The ozone layer and ultraviolet (UV) fluxes are tightly coupled. UV radiation photolyzes O2 into atomic oxygen, which can then bond with O2 to form O3. UV is also strongly absorbed by the ozone that has been formed. This absorption protects life at the surface while also photolyzing the O3, reversing the formation reaction and feeding back onto the structure of the ozone layer. Thus does the absorption of UV lead to the continuous destruction and reformation of the ozone layer, in the process attenuating the incoming UV flux at certain wavelengths by more than 30 orders of magnitude.

The coupling between UV and O3 can lead to counterintuitive responses to perturbations. As was perhaps first noted by , emitting an ozone-depleting substance whose local chemical effects strictly reduce ozone can nonetheless cause ozone to increase at certain altitudes subsequent treatments:. This phenomenon is known as self-healing. Figure a provides a canonical example of self-healing in response to ozone-depleting substances (specifically, halocarbons including CFCs). The self-healing effect is visible as increases in O3 in the tropical lower stratosphere and tropical tropopause layer. Similarly, perturbations that locally increase O3 can lead to decreases in O3 known as reverse self-healing . Figure b provides a canonical example of reverse self-healing in response to stratospheric cooling from the direct radiative effects of elevated CO2, the cooling from which changes collisional reaction rates to generally increase O3, which then leads to reductions in the tropical lower stratosphere (op. cit.).

Self-healing and reverse self-healing have been invoked in hundreds of papers, covering the ozone layer response to perturbations ranging from CFCs e.g., and stratospheric cooling e.g., to atmospheric oxidation e.g., conceptually in. However, despite being frequently invoked, self-healing and reverse self-healing are typically treated as curiosities only needed to explain unexpectedly signed responses of ozone to perturbations. They are only explained qualitatively, even in textbooks e.g.,.

Self-healing is typically explained as resulting from ozone depletion aloft, such as from CFCs, allowing photons that would have been absorbed aloft to penetrate more deeply into the atmosphere, photolyzing O2 down below to increase the source and concentration of O3 (self-healing). This mechanism relies on the spectral overlap between absorption by O3 and O2 at wavelengths less than 240 nm e.g.,. The increased ozone from self-healing partially stabilizes the downwelling ultraviolet flux against the initial depletion of ozone. Reverse self-healing is explained as resulting because ozone enhancement aloft, such as from stratospheric cooling, blocks photons that would have been absorbed by O2 below, reducing the source and concentration of O3 below. Both self-healing and reverse self-healing partially stabilize the downwelling ultraviolet flux against the initial depletion of ozone and are shown schematically in the top row of Fig. .

This standard explanation neglects the sensitivity of the ozone sink to perturbations in UV fluxes. One reason that the ozone sink has been neglected is that photolysis of O3 is typically considered to have a neutral effect on the ozone layer. This is because photolysis of O3 liberates an atomic oxygen that typically bonds with O2 to reform O3, completing a null cycle. Because the atomic oxygen is prone to reforming O3, it is usual to analyze ozone photochemistry in terms of odd oxygen (Ox ≡ O + O3), which is longer-lived than ozone and preserved by photolysis of O3 e.g.,. However, this null cycle does not close perfectly, and leakage from the null cycle occurs if the atomic oxygen bonds with O3 as in or, as happens more often, with catalysts of O3 depletion such as HO2 or NO2 . Although small compared to the null cycle, this leakage means that UV can drive a photolytic sink of O3. In other words, although odd oxygen is preserved by photolysis of O3, the sink of odd oxygen is nonetheless sensitive to such photolysis.

The photolytic sink of O3 opens up unconventional possibilities for the O3 response to perturbations in overhead column O3. If at some altitude the photolytic sink of ozone is more sensitive than the photolytic source, then O3 depletion aloft would lead to a net enhancement of the O3 sink below, further depleting O3 below (self-amplified destruction). Likewise, O3 addition aloft would lead to a net reduction in the O3 sink below, further adding O3 below (self-amplified production). Both of these responses are photochemically destabilizing, causing photochemical perturbations to amplify towards the surface. Figure  (bottom row) illustrates these two mechanisms of photochemical destabilization.

Photochemical destabilization has been noted before in , who identified significant photochemical destabilization above 40 km in a modified Chapman cycle model. However, they disclaimed their results as unrealistic, and these have since been neglected, perhaps for two main reasons: (1) they were considered theoretically impossible due to conceptual neglect of the photolytic sink of O3, and (2) they were hiding, because self-healing and reverse self-healing demand an explanation by virtue of their unexpected sign compared to that of the initial perturbation, whereas photochemical destabilization does not change the sign of the ozone response to a perturbation.

We find that photochemical destabilization is not only theoretically possible but is also actually revealed in the coefficients of two linear ozone models (Cariolle v2.9 and LINOZ) in the tropical stratosphere above 40 km, exactly where it was first noted in (Sect. ). To better characterize these sensitivities, we generalize photochemical stabilization and destabilization as manifesting the broader phenomenon of photochemical adjustment, defined as the component of the O3 response to a perturbation that is mediated by changes in UV from overhead column O3 responses to that same perturbation (Sect. ). Photochemical adjustment is quantified by the difference between the response to a perturbation under interactive versus locked UV. The region of photochemical destabilization above 40 km is then reproduced in a highly simplified model of the Chapman cycle augmented with two generalized sinks of O and O3 to represent catalytic cycles and transport – the Chapman+2 model (Sect. ). The Chapman+2 model facilitates the development of a theory for the transition altitude between photochemical destabilization and photochemical stabilization (Sect. ). This theory reproduces the latitudinal structure of the region of photochemical destabilization. In Sect. , we develop a new qualitative explanation for photochemical adjustment that is consistent with these quantitative insights.

To assess whether the ozone layer is photochemically stabilizing or destabilizing at a given location, we evaluate the sensitivity of the local net production rate of ozone (production minus loss) to a UV perturbation induced by a change in overhead column O3, keeping all else fixed (including tendencies from transport). Increasing the overhead column O3 decreases the photons reaching a given altitude in accordance with the spectrally varying absorption of ozone and the magnitude of the perturbation, reducing the photolysis rates of both O2 and O3 that drive the net production rate. If the increase in overhead column O3 reduces the net production rate, this leads to photochemical stabilization. If the increase in overhead column O3 increases the net production rate, this leads to photochemical destabilization. To characterize a climatology of photochemical regimes, this test must be repeated at all latitudes, altitudes, and seasons.

This exact battery of tests has been performed in chemical transport models by previous studies that developed linear ozone models, two independent coefficient sets of which are used throughout this study: Cariolle v2.9 and LINOZ . Linear ozone models are tools for computationally speeding up chemistry–climate modeling of ozone. In a linear ozone model, the net tendencies of ozone from a chemical transport model with tens to hundreds of (photo)chemical reactions are linearized with respect to finite perturbations in local ozone concentration, temperature, and overhead column ozone. Then, for computational efficiency, the ozone module can be replaced with these linear functions evaluated using their table of coefficients. A standard linear ozone model equation, first proposed in , is as follows: 1drO3dt=A1+A2(rO3-A3)+A4(T-A5)+A6(χO3-A7), where rO3 is the ozone mixing ratio, A1=P-L is the basic-state photochemical production minus the loss rate, A2=∂(P-L)/∂rO3, A3 is the basic-state ozone mixing ratio, A4=∂(P-L)/∂T, A5 is the basic-state temperature, A6=∂(P-L)/∂χO3 where χO3 is the overhead column ozone ∫z∞[O3]dz (molec. cm-2) and [O3] is the ozone number density (molec. cm-3), and A7 is the basic-state overhead column ozone.

The linear ozone model coefficients are interpreted as classifying the photochemical regime based on the sign of the sensitivity to perturbations in column ozone (A6). Photochemical stabilization occurs where A6<0, meaning that an increase in overhead ozone reduces the net ozone production. Photochemical destabilization occurs where A6>0, meaning that an increase in overhead ozone increases the net ozone production.

Previous studies have calculated the A parameters within chemical transport models as functions of altitude, latitude, and month. We have globally analyzed the A6 coefficients in two models. The first (and primary) linear ozone model we evaluate is the Cariolle v2.9 linear ozone model (coefficients obtained by personal communication with Daniel Cariolle). The Cariolle linear ozone model is linearized with respect to the chemical transport model MOBIDIC first described in . MOBIDIC is driven by two-dimensional transport based on the residual circulation. The first linear ozone model was described in , from which the Cariolle v2.9 linear ozone model descended, with a major update to specify the two-dimensional circulation from the ARPEGE-Climat model and to include heterogeneous chemistry in . The recent version of MOBIDIC to which the Cariolle v2.9 linear ozone model is calibrated includes the main gas-phase reactions driving the NOx, HOx, ClOx, and BrOx catalytic cycles, with 30 transported long-lived species and 30 short-lived species computed diagnostically . The Cariolle linear ozone model has been shown to perform well compared to state-of-the-art comprehensive chemistry–climate models and is used to prognose ozone in the ERA5 reanalysis . The second linear ozone model we evaluate is the LINOZ scheme, based on the UC Irvine chemical transport model e.g., as used in driven by the general circulation from NASA GISS ModelE (coefficients obtained by personal communication with Clara Orbe). LINOZ is documented in , and recent implementations include and .

The values of A6 during the month of March (chosen as an equinoctial month) are shown for Cariolle v2.9 and LINOZ in Fig. a, b. Negative values indicate photochemical stabilization, and positive values indicate photochemical destabilization. A major result is that there is significant and large photochemical destabilization, primarily above 40 km. This means that ozone depletion above 40 km removes additional ozone down to 40 km. Because these two linear ozone models agree so strongly, further analyses will focus on the Cariolle v2.9 model unless otherwise stated.

Photochemical destabilization occurs well above the bulk of the ozone layer; as evaluated using the climatological structure of O3 in the Cariolle v2.9 coefficients, 4 % of ozone molecules in the deep tropics (from 20° S to 20° N) are in a photochemically destabilizing regime above 40 km. Despite including only a modest fraction of O3, this region of photochemical destabilization challenges the prevailing theory, which only emphasizes the photochemical sensitivity of the ozone source and therefore cannot account for destabilization.

Intriguingly, the photochemical destabilization above 40 km in the tropics is located where it was first noted by in their modified Chapman cycle model. We reproduce the transition from destabilization aloft to stabilization below in our own version of the Chapman cycle augmented with generalized sinks of O and O3 from transport and catalytic cycles. These sinks are represented as two generalized chemical reactions, and hence our model is called the Chapman+2 model. The photochemical sensitivity of the Chapman+2 model is shown in Fig. c, which reproduces key features from the linear ozone models, which are in turn based on much more complex photochemical models. The details of the Chapman+2 model results will be presented later in Sect. .

The coefficients of the Cariolle v2.9 linear ozone model have provided exactly the evidence needed to classify regions of the atmosphere as photochemically stabilizing or destabilizing. One striking feature of Fig. a, b is that the sensitivity of the net ozone production rate to perturbations in column ozone has a larger magnitude in the destabilizing region than in the stabilizing region. This might seem to imply that destabilization is stronger than stabilization. However, the basic-state production and loss are also larger in the upper atmosphere, where the UV flux has not been attenuated as strongly, so therefore the ozone equilibration timescale may also be relevant to considering the magnitude of photochemical stabilization. Questions about the magnitude of photochemical stabilization demand a method to quantify the full vertical profile of photochemical adjustment in general, which is developed in the following section.

The idea behind photochemical stabilization or destabilization is that changes in ozone aloft can lead to a downward cascade of perturbations in ozone, yet this idea has not been previously formalized in a quantitative way. Here, we define photochemical adjustment as the component of the ozone response to a perturbation that results from changes in photolysis due to changes in column ozone aloft. Photochemical adjustment is therefore quantified as the difference between a fully interactive simulation of ozone photochemistry in which ozone and UV are coupled in the column through the photolysis rates, compared to one where the UV fluxes (and hence photolysis rates) are locked at their unperturbed values: 2photochemical adjustment≡[O3]|fully interactive-[O3]|UV-locked. This UV-locking method can in principle be implemented in any modeling context for atmospheric chemistry. Intuitively, a UV-locked simulation can be obtained in a photochemical model by locking the overhead column ozone when calculating photolysis rates, where the locked ozone could be steady or climatologically evolving, depending on the context. This ensures that the photolysis rates do not respond to any changes in ozone resulting from the perturbation, but it allows all other photochemical responses.

In this paper, we implement this approach using two methods. First, we use the Cariolle v2.9 linear ozone model coefficients to develop a linear emulator of photochemical adjustment. Later, we will perform various UV-locking experiments in the Chapman+2 model, which will be shown to reproduce essential results from the linear ozone model. Both of these analyses consider the equilibrated response to steady perturbations.

We begin our derivation for the linear emulator of the perturbation ozone equation by converting ozone anomalies in the linear ozone model from mixing ratio (Eq. ) to number density (for convenience) by multiplying by the number density of air, denoted as na (molec. cm−3). We then decompose the variables in our prognostic ozone number density equation into basic-state and perturbation components, x=x‾+x′, where x‾ is the basic-state component and x′ is the perturbation. Subtracting the basic-state component from the total equation and assuming a quasi-steady state, we solve for the perturbation ozone number density as a function of height in the presence of some prescribed perturbation, G: 3[O3]′=-A4naT′A2-A6naχO3′A2+G. On the right-hand side, the first term captures the sensitivity to temperature perturbations, the second term captures the sensitivity to overhead column ozone perturbations (thereby coupling in the photochemical adjustment), and the third term is the prescribed perturbation in ozone. A2 (defined as ∂(P-L)/∂rO3) tends to be negative, reflecting the fact that local perturbations in ozone tend to decay on a timescale of −1/A2. Although Eq. () is linear at any given height, it is mathematically implicit because the perturbation overhead column ozone is the integral of the ozone number density perturbation (i.e., χO3′=∫z∞[O3]′dz). Photochemical adjustment at height thus influences lower levels, introducing a spatial nonlinearity encoded in the A6 term, and Eq. () must be solved from the top of the atmosphere downwards.

We assess the response of tropical ozone to highly idealized forcing by ozone depletion (e.g., from ozone-depleting substances) and stratospheric cooling (e.g., from the direct radiative effects of CO2). The response to such perturbations is generally known to have a nontrivial vertical structure (e.g., Fig. ), although this response already includes the effects of photochemical adjustment, whose structure we seek to isolate. In order to illustrate how photochemical adjustment can induce a nontrivial vertical structure even in response to uniform perturbations, we consider constant (or piecewise-constant) perturbations. Ozone depletion is represented as a uniform reduction of ozone below its basic-state value (G=-G0, T′=0), which in turn can induce photochemical perturbations by perturbing the UV flux that drives ozone at lower levels. Thus, the fully interactive linear response to this uniform perturbation in ozone includes the perturbation itself plus the nonlocal effects of perturbed UV flux. Stratospheric cooling is represented as a uniform cooling (G=0, T′=-ΔT), which tends to locally increase ozone. This cooling is imposed uniformly, even extending into the troposphere, where the response is small but should not be considered a realistic response to elevated CO2, which instead (as is well known) warms the troposphere. The local increases in ozone from these perturbations then perturb the UV fluxes, leading to a fully interactive response that includes the local effects of cooling and the nonlocal effects of changes in overhead column ozone.

These two perturbations are explored by using the coefficients of the linear ozone model to perform an offline calculation of the response of a steady-state ozone layer to ozone depletion or stratospheric cooling. The linear ozone model distills the relative importance of the local effects of these perturbations from the nonlocal effects of the UV flux perturbations from aloft, as conveyed by the linear sensitivity to overhead column ozone. Both of these offline calculations have been performed on the discrete grid of the Cariolle v2.9 linear ozone model, with levels zi, i=1,2,…,N (where N=91) numbered from the top of the atmosphere downwards, each with a thickness of Δzi ranging from >3 km above 55 km to less than 1 km below the ozone maximum around 26 km. Uniform ozone depletion with a magnitude G0 has been imposed at and below z5=60 km. The fully interactive ozone response to this perturbation has been calculated by iterating between calculating the ozone response at level i and the resulting overhead column ozone anomaly at level i that is then seen by level i+1. The initial anomaly is therefore [O3]′(z5)=-G0, which leads to an overhead column ozone anomaly of χO3′(z5)=-G0Δz5. The fully interactive response at z6 can then be calculated as [O3]′(z6)=-G0-A6naχO3′(z5)/A2. This ozone anomaly is used to update the overhead column ozone perturbation as χO3′(z6)=χO3′(z5)+[O3]′(z6)Δz6. The solution can then proceed iteratively, where at each lower altitude we first calculate the ozone perturbation and then add that ozone perturbation (multiplied by the layer thickness) to the overhead column ozone perturbation. In this way, our calculation is locally linear in the overhead column ozone perturbation, but the dependence on overhead column ozone means that the ozone response at any given altitude depends nonlocally on the changes aloft.

A similar iterative method is used to calculate the response to stratospheric (and tropospheric) cooling. Our iterative calculation begins at the top of the model (z1=80 km) with a local ozone anomaly of [O3]′(z1)=A4naΔT/A2. This local ozone anomaly leads to an overhead column ozone perturbation of χO3′(z1)=[O3]′(z1)Δz1. The ozone perturbation at the next lower altitude can then be calculated in general as [O3]′(zi)=A4naΔT/A2-A6naχO3′(zi-1)/A2. The overhead column ozone perturbation can then be updated in general as χO3′(zi)=χO3′(zi-1)+[O3]′(zi)Δzi.

Using this approach, we calculated the linear response of ozone to uniform ozone depletion and stratospheric cooling. The response to these perturbations in the absence of photochemical adjustment can also be calculated directly as the UV-locked response by repeating the calculation with χO3′ overwritten to zero everywhere. For uniform ozone depletion, the UV-locked response is simply the prescribed ozone depletion, a reduction by G0 at all altitudes below 60 km. For stratospheric cooling, the UV-locked response is the direct thermal response given by the first term on the right-hand side of Eq. (). Knowing the UV-locked responses, it is then straightforward to calculate the photochemical adjustment, which (per Eq. ) is the fully interactive response minus the UV-locked response.

The results are shown in Fig. , as calculated using the linear ozone model coefficients in March for an equatorial atmospheric column. The response to uniform ozone depletion below 60 km of G0=108 molec. cm-3 is shown in Fig. a, with the prescribed depletion shown in blue. The fully interactive response (black) differs substantially from the prescribed perturbation. The fully interactive response shows reductions in ozone in the upper stratosphere that are larger in magnitude than those prescribed, peaking at 42 km with an amplitude 75 % larger than what is prescribed. This is a consequence of self-amplified destruction in the region of photochemical destabilization above 40 km. Below 40 km, the response is no longer photochemically destabilizing, and the fully interactive response is more positive than the prescribed reduction. At 35 km, the fully interactive response becomes positive in absolute terms – self-healing. The absolute increase in ozone peaks at a value around 2G0 at 29 km; the associated photochemical adjustment here is 3G0. The photochemical adjustment decays towards the lower stratosphere and troposphere, where the ozone response eventually resembles the prescribed depletion. By integrating these curves, it is evident that the overall column response of ozone is substantially modified by photochemical adjustment. The column integral of the prescribed perturbation is -G0×60 km, whereas the column integral of the fully interactive response is only half as large. Thus, photochemical adjustment significantly compensates for the initial perturbation.

The response to a uniform stratospheric cooling of ΔT=10 K is shown in Fig. b. The UV-locked response (blue) is a strict increase in ozone. Cooling approximately re-scales ozone by a constant factor, so the ozone response is shaped approximately like the unperturbed ozone profile. The fully interactive response (black) differs substantially from the UV-locked response, especially in the lower stratosphere. The maximum increase in ozone is predicted in both cases to occur around 30 km, but the fully interactive response is only half that predicted under UV locking. This discrepancy is due to photochemical adjustment, which is large and stabilizing throughout much of the stratosphere. Below 20 km, ozone is reduced in absolute terms (reverse self-healing). Integrating the column responses, the increase in total column ozone in the fully interactive case is only 43 % as large as the increase in the UV-locked case. Again, photochemical adjustment has halved the perturbation compared to in its absence.

A major result of this analysis is that photochemical adjustment is large and significant throughout the stratosphere and not just in the lower stratosphere, where self-healing and reverse self-healing tend to be found. It is important here to distinguish between photochemical adjustment and self-healing or reverse self-healing. We can express the colloquial definition of self-healing or reverse self-healing as follows: (reverse) self-healing≡[O3]fully interactive′if sign([O3]fully interactive′)⋅sign([O3]UV-locked′)<0,0otherwise. This definition shows that self-healing and reverse self-healing are given by the ozone perturbation in a fully interactive simulation wherever the ozone anomaly has the opposite sign to what is expected from the imposed perturbation. Expressed in this way, it is clear that self-healing and reverse self-healing are not the same as photochemical adjustment (defined in Eq. ). Indeed, self-healing and reverse self-healing are often just the tip of the iceberg of much larger photochemical stabilization. This is especially clear in the response to stratospheric cooling (Fig. b), in which the column-integrated reverse self-healing is only 14 % as large as the column-integrated photochemical stabilization.

The two main results from this analysis of linear ozone models are that (1) photochemical adjustment is destabilizing above 40 km and (2) photochemical adjustment can be large throughout the stratosphere, which is much greater than implied by conventional self-healing and reverse self-healing. Photochemical destabilization is inconsistent with the standard explanation for self-healing and reverse self-healing and therefore demands a revision of the conceptual understanding of these ubiquitous phenomena. This new conceptual understanding will also provide quantitative insights.

The large photochemical destabilization above 40 km and the large photochemical adjustment throughout the stratosphere (not merely in regions of self-healing or reverse self-healing) both demand a revision to present understanding. New understanding is challenging to achieve in comprehensive chemistry–climate models with tens of prognostic chemical species undergoing hundreds of reactions. However, some basic properties of photochemical adjustment do not depend on this complexity and are reproducible from simpler models. In particular, the prospect of photochemical destabilization was first raised in , who found such behavior in a modified version of the Chapman cycle above 40 km. It is at precisely those altitudes where the linear ozone models also simulate photochemical destabilization, suggesting that radically simplified photochemical models might support quantitative insights into photochemical adjustment.

We have analyzed photochemical adjustment in such a radically simplified model, the Chapman+2 model, which begins with the Chapman cycle but then augments it with two chemical reactions representing the generalized damping of ozone from sinks of O and O3 due to catalytic cycles and transport. The Chapman+2 model is comprehensively introduced in recent work focusing on the structure of the ozone layer , complementing our focus here on sensitivities. The Chapman+2 model was shown in Fig.  to reproduce the photochemical regimes from two chemical transport models. We now explain that calculation and use it to develop physical intuition and quantitative insights into photochemical adjustment.

The linear ozone models and the Chapman+2 model robustly agree on the altitude of the photochemical regime transition from destabilization aloft to stabilization below. Thus, this regime transition is likely explained by the simple physics that is shared by these models. Indeed, we find that the regime transition is controlled by which parts of the absorption spectrum for O3 and O2 have been attenuated versus which parts of the absorption spectrum are still active. Two key spectral windows will turn out to determine the overall photochemical regime: (1) the overlap window, which has absorption by both O2 and O3, occurring for λ<240 nm; and (2) the extension window, which has absorption by only O3, occurring for λ>240 nm. These absorption spectra are shown in Fig. b.

The overlap window can produce either photochemical stabilization, where photons switch between being absorbed by O2 and O3 e.g.,, or photochemical destabilization, where photons are absorbed by O3 in both the control and perturbed cases. The extension window can only support photochemical destabilization, because photons must be absorbed by O3 in both cases. Thus, the photochemical sensitivity is determined by the relative sensitivity of absorption in these two windows to perturbations in overhead column O3. This relative sensitivity is in turn controlled by a single variable endogenous to the ozone dynamics – overhead column ozone – leading to the following photochemical regimes.

Photochemically neutral regime. When overhead column ozone is so small that the ozone layer is optically thin at all wavelengths, absorption in both windows varies linearly with overhead column ozone, and the ozone layer is photochemically neutral.

The bottom of the destabilization layer occurs robustly around 40 km in the tropics because that is where overhead column ozone surpasses the stabilization threshold of 1018 molec. cm-2. These overhead column ozone thresholds have been validated with mechanism denial experiments using the Chapman+2 model. For example, we flattened the absorption coefficients in the overlap window and then artificially varied them across 2 orders of magnitude. As expected, destabilization begins once the peak absorption of the Hartley band saturates and stabilization begins once the overlap window saturates, as shown in Fig. . Thus, if the overlap window is forced to have an absorption coefficient comparable to the peak absorption of the Hartley band, then destabilization vanishes (Fig. d).

The principle that destabilization occurs where the overlap window is optically unsaturated has been validated in the Cariolle v2.9 and LINOZ linear ozone models. Figure  includes magenta curves corresponding to the slant overhead column ozone threshold of 1018 molec. cm-2, where slant overhead column ozone has been calculated as χO3/cos⁡(θ), with θ taken as the latitude (noting that we chose an equinoctial month to approximately equate latitude with zenith angle while neglecting the diurnal cycle in the Sun angle). In the linear ozone models, the climatological overhead column ozone is given by the parameter A7, and in the Chapman+2 model the climatological ozone is calculated at each latitude, approximating θ with latitude. Although imperfect, the theoretical curve approximately reproduces the transition from destabilization to stabilization, including its latitudinal structure (Fig. ). At high latitudes, the transition from destabilization to stabilization occurs at a higher altitude due to the oblique angle of the sunlight, which reaches the slant overhead column ozone threshold more rapidly for a given ozone profile.

Photochemical models produce photochemical adjustment as a natural consequence of accurately representing photochemistry. Thus, the key results of this paper are primarily conceptual, since they inform how the sensitivity of the ozone layer to perturbations is interpreted and explained. These results could also have implications for certain decisions made when formulating photochemical models, which is considered in the Discussion section. However, the main conceptual advances from this paper suggest that some of the previous explanations of ozone self-healing and reverse self-healing could distort understanding of photochemical adjustment.

Most explanations suggest that self-healing and reverse self-healing can be understood by considering the effect of the perturbed ultraviolet fluxes on the photolytic ozone source. For example, self-healing is explained in as follows: “O3 destruction at the upper levels in the stratosphere is partially compensated by the increase in O3 at the lower levels due to deeper penetration of solar UV radiation.” Similarly, in one of the few textbook explanations of self-healing, wrote that “When stratospheric O3 is removed ... there is more light available for photolysis of O2 and the formation of more ozone.” Although not strictly wrong, these explanations might lead to the incorrect impression that deeper penetration of solar UV radiation generally leads to increased ozone. Instead, we have shown that this common explanation only gives correct intuition for the stabilizing regime of ozone photochemistry but not the destabilizing regime. Photochemical adjustment cannot generally be understood by only considering the effects of the perturbation ultraviolet flux on the ozone source. Neglecting the effects of the perturbation ultraviolet flux on the ozone sink was shown to lead to errors in the magnitude and vertical structure of the photochemical adjustment (Fig. ).

Thus, it seems plausible to formulate a minimal explanation for self-healing and reverse self-healing as follows:

Self-healing. Ozone depletion enhances ultraviolet fluxes penetrating to lower altitudes, increasing both the ozone source and the ozone sink. Ozone exhibits a local net increase (self-healing) if the photolytic ozone source increases more than the photolytic ozone sink and that increase is large enough to overcome any local ozone depletion.

It has long been known that the photochemical nature of the ozone layer causes it to respond counterintuitively to perturbations. Ozone-depleting substances can lead to increases in ozone at some altitudes (known as self-healing), which have been argued to result from ultraviolet fluxes reaching deeper into the atmosphere. Processes that increase ozone, such as stratospheric cooling, can lead to decreases in ozone below (known as reverse self-healing), which have been argued as resulting from the decreased ultraviolet fluxes reaching lower altitudes. We have pursued a quantitative characterization and understanding of the photochemical processes that lead to self-healing and reverse self-healing. To do so, we have defined photochemical adjustment as the component of the ozone response to a perturbation that results from changes in photolysis due to changes in overhead column ozone. Photochemical adjustment is quantified as the difference in the ozone response to a perturbation in a fully interactive photochemical experiment versus with UV fluxes locked to their unperturbed values.

Photochemical sensitivities were quantified in two linear ozone models: Cariolle v2.9 and LINOZ. Photochemical adjustment was further quantified in column calculations using Cariolle v2.9 for the response to ozone depletion and stratospheric cooling. Photochemical adjustment can be stabilizing, damping overhead column ozone perturbations towards the surface and potentially leading to self-healing and reverse self-healing. Self-healing and reverse self-healing only occur for the subset of photochemical stabilization in which the photochemical adjustment dominates the local effects of the perturbation, making them just the tip of the iceberg for often large photochemical adjustment. We have also characterized a new and unconventional region of photochemical destabilization above 40 km in the tropical stratosphere and even farther aloft at high latitudes.

The regimes of photochemical stabilization and destabilization in the linear ozone models (Cariolle v2.9 and LINOZ) were successfully emulated using a Chapman+2 model of the ozone layer, which augments the Chapman cycle with generalized destruction of O and O3 by catalytic cycles and transport. A column-by-column calculation using the Chapman+2 model reproduces the full latitudinal structure of the transition from destabilization to stabilization (Fig. ). Photochemical destabilization in the Chapman+2 model arises when the photolytic sink of ozone (absorption by O3) is more sensitive than the photolytic source (absorption by O2) to perturbations in overhead O3. The sensitivity of the photolytic source and sink can in turn be related directly to the absorption spectra of O2 and O3. Photochemical destabilization occurs when absorption in the extension window (λ>240 nm) becomes optically saturated (τO3=1) while absorption in the overlap window (λ<240 nm) remains unsaturated. Photochemical stabilization occurs once absorption by O3 in the overlap window saturates. This spectral intuition leads to a simple theory that photochemical destabilization should occur below a threshold of slant overhead column ozone of approximately 1018 molec. cm-2, which reproduces the latitudinal structure of the transition altitude between destabilization and stabilization in the linear ozone models and the Chapman+2 model.

Roughly 4 % of ozone molecules in the tropics today are in a photochemically destabilizing regime. As considered in the Discussion section as a subject for future work, an atmosphere with less total ozone will have a higher fraction of its ozone layer in a destabilizing regime below the overhead column ozone threshold of 1018 molec. cm-2. Over Earth's history, atmospheric O2 has increased by at least 7 orders of magnitude, leading to the formation of the ozone layer e.g.,. Paleoclimatic ozone layers with total column ozone below the destabilization threshold could have been completely destabilizing, amplifying ozone perturbations and increasing the variability of the UV light experienced by early life.