. (2013) models. This makes sense, since Antarctica is a dry, desert environment. Similarly, the Rugheimer et al. (2013) model has an ozone total column depth of 5.3 × 10¹⁸ cm⁻² or 200 Dobson units (DU). For comparison, Earth's typical ozone total column density is around 300 DU (Patel et al., 2002), and a column depth of 220 DU is considered to be the start point for an ozone hole ⁹ . It is therefore unsurprising that matching the observed diffuse radiance in Antarctica requires scaling up the ozone abundance of Rugheimer et al. (2013) by a factor of 1.25. While our simple model, which excludes trace absorbers, clouds, and aerosols and is based on a globally averaged composition profile, cannot be expected to precisely replicate this measurement, we can reasonably expect it to identify major features of the modern surface UV environment.

Figure 5 presents the measured diffuse radiance observed by Wuttke and Seckmeyer (2006) and our model calculation smoothed by a 10-point moving average (boxcar) filter. Our code correctly replicated the major features of the modern terrestrial UV environment, such as the existence and location of the shortwave cutoff due to ozone. Figure 5 also presents the fractional difference between our model prediction and the measurement. The difference is within a factor of 2.2 and is highest in regions of strong atmospheric attenuation of UV. This accuracy is sufficient to distinguish between spectral regions of low and high (>100 ×) atmospheric attenuation, that is, to identify the UV fluence that is suppressed by atmospheric absorbers (e.g., Section 5.3). It is similarly sufficient to identify order-of-magnitude or greater changes in dose rates due to varying columns of a given absorber (e.g., Section 5.7), particularly because the highest error occurs at the lowest throughput and hence has the least weight in the dose rate calculation. We conclude that our code is sufficiently accurate for the applications considered in this work.

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FIG. 5.

Top: Zenith diffuse radiance measurement by Wuttke and Seckmeyer (2006) in Antarctica compared to the diffuse radiance calculated by our model for an atmosphere corresponding to the Rugheimer et al. (2013) modern Earth model, with the H₂O levels scaled down by a factor of 10 and the ozone column density scaled up by a factor of 1.25. Bottom: Fractional difference between the measurements of Wuttke and Seckmeyer (2006) and our model calculation. Our code recovers key features of the terrestrial UV environment, such as the shortwave cutoff due to ozone.

4.3.2. Reproduction of Toronto surface flux measurements

The World Ozone and Ultraviolet Radiation Data Centre (WOUDC; woudc.org) compiles measurements of UV surface flux. We compared our radiative transfer model calculations to a measurement of the UV surface flux at Toronto from 292 to 360 nm on 6/21/2003 at 11:54:06 (solar time). We chose this measurement to compare to as it corresponded approximately to the data presented by Kerr and Fioletov (2008) (i.e., a measurement in Toronto at noon in summer). The solar zenith angle at the time of measurement was 20.376°. We take the UV surface albedo to be 0.04, following the typical value suggested by Kerr and Fioletov (2008). We run our model from 292 to 360 nm at 0.5 nm resolution, matching the resolution of the measurements, from 0 to 60 km of altitude, at 600 m vertical resolution. We assume a T/P profile and atmospheric composition profile matching that of Rugheimer et al. (2013) for modern Earth. As in Section 4.3.1, we note that the Rugheimer et al. (2013) model has a total ozone column density of 200 DU, while the ozone column measured for this observation was 354 DU. We consequently scale our ozone mixing ratios by a factor of 1.77 to match the true column depth. As with Section 4.3.1, while we cannot expect our simple model to precisely replicate the surface flux measurement, we can reasonably expect it to identify major features of the modern surface UV environment.

Figure 6 presents the measured UV flux compared to our model prediction and the fractional difference between the two. Our model correctly replicates the shortwave UV cutoff due to ozone, which is characteristic of the modern surface UV environment. The relative difference between our model and the measurement is within a factor of 2.3, with the difference highest where the fluence is strongly suppressed. This performance is similar to that of our reproduction of Wuttke and Seckmeyer (2006) and is sufficient for the purposes of this paper.

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FIG. 6.

Top: Surface flux reported by a WOUDC station near summer noon in Toronto, compared to the surface flux calculated by our model for an atmosphere corresponding to the Rugheimer et al. (2013) modern Earth model with the ozone column density scaled up by a factor of 1.77. Bottom: Fractional difference between the measurements and our model. Our code clearly identifies and locates the shortwave cutoff due to ozone.

5.1. Action spectra and UV dose rates

To quantify the impact of the surface radiation environments on prebiotic chemistry, we follow the example of Cockell (1999) in computing biologically weighted UV dose rates. Specifically, we compute the biologically effective relative dose rate \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} \begin{align*} D = {{ \left( { \int_{{ \lambda _0}}^{{ \lambda _1}} {d \lambda A \left( \lambda \right) {I_{{ \rm{surf}}}} \left( \lambda \right) } } \right) } \mathord{ \left/ { \vphantom {{ \left( { \int_{{ \lambda _0}}^{{ \lambda _1}} {d \lambda A \left( \lambda \right) {I_{{ \rm{surf}}}} \left( \lambda \right) } } \right) } { \left( { \int_{{ \lambda _0}}^{{ \lambda _1}} {d \lambda A \left( \lambda \right) {I_{{ \rm{space}}}} \left( \lambda \right) } } \right) }}} \right. \kern \nulldelimiterspace} { \left( { \int_{{ \lambda _0}}^{{ \lambda _1}} {d \lambda A \left( \lambda \right) {I_{{ \rm{space}}}} \left( \lambda \right) } } \right) }} \end{align*} \end{document}

where A(λ) is an action spectrum, λ₀ and λ₁ are the limits over which A(λ) is defined, I _surf(λ) is the hemispherically integrated total UV surface radiance, and I _space(λ) is the solar flux at Earth's orbit. An action spectrum parametrizes the relative impact of radiation on a given photoprocess as a function of wavelength, with a higher value of A meaning that a higher fraction of the incident photons are being used in said photoprocess. Hence, D measures the relative rate of a given photoprocess for a single molecule at the surface of a planet, relative to in space at the location of the planet. If we compute the dose rate D_i , which corresponds to two UV surface radiance spectra I _surf,1 and I _surf,2 on a molecule that undergoes a photoprocess characterized by an action spectra A and find D ₁ > D ₂, we can say that the photoprocess encoded by A proceeds at a higher rate under I _surf,1 than I _surf,2.

Previous workers have used the modern DNA damage action spectrum (Cockell, 2002; Cnossen et al., 2007; Rugheimer et al., 2015) as a gauge of the level of stress imposed by UV fluence on the prebiotic environment. However, this action spectrum is based on studies of highly evolved modern organisms. Modern organisms have evolved sophisticated methods to deal with environmental stress, including UV exposure, that would not have been available to the first life. Further, this approach presupposes that UV light is solely a stressor and ignores its potential role as a eustressor for abiogenesis.

In this work, we used the action spectra that correspond to the production of aquated electrons from photoionization of tricyanocuprate and to the cleavage of the N-glycosidic bond in uridine monophospate (UMP, an RNA monomer) to compute our biologically effective doses. These processes are simple enough to have plausibly been in operation at the dawn of the first life, particularly in the RNA world hypothesis (Gilbert, 1986; Copley et al., 2007; McCollom, 2013) ¹⁰ . In the following sections, we discuss in more detail our rationale for choosing these pathways and how we construct the action spectra associated with them.

5.1.2. Stressor pathway: cleavage of N-glycosidic bond of UMP

UMP is a monomer of RNA, a key product of the Powner et al. (2009) pathway and critical molecule for abiogenesis in the RNA-world hypothesis for the origin of life. Shortwave UV irradiation of UMP cleaves the glycosidic bond that joins the nucleobase to the sugar (Gurzadyan and Görner, 1994), which destroys the biological effectiveness of this molecule. The reaction is difficult to reverse; indeed, the key breakthrough of the Powner et al. (2009) pathway was determining how to synthesize and incorporate this bond into the RNA monomers abiotically. Hence, this pathway represents a stressor for abiogenesis in the RNA-world hypothesis.

Glycosidic bond cleavage is not the only process operating in UMP at UV wavelengths. The (wavelength, QY) measured by Gurzadyan and Görner (1994) for glycosidic bond cleavage in UMP in an anoxic aqueous solution are (193 nm, 4.3 × 10⁻³) and (254 nm, (2–3) × 10⁻⁵). By comparison, the (wavelength, QY) they measure for chromophore loss (a measure of unaltered UMP abundance, based on absorbance at 260 nm) are (193 nm, 4 × 10⁻²) and (254 nm, 1.2 × 10⁻³), 1–2 orders of magnitude higher. The chromophore loss at 254 nm is well studied; for UMP, it is mostly due to photohydration, with a minor contribution from photodimer formation. The photohydration can be reversed with 90–100% efficiency via heating or lowering the pH (Sinsheimer, 1954), whereas further UV light (especially shortward of 230 nm) can cleave the photodimers. Since these processes are reversible via dark reactions, the UMP in some sense is not fully “lost,” unlike the glycosidic bond cleavage. We therefore argue the bond cleavage is more important than photohydration/photodimerization in measuring UV stress on UMP.

We define action spectra for the cleavage of the glycosidic bond in UMP by multiplying the absorption spectrum of UMP by the QY for the process. We take the absorption spectra from the work of Voet et al. (1963), which gives the absorption spectra of UMP at pH = 7.6. The QY of glycosidic bond cleavage as a function of wavelength has not been measured. To gain traction on this problem, we use the work of Gurzadyan and Görner (1994), which found the QY of N-glycosidic bond cleavage in UMP in neutral aqueous solution saturated with Ar (i.e., anoxic) to be 4.3 × 10⁻³ at 193 nm and (2–3) × 10⁻⁵ for 254 nm. We therefore represent the QY curve as a step function with value 4.3 × 10⁻³ for λ ≤ λ₀ and 2.5 × 10⁻⁵ for λ > λ₀. We consider λ₀ values of 193 and 254 nm, corresponding to the empirical limits from Gurzadyan and Görner (1994), as well as 230 nm, which corresponds to the end of the broad absorption feature centered near 260 nm corresponding to the π–π* transition and also to the transition to irreversible decomposition suggested by Sinsheimer and Hastings (1949). As shorthand, we refer to this photoprocess under the assumption that λ₀ = Y nm by UMP-Y.

Figure 7 shows the action spectra considered in our study. Action spectra are normalized arbitrarily (see, e.g., Cockell, 1999, and Rugheimer et al., 2015); hence they encode information about relative, not absolute, UV dose rate. We arbitrarily normalize these spectra to 1 at 190 nm.

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FIG. 7.

Action spectra for photolysis of UMP and photoionization of CuCN₃ ^2-, assuming a step-function form to the QY for both processes with step at λ = λ₀. The spectra are arbitrarily normalized to 1 at 190 nm.

5.2. Impact of albedo and zenith angle on surface radiance and prebiotic chemistry

In this section, we quantify the impact of varying albedo and zenith angle on surface radiance, and on prebiotic chemistry as measured by our action spectra.

The atmospheric radiative transfer computed for the prebiotic (3.9 Ga) Earth by Rugheimer et al. (2015) assumed a spectrally uniform albedo of 0.20 and a solar zenith angle of 60°. However, much broader ranges of albedos and zenith angles are available in a planetary context. In this section, we explore the impact of different albedos (A) and solar zenith angles (SZA) on the surface radiance (azimuthally integrated) on the 3.9 Ga Earth.

We calculate the surface radiance at SZA = 0°, 48.2°, and 66.5°, for a range of different surface albedos. SZA = 0° is the smallest possible value for SZA and corresponds to the shortest possible path through Earth's atmosphere. It is achieved at tropical latitudes. SZA = 48.2° corresponds to the insolation-weighed mean zenith angle on Earth (Cronin, 2014). SZA = 66.5° corresponds to the maximum zenith angle experienced at the poles (noon at the summer solstice) ¹² . Our choices of zenith angle thus encapsulate the minimum possible zenith angles and, hence, the shortest possible atmospheric path lengths over Earth's surface. As such, they may be understood as corresponding to the range of maximum possible UV surface radiances accessible at different latitudes on Earth's surface. It is of course possible to achieve arbitrarily large zenith angles (and hence arbitrarily low surface radiances) anywhere on Earth through the diurnal cycle and through seasonal variations at polar latitudes.

When considering albedos, we consider fixed uniform albedos of 0, 0.2, and 1. Albedos of 0 and 1 correspond to the lowest and highest possible values of A and, hence, the lowest and highest ¹³ surface radiance, respectively. The A = 0.2 case corresponds to the Rugheimer et al. (2015) base case. We also consider albedos that correspond to different physical surface environments, including ocean, tundra, desert, and old and new snow, including the dependence on z (see Appendix B for details). We consider this wide range of possible surface albedos because the climate state of the young Earth is minimally constrained by the available evidence, and climate states different than modern Earth's are plausible. For example, Sleep and Zahnle (2001) argued for a cold, ice-covered Hadean/early Archean climate, which would imply high-albedo conditions even at low latitudes.

Figure 8 presents the surface radiance computed for the Rugheimer et al. (2015) atmospheric model for these different zenith angles and surface albedos. The results match our qualitative expectations. Low-albedo surfaces correspond to lower surface radiances, with spectral contrast ratios as high as a factor of 7.4 between the A = 1 and A = 0 cases for λ > 204 nm (i.e., the onset of the CO₂ cutoff, see Ranjan and Sasselov, 2016). Similarly, small zenith angles correspond to higher surface radiances, with spectral contrast ratios as high as 4.1 between SZA = 0° and z = 66.5° for λ > 204 nm. Taken together, the effect is even stronger: for λ > 204 nm, the A = 1, SZA = 0° case (the highest-radiance case in the parameter space we considered) has spectral contrast ratios as high as a factor of 30 with respect to the A = 0, SZA = 66.5° case (the lowest-radiance case considered in our parameter space). When using more physically motivated albedos, the spectral contrast ratio between a model with SZA = 0° and albedo corresponding to fresh snow (i.e., the brightest natural surface included in our model) and a model with SZA = 66.5° and albedo corresponding to tundra (i.e., the darkest natural surface included in our model) was as high as a factor of 21. This means that at some wavelengths, 21 times more fluence would have been available on the equator of a high-albedo snow-and-ice covered “snowball Earth” compared to the polar regions of a warmer world with tundra or open ocean at the poles, for identical planetary atmospheres.

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FIG. 8.

Surface radiance for Earth at 3.9 Ga, assuming an atmosphere corresponding to the model of Rugheimer et al. (2015) and a range of solar zenith angles and surface albedos. Taken together, albedo and zenith angle can drive variations in spectral surface radiance as high as a factor of 20.6 for λ > 204 nm at 1 nm resolution.

We note that, somewhat non-intuitively, for some values of albedo and zenith angle, surface radiances exceeding the incident TOA radiance are possible (see, e.g., the A = 1, SZA = 0° case in Fig. 8). This is due to two factors. First, the downwelling diffuse radiance is enhanced by the backscatter of the upwelling diffuse radiance. Second, our flux conservation requirement coupled with our assumption of an isotropically scattering surface means that the upwelling radiance field is enhanced over the downwelling radiance field for low values of SZA and high values of A, meaning even more radiance is available to be backscattered. For a more thorough discussion of this phenomenon, see Appendix C. For a discussion of a similarly non-intuitive result for surface flux, see the work of Shettle and Weinman (1970).

We quantify the impact of albedo and zenith angle from a biological perspective by computing the biologically effective relative dose rates D_i for the photoprocesses described in Section 5.1 for the hemispherically integrated surface radiances corresponding to the different surface types and zenith angles considered in this study. These values are reported in Table 1. Variations in albedo can affect the BEDs of UV by factors of 2.7–4.4, depending on the zenith angle and the action spectrum used to compute the dose rate. Variations in zenith angle can affect the BED of UV by factors of 3.6–4.1, depending on the surface albedo and action spectrum. Taken together, variations in albedo and zenith angle can change the biologically effective dose of UV by factors of 10.5–17.5, depending on the action spectrum used to compute the dose rate. We conclude that local conditions like albedo and latitude could impact the availability of UV photons for prebiotic chemistry by an order of magnitude or more.

5.3. Impact of varying levels of CO₂ on surface radiance and prebiotic chemistry

Ranjan and Sasselov (2016) argued that shortwave UV light would have been inaccessible on the young Earth due to shielding from atmospheric CO₂. Specifically, we noted that atmospheric attenuation decreased fluence by a factor of 10 by 204 nm, with the damping increasing rapidly with the atmospheric cross section (driven by CO₂) at shorter wavelengths. This shielding is important because it screens out photons shortward of 200 nm that are expected to be harmful, while still permitting the potentially biologically useful flux in the >200 nm range (see, e.g., Guzman and Martin, 2008; Barks et al., 2010; Patel et al., 2015) to reach the planetary surface.

However, this argument is based on the models elucidated by Rugheimer et al. (2015). Rugheimer et al. (2015) assumed a CO₂ partial pressure at 3.9 Ga of 0.1 bar. This value is ad hoc: no direct geological constraints on CO₂ levels are available, and a variety of models with a wide range of CO₂ levels have been proposed that are consistent with the available climate constraints. Proposed CO₂ levels for the ∼3.9 Ga Earth range from 8 × 10⁻⁴ bar (Wordsworth and Pierrehumbert, 2013) to 7 bar (Kasting, 1987).

In this section, we examine the sensitivity of the shielding of UV shortwave fluence due to varying levels of CO₂ in the atmosphere. We compute radiative transfer through an atmosphere with varying levels of CO₂ and N₂ under irradiation by the 3.9 Ga Sun. We evaluate radiative transfer at (zenith angle, albedo) combinations of (SZA = 0°, A = fresh snow) and (SZA = 66.5°, A = tundra), corresponding to the extremal values of the range of plausible maximal surface radiances accessible on Earth assuming present-day obliquities. We omit attenuation due to other gases in our model (H₂O, CH₄, etc.) in order to isolate the influence of CO₂. We emphasize, therefore, that the UV throughputs we calculate should not be taken to correspond to the surface radiance plausibly expected on the 3.9 Ga Earth for a given CO₂ column, since they do not include attenuation from other gases and/or particulates or hazes that may have been present. Rather, these calculations represent the upper limits on surface radiance that are imposed by a given CO₂ column.

We assume a fixed background of N₂ gas, with column density \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document}$${N_{{{ \rm{N}}_2}}} = { \rm{ }}1.88{ \rm{ }} \times { \rm{ }}10^{25}{ \rm{ }}{\rm cm}^{ - 2}$$ \end{document} , corresponding to the 0.9 bar N₂ column assumed by the Rugheimer et al. (2015) atmospheric model. We choose this value for consistency with the model of Rugheimer et al. (2015), noting that it is also consistent with the deepest constraint on N₂ abundance in the Archean, that is, the finding of Marty et al. (2013) that pN₂ at 3–3.5 Ga was 0.5–1.1 bar based on analysis of fluid inclusions trapped in Archean hydrothermal quartz samples. Since N₂ does not absorb at UV wavelengths longer than 108 nm (Huffman, 1969; Chan et al., 1993a) and N₂ scattering is weak compared to, for example, CO₂ scattering, our results should be insensitive to the precise N₂ level.

We parametrize CO₂ abundance by scaling the CO₂ column calculated by Rugheimer et al. (2015) corresponding to 0.1 bar of CO₂, with total column density \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document}$${N_{{ \rm{C}}{{ \rm{O}}_2}}} = { \rm{ }}2.09{ \rm{ }} \times { \rm{ }}{10^{24}}{{\rm cm}^{ - 2}}$$ \end{document} . We calculate the UV radiance through CO₂ columns equal to the Rugheimer et al. (2015) column scaled by factors in the range from 10⁻⁶ to 10³. To link these columns to CO₂ partial pressures, we employ the relation that the partial pressure of a well-mixed gas in an atmosphere is \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document}$${p_i} = g \bar m{N_i}$$ \end{document} , where g is the acceleration due to gravity (g = 981 cm s⁻² for Earth), \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document}$$\bar m$$ \end{document} is the atmospheric mean molecular mass, and N_i is the column density of the gas. Figure 9 presents the UV surface radiances for atmospheres with \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document}$${N_{{{ \rm{N}}_2}}} = { \rm{ }}1.88{ \rm{ }} \times { \rm{ }}{10^{25}}{{\rm cm}^{ - 2}}$$ \end{document} and varying levels of CO₂. Table 2 presents the optical and atmospheric parameters associated with each model.

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FIG. 9.

Surface radiances for an atmosphere with \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document}$${N_{{{ \rm{N}}_2}}}$$ \end{document} = 1.88 × 10²⁵ cm⁻² and varying levels of CO₂, for (surface albedo, solar zenith angle) combinations of (tundra, 66.5°) and (new snow, 0°), corresponding to the range of maximum surface radiances available across the planetary surface. Solid lines correspond to CO₂ levels with motivation from climate models in the literature. The line corresponding to \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document}$${N_{{ \rm{C}}{{ \rm{O}}_2}}}$$ \end{document} = 2.09 × 10²⁴ cm⁻² (i.e., the fiducial 0.1 bar CO₂ level in the Rugheimer et al., 2015, model) is highlighted with a thicker line.

To place these column densities in context, we compute the CO₂ columns associated with different climate models in the literature.

We compute the surface radiance for N₂-CO₂ model atmospheres with \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document}$${N_{{ \rm{C}}{{ \rm{O}}_2}}}$$ \end{document} corresponding to the CO₂ columns computed for the above literature models, with a fixed N₂ background of \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document}$${N_{{{ \rm{N}}_2}}} = { \rm{ }}1.88{ \rm{ }} \times { \rm{ }}{10^{25}}\,{{\rm cm}^{ - 2}}$$ \end{document} as before. These models and the parameters associated with them are also shown in Fig. 9 and Table 2.

5.3.2. Biologically effective doses

Figure 10 presents the BEDs for the photoprocesses considered in our study under irradiation by surface fluences corresponding to attenuation by different levels of CO₂, normalized by the dose rates corresponding to \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document}$${N_{{ \rm{C}}{{ \rm{O}}_2}}}$$ \end{document}  = 2.09 × 10²⁴ cm⁻² (0.1 bar CO₂). With this normalization, a dose rate D > 1 means a higher dose rate than the 0.1 bar CO₂ case and hence a higher photoreaction rate, and D < 1 the opposite. Both the maximum radiance (A = new snow, SZA = 0°) and the minimum radiance (A = tundra, SZA = 66.5°) cases are presented.

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FIG. 10.

Biologically effective dose rates for UMP-X and CuCN3-Y as a function of \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document}$${N_{{ \rm{C}}{{ \rm{O}}_2}}}$$ \end{document} , normalized to their values at \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document}$${N_{{ \rm{C}}{{ \rm{O}}_2}}}\, $$ \end{document} = 2.09 × 10²⁴ cm⁻². The dashed line demarcates the level of CO₂ required by the climate model of Wordsworth and Pierrehumbert (2013), the lowest proposed so far. The plot truncates at the CO₂ level corresponding to volatilization of all crustal carbonates as CO₂, an upper bound on plausible CO₂ levels.

For the minimum radiance case, we observe that the BEDs uniformly decrease with increasing \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document}$${N_{{ \rm{C}}{{ \rm{O}}_2}}}$$ \end{document} , corresponding to uniforming decreasing fluence levels, as expected. D_i  > 1 for \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document}$${N_{{ \rm{C}}{{ \rm{O}}_2}}}$$ \end{document} < 2.09 × 10²⁴ cm⁻², and D_i < 1 for \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document}$${N_{{ \rm{C}}{{ \rm{O}}_2}}}$$ \end{document} > 2.09 × 10²⁴ cm⁻², meaning that both stressor and eustressor photoprocesses are slowed by increasing \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document}$${N_{{ \rm{C}}{{ \rm{O}}_2}}}$$ \end{document} .

In the maximum radiance case, the BEDs generally also follow the same trend with \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document}$${N_{{ \rm{C}}{{ \rm{O}}_2}}}$$ \end{document} , that is, decreasing as \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document}$${N_{{ \rm{C}}{{ \rm{O}}_2}}}$$ \end{document} increases. However, from \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document}$${N_{{ \rm{C}}{{ \rm{O}}_2}}}$$ \end{document} = 2.09 × 10²³–10²⁴ cm⁻², the dose rate of UMP-193 increases slightly, by 0.6%. This is because for \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document}$${N_{{ \rm{C}}{{ \rm{O}}_2}}}$$ \end{document} ≥ 2.09 × 10²³ cm⁻², photons shortward of λ₀ = 193 nm are effectively completely blocked from the surface, leaving only the longwave photons at the lower QY available to power the reaction. For high-albedo surfaces, this longwave fluence increases slightly with \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document}$${N_{{ \rm{C}}{{ \rm{O}}_2}}}$$ \end{document} due to enhanced backscattering of reflected light from the surface by atmospheric CO₂ ^[14], increasing slightly the effective dose. For \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document}$${N_{{ \rm{C}}{{ \rm{O}}_2}}}$$ \end{document} > 2.09 × 10²⁴ cm⁻², this effect is overwhelmed by the overall decrease in fluence levels, and the UMP-193 dose rate returns to the general trend.

High levels of atmospheric CO₂ can suppress prebiotically relevant photoprocesses as measured by our action spectra. For \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document}$${N_{{ \rm{C}}{{ \rm{O}}_2}}}$$ \end{document} = 9.84 × 10²⁶ cm⁻², corresponding to the volatilization of all CO₂ from crustal carbonates, the dose rates are suppressed by a factor of 10–100 relative to the dose rates at \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document}$${N_{{ \rm{C}}{{ \rm{O}}_2}}}$$ \end{document} = 2.09 × 10²⁴ cm⁻², depending on the surface conditions. UV-sensitive pathways relevant to prebiotic chemistry may be photon-limited in high-CO₂ cases. If assuming a high-CO₂ atmosphere for UV-dependent prebiotic pathways, it may be important to characterize the sensitivity of the prebiotic pathways to fluence levels to make sure that thermal back reactions will not retard the photoprocesses at low fluence levels.

Low levels of atmospheric CO₂ can modestly enhance prebiotically relevant photoprocesses as measured by our action spectra. For \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document}$${N_{{ \rm{C}}{{ \rm{O}}_2}}}$$ \end{document} = 1.87 × 10²² cm⁻² [corresponding to the low-CO₂ model of Wordsworth and Pierrehumbert (2013)], in the maximum radiance case the dose rates are 1.006–1.16 of the dose rates at \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document}$${N_{{ \rm{C}}{{ \rm{O}}_2}}}$$ \end{document} = 2.09 × 10²⁴ cm⁻². For the corresponding minimum radiance case, the dose rates are 1.19–1.31 of the dose rates at \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document}$${N_{{ \rm{C}}{{ \rm{O}}_2}}}$$ \end{document} = 2.09 × 10²⁴ cm⁻². If one allows CO₂ levels to decrease without regard for climatological or geophysical plausibility, higher dose rates are possible, but only to a point: assuming no CO₂ at all (only scattering from N₂), dose rates of 1.05–1.76 relative to the \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document}$${N_{{ \rm{C}}{{ \rm{O}}_2}}}$$ \end{document} = 2.09 × 10²⁴ cm⁻² base case are plausible (maximum radiance conditions). Hence, the variation in dose rate due to reducing CO₂ is less than a factor of 2. Pathways derived assuming attenuation from more conventional levels of CO₂ should function even with lower levels of CO₂ shielding.

Overall, across the range of possible CO₂ levels ( \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document}$${N_{{ \rm{C}}{{ \rm{O}}_2}}}$$ \end{document} ≤ 9.84 × 10²⁶ cm⁻²), the variation in BEDs is <2 orders of magnitude, for both stressor and eustressor pathways and all values of λ₀, assuming no other UV absorbers. Hence, as measured by these action spectra, UV-sensitive prebiotic photochemistry is relatively insensitive to the level of CO₂ in the atmosphere, assuming no other absorbers to be present.

5.4. Alternate shielding gases

In the previous section, we considered the constraints placed by varying levels of atmospheric CO₂ on the surficial UV environment. However, CO₂ is not the only plausible UV absorber in the atmosphere of the young Earth. Other photoactive gases that may have been present in the primitive atmosphere include SO₂, H₂S, CH₄, and H₂O. These gases have absorption cross sections in the 100–500 nm range, and as such if present at significant levels could have influenced the surficial UV environment. O₂ and O₃, while expected to be scarce in the prebiotic era, are strongly absorbing in the UV and might have an impact even at low abundances.

In this section, we explore the potential impact of varying levels of gases other than CO₂ on surficial UV fluence on the 3.9 Ga Earth. We consider each gas species G individually, computing radiative transfer through two-component atmospheres under insolation by the 3.9 Ga Sun, with varying levels of the photoactive gas G and a fixed column of N₂ as the background gas. We consider a range of column densities of G corresponding the levels computed by Rugheimer et al. (2015) scaled by factors of 10. Table 3 gives the abundance of each gas computed by Rugheimer et al. (2015).

As in the case of CO₂ (Section 5.3), we assume that G is well mixed, and we omit attenuation due to other gases in order to isolate the effect of the specific molecule G. We evaluate radiative transfer for an (A, SZA) combination corresponding to (fresh snow, 0°) only; hence, the surface radiances we compute may be interpreted as planetwide upper bounds. We assume a fixed N₂ background with column density of \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document}$${N_{{{ \rm{N}}_2}}}$$ \end{document} = 1.88 × 10²⁵ cm⁻², corresponding to the 0.9 bar N₂ column in the Rugheimer et al. (2015) atmospheric model. We again emphasize that the UV throughput we calculate should not be taken to correspond to the surface radiance plausibly expected on the 3.9 Ga Earth for a given column of G, since our calculations do not include attenuation from other gases that may have been present. Rather, these calculations represent the upper limits on surface radiance that are imposed by various levels of these gases.

The model metadata we secured from the work of Rugheimer et al. (2015) do not include H₂S abundances. We estimate an upper bound on the H₂S abundances by assuming that the relative abundance of H₂S compared to SO₂ traces their emission ratio from outgassing. Halmer et al. (2002) found the outgassing emission rate ratios of [H₂S]/[SO₂] = 0.1–2 for subduction zone–related volcanoes and 0.1–1 for rift zone–related volcanoes for modern Earth. Since the redox state of the mantle has not changed from 3.6 Ga and probably from 3.9 Ga (Delano, 2001), we can expect the outgassing ratio to have been similar at 3.9 Ga. Therefore, we assign an upper bound to the H₂S column of 2× the SO₂ column.

5.5. CH₄

Rugheimer et al. (2015) fixed by assumption a uniform CH₄ mixing ratio of 1.65 × 10⁻⁶ throughout their 1 bar atmosphere, corresponding to \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document}$${N_{{ \rm{C}}{{ \rm{H}}_4}}}$$ \end{document} = 3.45 × 10¹⁹ cm⁻². However, other authors have postulated a broad range of abundances for CH₄. Kasting and Brown (1998) estimated a methane abundance of 0.5 ppm (mixing ratio of 5 × 10⁻⁷) for a 1 bar N₂-CO₂ atmosphere assuming conversion of 1% carbon flux from mid-ocean ridges to CH₄ prior to the rise of life. Kasting (2014) echoed this estimated mixing ratio for a CH₄ source of serpentinization of ultramafic rock with seawater at present-day levels, while Guzmán-Marmolejo et al. (2013) estimated that serpentinization can drive CH₄ levels up to 2.1 ppmv. However, Kasting (2014) also noted that methane production from impacts could have outpaced the supply from serpentinization multiple orders of magnitude, and could have sustained abiotic CH₄ levels up to 1000 ppmv. Shaw (2008) also postulated that such high CH₄ levels might be plausible, hypothesizing that conversion of dissolved carbon compounds to methane might have produced methane fluxes an order of magnitude higher than the present day, enough to sustain an atmosphere with sufficient methane to maintain a habitable climate. Such estimates correspond to a broad range of CH₄, from \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document}$${N_{{ \rm{C}}{{ \rm{H}}_4}}}$$ \end{document} = 9.83 × 10¹⁸ cm⁻² to \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document}$${N_{{ \rm{C}}{{ \rm{H}}_4}}}$$ \end{document} = 1.97 × 10²² cm⁻². We consequently explore a range of CH₄ values corresponding to 10⁻² to 10³ × the Rugheimer et al. (2015) value, encompassing this range. Figure 11 shows the resultant spectra.

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FIG. 11.

Surface radiances for an atmosphere with \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document}$${N_{{{ \rm{N}}_2}}}$$ \end{document}  = 1.88 × 10²⁵ cm⁻² and varying levels of CH₄, for a surface albedo corresponding to new snow and SZA = 0°. The line corresponding to the CH₄ level assumed in the Rugheimer et al. (2015) model is presented as a solid, thicker line.

Absorption of UV light by CH₄ is negligible in an atmosphere with even trace amounts of CO₂, due to the extremely shortwave onset of absorption by CH₄ (165 nm). At CH₄ levels of \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document}$${N_{{ \rm{C}}{{ \rm{H}}_4}}}$$ \end{document} = 3.45 × 10²² cm⁻², 3 orders of magnitude higher than those assumed by Rugheimer et al. (2015) and at the upper end of what has been proposed in the literature, CH₄ extincts fluence shortward of 165 nm. A CO₂ level of \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document}$${N_{{ \rm{C}}{{ \rm{O}}_2}}}$$ \end{document} = 2.09 × 10¹⁹ cm⁻² is enough to extinct the fluence shortward of 167. This CO₂ level is 5 orders of magnitude less than the Rugheimer et al. (2015) value and 2 orders of magnitude less than the lowest level CO₂ suggested in the literature based on climatic constraints. We conclude that in an atmosphere with even trace amounts of CO₂, plausible levels of CH₄ do not further constrain the surface UV environment.

5.6. H₂O

There exist few constraints on primordial water vapor levels. The terrestrial water vapor profile is set by the temperature profile; evaporation rates and H₂O saturation pressures increase with temperature, meaning that a hot planet is likely to be steamier than a cold planet. Knauth (2005) used oxygen isotope data from cherts to argue that the ocean temperature was 328–358 K (55–85°C) at 3.5 Ga, though this is not universally accepted (Kasting, 2010), in part due to the extraordinary inventory of greenhouse gases that would be required to sustain such high temperatures. By contrast, Rugheimer et al. (2015) computed a surface temperature of 293 K for Earth at 3.9 Ga.

The model of Rugheimer et al. (2015) corresponds to an atmosphere with an H₂O column density of \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document}$${N_{{{ \rm{H}}_{ \rm{2}}}{ \rm{O}}}}$$ \end{document} = 9.96 × 10²² cm⁻². However, arbitrarily low H₂O abundances are possible depending on how cold the atmosphere and surface are. What of the upper limit? Kasting et al. (1984) computed, among other parameters, the H₂O mixing ratio for a planet with atmospheric composition that matches that of modern Earth under varying levels of insolation. In the case of 1.45× modern insolation, Kasting et al. (1984) computed a surface temperature of 384.2 K [greater than that suggested by Knauth (2005)], a surface pressure of 2.481 bar, and H₂O volume mixing ratio of ∼0.5. This corresponds to an atmosphere with a mean molecular mass of 3.89 × 10⁻²³ g and an H₂O column of 3.25 ×10²⁵ cm⁻². We interpret this value as an extreme upper limit for H₂O column density. We evaluate radiative transfer through N₂-H₂O atmospheres with total H₂O columns corresponding to 10⁻⁵ to 10³ of the Rugheimer et al. (2015) value, encompassing this upper bound. Figure 12 shows the resultant spectra.

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FIG. 12.

Surface radiances for an atmosphere with \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document}$${N_{{{ \rm{N}}_2}}}$$ \end{document} = 1.88 × 10²⁵ cm⁻² and varying levels of H₂O, for a surface albedo corresponding to new snow and SZA = 0°. The line corresponding to the H₂O level calculated in the Rugheimer et al. (2015) model is presented as a solid, thicker line.

H₂O is a robust UV absorber, with strong absorption for λ₀ < 198 nm. \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document}$${N_{{{ \rm{H}}_{ \rm{2}}}{ \rm{O}}}}$$ \end{document} = 9.96 × 10²¹ cm⁻² (0.1 × the Rugheimer et al., 2015, level) is enough to block fluence for λ₀ < 198 nm; for comparison, \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document}$${N_{{ \rm{C}}{{ \rm{O}}_2}}}$$ \end{document} = 2.09 × 10²⁴ cm⁻², the fiducial Rugheimer et al. (2015) level, blocks fluence for λ₀ < 201 nm. Even in the absence of attenuation from CO₂, attenuation from plausible levels of H₂O blocks UV flux with λ < 198 nm. Hence, no matter what the level of CO₂, fluence shortward of 198 nm would have been inaccessible to prebiotic chemistry, assuming warm enough surface temperatures to sustain \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document}$${N_{{{ \rm{H}}_{ \rm{2}}}{ \rm{O}}}}$$ \end{document}  = 9.96 × 10²¹ cm⁻² of atmospheric water vapor.

Figure 13 presents the dose rates D_i ( \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document}$${N_{{{ \rm{H}}_{ \rm{2}}}{ \rm{O}}}}$$ \end{document} )/D_i ( \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document}$${N_{{ \rm{C}}{{ \rm{O}}_2}}}$$ \end{document} = 2.09 × 10²⁴ cm⁻²), that is, the BEDs for UMP-193, UMP-230, and UMP-254, and CuCN3-254 and CuCN3-300 as a function of \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document}$${N_{{{ \rm{H}}_{ \rm{2}}}{ \rm{O}}}}$$ \end{document} ¹⁵ normalized by the corresponding dose rates calculated for a CO₂-N₂ atmosphere with 0.1 bar of CO₂. With this normalization, a value of D_i/D_i ( \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document}$${N_{{ \rm{C}}{{ \rm{O}}_2}}}$$ \end{document} = 2.09 × 10²⁴ cm⁻²) > 1 means that the given photoreaction is proceeding at a higher rate than for an atmosphere with \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document}$${N_{{ \rm{C}}{{ \rm{O}}_2}}}$$ \end{document} = 2.09 × 10²⁴ cm⁻². Across the range of \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document}$${N_{{{ \rm{H}}_{ \rm{2}}}{ \rm{O}}}}$$ \end{document} considered here, the dose rates are similar (within a factor of 1.7) to the dose rates in the \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document}$${N_{{ \rm{C}}{{ \rm{O}}_2}}}$$ \end{document} = 2.09 × 10²⁴ cm⁻² case. We therefore argue that the constraints on UV imposed by H₂O are similar to those imposed by \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document}$${N_{{ \rm{C}}{{ \rm{O}}_2}}}$$ \end{document} = 2.09 × 10²⁴ cm⁻². Prebiotic chemistry studies derived assuming a surface radiance environment primarily shaped by \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document}$${N_{{ \rm{C}}{{ \rm{O}}_2}}}$$ \end{document} = 2.09 × 10²⁴ cm⁻² should be robust to the level of water vapor in the atmosphere.

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FIG. 13.

Biologically effective dose rates for UMP-X and CuCN3-Y as a function of \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document}$${N_{{{ \rm{H}}_{ \rm{2}}}{ \rm{O}}}}$$ \end{document} , normalized to the dose rates at \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document}$${N_{{ \rm{C}}{{ \rm{O}}_2}}}$$ \end{document} = 2.09 × 10²⁴ cm⁻². The solid line corresponds to the H₂O level of Rugheimer et al. (2015).

5.7. SO₂

SO₂ absorbs more strongly and over a much wider range than CO₂ (Fig. A5). However, SO₂ is vulnerable to loss processes such as photolysis and reaction with oxidants (Kaltenegger and Sasselov, 2010); consequently, SO₂ levels are usually calculated to be very low on the primitive Earth. Assuming levels of volcanic outgassing at 3.9 Ga comparable to the present day, as did Rugheimer et al. (2015), SO₂ levels are low, with \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document}$${N_{{ \rm{S}}{{ \rm{O}}_2}}}$$ \end{document}  = 7.05 × 10¹⁴ cm⁻² in the calculation of Rugheimer et al. (2015). At these levels, SO₂ does not significantly modify the surface UV environment (Fig. 14).

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FIG. 14.

Surface radiances for an atmosphere with \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document}$${N_{{{ \rm{N}}_2}}}$$ \end{document} = 1.88 × 10²⁵ cm⁻² and varying levels of SO₂, for a surface albedo corresponding to new snow and SZA = 0°. The line corresponding to the SO₂ level calculated in the Rugheimer et al. (2015) model is presented as a solid, thicker line.

However, relatively little is known about primordial volcanism. During epochs of high enough volcanism on the younger, more geologically active Earth, volcanic reductants might conceivably deplete the oxidant supply. While an extreme scenario, if it occurred, SO₂ might plausibly build up to the 1–100 ppm level (Kaltenegger and Sasselov, 2010), at which point it might begin to supplant CO₂ as the controlling agent for the global thermostat ¹⁶ (cf. the model of Halevy et al., 2007, for primitive Mars). Assuming a background atmosphere of 0.9 bar N ₂ and 0.1 bar CO₂, this corresponds to column densities of \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document}$${N_{{ \rm{S}}{{ \rm{O}}_2}}}$$ \end{document}  = 2.09 × 10¹⁹–10²¹ cm⁻². We therefore explore a range of SO₂ values corresponding to 1–10⁷× the Rugheimer et al. (2015) value, encompassing this range. Figure 14 shows the resultant spectra. We considered lower SO₂ levels as well, but the resultant spectra were indistinguishable from the 1× case and so are not shown.

Such high SO₂ levels would be transient and would subside with volcanism. But while they persisted, SO₂ could dramatically modify the surface UV environment. At \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document}$${N_{{ \rm{S}}{{ \rm{O}}_2}}}$$ \end{document} = 7.05 × 10¹⁷ cm⁻², SO₂ starts to sharply reduce fluence at wavelengths λ≲200 nm. For \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document}$${N_{{ \rm{S}}{{ \rm{O}}_2}}}$$ \end{document}  ≥ 7.05 × 10²⁰ cm⁻² (∼36 ppm in the Rugheimer et al., 2015, model), all fluence shortward of ∼327 nm is shielded out. Such levels of SO₂ would correspond to very low-UV epochs in Earth's history.

We quantify the impact of high SO₂ levels on UV-sensitive prebiotic chemistry by again convolving our surface radiance spectra for an SO₂-N₂ atmosphere against our action spectra and computing the BEDs as functions of \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document}$${N_{{ \rm{S}}{{ \rm{O}}_2}}}$$ \end{document} . Figure 15 presents these values, normalized by the corresponding dose rates for the \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document}$${N_{{ \rm{C}}{{ \rm{O}}_2}}}$$ \end{document} = 2.09 × 10²⁴ cm⁻² case. As expected, higher levels of SO₂ reduce the BEDs. For \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document}$${N_{{ \rm{S}}{{ \rm{O}}_2}}}$$ \end{document} = 7.05 × 10²¹ cm⁻², the BEDs are suppressed by over 60 orders of magnitude, implying the corresponding photoreactions would have been quenched. UV-dependent prebiotic chemistry could not function in such high-SO₂ epochs.

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FIG. 15.

Biologically effective dose rates for UMP-X and CuCN3-Y as a function of \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document}$${N_{{ \rm{S}}{{ \rm{O}}_2}}}$$ \end{document} , normalized to the dose rates at \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document}$${N_{{ \rm{C}}{{ \rm{O}}_2}}}$$ \end{document} = 2.09 × 10²⁴ cm⁻². The solid line corresponds to the SO₂ level of Rugheimer et al. (2015).

These BEDs do not fall off at the same rates. Figure 16 plots the ratio between UMP-X and CuCN3-Y, for all X and Y, as a function of \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document}$${N_{{ \rm{S}}{{ \rm{O}}_2}}}$$ \end{document} . For \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document}$${N_{{ \rm{S}}{{ \rm{O}}_2}}}$$ \end{document}  ≥ 7.05 × 10¹⁸ cm⁻², for all values of λ₀, the CuCN3 photoionization BEDs decrease at lower rates than the UMP glycosidic bond cleavage BEDs. For \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document}$${N_{{ \rm{S}}{{ \rm{O}}_2}}}$$ \end{document} ≥ 7.05 × 10¹⁹ cm⁻², the UMP-230 BED is suppressed 2 orders of magnitude more than the CuCN3-X BEDs, relative to \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document}$${N_{{ \rm{S}}{{ \rm{O}}_2}}}$$ \end{document} ≤ 7.05 × 10¹⁵ cm⁻². Since the UMP-X BEDs measure a stressor for abiogenesis while CuCN3-X BEDs measure a eustressor for abiogenesis, one might argue that high-SO₂ environments present more clement environments for abiogenesis compared to low-SO₂ ones. However, these results are sensitive to the details of the action spectrum and photoprocess chosen. This is especially challenging given the paucity of data on the QY curves for these processes and the assumptions therefore required to construct them. Further, we have considered here only one stressor and eustressor photoprocess, whereas in reality there should have been many more photoprocesses. We therefore conclude that, as measured solely by UMP photolysis and cyanocuprate photoionization, high-SO₂ epochs might have been more clement environments for abiogenesis, but further laboratory constraints on the action spectra of these processes are required to reduce the sensitivity of this statement to assumptions.

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FIG. 16.

Ratio of biologically effective dose rates UMP-X/CuCN3-Y, for X = 193, 230, and 254 nm and Y = 254 and 300 nm, as a function of \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document}$${N_{{ \rm{S}}{{ \rm{O}}_2}}}$$ \end{document} .

5.8. H₂S

H₂S shares similar properties to SO₂. Like SO₂, H₂S is a stronger and broader absorber in the UV than CO₂. Like SO₂, H₂S is primarily generated through outgassing from volcanic sources and is lost from the atmosphere due to vulnerability to photolysis and reactions with oxidants. Consequently, H₂S is not expected to have been a major constituent of the prebiotic atmosphere.

Rugheimer et al. (2015) did not calculate an abundance for H₂S in their model. We estimate an upper bound on \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document}$${N_{{{ \rm{H}}_2}{ \rm{S}}}}$$ \end{document} ≤ 2 \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document}$${N_{{ \rm{S}}{{ \rm{O}}_2}}}$$ \end{document} by assuming that [H₂S]/[SO₂] traces their relative outgassing ratios, which vary from 0.1 to 2 in the modern day (Halmer et al., 2002). The redox state of the terrestrial mantle has likely not changed since 3.9 Ga (Delano, 2001; Trail et al., 2011), suggesting the proportion of outgassed gases from volcanogenic sources should not have changed either. Based on this reasoning, we assign an upper bound to \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document}$${N_{{{ \rm{H}}_2}{ \rm{S}}}}$$ \end{document} in an atmosphere corresponding to the Rugheimer et al. (2015) model of 1.41 × 10¹⁵ cm⁻², corresponding to 2 \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document}$${N_{{ \rm{S}}{{ \rm{O}}_2}}}$$ \end{document} . We explore a range of H₂S values corresponding to 1–10⁷× this value, corresponding to the range of SO₂ values we explore. Figure 17 shows the resultant spectra. We considered lower SO₂ levels as well, but the resultant spectra were indistinguishable from the 1× case and so are not shown.

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FIG. 17.

Surface radiances for an atmosphere with \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document}$${N_{{{ \rm{N}}_2}}}$$ \end{document} = 1.88 × 10²⁵ cm⁻² and varying levels of H₂S, for a surface albedo corresponding to new snow and SZA = 0°. The line corresponding to the 2 × SO₂ level calculated in the Rugheimer et al. (2015) model is presented as a solid, thicker line.

For \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document}$${N_{{{ \rm{H}}_2}{ \rm{S}}}}$$ \end{document}  = 1.41 × 10¹⁵ cm⁻², H₂S has minimal impact on the surface UV environment. However, as with SO₂, epochs of high volcanism might have depleted the oxidant supply and triggered the buildup of H₂S to higher levels, which could have occurred on a younger Earth. In this case, H₂S would have affected the surface UV environment. For \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document}$${N_{{{ \rm{H}}_2}{ \rm{S}}}}$$ \end{document}  ≥ 1.41 × 10¹⁹ cm⁻², H₂ suppresses the fluence at wavelengths shorter than 235 nm. For \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document}$${N_{{{ \rm{H}}_2}{ \rm{S}}}}$$ \end{document}  ≥ 1.41 × 10²² cm⁻², fluence shortward of 369 nm is shielded out. This reduction in fluence results in the expected decrease in BED with \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document}$${N_{{{ \rm{H}}_2}{ \rm{S}}}}$$ \end{document} , as shown in Fig. 18. For \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document}$${N_{{{ \rm{H}}_2}{ \rm{S}}}}$$ \end{document}  = 1.41 × 10²² cm⁻², all dose rates are suppressed by ≥11 orders of magnitude relative to the dose rates at \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document}$${N_{{{ \rm{H}}_2}{ \rm{S}}}}$$ \end{document}  = 1.41 × 10¹⁵ cm⁻². As with SO₂, high H₂S epochs in Earth's history would have been low-UV epochs, and UV-sensitive prebiotic pathways might have been photon-starved.

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FIG. 18.

Biologically effective dose rates for UMP-X and CuCN3-Y as a function of \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document}$${N_{{{ \rm{H}}_2}{ \rm{S}}}}$$ \end{document} , normalized to the dose rates at \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document}$${N_{{ \rm{C}}{{ \rm{O}}_2}}}$$ \end{document} = 2.09 × 10²⁴ cm⁻². The solid line corresponds to 2× the SO₂ level of Rugheimer et al. (2015).

Similarly as with SO₂, the various BEDs fall off at different rates with increasing \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document}$${N_{{{ \rm{H}}_2}{ \rm{S}}}}$$ \end{document} .

Figure 19 plots the ratio between UMP-X and CuCN3-Y, for all X and Y. The CuCN3-254 dose rate falls off faster than the other dose rates, and the CuCN3-300 dose rate falls off slower. This is because H₂S absorbs much more strongly at λ < 254 nm than for λ > 254 nm. As presently defined, the CuCN3-254 dose rate can only utilize λ < 254 nm radiation; the UMP-X dose rates can make use of λ > 254 nm fluence, though at a much lower efficiency; and the CuCN3-300 dose rate can fully utilize the λ > 254 nm radiation. Hence, D _UMP-X/D _CuCN3-254 increases with \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document}$${N_{{{ \rm{H}}_2}{ \rm{S}}}}$$ \end{document} for all X, while D _UMP-X/D _CuCN3-300 decreases. Depending on the value of the CuCN3 photoionization step function, high H₂S environments may have been much more or much less clement environments for abiogenesis, as measured by the balance between glycosidic bond cleavage in UMP and aquated electron production from CuCN3 photoionization. We conclude that it is critical to empirically constrain the action spectra of these photoprocesses in order to make robust use of them in estimating the favorability of high-versus-low H₂S environments for abiogenesis.

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FIG. 19.

Ratio of biologically effective dose rates UMP-X/CuCN3-Y, for X = 193, 230, and 254 nm and Y = 254 and 300 nm, as a function of \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document}$${N_{{{ \rm{H}}_2}{ \rm{S}}}}$$ \end{document} .

5.9. O₂

O₂ is a robust UV shield. In the prebiotic era, O₂ is thought to have been generated from photolysis of CO₂ and H₂O, with sinks from reactions with reductants. Measurements of sulfur mass-independent isotope fractionation (SMIF) imply O₂ concentrations <1 × 10⁻⁵ PAL prior to 2.3 Ga (Pavlov and Kasting, 2002), and Fe and U-Th-Pb isotopic measurements from a 3.46 Ga chert are consistent with an anoxic ocean during that era (Li et al., 2013). Rugheimer et al. (2015) calculated an O₂ abundance corresponding to \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document}$${N_{{{ \rm{O}}_2}}}$$ \end{document} = 5.66 × 10¹⁹ cm⁻², consistent with the Pavlov and Kasting (2002) limit. We explore a range of O₂ columns corresponding to 10⁻⁵ to 10⁵× the Rugheimer et al. (2015) column. We note the O₂ columns exceeding the Rugheimer et al. (2015) column are disfavored by the SMIF modeling of Pavlov and Kasting (2002) and should therefore be taken as strictly illustrative. Figure 20 shows the resultant spectra.

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FIG. 20.

Surface radiances for an atmosphere with \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document}$${N_{{{ \rm{N}}_2}}}$$ \end{document} = 1.88 × 10²⁵ cm⁻² and varying levels of O₂, for a surface albedo corresponding to new snow and SZA = 0°. The line corresponding to the O₂ level calculated in the Rugheimer et al. (2015) model is presented as a solid, thicker line.

At the Rugheimer et al. (2015) level of \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document}$${N_{{{ \rm{O}}_2}}}$$ \end{document} = 5.66 × 10¹⁹ cm⁻², O₂ blocks fluence at λ < 183 nm. \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document}$${N_{{ \rm{C}}{{ \rm{O}}_2}}}$$ \end{document} = 2.09 × 10²¹ cm⁻² is required to achieve a similar cutoff; \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document}$${N_{{ \rm{C}}{{ \rm{O}}_2}}}$$ \end{document} ≥ 1.87 × 10²² is expected based on the climate models we have found so far. Therefore, at the O₂ levels expected from photochemical models, O₂ does not further constrain the surface UV environment assuming a climatically plausible CO₂ inventory. But O₂ is a substantially stronger UV absorber than CO₂, and it is possible that in comparatively low-CO₂/high-O₂ scenarios, it could affect the surface UV environment. \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document}$${N_{{{ \rm{O}}_2}}}$$ \end{document} = 5.66 × 10²¹ cm⁻² of O₂ cuts off more fluence than \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document}$${N_{{ \rm{C}}{{ \rm{O}}_2}}}$$ \end{document} = 1.87 × 10²² (the minimum proposed from climate models). Hence, at O₂ levels of \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document}$${N_{{{ \rm{O}}_2}}}$$ \end{document} ≥ 5.66 × 10²¹ cm⁻², O₂ may begin to have noticeable impact on the surface UV environment. However, it is unlikely that such high O₂ inventories were achieved at 3.9 Ga, given the strong reductant sink from vulcanogenic gases, the lack of a strong O₂ source, and the empirical constraint from SMIF. It is most likely that attenuation from O₂ would have been negligible compared to that from CO₂.

5.10. O₃

Similarly to O₂, O₃ is a well known, strong UV shield. It is generated from 3-body reactions involving photolysis of O₂; hence its abundance is sensitive to O₂ levels, with sinks from photolysis and reactions with reducing gases. Rugheimer et al. (2015) estimated an O₃ column density of \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document}$${N_{{{ \rm{O}}_3}}}$$ \end{document} = 1.92 × 10¹⁵ cm⁻² for the 3.9 Ga Earth. At this level, O₃ does not significantly modify the surface UV environment. Figure 21 shows the surface radiance spectra for \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document}$${N_{{{ \rm{O}}_3}}}$$ \end{document} = 1.92 × 10¹⁵–10¹⁸ cm^−2[ 17 ^]. As the atmospheric O₃ inventory increases, so does its attenuation of UV fluence; at levels approaching the modern day ( \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document}$${N_{{{ \rm{O}}_3}}}$$ \end{document}  = 1.92 × 10¹⁸ cm⁻²), it suppresses the BEDs of the photoprocesses we consider by 2 orders of magnitude relative to \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document}$${N_{{ \rm{C}}{{ \rm{O}}_2}}}$$ \end{document}  = 2.09 × 10²⁴ cm⁻². However, such O₃ levels would require a very high O₂ inventory. It is most likely that attenuation from O₃ would have been negligible compared to that from CO₂ and/or H₂O.

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FIG. 21.

Surface radiances for an atmosphere with \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document}$${N_{{{ \rm{N}}_2}}}$$ \end{document} = 1.88 × 10²⁵ cm⁻² and varying levels of O₃, for a surface albedo corresponding to new snow and SZA = 0°. The line corresponding to the O₃ level calculated in the Rugheimer et al. (2015) model is presented as a solid, thicker line.

A.1. N₂

We compute the Rayleigh scattering cross-section of N₂ using the formalism of Vardavas and Carver (1984): σ = 4.577 × 10⁻²¹ × KCF × [A(1 + B/λ²)]/λ⁴, where λ is in μm and KCF is the King correction factor, where KCF = (6 + 3δ)/(6–7δ), where δ is the depolarization factor. This approach accounts for the wavelength dependence of the index of refraction but assumes a constant depolarization factor. We take the values of the coefficients A and B from Keady and Kilcrease (2000) and the depolarization factor of δ = 0.0305 from Penndorf (1957).

We take empirically measured N₂ extinction cross sections shortward of 108 nm from Chan et al. (1993a), who measure the extinction cross section from 6.2 to 113 nm (≤5 nm resolution). No absorption is detected longward of 108 nm (Huffman, 1969; Chan et al., 1993a); hence, we take Rayleigh scattering to account for the extinction for λ > 108 nm. Figure A1 presents the total and Rayleigh scattering cross sections for N₂ from 100 to 900 nm.

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FIG. A1.

Total extinction and Rayleigh scattering cross sections for N₂.

A.2. CO₂

We compute the Rayleigh scattering cross section of CO₂ using the formalism of Vardavas and Carver (1984): σ = 4.577 × 10⁻²¹ × KCF × [A(1 + B/λ²)]/λ⁴, where λ is in μm and KCF is the King correction factor, where KCF = (6 + 3δ)/(6–7δ), where δ is the depolarization factor. This approach accounts for the wavelength dependence of the index of refraction but assumes a constant depolarization factor. We take the values of the coefficients A and B from Keady and Kilcrease (2000) and the depolarization factor of δ = 0.0774 from Shemansky (1972).

We take empirically measured cross sections shortward of 201.6 nm from Huestis and Berkowitz (2010). Huestis and Berkowitz (2010) reviewed existing measurements of extinction cross sections for CO₂ and aggregated the most reliable ones into a single spectrum (<1 nm resolution). They tested their composite spectrum with an electron-sum rule and found it to agree with the theoretical expectation to 0.33%. From 201.75 to 300 nm, the measurements of Shemansky (1972) provide coverage. However, the resolution of these data ranges from 0.25 nm from 201.75–203.75 nm to 12–25 nm from 210–300 nm. Further, Shemansky (1972) found that essentially all extinction at wavelengths longer than 203.5 nm is due to Rayleigh scattering (Ityaksov et al., 2008, derive similar results). Therefore, we adopt the measurements of Shemansky (1972) from 201.75 to 203.75 nm and take Rayleigh scattering to describe CO₂ extinction at longer wavelengths. Figure A2 presents the total and Rayleigh scattering cross sections for CO₂ from 100 to 900 nm.

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FIG. A2.

Total extinction and Rayleigh scattering cross sections for CO₂.

A.3. H₂O

We compute the Rayleigh scattering cross section of H₂O following the methodology of von Paris et al. (2010) and Kopparapu et al. (2013). We compute the wavelength-dependent index of refraction of water vapor using the observation by Edlén (1966) that the refractivity of water vapor is 15% less than that of air (itself 1–2% water vapor by volume). We compute the refractivity of standard air from the formulae of Bucholtz (1995). von Paris et al. (2010) and Kopparapu et al. (2013) used a value for the depolarization factor of 0.17, based on the work of Marshall and Smith (1990); however, this value was measured for liquid water. We instead adopt δ = 0.000299 from the work of Murphy (1977). We note that the equations of Bucholtz (1995) have a singularity at 0.15946 μm (159.46 nm) due to a (39.32957−1/λ²) (λ in μm) term in the denominator, which causes the Rayleigh scattering cross section to go to infinity at that value. To circumvent this problem, in this term only, we adopt λ = 0.140 μm for 0.140 μm < λ < 0.15946 μm, and λ = 0.180 μm for 0.15946 μm < λ < 0.180 μm. This removes the singularity from the Rayleigh scattering curve (see Fig. A3).

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FIG. A3.

Total extinction and Rayleigh scattering cross sections for H₂O.

We take empirically measured cross sections shortward of 121 nm from the dipole (e,e) spectroscopy measurements of Chan et al. (1993b) (≤6 nm resolution). From 121 to 198 nm, we use the compilation of Sander et al. (2011), who surveyed the measurements of H₂O vapor cross section data to arrive at a recommended tabulation of cross sections for planetary science studies (<1 nm resolution). From 396 to 755 nm, we use the gas-cell absorption results of Coheur et al. (2002) and Fally et al. (2003), as combined by the MPI Atlas (mode of 0.0073 nm resolution). From 775 to 1081 nm, we use the measurements of Mérienne et al. (2003) (mode of 0.0077 nm resolution). At all wavelengths not covered by these data sets, we take the extinction to be due to Rayleigh scattering. Figure A3 presents the total and Rayleigh scattering cross sections for H₂O from 100 to 900 nm.

A.4. CH₄

We compute the Rayleigh scattering cross section of CH₄ using the formalism of Sneep and Ubachs (2005). This method accounts for the wavelength dependence of the index of refraction and assumes a constant depolarization factor of 0.0002, which is equal to the depolarization factor of CCl₄, which has a similar structure. Comparing their computations to data, Sneep and Ubachs (2005) found that their formalism overestimates the absorption cross section of CH₄ at 532.5 nm by 15%; therefore, we follow Kopparapu et al. (2013) in scaling down the Sneep and Ubachs (2005) estimate by 15% at all wavelengths.

We take empirically measured cross sections shortward of 165 nm from the dipole (e,e) spectroscopy measurements of Au et al. (1993) (<5 nm resolution for λ < 113 nm, 610 nm resolution thereafter). Absorption due to CH₄ has not been detected from 165 to 400 nm (Mount et al., 1977; Chen and Wu, 2004). Rayleigh scattering is taken to account for extinction at wavelengths longer than 165 nm. Figure A4 presents the total and Rayleigh scattering cross sections for CH₄ from 100 to 900 nm.

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FIG. A4.

Total extinction and Rayleigh scattering cross sections for CH₄.

A.5. SO₂

We compute the Rayleigh scattering cross section of O₃ using the formalism of Keady and Kilcrease (2000): σ = 1.306 × 10²⁰ × KCF × α ² /λ⁴, where σ is in cm² and λ is in μm, where KCF refers to the King correction factor, KCF =(6 + 3.δ)/(6–7δ) (Sneep and Ubachs, 2005), and where α refers to the polarizability of the molecule and δ is the depolarization factor. Bogaard et al. (1978) listed the polarizability α and depolarization ratio δ for SO₂ at 488, 514.5, and 632.8 nm. We use α _488nm and δ _488nm for λ < 501.25 nm, α _514.5nm and δ _514.5nm for 501.25 < λ < 573.65 nm, and α _632.8nm and δ _632.8nm for 573.65 nm < λ nm.

We take empirically measured cross sections of SO₂ shortward of 106.1 nm from the dipole (e,e) spectroscopy measurements of Feng et al. (1999a) (<5 nm resolution). From 106.1 to 403.7 nm, we take the cross sections for SO₂ extinction from the compendium of SO₂ cross sections of Manatt and Lane (1993) (0.1 nm resolution). Manatt and Lane (1993) evaluated extant UV cross sections for SO₂ extinction and aggregated the most reliable into a single compendium covering this wavelength range at 293 ± 10 K. From 403.7 to 416.7 nm, we take the Fourier transform spectrometer measurements of Vandaele et al. (2009) (<1 nm resolution). Many of the cross sections reported in this data set are negative, corresponding to an increase in flux from traversing a gas-filled cell. These cross sections are deemed unphysical and removed from our model. Figure A5 presents the total and Rayleigh scattering cross sections for SO₂ from 100 to 900 nm.

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FIG. A5.

Total extinction and Rayleigh scattering cross sections for SO₂.

A.6. H₂S

We compute the Rayleigh scattering cross section of H₂S using the formalism of Keady and Kilcrease (2000): σ = 1.306 × 10²⁰ × KCF × α ²/λ⁴, where σ is in cm² and λ is in μm, where KCF refers to the King correction factor, KCF = (6 + 3.δ)/(6–7δ) (Sneep and Ubachs, 2005), and where α refers to the polarizability of the molecule and δ is the depolarization factor. Bogaard et al. (1978) listed the polarizability α and depolarization ratio δ for H₂S at 488, 514.5, and 632.8 nm. We use α _488nm and δ _488nm for λ < 501.25 nm, α _514.5nm and δ _514.5nm for 501.25 < λ < 573.65 nm, and α _632.8nm and δ _632.8nm for 573.65 nm < λ nm.

We take empirically measured cross sections of H₂S shortward of 159.465 nm from the dipole (e,e) spectroscopy measurements of Feng et al. (1999b) (<10 nm resolution). From 159.465 to 259.460 nm, we take the cross sections for H₂S extinction from the gas cell absorption measurements of Wu and Chen (1998) (0.06 nm resolution), as recommended by Sander et al. (2011). From 259.460 to 370.007 nm, we take the gas cell absorption measurements of Grosch et al. (2015) (0.018 nm resolution). Many of the cross sections reported in this data set are negative, corresponding to an increase in flux from traversing a gas-filled cell. These cross sections are deemed unphysical and removed from our model. Figure A6 presents the total and Rayleigh scattering cross sections for H₂S from 100 to 900 nm.

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FIG. A6.

Total extinction and Rayleigh scattering cross sections for H₂S.

A.7. O₂

We compute the Rayleigh scattering cross section of O₂ using the formalism of Vardavas and Carver (1984): σ = 4.577 × 10⁻²¹ × KCF × [A(1 + B/λ²)]/λ⁴, where λ is in μm and KCF is the King correction factor, where KCF = (6 + 3δ)/(6 − 7δ), where δ is the depolarization factor. This approach accounts for the wavelength dependence of the index of refraction but assumes a constant depolarization factor. We take the values of the coefficients A and B from Keady and Kilcrease (2000) and the depolarization factor of δ = 0.054 from Penndorf (1957).

We take extinction cross sections of O₂ shortward of 108.75 nm from the work of Huffman (1969) (<12.6 nm resolution). Huffman (1969) reviewed previous literature measurements of vacuum UV extinction cross sections of O₂ and provided recommended values for aeronomic studies. From 108.75 to 130.0 nm, we use the gas absorption cell measurements for ground-state O₂ of Ogawa and Ogawa (1975) (<0.2 nm resolution). From 130.04 to 175.24 nm, we use the absorption cell measurements of Yoshino et al. (2005) (<0.42 nm resolution). From 179.2 to 202.6 nm, we use the gas absorption cell measurements of Yoshino et al. (1992) (300 K, 0.01 nm resolution). Duplicate values in this database (presumably due to rounding error) were removed. From 205 to 245 nm, we use the compilation of Sander et al. (2011), recommended by the Jet Propulsion Laboratory for use in planetary atmospheres studies (<1 nm resolution). From 245 to 294 nm, we use the gas absorption cell extinction cross sections measured by Fally et al. (2000) (<0.008 nm resolution.) From 650 to 799.6, we use the gas-cell absorption measurements of the SCIAMACHY calibration data from Bogumil et al. (2003) (<0.21 nm resolution,). As in the case of SO₂, several of the cross sections reported for this data set are negative; these cross sections are rejected as unphysical and removed from the model. Figure A7 presents the total and Rayleigh scattering cross sections for O₂ from 100 to 900 nm. We note that the cross sections presented here are for O₂ extinction only. Extinction due to molecular complexes, for example, the O₂-O₂ complexes observed by Greenblatt et al. (1990), are not included in our parametrization. This does not materially impact the fidelity of our model since the cross sections associated with these complexes are small at relevant partial pressures of O₂ (<3 × 10⁻²⁶ cm² for 1 atm of O₂).

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FIG. A7.

Total extinction and Rayleigh scattering cross sections for O₂.

A.8. O₃

We take the Rayleigh scattering cross section of O₃ using the formalism of Keady and Kilcrease (2000): σ = 1.306 × 10²⁰ × KCF × α ²/λ⁴, where σ is in cm² and λ is in μm, where KCF refers to the King correction factor, KCF = (6 + 3.δ)/(6–7δ) (Sneep and Ubachs, 2005), and where α refers to the polarizability of the molecule. From Brasseur and De Rudder (1986), KCF = 1.06 for ozone. We adopt α = 3.21 × 10⁻²⁴ cm³ based on the average electric dipole polarizability listed for ground state O₃ in Miller (2009). This formulation assumes constant polarizability (index of refraction) and depolarization factor.

We take empirically measured cross sections of O₃ shortward of 110 nm from the gas cell absorption measurements of Ogawa and Cook (1958) (<9.5 nm resolution). We take cross sections from 110 to 172 nm from the gas cell absorption measurements of Mason et al. (1996) (<2 nm resolution for λ ≤ 139.31, 3–17 nm resolution for λ = 139.31–172 nm). Following the recommendations of Sander et al. (2011), we take cross sections from 185 to 213 nm from the gas cell absorption measurements of Molina and Molina (1986) (0.5 nm resolution). Finally, we take the cross sections for 213–1100 nm from the gas cell absorption measurements recently published in joint papers by Serdyuchenko et al. (2014) and Gorshelev et al. (2014) (0.02–0.06 nm resolution, interpolated to 0.01 nm; 293 K). Gorshelev et al. (2014) compared this data set to previous measurements and find good agreement. Figure A8 presents the total and Rayleigh scattering cross sections for O₃ from 100 to 900 nm.

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FIG. A8.

Total extinction and Rayleigh scattering cross sections for O₃.

B.1. Ocean

We approximate the albedo of pure (ice- and land-free) ocean via the methodology of Briegleb et al. (1986), who in turn rely upon Payne (1972). Briegleb et al. (1986) took α _dif = 0.06 and α _dir = 2.6/(μ ^1.7 + 0.065) + 15(μ − 0.1)(μ − 0.5)(μ − 1.0).

Payne (1972) measured the reflectance of the ocean surface under a variety of conditions using a spectrometer with uniform sensitivity coverage from 280 to 2800 nm. Hence, albedos calculated from this work represent a fit to the mean albedo integrated 280–2800 nm, which includes 98% of solar flux. Briegleb et al. (1986) argued that the variation in ocean albedo as a function of wavelength is modest, due to the modesty of variations of the index of refraction of water across this wavelength range. Briegleb et al. (1986) modeled this variation and found the spectral corrections to the oceanic albedo due to the wavelength dependence of the optical properties of water to be +0.02 for 200–500 nm, −0.003 for 500–700 nm, −0.007 for 700–850 nm, and −0.007 for 850 nm to 4 μm. They calculated these corrections to have minimal impact on the TOA broadband albedo and, hence, ignored them.

However, for our applications (computing the spectral radiance over different surface environments), these corrections can be significant, especially in the case of diffuse radiation, where the shortwave correction is 1/3 of the diffuse albedo. Hence, we include these corrections by adding a correction term α _corr to α _dir and α _dif. Lacking any better assumption, we extend the 200–500 nm value to all wavelengths <500 nm. Hence, α _corr = 0.02 for λ < 500 nm, α _corr = −0.003 for λ = 500–700 nm, and α _corr = −0.007 for λ > 700 nm.

B.2. Snow

We approximate the albedo of pure snow using the methodology outlined by Briegleb and Ramanathan (1982) and reviewed by Coakley (2003). This methodology treats new-fallen and old snow separately (new-fallen snow is brighter).

From Table 1 of Briegleb and Ramanathan (1982), for new-fallen snow: \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} \begin{align*}{ \alpha _{{ \rm{dif}}}} ( \lambda { \rm{ }} = { \rm{ }}200 - 500 \;{ \rm{nm}} ) { \rm{ }} = { \rm{ }}0.95 \end{align*} \end{document} \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} \begin{align*}{ \alpha _{{ \rm{dif}}}} ( \lambda { \rm{ }} = { \rm{ }}500 - 700 \;{ \rm{nm}} ) { \rm{ }} = { \rm{ }}0.95 \end{align*} \end{document} \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} \begin{align*}{ \alpha _{{ \rm{dif}}}} ( \lambda { \rm{ }} = { \rm{ }}700 - 4000 \;{ \rm{nm}} ) { \rm{ }} = { \rm{ }}0.65 \end{align*} \end{document}

Whereas for old snow: \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} \begin{align*}{ \alpha _{{ \rm{dif}}}} ( \lambda { \rm{ }} = { \rm{ }}200 - 500 \;{ \rm{nm}} ) { \rm{ }} = { \rm{ }}0.76 \end{align*} \end{document} \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} \begin{align*}{ \alpha _{{ \rm{dif}}}} ( \lambda { \rm{ }} = { \rm{ }}500 - 700 \;{ \rm{nm}} ) { \rm{ }} = { \rm{ }}0.76 \end{align*} \end{document} \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} \begin{align*}{ \alpha _{{ \rm{dif}}}} ( \lambda { \rm{ }} = { \rm{ }}700 - 4000 \;{ \rm{nm}} ) { \rm{ }} = { \rm{ }}0.325 \end{align*} \end{document}

As before, we extend the 200–500 nm value to all λ < 200.

To compute the direct albedo, we follow Briegleb and Ramanathan (1982) in using the formalism of Dickinson et al. (1981) to account for zenith angle dependence: α _dir = α _dif + (1 − α _dif) × 0.5 × [3/(1 + 4μ) − 1] for μ ≤ 0.5, and α _dir = α _dif for μ > 0.5.

B.3. Desert

We approximate the albedo of desert environments following the methods of Briegleb et al. (1986), as reviewed by Coakley (2003). Following Tables 1 and 2 of Briegleb et al. (1986), \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} \begin{align*}{ \alpha _{{ \rm{dif}}}} ( \lambda { \rm{ }} < { \rm{ }}500 \;{ \rm{nm}} ) = { \rm{ }}0.5{ \rm{ }} \times { \rm{ }}0.28{ \rm{ }} + { \rm{ }}0.5{ \rm{ }} \times { \rm{ }}0.15{ \rm{ }} = { \rm{ }}0.22 \end{align*} \end{document} \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} \begin{align*}{ \alpha _{{ \rm{dif}}}} ( \lambda { \rm{ }} = { \rm{ }}500 - 700 \;{ \rm{nm}} ) = { \rm{ }}0.5{ \rm{ }} \times { \rm{ }}0.42{ \rm{ }} + { \rm{ }}0.5{ \rm{ }} \times { \rm{ }}0.25{ \rm{ }} = { \rm{ }}0.34 \end{align*} \end{document} \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} \begin{align*}{ \alpha _{{ \rm{dif}}}} ( \lambda { \rm{ }} = { \rm{ }}700 - 850 \;{ \rm{nm}} ) = { \rm{ }}0.5{ \rm{ }} \times { \rm{ }}0.50{ \rm{ }} + { \rm{ }}0.5{ \rm{ }} \times { \rm{ }}0.35{ \rm{ }} = { \rm{ }}0.43 \end{align*} \end{document} \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} \begin{align*}{ \alpha _{{ \rm{dif}}}} ( \lambda { \rm{ }} = { \rm{ }}850 - 4000 \;{ \rm{nm}} ) = { \rm{ }}0.5{ \rm{ }} \times { \rm{ }}0.50{ \rm{ }} + { \rm{ }}0.5{ \rm{ }} \times { \rm{ }}0.40{ \rm{ }} = { \rm{ }}0.45 \end{align*} \end{document}

where we have again extended the Briegleb et al. (1986) 200–500 nm albedos to all wavelengths <200 nm.

To compute the direct albedo, we follow Briegleb et al. (1986) in including zenith angle dependence by writing α _dir = α _dif × (1 + d)/(1 + 2dμ), where d is a parameter derived from a fit to data for different terrain types. For desert, d = 0.4.

B.4. Tundra

We approximate the albedo of tundra environments following the methods of Briegleb et al. (1986), as reviewed by Coakley (2003). \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} \begin{align*}{ \alpha _{{ \rm{dif}}}} ( \lambda { \rm{ }} < { \rm{ }}500 \;{ \rm{nm}} ) = { \rm{ }}0.5{ \rm{ }} \times { \rm{ }}0.04{ \rm{ }} + { \rm{ }}0.5{ \rm{ }} \times { \rm{ }}0.07{ \rm{ }} = { \rm{ }}0.06 \end{align*} \end{document} \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} \begin{align*}{ \alpha _{{ \rm{dif}}}} ( \lambda { \rm{ }} = { \rm{ }}500 - 700 \;{ \rm{nm}} ) = { \rm{ }}0.5{ \rm{ }} \times { \rm{ }}0.10{ \rm{ }} + { \rm{ }}0.5{ \rm{ }} \times { \rm{ }}0.13{ \rm{ }} = { \rm{ }}0.12 \end{align*} \end{document} \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} \begin{align*}{ \alpha _{{ \rm{dif}}}} ( \lambda { \rm{ }} = { \rm{ }}700 - 850 \;{ \rm{nm}} ) = { \rm{ }}0.5{ \rm{ }} \times { \rm{ }}0.25{ \rm{ }} + { \rm{ }}0.5{ \rm{ }} \times { \rm{ }}0.19{ \rm{ }} = { \rm{ }}0.22 \end{align*} \end{document} \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} \begin{align*}{ \alpha _{{ \rm{dif}}}} ( \lambda { \rm{ }} = { \rm{ }}850 - 4000 \;{ \rm{nm}} ) = { \rm{ }}0.5{ \rm{ }} \times { \rm{ }}0.25{ \rm{ }} + { \rm{ }}0.5{ \rm{ }} \times { \rm{ }}0.28{ \rm{ }} = { \rm{ }}0.27 \end{align*} \end{document}

where we have again extended the Briegleb et al. (1986) 200–500 nm albedos to all wavelengths <200 nm.

To compute the direct albedo, we follow Briegleb et al. (1986) in including zenith angle dependence by writing α _dir = α _dif × (1 + d)/(1 + 2dμ), where d is a parameter derived from a fit to data for different terrain types. For tundra, d = 0.1.