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Weather impacts on air quality (weather penalties)
We used a framework proposed by (Jhun et al. 2015)6 to quantify the past weather-related changes in air pollution concentration. This framework derives “weather penalty” by accounting for the differences of the β values among a model adjusted by weather variables and a model unadjusted. Any difference of these models is attributable to the long-term impact of the weather variables. A positive penalty suggests that an increase in air pollution is associated with long-term weather changes. Jhun et al. (2015) used this approach to quantify past weather-related changes (weather penalty) in tropospheric ozone (O3) and PM2.5 in the US during 1994–2012. Then, further investigations used this same framework in several other analyses, including a study looking at the weather-related impacts in PM2.5 elemental concentration in the US19, a study that identified where air quality has been impacted by weather changes in the US20, a study that quantified the weather-related changes in air pollution in Spain17, and a recent study looking at the weather impacts on air quality in Brazil21. This recent work in Brazil estimated weather penalties stratified by Brazilian regions (there are five regions in Brazil). In this current study, we estimated weather penalties by municipality, since a fine spatial scale was required to calculate the disparities analyses with better spatial accuracy. There are 5572 municipalities in Brazil, representing the most minor areas considered by the Brazilian political system. We describe below the framework that we used.
We used two datasets, air pollution (PM2.5) and weather data. We accessed PM2.5 concentration from the Copernicus Atmosphere Monitoring Service (CAMS)-Reanalysis (from the European Centre for Medium-Range Weather Forecasts – ECMWF) for 2003–2018. The data was retrieved at a spatial resolution of 0.125 degrees (approximately 12.5 km), covering Brazil, and a temporal resolution of 6 h, including daily estimates for 00, 06, 12, and 18 UTC—Universal Time Coordinated. We calculated the daily mean concentration for each pollutant. Then, we aggregated air pollution data spatially at the municipality level, considering only the average value of the headquarters of each municipality in Brazil.
Weather data included surface temperature (°C), precipitation (mm), relative humidity (%), and wind speed (m/s). The data were collected from the ERA-Interim model consisting of a global atmospheric reanalysis performed by the ECMWF. The meteorological dataset was also retrieved at a temporal resolution of 6 h and a spatial resolution of 12.5 km. As for PM2.5, we calculated the daily means over the entire period of interest for each weather variable, then aggregated the data by the municipality.
As we mentioned above, the weather penalty was derived by the differences of the β values between two models – one model adjusted by weather variables and one model unadjusted. We applied generalized additive models (GAMs) to fit the adjusted and unadjusted models. Both models were controlled for temporal terms, including yearly, monthly, weekday, and daily variation. The adjusted and unadjusted models are described in Eqs. 1 and 2, respectively.
$$ Y_{{i,j}} = \alpha + \beta _{{adjusted}} year_{{i,j}} + \gamma month_{{i,j}} + \delta week\;day_{{i,j}} + \varepsilon day_{{i,j}} {\text{ }} + {\text{ }}s_{1} \left( {temp} \right){\text{ }} + {\text{ }}s_{2} \left( {ws} \right){\text{ }} + {\text{ }}s_{3} \left( {rh} \right){\text{ }} + {\text{ }}s_{4} \left( {pr} \right){\text{ }} + {\text{ }}e_{{i,j}} $$
(1)
$$ Y_{{i,j}} = \alpha + \beta _{{unadjusted}} {\text{ }}year_{{i,j}} + \gamma month_{{i,j}} + \delta week\;day_{{i,j}} + \varepsilon day_{{i,j}} {\text{ }} + {\text{ }}e_{{i,j}} $$
(2)
where Y represents the daily concentration of PM2.5 in the municipality i on date j; α is the intercept of the GAM model; βunadjusted and βadjusted represent the linear weather-unadjusted and adjusted PM2.5 trends, respectively, expressed in μg/m3 per year; \(\gamma \), δ, and Ɛ are the vectors of coefficients that explain monthly, weekday, and daily variability within the time series, respectively; e are normal residual errors with homoscedastic residual variance; and s1, s2, s3 and s4 are the default smoothing spline functions from the mgcv R package, that take into account the nonlinear relationships between daily concentration of PM2.5 and weather variables, including temperature (temp), wind speed (ws), relative humidity (rh), and precipitation (prec), respectively in the weather-adjusted model (Eq. 1).
Then we used the \({\beta }_{adjusted}\) and \({\beta }_{unadjusted}\) values to quantify past weather-related changes (“weather penalty”, expressed in µg/m3 per year) in PM2.5. We derived the weather penalties for each municipality by obtaining the differences between \({\beta }_{unadjusted}\) and \({\beta }_{adjusted}\) (\({\beta }_{unadjusted}\) − \({\beta }_{adjusted}\)). While the weather impact is incorporated into the unadjusted trends (Eq. 2), the control by weather variables in model 1 removes the impact of inter-annual weather variation on PM2.5 trends. Therefore, we considered that any differences between the unadjusted and weather-adjusted trends are entirely attributable to long-term weather changes. A positive penalty (\({\beta }_{unadjusted}\) > \({\beta }_{adjusted}\)) suggests that an increase in PM2.5 is associated with long-term weather changes between 2003 and 2018. On the other hand, a negative penalty indicates that variation in weather variables over the study period was associated with decreased pollution.
Finally, we applied bootstrap analysis to compute the confidence intervals for the coefficients estimated above. The bootstrap was based on randomized subsets (pseudo-datasets) of the input dataset that accounted for serial correlation structures among the observations. We created 1000 pseudo-datasets for each municipality. Then, for each pseudo-dataset, we applied the same models described in Eqs. 1 and 2 (adjusted and unadjusted, respectively). Then, we estimated standard error by obtaining standard deviation from the 100 estimates in the bootstrap analysis.
Disparities analyses
The disparities analyses were divided into three steps, including (i) the calculation of the population-weighted weather penalty, (ii) the calculation of the difference between exposure for the most-exposed group versus the least exposed group, and (iii) the estimation of the weighted Gini coefficients. All these analyses were performed on a national and regional scale.
Population-weighted weather penalty
The population-weighted weather penalty was calculated for two groups—racial and income. For both groups, we used population census data provided by the Brazilian Institute of Geography and Statistics—BIGS (https://www.ibge.gov.br/en/). The BIGS classifies the race group into four groups, including white, black, pardo (mainly used to refer to the people of light brown skin color), and amarelo (direct translation to English, it means “yellow”; technically, according to the BIGS, it refers to Asian people). These race categories were the option available chosen by the participants of the census. The national population-weighted weather penalty for racial group k was calculated as:
$$ \overline{WP}_{k} = \frac{{\mathop \sum \nolimits_{j = 1}^{n} WP_{j} P_{k,j} }}{{\mathop \sum \nolimits_{j = 1}^{n} P_{k,j} }} $$
(3)
where \({\overline{WP} }_{k}\) is the national population-weighted Weather Penalty (WP) for racial group k (White, Black, Pardo, or Asian), measured in µg/m3; \({WP}_{j}\) is the weather penalty for municipality j; \({P}_{k,j}\) is the number of people in racial group k living in the municipality j; and n is the number of municipalities in Brazil. For the income groups, the population-weighted weather penalty was calculated as:
$$ \overline{WP}_{i} = \frac{{\mathop \sum \nolimits_{{j = 1 \left( {j \in i} \right)}}^{n} WP_{j} P_{j} }}{{\mathop \sum \nolimits_{{j = 1 \left( {j \in i} \right)}}^{n} P_{j} }} $$
(4)
where \({\overline{WP} }_{i}\) is the national population-weighted Weather Penalty (WP) for income group i, also, measured in µg/m3. Here, we accounted for two income groups, including the group categorized as low income (< quartile 25th) and the group defined as high income (> quartile 75th); \({WP}_{j}\) is the weather penalty for municipality j; \({P}_{j}\) is the total population of municipality j. Note that the summation occurs only across municipality j belonging to income group i. Thus, n represents these municipalities.
Difference between exposure for the most-exposed group versus the least exposed group
In the second stage, we calculated the exposure disparity based on three metrics, absolute disparity, percent difference, and relative disparity (ratio). The absolute disparity was calculated as the difference between the exposure for the most-exposed group (racial and income) and the exposure for the least-exposed group (racial and income). For example, considering that black population were more exposed to weather penalties than the white population (\({\overline{WP} }_{black}>{\overline{WP} }_{white}\)), thus, the absolute disparity would be calculated as \({\overline{WP} }_{black}-{\overline{WP} }_{white}\). This metric is linked to exposure-specific health impacts22. For the second metric, still considering the example mentioned above (\({\overline{WP} }_{black}>{\overline{WP} }_{white}\)), the percentage difference would be calculated as [(\({\overline{WP} }_{black}-{\overline{WP} }_{white}\))/national mean weather penalty] × 100%. Finally, the relative disparity would be calculated as \({\overline{WP} }_{black} / {\overline{WP} }_{white}\). The metrics of percent difference and relative disparity are used to quantify disproportionality in exposure burdens22.
Estimation of the weighted Gini coefficients
Note that the metrics described in the previous topic are based on population-weighted mean weather penalty exposures. A limitation of these metrics is that the disparities are not calculated across the full weather penalty distribution. Therefore, to address this limitation in a way that we can verify the consistency of our primary metrics (mentioned in the previous section), in this third stage, we calculated the inequality metric considering the full weather penalty exposure distribution by estimating weighted Gini coefficients for each racial group and for the overall population. The weighted Gini coefficient was calculated using the weighted.gini function in the R package “acid”. In this function, we used as inputs the weather penalties and the population for the racial group (and total population) for each municipality.
Ethical approval
All experiments were performed in accordance with relevant guidelines and regulations.
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