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 The effects of sulfate aerosols produced as a result of an asteroid impact on the ultra-violet (UV) radiation are investigated by radiative transfer calculations. After an impact, a reduction in the solar incident radiation and ozone depletion are expected to occur, each of which, in turn, are counteract their on effects on the UV radiation. We estimate reasonable ranges for the amounts of sulfate aerosols and ozone depletion after an impact, and calculate the UV radiation at the Earth's surface, besides absorption in the stratosphere, by changing the aerosol and ozone concentrations within the ranges. The calculation results reveal that the UV-B (0.28–0.315 μm) radiation depends on both aerosol and ozone concentrations. The reflection of UV-B radiation by sulfate aerosols cancels out the increase in surface UV-B radiation due to ozone depletion. This study suggests that, immediately after the Chicxulub impact event, the UV-B radiation at the Earth's surface would not increase as compared to the pre-impact levels, since large amount of sulfate aerosols would exist in the stratosphere. Several years after the impact, the UV-B radiation would increase, because most of the sulfate aerosols would be removed from the atmosphere but their amount would still be enough to destroy ozone and keep it below the harmful level for terrestrial life. In case of the Chicxulub impact, an increase in the UV-B radiation would have occurred several years after the impact and might have contributed to the mass extinction at the end of the Cretaceous period.
 An impact of a large asteroid would abruptly change the environment of the Earth. For example, the Chicxulub impact event that occurred near the Cretaceous-Tertiary boundary might lead to the mass extinction of life [e.g., Alvarez et al., 1980]. One of the significant phenomena that would arise as a result of such an impact is the massive production of sulfate aerosols in the stratosphere. It is suggested that a large amount of sulfuric gases would be injected into the middle and upper stratosphere by plumes following the explosion after the impact [Pierazzo et al., 1998]. The ejected sulfurous acid gases would eventually be oxidized and converted to sulfate aerosols in the stratosphere [Turco et al., 1979]. The amount of aerosol may be extremely higher than that in an ordinary atmosphere. [e.g., Pierazzo et al., 2003].
 A primary effect of the sulfate aerosols in the stratosphere is the reduction of solar energy reaching the Earth's surface, especially in the ultra-violet (UV) and visible region. A large amount of impact-induced aerosols is expected to cause a tremendous temperature drop in the troposphere and to inhibit photosynthesis by plants. In addition, an impact is expected to generate a large amount of nitrogen oxide, which depletes the ozone layer. Toon et al.  suggested that the Chicxulub impact might have caused a reduction in the amount of ozone by about 50%. Sulfate aerosols also aid in accelerating the conversion of nitrogen oxides to nitric acid. This effect activates chlorine and results in destroying the ozone if chlorine is present in sufficient amounts in the stratosphere [Hanson et al., 1994; Tie and Brasseur, 1995]. For the Chicxulub impact event, the amounts of Cl injected by the impact was estimated to be enough for destroying all the stratospheric ozone [Kring, 1999]. Several numerical experiments and observations have also provided evidences of the increases in reactive chlorine and the ozone depletion after the eruption of Pinatubo in 1991 [e.g., Tie et al., 1994; Solomon et al., 1996; Randel et al., 1995]. Ozone depletion in the stratosphere leads to an increase in UV radiation on the surface of the Earth. In particular, the UV-B wavelengths (0.28–0.315 μm), which is harmful radiation for animals and plants, are more sensitive to the amount of ozone rather than the UV-A (0.315–0.40 μm) radiation, which is less dangerous. However, an increase in UV radiation by ozone depletion opposes the reduction in UV radiation by aerosols. Besides, sulfate aerosols can enhance the absorption of UV radiation in the stratosphere but the ozone depletion may reduce the absorption. These effects also counteract each other. Therefore, it is not clear how the sulfate aerosols effect UV radiation under the conditions of ozone depletion.
 The purpose of this study is to quantitatively evaluate the effects of an impact-induced sulfate aerosols on UV radiation at the Earth's surface and in the atmosphere, via radiative transfer calculations, by taking into account the changes of both ozone and aerosol amount.
2. Atmospheric Models After an Asteroid Impact
 We carry out radiative transfer calculations for the atmosphere after a large asteroid impact, for evaluating the UV radiation as a function of the concentrations of both ozone and aerosols. We use the discrete-ordinate scheme [Nakajima and Tanaka, 1986; Nakajima and Tanaka, 1988], which allows us to take into account the radiation processes with aerosols as well as air molecules. This method assumes that the atmosphere is horizontally homogeneous. Since chemical processes involved in the stratospheric ozone depletion following an impact has a complex nature, it is difficult to determine the precise amount of ozone and its vertical profile in the atmosphere. Further, an estimation of the relation between the concentrations of ozone and the aerosols is beyond the scope of this study. Therefore, we simply assume plausible ranges for the concentrations of ozone and aerosols in the model atmosphere independent of each other. The range for the concentration of the aerosol amount was estimated from studies of aerosol production due to impacts and that for ozone amount was deduced from observations and numerical experiments of ozone depletion following a volcanic eruption.
 The amount of released sulfur depends on various factors, such as diameter, porosity of the impact object, velocity, chemical compositions at the impact site, and so on. Hydrocode simulations [Pierazzo et al., 1998] provided the amounts of sulfur injected into the atmosphere as a result of an impact. The mass of the sulfur gas released by an object whose size was enough to create a transient cavity of the size of Chicxulub one (about 100 km), was estimated to be in the range from about 25 Gt to 200 Gt, based on the factors mentioned above. Pierazzo et al.  estimated the amount of aerosols after the Chicxulub impact using the Sulfate Aerosol Model (SAM), which was able to simulate the evolution of sulfate aerosols. As an intermediate case, if 100 Gt of sulfur gas, having a composition of 20% SO3 and 80% SO2 is released uniformly in the whole stratosphere, the initial amount of sulfate aerosols whose solution ratio of sulfate to water is 75 wt% could reach up to about 10−2 g/cm2. Pierazzo et al.  also suggested that the radiative forcing by the injected sulfate aerosols would be saturated at 100 Gt of sulfur gas. Sulfate aerosols will be removed from the stratosphere with time and fall into the troposphere, where the sulfate aerosols are considered to rain out immediately. Therefore, we assume that sulfate aerosols only exist in the stratosphere and set the range of the columnar aerosol mass to be between 10−6 and 10−2 g/cm2. A columnar aerosol mass of about 3 × 10−6 g/cm2 corresponds to about 0.1 of the optical thickness at the wavelength of 0.5 μm. In the present atmosphere, the maximum for the optical thickness of aerosols in the visible region is of the order of 0.1.
 An impact leads to deposition of a large amount of energy into the atmosphere and will raise temperature of the atmosphere [Kring and Durda, 2002]. In general, increase of air temperature results in evaporation of sulfate aerosols [Hamill et al., 1997]. This study targets the atmosphere after sufficient cooling has taken place. The deposition of energy is also expected to generate fires, which produces large amounts of soot [e.g., Wolbach et al., 1988]. Soot absorbs radiation in the UV region and leads to a reduction in the downward flux at the surface and the absorption of UV radiation in the stratosphere. However, the period for the lasting effects of soot will be shorter than that for sulfate aerosols, because soot is expected to fall down more quickly than sulfate aerosols. Therefore, we neglect the effects of soot in this study.
 It is also difficult to estimate the amount of ozone depletion after an impact. A numerical simulation [Tie et al., 1994] revealed that large decreases in ozone after the Mt. Pinatubo eruption in 1991 has occurred during winter at the middle stratosphere of the high latitude northern hemisphere. For example, during the year following this eruption, the change in ozone amount at this area and the season reached about −18% of the pre-eruption level and the aerosol surface area density was about 15 μm2/cm3. If the number density of the aerosol is constant in the aerosol layer, 15 μm2/cm3 of the aerosol surface area density corresponds to an order of 10−6 g/cm2 in the columnar aerosol mass. In the second year, the change in the concentration of ozone at this area and for this season was about −12%, with the aerosol surface area density being ∼10 μm2/cm3: In the third year following the eruption, the change in ozone amount was about −6% and the corresponding aerosol surface area density was ∼5 μm2/cm3. Satellite observations also presented similar decreases in ozone after the Mt. Pinatubo eruption [e.g., Randel et al., 1995]. It suggests that even the aerosol amount of the order of 10−6 g/cm2 can cause about 20% decreases in the ozone if other conditions (such as temperature and chemical properties of the atmosphere) are appropriate for ozone destruction. Nitrogen oxide generated by an impact will also cause additional destruction of the ozone. Therefore, we set the range of the ratio of ozone amount to that of the present-day value to be between 100% and 20%.
 We assume the relative shape of the ozone profile to be similar to that of the US-standard atmosphere, in which the maximum of the number concentration of ozone is at the altitude of ∼20 km, and only its amount is varied. This means that the ratio of the amount of ozone to its present-day value would be constant throughout the height regime. It is assumed that the vertical profiles of other radiatively active molecular species in the atmosphere are the same as those seen in the present-day atmosphere and without the existence of any water/ice cloud. The optical parameters of a sulfate aerosol, such as the absorption coefficients and scattering phase function, were determined following Mie theory, and with reference to the refractive index data obtained from laboratory observations [Palmer and Williams, 1975]. The solution ratio of sulfate to water was assumed to be 75 wt%. The number-size distribution for sulfate aerosols was assumed to obey a log-normal distribution function with an effective radius of 0.2 μm and a standard deviation of 2.0. These are representative for sulfate aerosols following a volcanic eruption [e.g., Goodman et al., 1994]. The assumed effective radius (0.2 μm), in turn makes the reflectance of the aerosol layer largest (and the transmittance smallest). The spectrum of the solar radiation at the top of the atmosphere used in the radiative transfer calculation is assumed to be similar to the present-day values.
3. Effects of Aerosol and Ozone Depletion
 First, we calculate the downward fluxes of the UV radiation at the Earth's surface in the model atmosphere, which contains sulfate aerosols between altitudes of 15 km and 30 km (corresponding to the middle and upper stratosphere). In the present (normal) atmosphere, the formation of sulfate aerosols occurs almost at these altitudes, because of the high temperature above this layer leading to the evaporation of sulfate aerosols [Hamill et al., 1997]. However, the reflectance of the aerosol layer for the UV radiation is almost independent of altitude and the thickness of the layer. In the aerosol layer, the number density of aerosols was simply assumed to be constant in the vertical direction and also that the troposphere is devoid of any aerosols. The incident solar zenith angle was set at 30°. Figure 1 shows the downward fluxes at the Earth's surface, for the wavelengths of UV-B region and UV-A regimes, as a function of the columnar aerosol mass and the ratio of the concentration of ozone to its current value. The “columnar aerosol mass” gives the total mass of aerosols existing in a vertical column of the atmosphere. The surface downward fluxes for the atmosphere that has no aerosol and no ozone depletion are about 1.4 W/m2 for the UV-B region and about 63 W/m2 for the UV-A region (hereinafter, we refer to these flux values as “unperturbed case”). Figure 1 indicates that the UV-B radiation at the Earth's surface depends on the concentrations of both aerosols as well as ozone. When the concentration of the aerosol is smaller than about 10−5 g/cm2, the surface UV-B radiation is more sensitive to the ozone amount as compared to that of aerosol. When the columnar aerosol mass is between ∼10−5 g/cm2 and 10−4 g/cm2, the ozone depletion as well as the sulfate aerosols are seen to be important for the UV-B radiation. Thus, the critical amount of ozone that makes the UV-B radiation exceed the unperturbed case is dependent on the amount of aerosol. However, when the columnar aerosol mass is larger than about 2 × 10−4 g/cm2, corresponding to an aerosol optical thickness at wavelength of 0.5 μm of about 10, the downward flux of the UV-B region is found to be smaller than the unperturbed case, even if the ratio of the ozone amount to its current value is 0.2. The combination of the values of aerosol mass and the amount of ozone, which makes the UV-B radiation equivalent to the unperturbed case (thick line in Figure 1), is found to be almost independent of the solar zenith angle. On the other hand, the surface UV-A radiation is almost independent of the ozone amount, especially when the columnar aerosol mass is larger than 10−5 g/cm2.
 Next, we estimate the effects on the absorption of UV-B radiation in the aerosol layer (15 to 30 km) and in the atmosphere above the aerosol layer (30 to 50 km), as a function of the concentration of aerosols and ozone. The absorbed energy in the case of the UV-B radiation for the unperturbed case within the aerosol layer and above the aerosol layer are about 4.1 W/m2 and 7.3 W/m2, respectively. Figure 2 shows that when the columnar aerosol mass is larger than 10−4 g/cm2, the absorption in the aerosol layer (Figure 2a) decreases with the increase in the aerosol amount. This is because of the fact that the increased amount of aerosols would reflect a large part of the incident solar UV-B radiation before it gets absorbed by ozone in the aerosol layer. The maximum absorption in the aerosol layer occurs near where the ratio of the ozone concentrations is 0.4 and the columnar aerosol mass, 10−4 g/cm2. This is because of the decrease in absorption as a result of the ozone depletion above the aerosol layer and in turn causes an increase of incident UV-B radiation into the aerosol layer. However, when the columnar aerosol mass is larger than ∼10−4 g/cm3, the absorption in the aerosol layer has little dependence on changes in the ozone amount. On the other hand, the UV-B absorption above the aerosol layer (Figure 2b) linearly varies with the amount of ozone. The absorption also increases with an increase in the aerosol amount, and this dependency becomes larger as the columnar aerosol mass becomes larger than 10−4 g/cm2. Further, when the columnar aerosol mass is larger than ∼10−3 g/cm2, the absorption above the aerosol layer is found to be larger than that within the aerosol layer. This suggests that the UV-B radiation reflected by the aerosol layer is the dominant factor for the absorption of UV-B radiation, provided a large amount of aerosols is injected.
4. Discussion and Conclusions
 An asteroid impact is considered to affect UV radiation through two counteracting phenomena, the production of sulfate aerosols and the ozone depletion. This study indicated that the UV-B radiation is sensitive to both of the effects, especially between ∼10−5 g/cm2 – 10−4 g/cm2 of the columnar aerosol mass, and also suggested the combination of the aerosol and ozone concentrations that cause the UV-B radiation at the surface to increase as compared to the unperturbed case. For example, if the columnar aerosol mass is about 6 × 10−5 g/cm2 (which corresponds to an optical thickness at wavelength of 0.5 μm of about 2), the UV-B radiation is equivalent to the unperturbed case when the ozone amount is half of its current value. Similarly, there is a 20% increase of the UV-B radiation at the Earth's surface as compared to the unperturbed case, if there is a ∼60% decrease of ozone from its current value. On the other hand, if the columnar aerosol mass is ∼10−6 g/cm2, a ∼20% decrease of ozone from its current value results in about 20% increase of the UV-B radiation. As mentioned before, 10−6 g/cm2 of the columnar aerosol mass has the potential to destroy ∼20% of the ozone, if the chemical conditions in the stratosphere are sufficient for ozone destruction. Several field experiments have investigated the effects of UV-B radiation on some crops, and have revealed that a 20% increase in UV-B radiation caused a significant decrease in the productivity [e.g., Caldwell et al., 1998]. This implies that ozone depletion by such an impact is dangerous for lives on Earth if the amount of sulfate aerosols is relatively small. However, when the columnar aerosol mass is larger than about ∼2 × 10−4 g/cm2, the increase in UV-B radiation due to ozone depletion is nullified by the reflection of sulfate aerosols even when 80% of the ozone is destroyed.
 Our calculation results also indicate that the absorption of UV-B radiation in the stratosphere depends on the concentration of both aerosols and the ozone. Sulfate aerosols tend to enhance the absorption of UV-B radiation above the aerosol layer, thus compensating the decrease in absorption due to ozone depletion. If sulfate aerosols did not exist in the stratosphere, the ozone depletion would reduce the absorption of UV-B and cause cooling of the stratosphere. An increase in the absorption of radiation in the stratosphere is expected to cause heating of the stratosphere, and then the circulation of the atmosphere and global climate will finally be changed [e.g., Kirchner et al., 1999]. This implies that not only the ozone depletion, but also the existence of sulfate aerosols is important for determining the heat budget in the stratosphere and the climate of the Earth following an impact.
 We investigated the perturbations in the environment following the Chicxulub impact event. Figure 3 is a schematic of the change in the concentration of aerosols and ozone with time. The sulfate aerosols are expected to be removed from the stratosphere by diffusion or downward gravitational motion gradually over several years. Pierazzo et al.  provided a scenario for the change in aerosol amount following the Chicxulub impact event, from simulations using a SAM. During the time, and after four years following the impact, the initial amount of sulfate aerosols, (∼10−2 g/cm2), would drop to less than 10−4 g/cm2. About 6 years after, the columnar aerosol mass became less than 10−6 g/cm2. Our calculations suggest that during the first 4 years after the impact, the increases in UV-B radiation at the Earth's surface due to ozone depletion was not significant. However, the amount UV-B radiation was seen to differ from the unperturbed case only ∼4 years following the impact. If the ozone amount was 20% of its current value, the UV-B radiation would rise by a factor of about 1.5 as compared to the unperturbed case. Six years later, the UV-B radiation would be at the same level even if the ozone amount would recover to 60% of its current value. Such a harmful condition for terrestrial life with increased UV-B radiation might continue until the ozone amount was recovered to the pre-impact levels. This implies that the sulfate aerosols might still have an effect on the mass extinction through ozone depletion, even after the solar incident radiation at the surface returned to almost normal.
 The present study was supported by the 21st Century COE Program, Advanced Science and Technology Center for the Dynamic Earth, Tohoku University. We thank T. Nakajima and his collaborators for providing the radiative transfer calculation code RSTAR-5b.