Health and equity implications of individual adaptation to air pollution in a changing climate

Significance Air pollution is the leading environmental risk factor for early death. Alerts guide people to stay indoors when air quality is poor. Climate change can worsen air quality over this century. We show that this creates conditions for rising air quality alerts, disproportionately for racialized, unhoused, and poorly housed populations. Relying on people to protect themselves likely offers minimal benefits compared to reducing emissions; however, boosting adaptation can offer additional health benefits even under stringent climate policy. New policy could, for example, compensate people for moving indoors, and improve access to clean indoor air. We address active policy questions about how to equitably protect health under climate change, identifying levers for action against an increasing, unfair burden of air pollution.


Supporting text Figures S1 to S2
Tables S1 to S15 SI References SUPPLEMENTAL METHODS PM2.5 Infiltration.The infiltration factor FINF has been shown to be variable in previous studies.A national study by Persily et al. (2010) estimates that leakage accounts for a varying amount of infiltration based on the age and type of the dwelling unit (1).Using 2015 U.S. Census American Community Survey data on housing age and the proportion of population living in single-family housing, we calculated the weighted average of ACH due to leakage across the country as approximately 0.33 (2).Based on the plots by Long et al. (2001), an ACH rate of 0.33 corresponds with a PM0.7-2.5 infiltration rate of approximately 20% (3).We set FINF = 0.2.Outdoor PM2.5 concentrations vary by climate policy, day, and grid cell, and are updated based on model outputs.
Time Use.We use an average daily time spent outdoors of one hour.To determine Tout, we reviewed the ATUS 2021 Activity Summary File, analyzing the data of each respondent, and the location of their activity data according to the classification system developed by Hoehne et al. (2018) (4).In their study, Hoehne et al. (2018) classified activities as occurring "Indoor", "Outdoor", or "Unknown" (4).It is important to note that outdoor work is not accounted for in that study, leading to an underestimate of total outdoor time.
By applying these classifications to the ATUS 2021 data, we found that Tout -meaning activities classified as "Outdoor" -varied among respondents from 0 -15.5 hours.The mean Tout value was 34 minutes per day.The mean time spent in "Unknown" locations was 45 minutes per day.This leads to a range of 34 -79 minutes per day before accounting for outdoor work.The study by Cox-Ganser and Henneberger (2021) reported that 14.5 million people worked jobs classified as outdoors in 2019 (5).Based on the 2019 U.S. population of 328.3 million, this represents about 4.4% of the population.If we estimate that these people work 8 hours per day on 5 out of 7 days per week, this leads to an increase in the population-weighted average time spent outside of about 15 minutes per day, which brings the range of average time outside to 49 -94 minutes per day.
To reduce the risk of being influenced too strongly by the COVID-19 pandemic, we also examined the ATUS 2019 Activity Summary File data (6).That data showed a range of daily time spent outdoors of 0 -17 hours.The mean time outdoors value was 29 minutes per day and the mean unknown time was 52 minutes per day.After accounting for the population who works outdoors, the range of average time spent outside would be between 44 -96 minutes a day.

Social Learning Model
Overview.Our social learning model represents the spread of adaptation behavior through a population through comparison of the utility between adapters and non-adapters.In this model, we define separate regions, i, which represent one 2 x 2.5-degree grid cell.Each region has a homogenous population of fixed size at each time step.Individuals in this population can either be adapters or non-adapters.We define the proportion of adapters as   , thus 1 −   is the proportion of non-adapters.In this population, social norms encourage the dominant behavior.The utilities of being adapters and non-adapters are: (S2) In these equations,   represents the cost associated with adaptation in region i.   is a function that represents the perceived risk of negative health effects due to air pollution in region i.An adapter believes they mitigate their risk of these negative health effects by adapting, whereas a non-adapter receives the full amount of this perceived health risk.  represents the weight of social norms in each U.S census region and (  ) is a function that determines the social norm that is predominant for grid cell i.
We subtract  , −  , to define ∆  as: ∆ , = − , +  , +   (2� , � − 1) (S3) Where the parameters remain as defined in equations S1 and S2.Since   and   are measured in dollars and take on large values of magnitude much greater than 1, they will be scaled to be unitless and close to the range of [-1, 1], which is a similar order of magnitude for the social norms term.We do so by dividing the difference between  , and  , by an empirically fitted constant,  0 .
Where  0 is an empirically fitted constant added to scale the difference between mitigated perceived risk and cost such that its influence is of similar magnitude to the influence of social norms.
In each grid cell, individuals will update their adaptation/non-adaptation decision based on the rate at which information is spread throughout their social networks, the proportion of the population who are currently adapters or non-adapters, and the difference in utility between the two strategies as calculated in equation S4.
Where  , is the proportion of adapters in grid cell i at time t, ∆ , is the difference in utility between adaptation and non-adaptation ( , −  , ).  denotes the social learning rate in each U.S. census region, and   is the population of gridcell i. Population is included because higher population areas lead to more diverse social networks for inhabitants which increases the spread of information (7).The proportion of adapters in a grid cell must be between 0 (no adapters in the population) and 1 (the entire population is an adapter).Equation S6 enforces that bound.
Determining Social Influence.In this model, we include the spread of information and influence across grid cells.We do this by defining (  ), the social behavioral norm for grid cell i, as: Where  , is the normalized Social Connectedness Index (SCI) between two grid cells.SCI is defined by Meta/Facebook as the relative likelihood of a friendship link between users in two locations (8).We use this as a proxy for information spread between two locations, which influences social norms.To calculate  , , we retrieved SCI values at the U.S. county-county level from Facebook.Then, we aggregated the county-county connections to the grid cell -grid cell level using the process introduced in ( 9).The process begins by calculating the portion of counties that are in each grid cell.We then weight each county by its proportion of the total grid cell population.For each grid cell pair, we multiply countyi -countyj SCI values by the proportion of population that countyi and countyj make up.We sum these values to get the SCI between grid cells.Then, we multiply the SCI value between two grid cells by the population of both grid cells to get a relative number of connections between the grid cells.We then calculate the sum of the connections each grid cell has and normalize each grid cell connection total to determine the relative influence that each cell has on each other.The social norm for a grid cell is then calculated as the product of relative influence from grid cell to grid cell (  ) and the proportion of adapters in each influencing grid cell (  ).

Calculating Marginal Costs.
Marginal costs within the Social Learning Model are calculated similarly to the Rational Actor Model.As most literature surveys show that curtailing outdoor activities is the predominant adaptation strategy in the general population, we set the cost of adaptation to be proportional to the reduction of time spent outdoors by adapters.We value lost time outdoors at the average wage rate.The cost of adaptation can be represented as: Where   is the mean hourly wage rate in grid cell i.   is the proportion of an air quality alert day that an adapter chooses to spend indoors and is empirically fit by U.S. census region.  is the proportion of PM2.5 -driven air quality alert days within grid cell i over the current time period.  is the national average time spent outdoors, which is 2 hours per day over 365 days per year.
Calculating Perceived Risk.The perceived risk function  , includes a term for likelihood of risk, which is a function of the proportion of bad air days in the current time step,  , , a term for severity of risk,  , , and a scaling factor s.
The term for the severity of risk is based on   ~, which is defined as the annual per-capita costed premature mortality burden due to PM2.5, which is updated at quarterly intervals.
The costed premature mortality burden experienced by a grid cell of adapters and non-adapters is dependent on several factors.First is c, the Value of a Statistical Life, which is based on a population's willingness to pay to reduce their risk of premature death.Second is  , , which is the proportion by which adapters reduce their PM2.5 exposure across the time period by adapting.Third is xi,t, the proportion of the population who are adapters in the current time period.Last is  , ~, which is the incidence of PM-driven premature mortality for a population of non-adapters.
The adaptation strategy for adapters is to reduce their time outdoors on days with an AQI > 100.
The proportion of days with AQI > 100 also termed "Air Quality Alert Days" in each grid cell/time period is  , .AQI > 100 is the threshold for "Unhealthy for Sensitive Groups" and is the point where the U.S. EPA begins recommending behavior change.When projected AQI exceeds this threshold, health ministries may generate an alert to people living nearby.Therefore, the term  , is calculated as: Where, similarly to the Rational Actor Model, the term  is the ratio of the exposure an adapter would experience when staying indoors on an alert day to the exposure one has when they do not stay indoors.This term is dependent on   and FINF and is defined as: PM is the set of daily 24-hour mean PM2.5 concentrations over a given year.The set is separated into two subsets, one that includes the PM2.
Where r is one of the four U.S. census regions and μi,r represents the proportion of cell i in region r.We use a national, population-weighted hourly wage rate, ϕ, as we found that fitting using average wage by grid cell led to unrealistic results that were highly sensitive to grid-level wage values.Low-wage grid cells tended to equilibrate to full adaptation and high-wage grid cells tended to equilibrate to pure non-adapters within the fitting period of 2014-2020.Since adapters are updated quarterly and our data on adapters is yearly, Xr is interpolated to quarterly data.Also, throughout the fitting process, Xr,0 are fit and allowed to vary by 25% of their empirical value.

SUPPLEMENTAL RESULTS
Projection Into Future.For running the model in the years 2050 and 2100, the proportion of adapters is initialized to the last values from the previous time period.For 2050, the proportion of adapters from 2020 taken from the historical fitting process is used.Additionally, population and economic values are adjusted for predicted future growth, which are period and sometimes policy dependent and summarized in Tables S6 though S9.
Comparison to Start-of-Century.Table S10 compares PM2.5 exposure, adaptation days, exposure reduction per adaptation, adaptation benefits, adaptation costs, and adaptation net benefits between different policy/time period combinations and the beginning of the 21 st century.Table S10 shows that in both the REF and P3.7 scenarios, exposure to PM2.5 without adaptation will increase by the year 2050.P3.7 reduces the climate penalty on PM2.5 pollution by approximately half at 2050 and maintains pollution levels throughout the remainder of the century.Under REF, PM2.5 exposures continue to rise, leading to a climate penalty that is over five times worse than P3.7.Rational adaptation is shown to mitigate PM2.5 exposure in the future.At 2050, rational adapters would, on average, adapt 27 more days per year than they would under REF and 25 more days per year than they would under P3.7.This increase in adaptation is caused by higher PM2.5 pollution concentrations and an older population who will be more strongly affected by PM2.5 pollution.We see that these populations are willing to adapt when pollution reductions per adaptation day are lower than they would be at the start-of-century.The adaptation benefits, costs, and net benefits show that adaptation net benefits are highest in the REF scenario when pollution levels are highest and decrease under stringent climate policy.
Quantifying the Comparison to Previous Research.The most similar previous research to this is Buonocore et al. ( 2021), who investigated the potential health benefits of air quality alerts (10).Buonocore et al. ( 2021) consider both long-and short-term mortality risk changes due to ozone and PM2.5 in the population aged 65 years and older.When the Air Quality Index exceeds 100, assuming no infiltration or offsetting indoor sources, they find per capita benefits to be no higher than $14 per person per hour.Here, we find an average benefit of $31 per person per hour for adults aged 30 and over at the start-of-century across the U.S. Several differences in study design help to explain this difference; however, the dominant factor is the treatment of exposure reduction.Buonocore et al. allows a single hour of adaptation per day between 6 am and 9 pm, with exposure to outdoor air at all other hours of the day.This leads to differing exposure reductions based on how much worse the most polluted hour is than the other 23 hours.Our adaptation model, due to using 24-hour mean concentrations and accounting for exposure differences indoors and outdoors, results in a constant exposure reduction of approximately 15%.
In Buonocore et al. (2021), to achieve that level of reduction, the worst hour would have to be four times higher than the average of the remaining 23 hours.When we reproduce Buonocore et al.'s findings but with our exposure reduction assumptions, we find up to a 1.5-fold (or 50%) increase in benefits.Cost of adaptation in grid cell i at time t.

𝝋𝝋 𝒊𝒊
Mean hourly wage in gird cell i.
Daily time that the population spends adapting.

𝝃𝝃 𝒓𝒓
The portion of Tout that the population switches to Tin when adapting.

𝝆𝝆 𝒊𝒊,𝒐𝒐
The proportion of days with AQI over the relevant threshold (100 or 150) in a grid cell i at time t.

𝒔𝒔
An empirically fit scaling factor relating perceived risk to actual risk.

𝑷𝑷 𝒊𝒊,𝒐𝒐
Represents the economic value of the severity of risk of premature death due to PM2.5 pollution in grid cell i at time t.

𝜼𝜼 𝒊𝒊,𝒐𝒐
The proportion by which adapters reduce their PM2.S11.Effect of optimal adaptation on health effects of policy.The "Mitigate" scenarios are the costs and benefits accrued by enacting climate change mitigation policy and not considering PM2.5 adaptation.The "Rational Adapt" cases look at how including rational adaptation in the analysis reduces the cost (by reducing adaptation days from REF to P3.7) and reduces the benefits (because adaptation reduces the PM2.5 health burden).Policy benefits are reduced more than policy costs, leading to smaller benefit / cost ratios.

Figure S1 .
Figure S1.Best fit for Social Learning Model parameters based on fitting to SummerStyles survey data by region (11).Top row of plots show the national proportion of adapters based on survey data along with the modeled best fit and difference in utility between adapters and nonadapters.The bottom row of plots show the proportion of adapters by grid cell over the fitting period (2014-2020).

Figure S2 .
Figure S2.Comparison of modeled AQI days vs measured AQI days.Measured AQI days based on PM2.5 concentrations from US EPA monitors interpolated with Voronoi neighbor averaging performed in BenMAP-CE. .

Table S3 . Parameter definitions for Social Learning Model.
Raw proportion of adapters in grid cell i one time step into the future.Gets bound by minimum and maximum values.,Proportion of adapters in grid cell i in the current time step.

Table S4 .
(7)tion of health burden valuation driven by PM2.5 mortality.Calculated by isolating the valued health burden from PM2.5 mortality and dividing that by the total health burden from PM2.5 and O3.Data for calculations are in Saari et al. (2019)(7).

Table S6 .
Climate mitigation policy scenarios included in this study.

Table S7 .
Population projection factors and data sources.

Table S10 .
Changes in population weighted national mean attributes compared to start-ofcentury.The values in this table are the difference in national population weighted exposure data and adaptation benefits and costs between future time periods and the reference period for the year 2000.