Saturday, July 9, 2022

Nudges didn't work with vaccination intentions against COVID-19

Can vaccination intentions against COVID-19 be nudged? Elena Kantorowicz-Reznichenko, Jaroslaw Kantorowicz, Liam Wells. Behavioural Public Policy, July 8 2022. https://doi.org/10.1017/bpp.2022.20

Abstract: Once vaccines against COVID-19 became available in many countries, a new challenge has emerged – how to increase the number of people who vaccinate? Different policies are being considered and implemented, including behaviourally informed interventions (i.e., nudges). In this study, we have experimentally examined two types of nudges on representative samples of two countries – descriptive social norms (Israel) and saliency of either the death experience from COVID-19 or its symptoms (UK). To increase the legitimacy of nudges, we have also examined the effectiveness of transparent nudges, where the goal of the nudge and the reasons of its implementation (expected effectiveness) were disclosed. We did not find evidence that informing people that the vast majority of their country-people intend to vaccinate enhanced vaccination intentions in Israel. We also did not find evidence that making the death experience from COVID-19, or its hard symptoms, salient enhanced vaccination intentions in the UK. Finally, transparent nudges as well did not change the results. We further provide evidence for the reasons why people choose not to vaccinate, and whether different factors such as gender, belief in conspiracy theories, political ideology, and risk perception, play a role in people's intentions to vaccinate or susceptibility to nudges.

Discussion and conclusion

In this article, we aimed to examine a number of soft interventions to increase people's intention to vaccinate. Vaccination is currently considered the main solution to the global pandemic and vaccinating the majority of the population is a key public policy goal. At least in democratic countries, governments do not wish to force people to vaccinate, respecting their freedoms and rights over their bodies. Therefore, other methods to encourage vaccination are necessary. Nudging is one popular method, which has been used in many countries around the world for different public policies (e.g., increasing tax compliance, organ donation, savings). Therefore, it has been also discussed and considered in the context of vaccination against COVID-19.

We have experimentally examined three nudges, in two countries, which at the initial period of vaccination availability appeared to be leading in rates of vaccination. Those countries are also similar in terms of their public being generally supportive of different nudges (Reisch & Sunstein, Reference Reisch and Sunstein2016; Pe'er et al.Reference Pe'er, Feldman, Gamliel, Sahar, Tikotsky, Hod and Schupak2019). General support of nudges was also found in many other countries (e.g., Jung & Mellers, Reference Jung and Mellers2016; Sunstein et al.Reference Sunstein, Reisch and Rauber2018Reference Sunstein, Reisch and Kaiser2019), thus constituting an instrument that has a potential to direct people's behaviour across different countries. First, we examined the effectiveness of a descriptive social norm on a representative sample of the Israeli (Jewish)Footnote18 population. In particular, we have utilized findings from psychology indicating that people follow the behaviour of others, in order to encourage vaccination intentions. Overall, the average intention of people to vaccinate was high, which is a promising result. However, the nudge itself did not make a difference. Also, a more ‘legitimate’ nudge which was transparent about its method and goal did not change people's choices.

We have also run an experiment to examine two additional nudges on a representative sample of the population in the UK. This experiment used the saliency nudge, utilizing findings from psychology that making certain factors more salient might affect how people treat probabilities, and in turn, which choices they make. The experiments made either the death experience very vivid and alarming or stressed the symptoms of COVID-19. Also, in the UK already in the baseline people had high intentions to vaccinate on average. The saliency nudges had very limited effect to none at all. In particular, when considering the full sample, none of the nudges changed the choices. Looking at the restricted sample (those participants who passed the manipulation check) showed a very small effect of the transparent death saliency nudge. Even though statistically significant, the small effect does not seem to be promising. In addition, we have examined the choices of different subgroups in the two countries but found no differences in the effectiveness of the nudge.

Our studies were well powered as we have based our sample sizes on a power analysis. Therefore, the null results are unlikely to be the result of lack of statistical power. One explanation might be that nudges are effective when people do not have strong preferences either way. In that case, it is not costly to follow a certain nudge. Some studies suggested that the inability of the nudge to change the behaviour of some people might be derived from a stronger preference of those people against the direction of the nudge (Bronchetti et al.Reference Bronchetti, Dee, Huffman and Magenheim2013; Beshears et al.Reference Beshears, Choi, Laibson, Madrian and Milkman2015; Jachimowicz et al.Reference Jachimowicz, Duncan, Weber and Johnson2019). For example, Bronchetti et al. (Reference Bronchetti, Dee, Huffman and Magenheim2013) raised the possibility that people with lower income are more resistant to default nudges that direct them to allocate money for savings because they already have plans how to use this money.

The context of the new vaccination is sensitive. On the one hand, there is an ongoing (threatening) pandemic with many uncertainties in respect of its long-term effects. On the other hand, the developed vaccine (which at the time of the study was not approved yet) is novel and entails many uncertainties with respect to the long-term effects. People are either more afraid of the former, or more of the latter. Therefore, it is difficult to affect their choices with nudges that target their intuitive system of decision making, instead of the deliberative process of decision making. In other words, it might be necessary to first address people's concerns, before having an effect on their behaviour. Our results seem to support the recently expressed opinion of one of the ‘founders’ of the concept of nudges himself, that nudges might not be a sufficient instrument to enhance vaccination to end the current pandemic,Footnote19 even though there is evidence that at least using reminders and simplifying the process of vaccination has a positive effect (Dai et al.Reference Dai, Saccardo, Han, Roh, Raja, Vangala, Modi, Pandya, Sloyan and Croymans2021).

Our results demonstrate that many people are willing to vaccinate. But there is also a smaller group which is hesitant. From our investigation of the reasons for this hesitation, it seems that the primary reason is the concern about the side effects. Even at the stage of our experiments it was clear that once the vaccine will be available, there will not be sufficient evidence of their long-term effects. This is due to the urgency in approving this vaccine and saving the world from the pandemic. Therefore, this concern is understandable.

Consequently, to encourage vaccination, governments should invest more in understanding people's concerns and trying to address them. For example, by investing in campaigns where people receive more information on the trade-offs between the uncertain long-term effects of the vaccine, and the uncertain (probably worse) long-term effects of contracting COVID-19. Relying solely on soft interventions such as nudges seems not to be sufficient.

One limitation of this study is that we focus on people's intentions rather than vaccination uptake, thus potentially facing the problem of intention-behaviour gap (Sheeran, Reference Sheeran2002). In the specific context of vaccinations for example, several studies have found that even when people intend to vaccinate, they do not always follow through (e.g., Bronchetti et al., Reference Bronchetti, Dee, Huffman and Magenheim2013; Chang et al.Reference Chang, Jacobson, Shah, Pramanik and Shah2021). Nevertheless, there are many studies demonstrating that an intention to vaccinate is generally a strong predictor of an actual uptake of vaccines (daCosta DiBonaventura & Chapman, Reference daCosta DiBonaventura and Chapman2005; Lehmann et al.Reference Lehmann, Ruiter, Chapman and Kok2014; Fall et al.Reference Fall, Izaute and Chakroun-Baggioni2018; Jensen et al.Reference Jensen, Ayers and Koskan2022). In the specific context of this article, at the time of the study we have found that 63.6% of the Israeli participants and 75.3% of the UK participants (control groups), respectively, either ‘strongly agreed’ or ‘agreed’ that they would vaccinate themselves against COVID-19. Looking at the most recent data to date of vaccination uptake we see that nearly 77 persons per 100 population have taken the first dose and around 69 per 100 are fully vaccinated in Israel. In the UK, almost 78 persons per 100 population have taken the first dose, and nearly 73 in 100 are fully vaccinated.Footnote20 Therefore, the baseline intentions in our studies (which were expressed before the vaccine became available) seem to be overall aligned with the actual rate of vaccination as reported by WHO for the beginning of the year 2022.

Furthermore, even though we do not have a way to directly translate our results from intentions to behaviour, our findings seem to be conservative in this respect. From the studies of the intention-behaviour gap, it seems that the gap is mostly driven by people who intend to act but eventually fail to do so (Sheeran, Reference Sheeran2002).Footnote21 Therefore, it is reasonable to expect that if the investigated nudges in this article did not change people's intention, it probably would not change people's behaviour.

A related potential concern is that currently there is more knowledge about the effectiveness of the vaccine and its short-term safety.Footnote22 The fact that uncertainty regarding those two factors were the main reasons for some of our subjects not to intend to vaccinate, might suggest our results would change at this stage. However, the level of uncertainty was similar for all participants in our studies. And yet many indicated an intention to vaccinate. Those who were hesitant or reluctant did not seem on average to change their minds in response to the employed nudges. Whereas the new information may have on itself encouraged people to vaccinate, there is no immediate reason to believe it would influence the level of effectiveness of the nudge. For example, in Israel, even after the vaccines against COVID-19 were made available, and evidence of its efficacy and short-term safety had emerged, the two main concerns of the people who were still hesitant about vaccination remained its effectiveness and safety (e.g., Heller et al.Reference Heller, Chun, Shlomo, Gewirtz-Meydan, Acri, Kulkarni and Grinstein-Weiss2022). Also in the UK, the long-term safety was still a major concern for people who were choosing not to vaccinate themselves (Majeed et al., Reference Majeed, Papaluca and Molokhia2021). However, Majeed et al. (Reference Majeed, Papaluca and Molokhia2021) stated that the emerging data on the benefits of the vaccine also reduce vaccine hesitancy. Therefore, it might be reasonable to assume, that those who are still hesitating at this stage, more than a year after vaccines were introduced and with the current reliable information on the effectiveness and short-term safety of vaccines, are those who hold stronger preference against vaccinating. Consequently, our results might again be viewed as conservative, and suggest that other strategies, which are addressing the persisting concerns are needed, rather than simply using ‘system 1’ nudges to enhance vaccination.

Amygdala damage associated with smaller social network size

Amygdala but not hippocampal damage associated with smaller social network size. Janelle N.Beadle et al. Neuropsychologia, July 8 2022, 108311. https://doi.org/10.1016/j.neuropsychologia.2022.108311

Abstract: Social network size has been associated with complex socio-cognitive processes (e.g., memory, perspective taking). Supporting this idea, recent neuroimaging studies in healthy adults have reported a relationship between social network size and brain volumes in regions related to memory and social cognition (e.g., hippocampus, amygdala). Lesion-deficit studies in neurological patients are rare and have been inconclusive due to differences in participant sampling and measurement. The present study uses a multiple case study approach. We investigated patients with focal damage to the hippocampus and/or amygdala (two neural structures thought to be critical for social networks), and examined the patients’ social network size, loneliness, and life satisfaction relative to a non-injured comparison group. Patients with amygdalar damage had smaller social networks and reported higher levels of loneliness and lower life satisfaction, on average, than comparison participants. Patients with damage to the hippocampus reported more friends than the comparison participants, but did not differ in their ratings of loneliness or life satisfaction. This lesion study offers new evidence that the amygdala is critical for social networks, life satisfaction, and reduced loneliness.

Keywords: Social networksLesion studiesLonelinessAmygdalaHippocampus


Friday, July 8, 2022

Reading of literary fiction in early life is associated with a more complex worldview (increased attributional complexity, increased psychological richness), & with a decreased belief that contemporary inequalities are legitimate

Reading Literary Fiction Is Associated With a More Complex Worldview. Nicholas Buttrick, Erin C. Westgate, Shigehiro Oishi. Personality and Social Psychology Bulletin, July 7, 2022. https://doi.org/10.1177/01461672221106059

Abstract: What are the effects of reading fiction? We propose that literary fiction alters views of the world through its presentation of difference—different minds, different contexts, and different situations—grounding a belief that the social world is complex. Across four studies, two nationally representative and one preregistered (total n = 5,176), we find that the reading of literary fiction in early life is associated with a more complex worldview in Americans: increased attributional complexity, increased psychological richness, decreased belief that contemporary inequalities are legitimate, and decreased belief that people are essentially only one way. By contrast, early-life reading of narrative fiction that presents more standardized plots and characters, such as romance novels, predict holding a less complex worldview.

Keywords: attitudes, empathy, interpersonal processes, social judgment


Vegetarians have to grapple not only with the meatlessness of their diet, but also with the fact that it signals White privilege

Racialized Perceptions of Vegetarianism: Stereotypical Associations That Undermine Inclusion in Eating Behaviors. Daniel L. Rosenfeld, Tiffany N. Brannon, A. Janet Tomiyama. Personality and Social Psychology Bulletin, July 7, 2022. https://doi.org/10.1177/01461672221099392

Abstract: Shifting societal eating patterns toward a vegetarian diet offers promise for improving public health and environmental sustainability. Yet concerns exist about racial disparities in inclusion, as some sentiments suggest that vegetarianism is stereotypically associated with Whiteness. Through four studies (total N = 3,234), we investigated associations U.S. adults hold between race and vegetarianism, along with implications for behavior change and belongingness among Black individuals. Participants, across racial backgrounds, strongly associated vegetarianism with Whiteness, both explicitly and implicitly. A race prime led Black participants to report lower interest in becoming a vegetarian, whereas a prime of race-vegetarianism associations decreased Black participants’ feelings of belongingness in the vegetarian community. Exposure to racially inclusive messaging about vegetarianism, meanwhile, increased belongingness among Black participants. These findings provide the first quantitative insights into racial stereotypes about vegetarianism and pose future directions for theory, research, and practice at the intersections of race and eating behavior.

Keywords: race, stereotype, eating behavior, vegetarianism, belonging


Most have assumed that conservatism antecedes well-being without considering the alternative—that well-being may predict conservatism; this study says conservatism did not predict well-being over time

A Longitudinal Test of the Conservative-Liberal Well-Being Gap. Salvador Vargas Salfate et al. Personality and Social Psychology Bulletin, July 7, 2022. https://doi.org/10.1177/01461672221096587

Abstract: In this article, we test if conservatism predicts psychological well-being longitudinally. We based the study on previous findings showing that conservatives score higher on different measures of well-being, such as life satisfaction and happiness. Most explanations in the literature have assumed that conservatism antecedes well-being without considering the alternative—that well-being may predict conservatism. In Study 1, using multilevel cross-lagged panel models with a two-wave longitudinal sample consisting of data from 19 countries (N = 8,740), we found that conservatism did not predict well-being over time. We found similar results in Study 2 (N = 2,554), using random-intercept cross-lagged panel models with a four-wave longitudinal sample from Chile. We discuss the main implications of these results for the literature examining the association between conservatism and well-being.

Keywords: conservatism, well-being, longitudinal analysis, life satisfaction, happiness


Realism vs alarmism: Since the 1980s, there has been an ozone 'hole' over the tropics much larger than the Antarctic one; obviously, no harm has been reported related to this thinning despite affecting almost 50pct of the world's population

Observation of large and all-season ozone losses over the tropics featured. Qing-Bin Lua. AIP Advances 12, 075006 (Jul 5 2022); https://doi.org/10.1063/5.0094629

Abstract: This paper reveals a large and all-season ozone hole in the lower stratosphere over the tropics (30°N–30°S) existing since the 1980s, where an O3 hole is defined as an area of O3 loss larger than 25% compared with the undisturbed atmosphere. The depth of this tropical O3 hole is comparable to that of the well-known springtime Antarctic O3 hole, whereas its area is about seven times that of the latter. Similar to the Antarctic O3 hole, approximately 80% of the normal O3 value is depleted at the center of the tropical O3 hole. The results strongly indicate that both Antarctic and tropical O3 holes must arise from an identical physical mechanism, for which the cosmic-ray-driven electron reaction model shows good agreement with observations. The whole-year large tropical O3 hole could cause a great global concern as it can lead to increases in ground-level ultraviolet radiation and affect 50% of the Earth’s surface area, which is home to approximately 50% of the world’s population. Moreover, the presence of the tropical and polar O3 holes is equivalent to the formation of three “temperature holes” observed in the stratosphere. These findings will have significances in understanding planetary physics, ozone depletion, climate change, and human health.

The present finding of a tropical ozone hole is closest to the observation by Polvani et al.26 of large O3 losses at the altitude of 18.5 km or 67/68 hPa over the tropics (30°S–30°N) from 1979 to 1997 with data from three independent datasets (TOST, BDBP, and GOZCARDS)28–30 although they did not reveal the tropical O3 hole. Polvani et al.26 also showed that global and tropical LST cooling had disappeared since 1997, while the tropical O3 concentration reached the minimum around 2005. When explaining their observed results, however, Polvani et al. argued for the low abundance of active chlorine and hence no local chemical O3 destruction in the tropical lower stratosphere. Instead, they argued that the observed tropical O3 and cooling trends were primarily driven by tropical upwelling caused by ODSs rather than greenhouse gases (GHGs) (mainly non-halogenated GHGs, as widely believed). As we have noted in the Introduction and will further discuss later, however, even a low level of active halogen can cause significant ozone depletion in the tropical lower stratosphere.
Interestingly, Polvani et al.26 also performed simulations from a chemistry–climate model (CCM) with incrementally added single forcings (sea surface temperatures—SSTs, GHGs, ODSs, volcanic eruptions, and solar variations) to detail the contribution of each forcing to tropical ozone and LSTs. Although their simulated results showed that ODSs were the dominant forcing of tropical ozone loss over GHGs, it must be pointed out that their simulated values of sum ozone loss (−28 ± 13 ppbv per decade; see their Table 1) were about five times smaller than their observed results (∼−150 ppbv per decade for the 1980s and 1990s), even ignoring that not all individual ensemble members showed statistically significant trends (see their Table 2). Moreover, in contrast to their claim that tropical lower stratospheric ozone would be closely tied to tropical upwelling w*, their simulated value of the w* increase by ODSs is not dominant but very close to that by GHGs, each force contributing to an increment by ∼0.1 km yr−1 decade−1 at 85 hPa, namely, 0.04 ± 0.09 for SSTs, 0.10 ± 0.11 for SSTs + GHGs, and 0.21 ± 0.11 for SSTs + GHGs + ODSs (see their Table 1). The results of the latter were also consistent with their simulated results of tropical LST trends (see their Fig. 3).
The simulated results of CCMs by Randel and Thompson37 and others38 had some differences from but were overall similar to the above-mentioned CCM results by Polvani et al.26 In most simulated results of CCMs, the strength of tropical upwelling was projected to increase from 1960 to 2100 by ∼2% per decade with the largest trends occurring in JJA, corresponding to tropical O3 reductions at 50 hPa of 0.15–0.35 ppmv (11–25 ppbv per decade).38 This ozone loss trend resulting from CCM simulations is about 10 times less than the observations by Polvani et al.26 and the present observations shown in Figs. 15. More crucially, the observed data have robustly shown that significant tropical ozone loss and LST cooling occurred in the 1980s and 1990s only, which is in drastic discrepancy from the simulated results of CCMs. Polvani et al.26 were then led to the open question: How could ODSs affect the stratospheric circulation? They conceded that the underlying mechanism for ODSs being a key forcing for tropical lower stratospheric O3 and temperature trends remained largely unexplored. Knowing the wide belief in CCMs that the key drivers of tropical upwelling and thus tropical O3 or LST trends since 1960 are non-halogenated GHGs (mainly CO2), Polvani et al.26 were forced to suggest that polar O3 depletion caused by ODSs would cause tropical upwelling and hence large tropical O3 losses. This explanation cannot be correct either, as the polar O3 hole is seasonal and appears only in the springtime, whereas the tropical O3 hole is all-season and has no changes in its central location over the seasons and over the decades since its appearance in the 1980s [Figs. 13 and 4(e)].
The present observed results in Figs. 16 and Figs. S1–S4 strongly indicate that, like the Antarctic O3 hole that was once incorrectly explained by the misconceived air transport mechanism (“dynamical theory”), the tropical O3 hole must not result from changes in normal atmospheric circulation patterns over the tropics since the 1960s or 1970s but result from an identical physical/chemical mechanism to that for the polar O3 hole. Obviously, the tropical O3 hole varies closely with the atmospheric level of CFCs [as seen in Fig. 4(b)], so it must originate from a CFC-related mechanism. The postulated stratospheric cooling and tropical upwelling effects of increasing non-halogenated GHGs have disappeared in observed O3 and temperature data for the Antarctic lower stratosphere6–8 and for the tropical lower stratosphere.26 It is obvious that the simulated results from CCMs26,37,38 do not agree with the observed results shown in Figs. 4(b)5(a)5(b), and 6(f), which show that the negative O3 trends were about 10 times larger (−25 to −30% per decade) in the 1980s and 1990s and there have been no significant O3 or LST trends in the tropical/Antarctic since the mid-1990s. The latter are actually consistent with the observations summarized in the newest IPCC report (Chap. 2).36 Moreover, the proposed enhanced tropical upwelling directly contradicts with the observed CFC depletion in the lower tropical stratosphere [Fig. 4(d)], as increased upward motion would transport CFC-rich air from the troposphere. Indeed, the observed data robustly show no shifts in the positions of both Antarctic and tropical O3 holes that have constantly been centered in the altitude region corresponding to the CR ionization peak since the 1960s/1980s and circularly symmetric O3 depletion cyclones are formed with the largest depletion at the centers [Figs. 13 and 4(e)]. These major features cannot be explained by tropical upwelling due to non-halogenated GHGs (mainly CO2) that have kept rising since the industrial revolution starting in 1760. All the observed data strongly indicate that tropical upwelling cannot be the major mechanism for the observed large, deep, and all-season tropical O3 hole. The simultaneous depletions of both CFCs and O3 in the lower tropical stratosphere are most likely due to a physical reaction mechanism that occurs locally. For the latter, the CRE mechanism, supported by the observed data in Figs. 16 and the substantial datasets obtained from both laboratory and atmospheric measurements,3–9,39–41 has provided the best and predictive model.
It is well known that the presence of PSCs is crucial for the formation of the Antarctic O3 hole.42–45 It was proposed that on the surfaces of PSCs, chlorine reservoir molecules (HCl and ClONO2) are converted into photoactive forms (Cl2) that can then undergo photolysis to destroy O3. There are two types of PSCs, namely, Type I and Type II PSC. The composition of Type II PSC is water ice, while Type I PSC is composed of mixtures of nitric acid (HNO3), water vapor (H2O), and sulfuric acid (H2SO4). The temperatures required for the formation of Type I and II PSCs are 195 and 188 K, respectively. Thus, it is very likely that TSCs, at least Type I PSC-like TSCs, can also form in the tropical lower stratosphere over the seasons due to the observed low temperatures of 190–200 K [Figs. S4 and Fig. 4(f)]. CRs may also play a certain role in forming PSCs and PSC-like TSCs.16,19 Note that the tropical lower stratosphere is very different from the polar lower stratosphere in both composition and climate. The former is rich in CFCs and other halogen-containing gases, whereas the latter are composed of inorganic chlorine species and lower-level CFCs. However, the CRE mechanism put forward two decades ago has proposed that O3-depleting reactions of both CFCs and inorganic halogen species can effectively occur on the surfaces of PSCs.3–9,39–41 Therefore, there are required and sufficient conditions for O3-depleting reactions occurring on the surfaces of proposed PSC-like TSCs in the tropical lower stratosphere. As noted in the Introduction, the constant co-presence of low-temperature TSCs and intense sunlight should lead to a unique active halogen evolution in the tropical lower stratosphere, in which halogen-catalyzed reactions are much more efficient for O3 destruction than those in the polar lower stratosphere.
The tropics (30°N–30°S) constitutes 50% of the Earth’s surface area, which is home to about 50% of the world’s population. O3 depletion in the tropics could cause a great global concern. In areas where O3 depletion is observed to be smaller in absolute O3 value, UV-B increases are more difficult to detect as the detection can be complicated by changes in cloudiness, local pollution, and other difficulties. However, it is generally agreed that the depletion of the O3 layer leads to an increase in ground-level UV radiation because ozone is an effective absorber of solar UV radiation. Exposure to enhanced UV-B levels could increase the incidence of skin cancer and cataracts in humans, weaken human immune systems, decrease agricultural productivity, and negatively affect sensitive aquatic organisms and ecosystems.46 Indeed, there was a report called HIPERION published by the Ecuadorian Space Agency in 2008.47 The study using ground measurements in Ecuador and satellite data for several countries over 28 years found that the UV radiation reaching equatorial latitudes was far greater than expected, with the UV index as high as 24 in Quito. This Ecuadorian report concluded that O3 depletion levels over equatorial regions are already endangering large populations in the regions. Further delicate studies of O3 depletion, UV radiation change, increased cancer risks, and other negative effects on health and ecosystems in the tropical regions will be of great interest and significance.
Another important result is that the global lower stratospheric temperature is essentially governed by the O3 layer, which is expected as ozone is the main and dominant molecule that absorbs solar radiation in the stratosphere. As a result, the presence of the tropical and polar O3 holes will play a major role in stratospheric cooling and regulating the global lower stratospheric temperature, as seen previously6–9,26 and in the results shown in Fig. S4 and Figs. 4(f) and 6(e)6(f). As seen in Fig. S4 and Fig. 4(f), this is equivalent to the formation of three “temperature holes” in the stratosphere, corresponding to the Antarctic, tropical, and Arctic O3 holes, respectively. This interesting result will be further explored in a subsequent paper.