A spatial causal analysis of wildfire-contributed PM 2.5 using numerical model output. Brian Reich, NC State
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1 A spatial causal analysis of wildfire-contributed PM 2.5 using numerical model output Brian Reich, NC State Workshop on Causal Adjustment in the Presence of Spatial Dependence June 11-13, 2018 Brian Reich, NC State Forest-fire contributed PM / 36
2 Collaborators Alex Larsen (NCSU) Shu Yang (NCSU) Ana Rappold (EPA) Brian Reich, NC State Forest-fire contributed PM / 36
3 Increase in wildfires in the US Since the 70 s, the rate of large wildfires (1000+ acres) has doubled In that time, the rate of very large wildfires (10,000+ acres) has increased fivefold 1 This poses an increasing health threat: NPR (9/11/17) Is All That Wildfire Smoke Damaging My Lungs? NYT (9/17/17): As Wildfires Burn West, Ash Rides Wind High Across the U.S.; Large Erratic Blazes are Posing a Bigger Threat to People 1 climatecentral.org, 2012 Brian Reich, NC State Forest-fire contributed PM / 36
4 Smoke plumes carry pollution across the continent Brian Reich, NC State Forest-fire contributed PM2.5 4 / 36
5 Wildfires contribution to air pollution Fine particular matter (PM 2.5 ) is a criteria pollutant monitored by the EPA to protect human health In the US, emissions of PM 2.5 from most sources are steadily declining Forest fire smoke remains a major contributor, and may increase with climate change, population, and land-use change Many studies are now investigating the health effects of fire smoke Brian Reich, NC State Forest-fire contributed PM / 36
6 Causal analysis using numerical models How much PM 2.5 is causally-attributed to wildfires? How much health burden is causally-attributed to wildfires? These questions are difficult to answer because only total PM 2.5 (background + fire) can be measured Observational data, long-range transport and confounding environmental factors are also challenges We combine numerical models and observational data Causal analysis lays bare the assumptions needed to interpret the results causally Brian Reich, NC State Forest-fire contributed PM / 36
7 Related work on spatial causal inference Downscaler methods (e.g., Berrocal et al 2 ) correct for spatially-varying bias in model output no treatment effects Zigler et al have a series of papers 3 on causal effects of air pollution regulation no numerical models or counterfactuals Detection and attribution climate studies 4 run models in different regimes only observe data in one regime 2 e.g., Berrocal, Gelfand, and Holland, AOAS, e.g., Zigler, Dominici, Wang, Biostatistics, 2012; Zigler and Dominici, AJE, 2014; Zigler et al, HEI, e.g., Katzfuss et al, JGR, 2017 Brian Reich, NC State Forest-fire contributed PM / 36
8 CMAQ: The Community Multiscale Air Quality Modeling System Brian Reich, NC State Forest-fire contributed PM / 36
9 Annual average CMAQ (12km 12km) Brian Reich, NC State Forest-fire contributed PM / 36
10 CMAQ run without fires Brian Reich, NC State Forest-fire contributed PM / 36
11 Difference between the runs (as % of total) Brian Reich, NC State Forest-fire contributed PM / 36
12 EPA Monitoring Stations (background + fire) PM 2.5 is measured every 3-6 days; this is the average Brian Reich, NC State Forest-fire contributed PM / 36
13 Time series plot for one site in Northern CA Brian Reich, NC State Forest-fire contributed PM / 36
14 Data sources and notation Monitor data at location s and day t: Y t (s) CMAQ non-fire run: ˆθ t (s) CMAQ fire run minus non-fire run: ˆδ t (s) Other confounders (emissions, wind, land type): X t (s) Binary indicator of a fire: A t (s) The collection a process across space is bold, e.g., A t = {A t (s); s D} Brian Reich, NC State Forest-fire contributed PM / 36
15 Potential outcomes framework The PM 2.5 at s depends on the fire status at all sites, A This is called interference or spill-over When envisioning counterfactual outcomes we must consider all sites simultaneously Brian Reich, NC State Forest-fire contributed PM / 36
16 Potential outcomes framework The treatment is the regime R = 0: world without forest fires R = 1: current world with forest fires Y t (s, 0) and Y t (s, 1) are the potential PM 2.5 outcomes Model: Y t (s, 0) = θ t (s) and Y t (s, 1) = θ t (s) + δ t (s) θ t and δ t are stochastic processes Brian Reich, NC State Forest-fire contributed PM / 36
17 Potential outcomes framework The causal effect is (s) = E[Y t (s, 1) Y t (s, 0)] = E[δ t (s)] where the average is over the distribution of covariates X and fires A over the entire spatial domain Challenge: we never observe data under R = 0 To address this we use CMAQ output Causal assumptions Brian Reich, NC State Forest-fire contributed PM / 36
18 Assumptions We assume there exist C t (s) {0, 1} where s is affected by smoke iff C t (s) = 1 Bias-correction functions B 0 and B 1 so that the following assumptions hold: (A1) Consistency: Y t (s) = Y t [s, C t (s)] (A2) No unmeasured confounders given model output: θ t (s) = B 0 [ˆθ t (s)] + e 1t (s) and δ t (s) = B 1 [ˆδ t (s)] + e 2t (s), where e t (s) = [e 1t, e 2t ] is independent of X, A and C Brian Reich, NC State Forest-fire contributed PM / 36
19 Assumptions (A1) Consistency: Y t (s) = Y t [s, C t (s)] (A2) No unmeasured confounders given model output: θ t (s) = B 0 [ˆθ t (s)] + e 1t (s) and δ t (s) = B 1 [ˆδ t (s)] + e 2t (s), where e t (s) = [e 1t, e 2t ] is independent of X, A and C Are these assumptions reasonable? (A1) assumes that we have some observations we are sure are not affected by fire smoke (including spillover)...probably OK? (A2) assumes that the CMAQ modelers have included the important drivers of fine particulate matter...maybe OK? Have the accounted for all feedbacks? Brian Reich, NC State Forest-fire contributed PM / 36
20 Causal interpretation Theorem 1:Under (A1) and (A2) and assuming that C t is not degenerate, then the parameters in the potential outcome model are identifiable via the distribution of observed data, Y t ˆθ t, ˆδ t, C t. By Theorem 1, causal parameter estimation only requires inspecting the implied model for Y t (s) and confirming parameter identification. We specify parametric models for the bias correction functions B 0 and B 1 and the spatial process e t (s). We then argue that all parameters, including the correlation between counterfactuals, are identifiable. This serves as a basis for using a Bayesian approach to estimating (s). Brian Reich, NC State Forest-fire contributed PM / 36
21 Spillover/interference Defining the intervention as the fire regime instead of individual fires is key for two reasons: 1. mimics the numerical model simulation 2. limits the number of potential outcomes An alternative is to define potential outcomes for each potential fire-presence vector, A t = [A t (s 1 ),..., A t (s n )] This would require 2 n potential outcomes, and very complicated modeling and marginalization Limitation: the proposed framework cannot estimate effects of individual fires or specific features of fires Brian Reich, NC State Forest-fire contributed PM / 36
22 Bayesian hierarchical model The model is: Y t (s) = θ t (s) + C t (s)δ t (s) + ε t (s) θ t (s) = B 0 [ˆθ t (s)] + e 1t (s) δ t (s) = B 1 [ˆδ t (s)] + e 2t (s) Measurement error (iid) is ε Background PM 2.5 bias adjustment: B 0 [ˆθ t (s)] = a 0 (s) + b 0 (s)ˆθ t (s) Fire-contributed PM 2.5 bias adjustment: B 1 [ˆθ t (s)] = a 1 (s) + b 1 (s)ˆδ t (s) Brian Reich, NC State Forest-fire contributed PM / 36
23 Bayesian hierarchical model The model is: Y t (s) = θ t (s) + C t (s)δ t (s) + ε t (s) θ t (s) = B 0 [ˆθ t (s)] + e 1t (s) δ t (s) = B 1 [ˆδ t (s)] + e 2t (s) Fire indicator: C t (s) = 1 if ˆδ t (s) > τ Spatial process e t (s) follows a bivariate Matern process Cov[e jt (s), e kt (s )] = M( s s ; ρ jk ) where M is the Matern covariance function and ρ jk are covariance parameters Brian Reich, NC State Forest-fire contributed PM / 36
24 Identification The mean is E[Y t (s)] is α 0 (s) + β 0 (s)ˆθ t (s) + α 1 (s)c t (s) + β 1 (s)[c t (s)ˆδ t (s)] Identification follows assuming {1, ˆθ t (s), C t (s), C t (s)ˆδ t (s)} are not perfectly collinear The covariance Cov[Y t (s), Y t (s )] is M( s s ; ρ 11 ) if C t (s) = C t (s ) = 0 M( s s ; ρ 12 ) if C t (s) C t (s ) M( s s ; ρ 22 ) if C t (s) = C t (s ) = 1 By examining the correlation between pairs separately by C t (s) the correlation parameters are identifiable Brian Reich, NC State Forest-fire contributed PM / 36
25 Posterior inference We approximate the causal effect E[C t (s)δ t (s)] by T (s) = C t (s)δ t (s) t=1 The Bayesian framework gives the full posterior for Under (A1) and (A2) this has a causal interpretation The model is fit separately in 9 subregions We assume independence across days Brian Reich, NC State Forest-fire contributed PM / 36
26 Data and estimates for one site in CA Brian Reich, NC State Forest-fire contributed PM / 36
27 Average θ t (s) over the wildfire season Brian Reich, NC State Forest-fire contributed PM / 36
28 Posterior mean slope, b 1 (s) Brian Reich, NC State Forest-fire contributed PM / 36
29 Causal estimate, (s), posterior mean Brian Reich, NC State Forest-fire contributed PM / 36
30 Causal estimate, (s), posterior SD Brian Reich, NC State Forest-fire contributed PM / 36
31 Fire-Contributed PM as % of Total Brian Reich, NC State Forest-fire contributed PM / 36
32 Causal Estimate vs. CMAQ at monitors in the NW Brian Reich, NC State Forest-fire contributed PM / 36
33 Estimated 5 number of attributable hospitalizations Age Group Region Method Central Bayesian CMAQ ENC Bayesian CMAQ South Bayesian CMAQ Southeast Bayesian CMAQ Southwest Bayesian CMAQ Relative risk of wildfire-contributed PM 2.5 taken from Delfino et al (2009) Brian Reich, NC State Forest-fire contributed PM / 36
34 Estimated number of attributable hospitalizations Age Group Region Method Northeast Bayesian CMAQ Northwest Bayesian CMAQ West Bayesian CMAQ WNC Bayesian CMAQ Brian Reich, NC State Forest-fire contributed PM / 36
35 Cumulative health burden by county Brian Reich, NC State Forest-fire contributed PM / 36
36 Conclusions/future directions The Bayesian model produces generally lower effect estimates compared to CMAQ Bayesian model gives uncertainty estimates Sensitivity testing for the causal assumptions is needed Thanks to the Joint Fire Science Program for support! Brian Reich, NC State Forest-fire contributed PM / 36
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