Formulation of the cosmic ray–driven electron-induced reaction mechanism for quantitative understanding of global ozone depletion

Significance

The stratospheric ozone layer absorbs harmful ultraviolet (UV) radiation and is therefore a vital protection layer to living creatures on the Earth’s surface. However, cosmic rays (CRs) from deep space may destroy the ozone layer, especially when there is a significant amount of chlorofluorocarbons (CFCs) in the atmosphere, leading to ozone holes. This paper formulates the CR–driven electron-induced reaction (CRE) mechanism to provide a quantitative understanding of global ozone depletion. A concise analytical equation is derived to give atmospheric chlorine atom concentration, which shows excellent agreement with observations. This work represents an important contribution to understanding global ozone depletion and the impacts of CRs on the Earth’s climate and environment.

Abstract

This paper formulates the cosmic ray–driven electron-induced reaction as a universal mechanism to provide a quantitative understanding of global ozone depletion. Based on a proposed electrostatic bonding mechanism for charge-induced adsorption of molecules on surfaces and on the measured dissociative electron transfer (DET) cross sections of ozone-depleting substances (ODSs) adsorbed on ice, an analytical equation is derived to give atmospheric chlorine atom concentration: $\left[Cl\right]={\displaystyle \sum _i}{k^i{\theta }_{\mathit{ODS}}^i\mathrm{\Phi }}_e^2,$ where Φ_e is the prehydrated electron (e_pre⁻) flux produced by cosmic ray ionization on atmospheric particle surfaces, ${\theta }_{\mathit{ODS}}^i$ is the surface coverage of an ODS, and kⁱ is the ODS’s effective DET coefficient that is the product of the DET cross section, the lifetimes of surface-trapped e_pre⁻ and Cl⁻, and the particle surface area density. With concentrations of ODSs as the sole variable, our calculated results of time-series ozone depletion rates in global regions in the 1960s, 1980s, and 2000s show generally good agreement with observations, particularly with ground-based ozonesonde data and satellite-measured data over Antarctica and with satellite data in a narrow altitude band at 13 to 20 km of the tropics. Good agreements with satellite data in the Arctic and midlatitudes are also found. A previously unreported effect of denitrification on ozone loss is found and expressed quantitatively. But this equation overestimates tropospheric ozone loss at northern midlatitudes and the Arctic, likely due to increased ozone production by the halogen chemistry in polluted regions. The results render confidence in applying the equation to achieve a quantitative understanding of global ozone depletion.

In research communities of astronomy, physics, and chemistry, there are apparent interests in studying the effects of cosmic rays (CRs) on Earth’s and interstellar climate and ecological environment including the depletion of the ozone layer on various time scales (1–9). Of particular interest are the dissociative electron attachment (DEA) and dissociative electron transfer (DET) reactions of halogen-containing ozone-depleting substances (ODSs) in the gas and various condensed phases and on ice surfaces (10–28). Based mainly on the observations of DET reactions (16, 17), the CR–driven electron-induced reaction (CRE) mechanism for forming the ozone hole was proposed about two decades ago (29–33). Subsequently, substantial data from both laboratory measurements and atmospheric observations have provided a sound physics and chemistry foundation for the CRE mechanism, as reviewed previously (32, 34). Furthermore, the CRE model’s prediction of 11-y cyclic variations in polar ozone loss and associated stratospheric cooling, including the predicted largest Antarctic/Arctic ozone hole in the recent CR peak in 2020 to 2021 (31), has been well observed. Moreover, the fingerprints of the CRE mechanism have recently been found from measured altitude profiles of ozone and temperatures in the springtime Antarctic ozone hole (35). In 2022, a critical review of the CRE mechanism also led to the surprising discovery of the largest and all-season ozone hole over the tropics (36).

Furthermore, an equation was derived from the CRE mechanism, approximately giving the percent change of total O₃ in the ozone hole by

$$\frac{\mathrm{\Delta }\left[O_3\right]}{\left[O_3\right]}=-k\left[C\right]I^2,$$ [1]

where [C] is the “equivalent effective chlorine” in the stratosphere, I is the CR intensity, and k is a fitting constant (32–34). Although Eq. 1 well reproduced the observed data of O₃ loss and associated stratospheric cooling (33–35), its inclusion of the fitting parameter k was a barrier to provide complete quantitative calculations of O₃ depletion. Moreover, since the vertical profiles of O₃ trends can provide a fingerprint for the mechanisms of O₃ depletion (35, 37), it is crucial to obtain quantitative estimates of vertical profiles of O₃ loss and to compare them with observations.

Although ozone depletion has been intensely studied over the past 4 to 5 decades, the status of research based on chemistry-climate models (CCMs), considering the photochemical effects of ODSs on the ozone layer, remains essentially unchanged. CCMs were able to reproduce the observed O₃ loss in the upper stratosphere, indicating good understanding of ozone depletion in this altitude range (37–39). However, large discrepancies between CCMs and observations persistently exist in the lower stratosphere (38, 39), in which the largest ozone losses (ozone holes) are found. Moreover, the uncertainties in the O₃ profile for both models and ground- and satellite-based observations of pre-1997 O₃ trends are very large (up to ±20% per decade) in the lowermost stratosphere [see, e.g., figures 5.9, 5.10, and 5.11 in the recent Stratosphere-troposphere Processes And their Role in Climate (SPARC)'s Long-term Ozone Trends and Uncertainties in the Stratosphere (LOTUS) Report (38), which was adapted in the 2018 World Meteorological Organization (WMO) Report (39), whereas the 2022 WMO Report (40) focused on reviews of no pre-1997 but post-1997 O₃ trends]. Researchers’ confidence in trend results is reduced in the lower stratosphere due to low O₃ values, decreased sensitivity of satellite observations, and large natural variability. Additional and independent research has been called to put the trend results in the lower stratosphere on more solid ground (38).

This article aims to derive an analytical quantifying equation with no fitting parameters of global O₃ depletion based on the proposed CRE mechanism (29–35), which comprises two major CR-driven processes: the charge-induced adsorption of ODSs on surfaces of atmospheric particles and the DET reaction of the thus adsorbed ODSs on the surfaces under atmospheric CR radiation. For the former process, we will apply and modify a universal electrostatic bonding mechanism proposed by van Driel and coworkers (41, 42) to find the coverages of ODSs adsorbed on the CR-caused charged surfaces of atmospheric particles. For the latter process, the DET reaction efficiencies of ODSs adsorbed on ice surfaces or water clusters have been well measured (16, 17, 22, 29, 30, 32, 34, 43, 44) and theoretically studied (19–21, 24, 26). Our theoretical results will then be compared with the observed vertical profiles of O₃ loss from both ozonesonde and satellite measurements. This study mainly focuses on global O₃ depletion in the stratosphere, while it may also have applicability to understanding O₃ loss in the troposphere, especially in unpolluted or less polluted regions.

Theory

The DEA/DET reactions of halogenated ODSs in the gas and various condensed phases and on ice surfaces have been well studied (10–30, 32, 34, 43–47)

$$\begin{array}{c}AB+e^{-}\left(\sim 0 eV\right)\to {\mathit{AB}}^{\ast -}\to A^{-}+B\left(\mathrm{D}\mathrm{E}\mathrm{A}\right),\hfill \end{array}$$ [2]

$$\begin{array}{c}AB+e_{\mathit{pre}}^{-}{{(H}_{2}O)}_n\to {\mathit{AB}}^{\ast -}\to A^{-}+B\left(\mathrm{D}\mathrm{E}\mathrm{T}\right),\hfill \end{array}$$ [3]

where e⁻/e_pre⁻ (prehydrated electron) is a free electron or a e_pre⁻ trapped in ice or water and the transient species AB*⁻ is a vibrationally-excited state of the molecule. The DEAs of most halogen(Cl/Br/I)-containing molecules such as chlorofluorocarbons (CFCs, the major ODSs) are exothermic, and the measured DEA cross sections of gas-phase CFCs to low-energy free electrons near zero eV are very large (11, 12). Remarkably, the giant enhancements in DEA of CFCs adsorbed on ice surfaces were observed by Lu, Madey, and Sanche (16, 17, 29, 30). This reaction is termed as DET as it involves the trapping and transfer of an e_pre⁻ on ice surface. The exothermic energies of the DET reactions on H₂O ice or in liquid water are enhanced by 1 to 2 eV due to the effect of the polarization potential (48). This leads to strong resonances of anion states of Cl-, Br-, and I-containing molecules with e_pre⁻ that is weakly bound at −1.5 to −1.0 eV (32, 46). Thus, highly effective resonant DET can occur for organic and inorganic Cl-, Br-, and I-containing molecules on H₂O ice or in liquid water (32, 34, 45, 46). At the temperature of about 25 K, the absolute DET cross sections of CFCs were measured to be 10⁶ to 10⁸ times their photodissociation cross sections (16, 17, 29, 30, 44). Our observations of highly effective DET reaction of CFCs on ice were later confirmed experimentally by Kim and coworkers (18) and Wolf and coworkers (22, 47), using real-time femtosecond laser spectroscopic methods, and theoretically by Tachikawa (19, 20), Bhattacharya et al. (21), and Fabrikant (24, 26).

The temperature dependences of DEA and DET reaction rates were studied by Hotop, Fabrikant and coworkers (49) and by Lu et al. (50). Rate coefficients k(T) for DEA and DET reactions of many molecules generally exhibit a rise with increasing temperature T, which is often represented by an Arrhenius or Arrhenius-like equation k(T) ∝ exp[−E_a/(k_BT)] with the activation energy E_a deduced from fits to the experimental data k(T). In a direct DEA process of halogenated ODSs including CCl₄, CFCs, and HCFCs, this behavior indicates an energy barrier of 0 to 0.6 eV for the anion on its path to the dissociated products (49). In a DET reaction involving electron harpooning on the surface, this energy barrier is much smaller and associated with the structural reorganization energy (0 to 0.1 eV) of the medium (ice or water) (50). In this study, we will simply use E_a = 0.05 eV for all ODSs and the DET cross sections measured at 25 K to extend the DET cross sections to various temperatures in the stratosphere and troposphere.

In the stratosphere and troposphere, the major source of electrons is simply the atmospheric ionization caused by CRs. Peyerimhoff and coworkers (13, 14) suggested that the DEA of CFCs must be considered as a factor in evaluating stratospheric O₃ depletion. However, the gaseous DEA process was thought to be insignificant for stratospheric ozone depletion due to the very low free electron density (51). On the other hand, the understanding of stratospheric anion chemistry was also believed to be rather speculative (52, 53). Then, the surprising observation of giant enhancements in DET of CFCs adsorbed on ice surfaces has stimulated continued studies (16, 29). The DEA/DET reactions of halogenated molecules can generate reactive neutral radicals and halogen anions (29, 34), and most halogen anions are trapped at ice surfaces due to the image potential (16–18, 22, 29, 30, 32, 34, 43, 44). It is known that ionic surface reactions can effectively convert Cl⁻/Br⁻ into photoactive XNO₂, X₂, and HOX (X = Cl, Br), as demonstrated on solid or aqueous sea-salt aerosols by Finlayson-Pitts and coworkers (54, 55) and on CF₂Cl₂ films by Hedhili, Lu, Madey, and coworkers (56). A known effective conversion of a Cl⁻ ion into an active chlorine species is the reaction with the nocturnal NO_X species, N₂O₅

$$\begin{array}{c}{N}_2{O}_5\left(g\right)+{\mathit{Cl}}^{-}\left(s\right)\to ClN{O}_2\left(g\right)+N{O}_3^{-}\left(s\right).\hfill \end{array}$$ [4]

This reaction produces a photolabile species (ClNO₂) with the yield approaching 100% (57). Although additional reaction channels may form Cl₂, ClNO, and HOCl (58, 59), ClNO₂ is the dominant active chlorine species (60–64). Thus, we will only consider the reaction 4 as the predominant mechanism for converting trapped Cl⁻ ions into active chlorine species in the gas phase. The latter rapidly liberates highly reactive Cl free radicals causing ozone depletion upon photolysis

$$Cl{\mathit{NO}}_2+h\nu \to Cl+N{O}_2.$$ [5]

Additionally, the reaction 4 plays a particular role in controlling the lifetime of adsorbed Cl⁻ on the surfaces and hence surface charging of atmospheric particles, as will be explored later.

The O₃ loss rate can be expressed in terms of Cl and Br atomic concentrations [Cl] and [Br] (65)

$$-\frac{d\left[O_3\right]}{\mathit{dt}}=\left(k_{\mathit{Cl}}\right[Cl]+k_{\mathit{Br}}\left[Br\right])\left[O_3\right],$$ [6]

where k_Cl (k_Br) is the rate constant for the reaction of Cl (Br) atom with ozone, with k_Cl = 2.9×10⁻¹¹exp(−260/T) cm³s⁻¹ (66). Eq. 6 has been used to study tropospheric ozone depletion during the “polar sunrise”, which is correlated with high average diurnal Cl and Br atom concentrations in polar regions (65) and midlatitudes (67). Integration of Eq. 6 over a 24-h period yields the amount of O₃ removed in each diurnal cycle (65). Since the atmospheric abundances of human-made CFCs and HCFCs have been dominant in all ODSs, the concentration of the Br-containing ODS (mainly CH₃Br), which has a main natural origin, has had no major changes since the 1960s. Also, the rate constant k_Cl is 10 times larger than k_Br at 298 K (65, 66). All these factors lead to a good approximation for quantitative estimates of time-series changes in anthropogenic ozone loss rate

$$-\frac{d\left[O_3\right]}{\mathit{dt}}{\approx k}_{\mathit{Cl}}\left[Cl\right]\left[O_3\right].$$ [7]

This equation will be used for this study, in which [Cl] will be theoretically derived from the CRE mechanism, which is schematically shown in Fig. 1.

Fig. 1.

Major reactions in the cosmic ray–driven electron-induced reaction (CRE) mechanism of ozone depletion. A cosmic ray–driven charge-induced adsorption of a halogen-containing molecule (CFCs, HCFCs, HCl, and ClONO₂) onto the charged surface of solid or liquid cloud or aerosol particles and the subsequent dissociative electron transfer (DET) reaction leads to the formation of mainly a Cl⁻ ion that is trapped at the surface. The Cl⁻ ion is then converted by reaction with reactive nitrogen species (mainly N₂O₅) to release photoactive ClNO₂ (Cl₂ or HOCl or ClNO) into the gas phase. The photolysis of the latter rapidly results in a Cl free radical to cause ozone destruction via the well-known Cl-catalyzed reaction cycles. For details, see Lu (32–35).

Quantitative Understanding of Global O₃ Depletion

To achieve a quantitative understanding of vertical profiles of O₃ depletion, we will need to obtain quantitative estimates of the following atmospheric processes: (i) electrons produced at surfaces of ice or aqueous cloud or aerosol particles under CR ionization; (ii) charged-induced adsorption of ODSs on particle surfaces; and (iii) the yield of gas-phase halogen (Cl) atoms converted from halogen anions (Cl⁻) produced by DET reactions of adsorbed ODSs on the surfaces.

(i) Atmospheric distribution of e_pre⁻. First, the flux of e_pre⁻ at the surface of cloud or aerosol particles, Φ_e, can be calculated from the measured CR fluxes (Φ_CR) and CR energetics in the stratosphere and troposphere. It should be reasonable to assume that all cloud or aerosol particles have a major composition of H₂O. In radiation chemistry of water or H₂O ice, the G value (the number of generated/altered species per 100 eV ionizing radiation energy deposited) for the production of e_pre⁻ is known to be ~4.8 (68, 69). Thus, we obtain

$${\mathrm{\Phi }}_e=4.8\left(1-f\right){\mathrm{\Phi }}_{\mathit{CR}}{\widehat{E}}_{\mathit{CR}}/100,$$ [8]

where Ê_CR is the most effective energy in eV of ionizing CRs in the atmosphere and f (≈0.15) is the fraction of energy loss by secondary particles emitted away from the surface. Note that despite the primary galactic CRs (GCRs) having very high energies up to several tens of GeV, the atmospheric ionization at altitudes below 50 km arises mainly not from the primary GCR particles but from secondaries of a nucleonic–electromagnetic cascade initiated by primary GCRs in the atmosphere (2, 70). For a certain latitude, the maximum ionization produced by CR particles in the atmosphere depends on the altitude and phase of the solar cycle. This Ê_CR peak moves toward higher energies with decreasing altitudes and toward slightly higher energies with increasing solar activity or decreasing latitudes due to the hardening of primary GCR spectrum. The Ê_CR value is about 1.0 to 2.2 GeV from solar minimum to solar maximum in the polar stratosphere, increasing to about 3 GeV at ~3 km altitude (70). In the equatorial stratosphere, Ê_CR should be slightly larger (≥2.2 GeV) and the solar modulation should be weakest due to the highest energies of primary GCRs reaching equatorial regions (the geomagnetic effect).

Using the measured CR fluxes as a function of altitude (2) and approximately Ê_CR = 1.0, 2.2, and 1.3 GeV for polar, tropical, and midlatitude stratospheres, respectively, we obtain the altitude profiles of e_pre⁻ that would be produced at the surfaces of ice or aqueous particles under CR ionization, as shown in Fig. 2A. These vertical profiles, however, must be corrected by the density distributions of cloud or aerosol particles if one wants to get the actual distributions of the e_pre⁻ production rate in the stratosphere and troposphere.

Fig. 2.

Calculated altitude profiles of (A) the prehydrated electron flux (Φ_e) on surfaces of cloud or aerosol particles, (B) the surface area density (μ) of the particles, and (C) the prehydrated electron production rate (= μΦ_e) in the atmosphere, in the winter Antarctic/Arctic and the annual tropics and midlatitudes.

Since the discovery of the Antarctic ozone hole, stratospheric clouds or aerosols have been intensively studied (71–73). Particularly Adrian et al. (71) made delicate measurements and characterizations of polar stratospheric clouds (PSCs) and aerosols in the winter lower stratosphere at McMurdo Station, Antarctica (78°S). The stratospheric particles observed above 11 km at temperatures below 198 K were divided into four classes based on their scattering properties and particle sizes. Namely, volcanic aerosol and nondepolarizing hydrated nitric acid particles were predominant with surface area densities in the range of 10 to 30 and 20 to 50 μm² cm⁻³, respectively, in the polar stratosphere below 16 to 17 km; above this altitude, depolarizing hydrated nitric acid and ice clouds were predominant with surface area densities of 5 to 15 and 5 to 100 μm² cm⁻³. It is known that the Arctic polar vortex in winter is much less stable in terms of PSC formation than its Antarctic counterpart and the year-to-year variability in the PSC spatial volume in the Arctic is much larger. In the Antarctic, the PSC season is longer and more regular with the presence of PSCs every year from mid-May to early October, while in the Arctic, PSCs may or may not form from December to March. On average, there were about 14 times more PSC occurrence during a season in the Antarctic than that in the Arctic (73). In terms of PSC compositions, the season-long mean vertical profile of relative composite spatial coverage is also very different between the two Poles (73). In the Antarctic, solid nitric acid trihydrate (NAT) particles are the predominant PSC composition (taking nearly 60%) with the peak around 22 km and there are significant percentages (nearly 25%) of H₂O ice particles below 24 km. In contrast, NAT mixtures (taking nearly 80%) peak at around 16 km and drop to about 20% in the upper troposphere near 12 km, whereas ice (cirrus) particles have the maximum (nearly 80%) near 12 km and drop to very low fractions (less than 5%) above 16 km in the Arctic (73).

The formation of atmospheric particles such as PSCs and aerosols depends on temperature and pressure. To simulate the surface area densities of cloud or aerosol particles in the global stratospheric and troposphere, we simply adopt an empirical equation

$$\mu ={\mu }_0\left(\frac{P}{P_0}\right)e^{-38(T-T_0)/T},$$ [9]

where μ₀ = 50 μm² cm⁻³, P₀ = 43.72 mb, and T₀ = 192 K. Our simulated results of particle surface area densities by Eq. 9 are shown in Fig. 2B. Interestingly, the surface area densities are calculated to be 20 to 56 μm² cm⁻³ at 10 to 25 km for cloud or aerosol particles in the winter Antarctic stratosphere, which are in good agreement with the measured ranges (71, 72). Our simulated results of atmospheric particles in the tropics give the maximum surface area density of 37 to 45 μm² cm⁻³ at 16 to 18 km, rapidly decreasing to less than 10 μm² cm⁻³ at higher or lower altitudes due to the sharp rises in temperature. This is reasonable, given that the measured temperature in the tropical lower stratosphere at 16 to 18 km is as low as 196 to 197 K, similar to the winter Antarctic lower stratospheric temperatures (36, 74). The calculated μ values are 1 to 3 μm² cm⁻³ at midlatitudes and 1 to 5 μm² cm⁻³ in the Arctic (approximately 10 times lower than that in the Antarctic) due to much higher stratospheric temperatures. Our simulated results in Fig. 2B show overall agreement with the above-described observations, particularly for the differences between the Antarctic and the Arctic.

The altitude distributions of the e_pre⁻ production rates (= μΦ_e) in the stratosphere and troposphere are shown in Fig. 2C. Of particular interest is that the simulated particle surface area density in the winter Arctic peaks at the attitude around 10 km, arising from the combined effects of temperature and air density/pressure (Fig. 2B), whereas the e_pre⁻ production rates in all regions, including the Arctic, peak at 16 to 20 km (Fig. 2C).

(ii) Charge-induced adsorption of ODSs on atmospheric particle surfaces. To find the amounts of charge-induced adsorption of ODSs such as CFCs and HCFCs that are nonsticky to an uncharged ice surface, we need to determine the surface charge density on the surface of atmospheric particles. A critical step is to estimate the lifetime of charges on the particle surface. Although the initial process of the CR ionization is the instantaneous production of electrons, electrons are rapidly captured by molecules via DEA or DET to yield anions. As mentioned above, the DET reactions of halogenated ODSs with e_pre⁻ are extremely effective to produce Cl⁻ (Br⁻ or I⁻) ions, most of which are trapped at the surface by the image potential. In addition, electron attachment to other atmospheric species can also lead to the formation of molecular anions such as N₂⁻ and O₂⁻, which can effectively trap charges on the particle surface, as we observed on ice surfaces (48). Moreover, van Driel and coworkers (41, 42) made an interesting observation that ambient O₂ serves as an effective trapping catalyst in enhancing electron trapping in ultrathin SiO₂ films and that surface charging can then induce effective adsorption of nonsticky and nonpolar gases (such as He, Ar, H₂, O₂, N₂, and CO) onto the surface at room temperature. A similar process is reasonably expected to occur on surfaces of cloud or aerosol particles under CR ionization, on which Cl⁻(Br⁻/I⁻), N₂⁻, and O₂⁻ can serve as trapping catalysts. Thus, the surface charge density σ_e can simply be written as

$${\sigma }_e={\mathrm{\Phi }}_e{\tau }_{\mathit{ion}},$$ [10]

where τ_ion is the lifetime of trapped anions at the surface of cloud or aerosol particles. Note that Eq. 10 takes no account of the cumulative effect of anions on the surface, which will lead to a much higher surface charge density.

Now, with the surface charge density given by Eq. 10, we can derive the amounts of ODSs adsorbed on atmospheric particle surfaces. For gas adsorption on the electron-trapped SiO₂ surface, van Driel and coworkers (42) suggested a universal bonding mechanism—an electrostatic bonding in which the adsorbed species become polarized in the electric field established by the negative charges on the surface and the interaction energy depends on the polarizability of the adparticle. This mechanism well explained their experimental results with the surface irradiated by a femtosecond laser, which was estimated to yield an electron flux at the Si–SiO₂ interface of 10¹³ to 10¹⁵ cm⁻² s⁻¹ (41). A similar magnitude of electron flux generated by alkali metal (potassium) predeposition on ice was also estimated in our experiment, which showed strong charge-induced adsorption of nonpolar CCl₄ on H₂O ice surface (34). As this electron flux is expected to be much higher than the ones produced by CR fluxes at the surface of atmospheric particles expressed in Eq. 8, we judge that the electric field–induced polarizability of the adspecies is unlikely to be significant in the stratosphere and troposphere. Thus, we will only consider the electrostatic bonding between the negative charges on the surface and the intrinsic dipole of the adspecies (an ODS), noticing that most of the ODSs, except CCl₄, are polar molecules with an electric dipole moment. For interaction of the adspecies with a single-charged surface anion of charge e, the binding (interaction) energy simply becomes

$$E_b=\frac{\delta e}{4\pi {\epsilon }_0{r}_0^2},$$ [11]

where e is the electron elementary charge, δ is the electric dipole moment of the adspecies, ε₀ is the vacuum permittivity, and r₀ is the equilibrium adsorption distance. This distance is approximately the sum of the radius of the surface anion and the van der Waals radius of the adspecies. The binding energy in Eq. 11 should be doubled for some ODSs such as CF₂Cl₂ and CFCl₃, which are expected to have two Cl atoms directed toward the surface and experience the electrostatic field caused by two surface charges. Given the measured dipole moments of ODSs (CFCs, HCFCs, HCl, ClONO₂, and N₂O₅) and taking the surface charge species to be Cl⁻, we calculate by Eq. 11 that the binding energies are 270 meV and 464 meV for ClONO₂ and N₂O₅, respectively, and are in the range of 342 to 540 meV for CFCs, HCFCs, and HCl, from CFC-11 with the smallest δ = 0.46 Debye (D) to HCFC-142b with the largest δ = 2.14 D. The actual E_b value will be much larger if one considers interactions with all the other charges on the surface and if one also includes field-induced chemisorption effects (42). For simplicity, we approximately use the binding energy E_bⁱ ≈ 400 meV for all HCl, CFCs, and HCFCs and the above-given binding energies for ClONO₂ and N₂O₅ in our calculations of the coverages of these ODSs on the surface of atmospheric particles.

Note that charge-induced adsorption based on the charge-dipole coupling, which can be considered as targeted reactive adsorption, is very different from conventional adsorption/uptake of gases on the particle surface according to Henry’s law. The latter was proposed to be the rate-limiting step for the heterogeneous chemical reaction of HCl and ClONO₂ on the surface of PSC ice (75–77). For the latter reaction, the reactive uptake coefficient (γ) or reaction probability is very complicated to determine, depending on complex steps on the gas, interface, and condensed phase environment of the particles and requiring the development and application of complicated models with multiple parameterizations to interpret γ [see a recent review by Wilson et al. (78), and references therein]. From Langmuir’s adsorption equation, in contrast, the charge-induced adsorbed surface density [ODS]_adⁱ of an ODS species with a partial pressure p_i in the atmosphere onto the particle surface is neatly given by

$${\left[ODS\right]}_{\mathit{ad}}^i={\sigma }_{\mathit{max}}{\theta }_{\mathit{ODS}}^i={\sigma }_e{\theta }_{\mathit{ODS}}^i.$$ [12]

Here, σ_max is the maximum surface concentration of the ODS (in molec/cm²), which is simply the surface charge density σ_e in this charge-attracted adsorption, i.e., σ_max = σ_e, and θ_ODSⁱ is the coverage of the ODS species on the surface, defined as

$${\theta }_{ODS}^i\equiv \frac{K_{eq}^i{p}_i}{\left(1+K_{eq}^i{p}_i\right)},$$ [13]

where K_eqⁱ is the equilibrium constant (in liter/mole) governed by two opposing adsorption–desorption steps and is equal to the ratio of their rate constants

$$K_{eq}^i\equiv \frac{k_{ad}^i}{k_{de}^i}=e^{E_b^i/k_{B}T},$$ [14]

where k_B is the Boltzmann constant.

(iii) Yield of halogen (Cl) atoms converted from the DET-produced anions (Cl⁻). To find the Cl radical yield, we need to know the lifetimes of e_pre⁻ and anions on atmospheric particle surfaces, τ_e and τ_ion. Long-lived trapped electrons on ultrathin ice films were implicitly observed in our electron-trapping experiments (17, 44, 50). Subsequently, Baletto et al. (79) found by their first-principles MD simulations that very stable trapped electron can exist on ice surface at temperatures of 150 to 200 K, similar to the lower-stratosphere temperatures measured in the winter Antarctic/Arctic or the all-season tropics. Moreover, Bovensiepen et al. (80) directly observed very long-lived trapped electrons with a lifetime up to minutes (10³ s) at the crystalline ice surface. In their time- and energy-resolved experiment, the stabilization of the trapped electrons was monitored continuously in timescales over 17 orders of magnitude from femtoseconds to minutes, exhibiting almost no shift in energy and no decay in yield of the trapped electrons up to 10⁻² s. For simplicity in this study, we will use τ_e ≈1.0 × 10⁻² s. Obviously, larger values of ozone loss can be obtained if one uses a longer lifetime τ_e.

The lifetime of anions is related to the loss process of anions in the atmosphere. In the general atmosphere below 50 km, the major sink of negative ions is recombination with positive ions and the rate constant for the recombination is essentially independent of species (52, 53). In the upper stratosphere, the ion recombination lifetime is very long, about 10⁴ s. With lowering altitudes, the lifetime decreases until about the tropopause and increases again in the troposphere, resulting in a minimum in the lowermost stratosphere; the ion–ion recombination lifetime in the stratosphere is approximately 10² to 10⁴ s (81). On the particle surface, we expect that the ion–ion recombination is dominated over by the reaction of anions with atmospheric species (mainly NO_X), as expressed in reaction 4. Unlike the previously proposed heterogeneous surface ionic reaction (54, 55, 58, 60–63, 82), we propose that N₂O₅ is first adsorbed onto the charged particle surface via the targeted electrostatic attraction rather than random collisions and then reacts with the trapped Cl⁻ to yield a photoactive ClNO₂. The second step is similar to a surface reaction scheme recently proposed to describe trace gas uptake and reaction with applications to aerosols and microdroplets by Wilson et al. (78). Through the conversion reaction 4, the lifetime of trapped Cl⁻ anions is governed approximately by the adsorbed N₂O₅ surface concentration, [N₂O₅]_ad

$${\tau }_{\mathit{ion}}=1/\left[k_{\mathit{Cl}}^{-}\mu {[N_2{O}_5]}_{ad}\right],$$ [15]

where k_Cl⁻ is the rate constant in cm³s⁻¹ for reaction 4

$$k_{\mathit{Cl}}^{-}=1.07\times {10}^{-15}{e}^{-E_a/k_{B}T},$$ [16]

with the calculated activation energy being E_a = −354 meV and the measured k_Cl⁻ value at 300K being k_Cl⁻ = 9.4 × 10⁻¹⁰ cm³s⁻¹ (83). Combining Eqs. 10, 12, and 15, we obtain a more meaningful expression

$${\tau }_{\mathit{ion}}=1/\sqrt{k_{\mathit{Cl}}^{-}\mu {\mathrm{\Phi }}_e\theta \left(N_2{O}_5\right)},$$ [17]

where θ(N₂O₅) is the surface coverage of adsorbed N₂O₅ given by Eqs. 13 and 14. Like long-lived trapped electrons, anions trapped at the surfaces of atmospheric particles are expected to have a longer lifetime than the ion–ion recombination lifetime in the gas phase or the bulk. Also, it is expected that owing to involving surface reactions, the lifetime of surface-trapped anions will be more sensitive to atmospheric temperature than the free anions.

To find the lifetime of trapped anions on the surface by Eq. 17, an additional important factor is the “denoxification” reducing the concentrations (partial pressures) of gaseous NO₂ and N₂O₅ in the coldest stratosphere, which is dependent on the surface area density μ of the atmospheric particles

$$\left[N_2{O}_5\right]={\left[N_2{O}_5\right]}_0\left(1-k_{\mathit{den}}\mu \right)={\left[N_2{O}_5\right]}_0/\alpha ,$$ [18]

where k_den or α is a reducing constant or factor of denitrification and [N₂O₅]₀ is the gas-phase N₂O₅ concentration if there are low densities of particles (k_denμ « 1). High-quality satellite data of N₂O₅ data with a good altitude resolution are needed to determine the factors of denitrification. The NASA’s High Resolution Dynamics Limb Sounder (HIRLDS) (v7) N₂O₅ data are unique in having a vertical resolution of ~1 km, but they only cover the stratosphere at altitudes ≥20 km and latitudes 63°S to 80°N for the period January 2005 to March 2008 (84, 85), with no data available for the main Antarctic (60°S to 90°S). To overcome this challenge, we fit Eq. 18, with the particle surface area density μ given by Eq. 9, to the HIRLDS satellite data in the tropics and obtain the constant k_den = 1.5 × 10⁶ cm. This k_den value gives the factors α of reduction in N₂O₅ concentration in the lower stratosphere at 10 to 25 km to be 1.0 to 3.0 in the annual tropics, relative to the measured N₂O₅ concentrations in March. The extending of this k_den value to the winter Antarctic is justified by the observation that the lower-stratospheric temperatures in the tropics are very close to those in the winter Antarctic (36, 74). The thus obtained α values lie in 1.3 to 6.4 in the winter Antarctic. The α values determined from the available HIRLDS satellite data are ~3.0 for the winter Arctic and ~2.0 for annual midlatitudes in the lower stratosphere. It is known that the observed winter NOx is reduced by up to a factor of ~10 with respective to summer observations in the 20 to 27 km altitude region (66). Given the differences in lower-stratospheric temperature in these regions, these denitrification factors are very reasonable and will be used in our calculations of ozone loss rates.

As plotted in Fig. 3, our calculations of the reactive Cl⁻ anion lifetimes show very interesting results that despite the expected differences from the ion–ion recombination lifetimes in the gas phase, the lifetimes of surface-trapped Cl⁻ given by Eqs. 16–18 well reproduce not only the measured ion lifetimes of 10² to 10⁴ s in the lower stratosphere but also the observed altitude profiles, exhibiting a minimum lifetime in the lower stratosphere (81). Moreover, it is particularly interesting to note that the use of our simulated factors of denitrification by Eq. 18, together with the particle surface area densities given by Eq. 9, also leads to our calculated ozone depletion rates in excellent agreement with those using the actual satellite-measured N₂O₅ concentrations available at altitudes above 20 km except the Antarctic, as will be presented later.

Fig. 3.

Calculated altitude profiles of the reactive lifetime of Cl⁻ anions trapped at atmospheric particle surfaces in the winter polar regions and the annul tropics and midlatitudes. Also shown is the measured altitude profile (the dash curve) of the ion–ion recombination lifetime in the general atmosphere.

In the CRE mechanism of ozone depletion, the DET reaction 3 is clearly the rate-limiting step, which is solidly indicated from the above-mentioned observations of pronounced 11-y cyclic variations of ozone loss and associated cooling in the lower stratospheric region where the CR ionization mainly occurs (34, 35, 86). As mentioned above, it is well known that ClNO₂ formed from the Cl⁻ conversion reaction 4 is rapidly photolyzed to yield a Cl atom with sunlight via reaction 5. As a result, the average diurnal sum concentration of Cl atoms yielded from the CRE mechanism of all ODSs, expressed as a volumetric concentration by the particle surface area density μ in the atmosphere, is given by

$$\left[Cl\right]=\sum _i\mu k_e^i{\left[ODS\right]}_{\mathit{ad}}^i{\mathrm{\Phi }}_e{\tau }_e,$$ [19]

where k_eⁱ is the DET cross section for an adsorbed ODS species with e_pre⁻ produced by CR ionization on the particle surface. Note that Eq. 19 actually takes account of the catalytic (cumulative) effect of Cl⁻ on the adsorption of an ODS onto the surface by assuming that the ODS is not depleted during the lifetime of e_pre⁻. Substituting Eqs. 10 and 12 into Eq. 19, we obtain

$$\left[Cl\right]=\sum _i\mu k_e^i{\tau }_e{\tau }_{\mathit{ion}}{\theta }_{\mathit{ODS}}^i{\mathrm{\Phi }}_e^2\equiv \sum _i{k^i{\theta }_{\mathit{ODS}}^i\mathrm{\Phi }}_e^2,$$ [20]

where $k^i=\mu k_e^i{\tau }_e{\tau }_{\mathit{ion}}$ is defined as the effective (volumetric) DET coefficient of an ODS (adsorbed on the particle surface) in the atmosphere. This equation, together with Eq. 7, provides a complete quantitative estimate of global ozone depletion in the atmosphere.

Provided with the measured DET cross sections (17, 29, 30, 34, 43, 44) and altitude profiles (66, 87) of ODSs (CFCs, HCFCs, HCl, ClONO₂, and N₂O₅), and the calculated values of Φ_e, μ, θ_ODSⁱ, and τ_ion by Eqs. 8, 9, 13, 14, and 16–18, respectively, with the binding energies E_b given in the above and τ_e ≈1.0 × 10⁻² s, we can now use Eqs. 7 and 20 to calculate the altitude profiles of ozone depletion rate at various regions of the globe. The good reproductions of measured values including surface area densities, magnitudes of denitrification, and anion lifetimes by our simulated results mentioned above give us confidence to make quantitative calculations of global ozone loss.

Observed and Calculated Results

The details for observations and our theoretical calculations are given in Data and Methods. Here, measured altitude profiles of ozone depletion from the ground-based WOUDC (World Ozone and Ultraviolet Radiation Data Centre)'s Trajectory-mapped Ozonesonde dataset for the Stratosphere and Troposphere (TOST) datasets (TOST_SM) (88) and the NASA's Global ozone chemistry and related trace gas data records for the stratosphere (GOZCARDS) satellite datasets (GOZCARDS _source and _merged) (89) are shown in SI Appendix, Fig. S1 and Fig. 4, together with our theoretical results. Note that in our time-series calculations, we simply assumed that the only variable is the levels of ODSs (CFCs, HCFCs, HCl, and ClONO₂), and no enhanced ozone production by halogen radicals is included. Despite these major simplifying assumptions, our calculated results exhibit overall good quantitative agreement with the observed stratospheric ozone data, particularly with the GOZCARDS satellite data. Here, we highlight the key features. i) For the ozone depletion rate in the Antarctic stratosphere, nearly equally excellent agreements among calculated results, TOST_SM, and GOZCARDS source data are found. ii) In the stratospheres of the Arctic and both southern and northern midlatitudes, excellent agreements between calculated and measured results, especially GOZCARDS data, are also found, provided with the well-known large year-to-year dynamic variability in Arctic ozone loss. iii) In the tropics, a remarkable agreement between calculated results and GOZCARDS data is found, both showing a much narrower peak in altitude profile of significant ozone loss rates at 13 to 20 km than the TOST data. iv) It is also very noteworthy that our calculated ozone depletion rates using the given factors of denitrification show excellent agreement with those calculated directly with the actual satellite-measured data of N₂O₅ concentrations available at altitudes above 20 km except the Antarctic (Fig. 4 B–F). v) It is also worthwhile noting that our CRE theoretical results show nearly equally excellent agreements with observed data in the tropics and the Antarctic/Arctic/midlatitudes. This fact indicates the reliabilities of the observed data and our calculated results on ozone loss in the tropics, which was, in contrast, given with the largest uncertainties in previous studies (37–39). Of particular interest is to compare our current results with those observed by Randel et al. (37), who analyzed the Stratospheric Aerosol and Gas Experiment (SAGE) II satellite data for the period 1984 to 98 and showed negative trends over much of the globe in the lower stratosphere, with largest percentage changes (on the order of −10% per decade) in the tropics below 20 km. They also noted that such large tropical O₃ depletion was not predicted by photochemical model calculations (37). vi) In the troposphere of northern midlatitudes and the Arctic, large differences between calculated results and TOST data (no GOZCARDS data available) are seen and the calculated results indeed overestimate tropospheric ozone depletion, as we expected from excluding enhanced ozone production by halogen radicals (Data and Methods). vii) Last but not least, our calculated results show very small differences in stratospheric ozone depletion rate between (annual mean) northern midlatitudes and the (springtime) Arctic. Given the known strong seasonal variation in trends over northern midlatitudes in the altitude range 10 to 18 km, with the largest ozone loss during winter and spring (37), the O₃ loss rates at northern midlatitudes in winter and spring are likely slightly larger than those in the Arctic. This behavior appears surprising. However, this result is very unlikely to be artificial, as it is found with great consistency between calculated results and GOZCARDS data, and given an O₃ lifetime of ~30 d in the stratosphere, our calculated maximum O₃ loss rates of 0.42 to 0.66% per day at 16 km altitude at northern midlatitudes, which has been most studied, in the 2000s relative to 1960s/1980 or to the 1980s (SI Appendix, Fig. S1C and Fig. 4D), are in good agreement with the widely accepted values of 7.0 to 7.3% per decade in the 1980s and 1990s (37, 90). For the cause of this surprising result, one can see that the e_pre⁻ production rate at midlatitudes is slightly smaller than that in the Arctic (Fig. 2C) and the lifetime τ_ion of trapped anions on particle surfaces at midlatitudes is nearly identical to that in the Arctic at altitudes around 15 km (Fig. 3), whereas the concentrations of ODSs in the lower stratosphere at midlatitudes are known to be larger than those in the polar region (Arctic). The combination of these factors is likely to lead to the small differences in O₃ loss rate between the two regions, as shown in SI Appendix, Fig. S1 and Fig. 4.

Fig. 4.

Observed (TOST_SM and GOZCARDS_Source and _Merged) (symbols) and theoretical (green curves) altitude profiles of ozone loss rates in the Antarctic (60°S to 90°S), the Arctic (60°N to 90°N), the tropics (30°S to 30°N), and southern and northern midlatitudes (30°S to 60°S and 30°N to 60°N), in the 2000s relative to the 1980s (A–E). Except for the Antarctic (A) in which no HIRDLS data of N₂O₅ are available, the theoretical ozone loss rates (the blue curves) calculated directly with the satellite-measured HIRDLS N₂O₅ concentrations at altitudes ≥20 km are also shown. In F, the results for the tropics are for the 2000s relative to the 1960s (theoretical and TOST) and to the 1980 (GOZCARDS), same as in SI Appendix, Fig. S1. Horizontal error bars in observed data are ±20%, approximately 2 times the SDs (uncertainties), in the decadal mean values.

Discussion

The good agreement between the observed and calculated results in SI Appendix, Fig. S1 and Fig. 4 is the most compelling message delivered by this study. Of special note is the good agreement between calculated results and GOZCARDS data in the tropics. Both consistently show a sharp altitude band at 13 to 20 km of large ozone depletion. These results strongly support our recent discovery of the large and deep tropical ozone hole based on the zonal mean TOST ozonesonde data at the altitude band 13.5 to 20.5 (14–21) km. In spite of showing the much broader peak in altitude profile of tropical ozone loss at 8 to 25 km, the TOST data that were used to reveal the tropical ozone hole in our recent study (36, 86) lie in the altitude range of 13.5 to 20.5 km (14 to 21 km), which well matches the narrow band at 13 to 20 km of large ozone loss rates in both calculated and GOZCARDS data, as shown in Fig. 4 C and F. These results not only strongly validate our recent application of the TOST dataset in discovering the tropical ozone hole but are strong evidence of the CRE mechanism responsible for global ozone depletion.

Another important finding from our results is a previously-unreported effect of denitrification. It has been known for some time that denitrification is a requirement for observing a large Antarctic ozone hole, which was suggested to reduce the deactivation and removal of ClO radicals by NO_x from the catalytic reaction cycles for ozone depletion (91, 92). In contrast to this suggestion, ClO radicals are predominantly formed in the springtime polar lower stratosphere with the presence of sunlight, during which the level of ClONO₂ is actually observed to be at its maximum in the whole year (34, 66). In this study, we have provided an alternative explanation, that is, denitrification directly increases the lifetime of trapped anions on the surface of atmospheric particles and hence the surface charge density. This can then lead to the enhanced adsorption of ODSs on particle surfaces and the final yield of Cl atoms from the DET reactions of adsorbed ODSs. Importantly, we have presented this explanation quantitatively, straightforwardly through Eqs. 15, 18, and 20. This effect may play a key role in controlling ozone depletion, as both denitrification and DET reactions simultaneously occur in the winter polar lower stratosphere mainly.

We are now left with theoretical uncertainties arising mainly from three categories: temperature-dependent reaction rate constants (k_e and k_Cl⁻), binding energies between ODSs and the charged surface of atmospheric particles, and lifetimes of e_pre⁻ and anions on the particle surface (τ_e and τ_ion). It is worthwhile noting that the identical estimated values of these physical quantities are constantly used in our calculations of ozone depletion rates in all the atmospheric regions of the globe from the polar regions to midlatitudes and the Equator. Despite the potential existence of identified or unidentified uncertainties due to complex atmospheric processes leading to ozone depletion, here the key and convincing conclusion is that our calculated results exhibit nearly equally good agreement with the observed data in all these regions. We estimate that the uncertainties lead to an overall uncertainty of approximately ±20% of the mean values in the determination of O₃ loss. This uncertainty is considerably larger than what would be expected from tropical ozone loss due to dynamic changes in the Brewer–Dobson circulation, which have been simulated to be 2 to 3% per decade by CCMs (93), corresponding to an ozone loss rate of 0.13 to 0.20% per day in the tropics in the results shown in Fig. 4 C and F. In our analyses for lower-stratospheric altitudes at 15 to 17 km where ozone loss has the maximum, we find that over 80% (88%) of the observed springtime O₃ loss rate in the Antarctic (Arctic) and over 96% of the observed annual mean O₃ loss rate in the tropics result from the DET reactions of adsorbed CFCs and HCFCs alone and that the sum of the DET reactions of all adsorbed ODSs including organic ODSs (CFCs and HCFCs) and inorganic chlorine reservoirs (HCl and ClONO₂) on surfaces of cloud or aerosol particles leads to catalytic loss rates in good agreement with the observed results in all the polar regions, the tropics, and midlatitudes. The relative contributions from HCl and ClONO₂ (mainly HCl) increase with rising altitudes up to about 94% in the middle stratosphere at 33 km in the Antarctic/Arctic and up to 75% at 34 km in the tropics. Thus, our results lead to an important conclusion that both springtime polar and all-season tropical ozone holes observed in the lower stratosphere are predominantly caused by DET reactions of CFCs and HCFCs adsorbed on atmospheric particle surfaces. This directly answers the key question why the large ozone hole with a similar depth to the Antarctic ozone hole is formed in the tropical lower stratosphere where the concentrations of HCl and ClONO₂ are very low.

Conclusion

A quantitative understanding of global ozone depletion based on the CRE reaction as a universal mechanism gives rise to a concise and elegant equation with two major inputs only, the stratospheric concentrations of ODSs and the cosmic ray flux. Using this equation, our time-series calculations of decadal mean ozone depletion rates in the Antarctic, Arctic, tropics, and midlatitudes with the simplifying assumption taking the variation of halogenated ODSs’ concentrations as the sole input impressively yield results in good agreement with observed data, especially with the GOZCARDS satellite data. Excellent agreements among calculated results, TOST_SM, and GOZCARDS source data are found for the spring Antarctic ozone hole. A remarkable agreement between calculated results and satellite data is found for the all-season tropical ozone hole, which is located within a narrow altitude band at 13 to 20 km. This agreement puts our recent finding of the largest ozone hole in the tropical lower stratosphere at 14 to 21 km on solid ground. Given the known large dynamic variability in Arctic ozone loss, our calculated results also show good agreement with satellite data in the Arctic. Excellent agreements between calculated and measured results, especially GOZCARDS data, are also found in both southern and northern midlatitudes. We have also provided an insight into the effect of denitrification. Our results show that denitrification can directly increase the lifetime of trapped anions on the surface of atmospheric particles and thus increase the final yield of Cl atoms from the DET reactions of adsorbed ODSs. This effect is quantitatively expressed in the equations, playing a key role in controlling ozone depletion. Interestingly our calculated results, consistent with the GOZCARD data, show very small differences in ozone depletion rate in the lower stratosphere between annual mean northern midlatitudes and the winter Arctic. This behavior is likely due to the combined effect of the e_pre⁻ production rate and the ODS concentrations in the stratospheres of the two regions.

We should note that the analytical Eq. 20 derived in this study seems to generally overestimate ozone depletion in the troposphere, particularly in polluted regions (e.g., northern midlatitudes and the Arctic). In the latter, large differences between calculated results and ground-based TOST data are found, albeit no satellite data on tropospheric ozone are available for a second examination. These overestimates are most likely caused by the enhanced ozone production due to the halogen chemistry in the troposphere (57, 60, 62), which must be included in future model development if one desires to achieve a precise estimate of ozone loss in this lower altitude region. We should also note that further improvements may be achieved if time-series variations of lower stratospheric and tropospheric temperatures are included in the calculations of ozone trends. Also, the spatial resolution in theoretical calculations of global ozone depletion by the derived equation can be improved to individual latitudes instead of the broad latitude bands if the cosmic ray flux as a function of latitude is used. Given the important role of N₂O₅ in controlling ozone loss revealed from this study, there is a compelling need for precise measurements of this reactive nitrogen species in the atmosphere.

Finally, we would like to note here that although this study was not intended to provide accurate calculations of global ozone depletion due to its inclusion of simplifying assumptions, the parameter-free CRE analytical equation has given theoretical results in satisfactory agreements with observations in the global stratosphere, ranging from the Antarctic, the Arctic, and the tropics to both northern and southern midlatitudes. This achievement renders us confidence in validating our recent discovery of the tropical ozone hole and in applying the equation to achieve quantitative understanding of global ozone depletion. To our understanding, no previous CCMs have been able to provide a better agreement with observations in the global lower stratosphere including all the polar regions, the tropics, and midlatitudes simultaneously and consistently (38–40, 66, 94). The results presented in this article have demonstrated that the CRE mechanism can remove the persistent discrepancies between CCMs and observations, particularly in the lower stratosphere. Further research on the CRE mechanism will be of interest.

Data and Methods

Observed Data.

There are two available satellite datasets covering the periods starting from the 1970 or late 1970s, NASA/NOAA's Solar Backscatter Ultraviolet Radiometer (SBUV) and NASA’s Stratospheric Aerosol and Gas Experiment (SAGE) I/II datasets. However, the SBUV profile data are not useful particularly in the lower stratosphere and troposphere, due to the instrument’s poor vertical resolution, which is 6 to 7 km near 3 hPa and degrades to 15 km in the troposphere. Therefore, all satellite merged profile records rely mostly on SAGE I/II data for pre-2000 periods, as reviewed in the recent SPARC’s LOTUS Report (38). The NASA’s GOZCARDS is a combination of various high-quality space-based monthly zonal mean ozone profile data (89). It is worth noting that among long-term merged satellite datasets, GOZCARDS is the only merged satellite dataset that extends to the lowermost stratosphere and covers the early satellite era starting in 1979 (38).

The measured altitude profiles of ozone depletion were obtained from the ground-based WOUDC ozonesonde (TOST_SM) (88) and the NASA satellite (GOZCARDS _source and _merged) (89) datasets, which are shown in Fig. 4 and SI Appendix, Fig. S1. We show the data of ozone loss in the 2000s with respect both to the 1960s in SI Appendix, Fig. S1 and to the 1980s in Fig. 4, as we presented in recent papers (36, 86). Prior to 1979, there was a lack of reliable satellite data. Thus, we similarly present the GOZCARDS data of ozone loss in the 2000s relative both to the 3-y mean satellite-measured data for the first 3 y 1979 to 1981 as the starting point of the satellite era in SI Appendix, Fig. S1, as we (86) and others (95) presented previously, and to the decadal mean data in the 1980s in Fig. 4. For measured ozone data, the SDs were reported to be typically within 10% of the means (88, 89). To consider the instrumental errors and other uncertainties such as bias uncertainties and altitude correction uncertainties, we apply a total error bar of ±20% to the mean values. To derive the measured and theoretical vertical profiles of ozone loss rate averaged in a diurnal cycle (per day), we take the lifetime of ozone in the stratosphere and troposphere to be about 30 d (66, 88). This leads to the maximum average diurnal ozone depletion rate of about 2.5% per day in the springtime Antarctic ozone hole in September–October–November (SI Appendix, Fig. S1A), which is consistent with the values reported in the literature (90, 96), and of 2.3% per day in the annual tropical ozone hole (Fig. 4F). As plotted in SI Appendix, Fig. S1 and Fig. 4, the results of vertical profiles of ozone loss from the independent TOST and GOZCARDS datasets show overall consistency. However, some differences between the datasets are also seen, especially for the vertical profiles of ozone loss in the spring Arctic in March–April–May and the annual tropics. It is well known that the year-to-year variability in PSC formation and ozone loss in the Arctic is much larger than that in the Antarctic, with very large dynamic variabilities for most winter and spring days. This factor could contribute to the large discrepancy between TOST and GOZCARDS data for ozone loss in the Arctic. In the tropics, the TOST data exhibit a very broad peak in altitude profile of ozone loss at altitudes 8 to 25 km, whereas the GOZCARDS data show a much narrower peak centered around 16 km though no satellite data are available below 14 km. This large discrepancy might be caused by the domain-filling trajectory approach used in generating the TOST dataset. There are overall excellent agreements between GOZCARDS raw (source) and merged datasets, though some minor differences between the two datasets also exist, likely caused by the bias removal and averaging in generating the merged data. Nevertheless, the observed data from both ground-based TOST and satellite-measured GOZCARDS datasets should reasonably represent ozone trends from the 1960s/1980 or the 1980s to the 2000s.

Theoretical calculations.

We have calculated the average diurnal Cl atom concentration produced by the CRE mechanism via Eq. 20 and then the ozone loss rate via integration of Eq. 7 over a 24-h period to yield the percentage of O₃ depleted in each diurnal cycle (65). Here, we note the following: i) Since we are interested in studying anthropogenic ozone depletion, the effects of natural halogenated species such as CH₃Cl and CH₃Br, which have had only small changes in concentration since 1960s, are not included. Also, CCl₄ is not included since it is a nonpolar molecule and no electric field–induced polarizability is considered in our current CRE mechanism. ii) We simply assume that the stratospheric concentrations of organic halocarbons (CFCs and HCFCs) and inorganic halogen reservoirs (HCl and ClONO₂) above 10 km in the Antarctic/Arctic in the beginning of the winter are approximately 0.75 and 2.5 times the measured concentrations at 30°N in March, respectively, while the corresponding concentrations at midlatitudes are about 0.85 and 1.5 times; the concentrations in the tropics are approximately the same as those at 30°N. The thus given ODS concentrations are in generally good agreement with the satellite-measured data (36, 66, 87, 97). For example, the given HCl concentrations at 22 to 24 km in the early winter Antarctic/Arctic is 2.02 to 2.35 ppbv, while the satellite measured value is about 2.0 ppbv at 31.6 hPa (~24 km) at 80°S/N (97); the satellite-measured CF₂Cl₂ concentrations in the fall Antarctic/Arctic at 16 to 24 km are about 0.74 to 0.76 times those in the annual tropics (36). The predenitrified stratospheric NO₂/N₂O₅ concentrations in the Antarctic/Arctic, midlatitudes, and the tropics are, respectively, about 2.0, 1.5, and 0.83 times the concentrations at 30°N in March (66, 98). The above-given denitrification factors in the lower stratosphere at altitudes above 10 km in various regions are used in our calculations. There is no denitrification to occur in the warmer troposphere, in which the gaseous N₂O₅ concentration is essentially constant with altitude and is simply fixed at 20, 17.5, and 15 pptv in the Antarctic/Arctic, midlatitudes, and the tropics, respectively. Except for the Antarctic, the satellite-measured data of N₂O₅ concentrations available at altitudes above 20 km obtained from the NASA’s HIRLDS (v7) dataset (84, 85) are also directly used in our calculations, in addition to those with respect to the measured concentrations at 30°N in March and applying the factors of denitrification. iii) We assume that there is a lag time of about 10 y for transport and mixing associated with transport from the measured lower tropospheric global mean abundances to the global stratospheric levels of ODSs (35, 36, 74). iv) Since air downward movement occurs in the winter polar vortex, the calculated reactive Cl yield for springtime ozone depletion resulting from the DET reactions on the surfaces of PSC ice particles in the winter Antarctic stratosphere are shifted downward by 3.2 km, according to the field measurements of PSCs, which showed an altitude displacement of approximately 1.0 km per month (71). In contrast, our simulated results by Eq. 9 show that the particle surface area density in the Arctic peaks near the tropopause (Fig. 2B), and both NAT and ice (cirrus) particles predominantly form in the Arctic lowermost stratosphere at altitudes 12 to 16 km (73). Therefore, no displacements are applied to the CRE-produced Cl atom yield in the Arctic. (v) We use the available satellite-measured altitude profiles of stratospheric and tropospheric temperatures in the winter Antarctic/Arctic and the annual tropics and midlatitudes in the 2000s and assume no changes in the temperature profiles from the 1960s or 1980s to the 2000s. In other words, the only variable is the levels of ODSs (CFCs, HCFCs, HCl, and ClONO₂ ) in our time-series calculations. This is certainly a rough simplifying assumption since ozone depletion is well known to cause a cooling trend in lower stratospheric temperature, and increased levels of greenhouse gases can also cause a direct radiative cooling in the upper stratosphere particularly at altitudes above 25 km (74, 99, 100). Fortunately, however, unlike the spring season, ozone depletion in the winter polar lower stratosphere has been limited and there have been no significant changes in the measured season-mean lower-stratospheric temperatures over Antarctica in the winter or fall since the 1960s up to date (32, 34, 86). Thus, this assumption should have a negligible effect on our calculations of polar ozone depletion. In the tropics and midlatitudes, however, this assumption may somewhat overestimate lower-stratospheric ozone loss in the 1960s or 1980s and correspondingly underestimate relative ozone loss in the 2000s, due to the relatively low stratospheric temperatures and high tropospheric temperatures measured in the 2000s being used in all the calculations. Oppositely, the latter may lead to overestimates of ozone loss in the troposphere in the 2000s relative to the 1960s or 1980s. vi) Finally, no enhanced ozone production by halogen radicals (57, 60, 62) is included in our CRE calculations. This likely results in overestimates of tropospheric ozone depletion caused by halogenated ODSs in the polluted regions, e.g., at northern midlatitudes. Thus, our calculated ozone loss rates in the stratospheres of the tropics and midlatitudes are the lower limits and in the troposphere are the upper limits.

Supplementary Material

Appendix 01 (PDF)

Data, Materials, and Software Availability

The data used for this study were obtained from the following sources:the TOST data (88) were obtained from the WMO’s WOUDC (https://woudc.org/archive/products/ozone/vertical-ozone-profile/ozonesonde/1.0/tost/); the GOZCARDS data (89) were obtained from the NASA EARTHDATA dataset (https://disc.gsfc.nasa.gov/datasets?keywords=GOZCARDS); the zonal mean N₂O₅ HIRDLS satellite data (85) were obtained the SPARC Data Initiative (https://www.sparc-climate.org/data-centre/data-access/sparc-data-initiative/); the altitude profiles and DET cross sections of ODSs were obtained from refs. 66 and 87 and refs. 17, 29, 30, 34, 43, and 44, respectively; the RO lower stratospheric temperature satellite datasets were obtained from the ROM SAF (https://www.romsaf.org/product_archive.php); the cosmic ray flux data were obtained from ref. 2; tropospheric data of ODSs were obtained from the 2021 IPCC AR6 Report (https://www.ipcc.ch/assessment-report/ar6/).