USING BAYESIAN HIERARCHICAL MODELLING TO PRODUCE HIGH RESOLUTION MAPS OF AIR POLLUTION IN THE EU Gavin Shaddick University of Bath RSS Avon Local Group October 2006

Air Pollution Modelling for Support to Policy on Health, Environment and Risk Management in Europe A PMoSPHERE APMoSPHERE is a thematic project, funded under the Global Monitoring for Environment and Security initiative, as part of the European Union’s Fifth Research Framework Programme. Its aim is to compile high resolution maps of air pollution across the EU, as a basis for scientific research and policy support.

Air Pollution Modelling for Support to Policy on Health, Environment and Risk Management in Europe A PMoSPHERE APMoSPHERE is a thematic project, funded under the Global Monitoring for Environment and Security initiative, as part of the European Union’s Fifth Research Framework Programme. Its aim is to compile high resolution maps of air pollution across the EU, as a basis for scientific research and policy support.

Partners A PMoSPHERE Department of Epidemiology and Public Health, Imperial College Institute for Risk Assessment Sciences, University of Utrecht Institute for Environmental Research and Sustainable Development, National Observatory of Athens Centre for International Climate and Environmental Research, Oslo Department of Mathematical Sciences, University of Bath AEA Technology Netcen

What APMoSPHERE will do Key objectives of APMoSPHERE are:  to produce a detailed (1km) inventory of atmospheric emissions by major sector for the EU  to develop and test a range of different methods for mapping air pollution on the basis of these emissions estimates, in combination with other routinely available data sets (including air pollution monitoring data)  using these various methods and data sets to generate detailed (1km) and updatable maps of air pollution, together with a set of policy-related indicators on potential ecological and health risks  based on these results, to provide an assessment of the air pollution situation in the EU, and implications for future air quality monitoring and policy The pollutants: Particulates (PM 10 and black smoke) Nitrogen oxides (NO x and NO 2 ) Carbon monoxide Sulphur dioxide Ozone

What APMoSPHERE will do Key objectives of APMoSPHERE are:  to produce a detailed (1km) inventory of atmospheric emissions by major sector for the EU  to develop and test a range of different methods for mapping air pollution on the basis of these emissions estimates, in combination with other routinely available data sets (including air pollution monitoring data)  using these various methods and data sets to generate detailed (1km) and updatable maps of air pollution, together with a set of policy-related indicators on potential ecological and health risks  based on these results, to provide an assessment of the air pollution situation in the EU, and implications for future air quality monitoring and policy Particulates (PM 10 and black smoke) Nitrogen oxides (NO x and NO 2 ) Carbon monoxide Sulphur dioxideSulphur dioxide Ozone

Geographic Information System Study Area EU15 + Norway Concentration data AIRBASE & EMEP * 1 km predictors Topography Meteorology Roads * Land cover * Light intensity * Modelled Emissions * Population data 1 km modelled population*

Aims Provide modelled exposures (and measures of uncertainty). Provide modelled exposures (and measures of uncertainty). Impute missing values Impute missing values Unmeasured locations Unmeasured locations Combine information from multiple sources Combine information from multiple sources Investigate the spatio-temporal modelling of pollutants. Investigate the spatio-temporal modelling of pollutants. Assessing the contribution of spatial, temporal and random variabilty. Assessing the contribution of spatial, temporal and random variabilty.

Data dependencies  Relationship with covariates Climate, e.g. temperature Climate, e.g. temperature Local emissions, e.g. land cover Local emissions, e.g. land cover Topography, e.g. altitude Topography, e.g. altitude Temporal dependencies. Temporal dependencies. Spatial dependencies. Spatial dependencies. Distance between monitoring sites. Distance between monitoring sites. Site type (e.g. background, traffic). Site type (e.g. background, traffic).

Model framework Bayesian Hierarchical Model. Bayesian Hierarchical Model. Pollutants (log) modelled as a function of the ‘true’ underlying level with unstructured error. Pollutants (log) modelled as a function of the ‘true’ underlying level with unstructured error. Incorporate covariate information Incorporate covariate information True underlying level is a function of the previous year’s level. True underlying level is a function of the previous year’s level. Missing values treated as unknown parameters within the Bayesian framework and can be estimated. Missing values treated as unknown parameters within the Bayesian framework and can be estimated.

Priors Information from previous studies or years Information from previous studies or years Expert opinion Expert opinion Physical science Physical science ‘vague’ ‘vague’

Posteriors and parameter estimates In simple cases, e.g. where both prior and likelihood are conjugate, exact expressions for the posterior distributions can be found In simple cases, e.g. where both prior and likelihood are conjugate, exact expressions for the posterior distributions can be found In more complex cases, the posterior may be intractable In more complex cases, the posterior may be intractable Can use simulation to ‘build up’ the posterior Can use simulation to ‘build up’ the posterior MCMC (WinBUGS) MCMC (WinBUGS)

Model stages Level 1 : Observed data stage. Level 1 : Observed data stage. Y t =  t + covariates + site effect + v t, v t ~ N(0,  v ) Y t =  t + covariates + site effect + v t, v t ~ N(0,  v ) Level 2(a) : Temporal/system stage. Level 2(a) : Temporal/system stage.  t = α  t-1 + w t, w t ~ N(0,  w )  t = α  t-1 + w t, w t ~ N(0,  w ) Level 2(b) : Spatial stage Level 2(b) : Spatial stage Site random effects modelled as multivariate normal with correlations proportional to the distance,d, between sites. Site random effects modelled as multivariate normal with correlations proportional to the distance,d, between sites. f(d) = exp(-  d) f(d) = exp(-  d) Site effects can be estimated at unmeasured locations conditional on the measured values. Site effects can be estimated at unmeasured locations conditional on the measured values. Level 3 : Hyperparameters. Level 3 : Hyperparameters. Assign prior distributions to covariate effects and variances. Assign prior distributions to covariate effects and variances.

Prior information For the spatial effect For the spatial effect Φ given a uniform (1.3-4) distribution Φ given a uniform (1.3-4) distribution Corresponds to correlations falling to between 0.13 and 0.52 at a distance of 50km Corresponds to correlations falling to between 0.13 and 0.52 at a distance of 50km Normal distributions for covariate effects Normal distributions for covariate effects Gamma distributions for (inverse of) variances [precisions] Gamma distributions for (inverse of) variances [precisions]

Results UK data for SO2, UK data for SO2,

Components of variation Random (unstructured) error – 26% Random (unstructured) error – 26% Temporal – 13% Temporal – 13% Spatial – 61% Spatial – 61% Random error

Posterior estimates – temporal components

Spatial effects Posterior median for Φ : 3.79, 95% CrI ( ) Posterior median for Φ : 3.79, 95% CrI ( )

Predictions for UK Overall mean + temporal (2001) effect + covariate effect + spatial effect

Extending methodology to EU level  Increased number of sites brings large computational burden Following analysis performed on NO2 in 2001 Following analysis performed on NO2 in % dataset (sites) used to build models 75 % dataset (sites) used to build models 25 % for validation 25 % for validation

Modelling at different scales Based on theoretical and empirical environmental models Based on theoretical and empirical environmental models Variograms Variograms Scales defined by site type and associated covariates Scales defined by site type and associated covariates Global (climate and topological) Global (climate and topological) Rural (transport, population density, agriculture) Rural (transport, population density, agriculture) Urban (transport, population density, urban greenery) Urban (transport, population density, urban greenery) Eases computational burden Eases computational burden

Covariates

Model stages Global model Global model Y Gs =  G + global covariates S + site effects + v Gs, v Gs ~ N(0,  2 G ) Y Gs =  G + global covariates S + site effects + v Gs, v Gs ~ N(0,  2 G ) Rural model Rural model (Y Rs – predicted(Y Rs ) ) =  R + rural covariates S + v Rs, v Rs ~ N(0,  2 R ) (Y Rs – predicted(Y Rs ) ) =  R + rural covariates S + v Rs, v Rs ~ N(0,  2 R ) Urban model Urban model (Y Us – predicted(Y Us ) ) =  U + urban covariates S + v Us, v Us ~ N(0,  2 U ) (Y Us – predicted(Y Us ) ) =  U + urban covariates S + v Us, v Us ~ N(0,  2 U ) Predictions were made using the global models for every one of the 1km x 1km cells ( ) Predictions were made using the global models for every one of the 1km x 1km cells ( ) additional effects of rural ( cells) additional effects of rural ( cells) urban (65662 cells) urban (65662 cells) used to create an further two sets of predictions which were then combined to create a composite map. used to create an further two sets of predictions which were then combined to create a composite map.

Results – global model Increases with distance Increases with distance from sea and for climate from sea and for climate variables 2 & 5 – areas variables 2 & 5 – areas with warm or hot summers with warm or hot summers  Decreases with altitude Posterior median for , 0.037, corresponds to fall in correlation to at 100km Posterior median for , 0.037, corresponds to fall in correlation to at 100km Without any geograpahical covariates,  much smaller (by factor of ten), indicating much more ‘spatial’ residual error Without any geograpahical covariates,  much smaller (by factor of ten), indicating much more ‘spatial’ residual error

Results – rural and urban Rural - significant effect of major roads Rural - significant effect of major roads Urban - clear overall increase (intercept term) Urban - clear overall increase (intercept term)  transport (major, minor roads) minor roads)  population density  negative association with altitude with altitude

Pollutant NO 2 Scale Composite of global, rural and urban background Time period 2001, annual average Geographic extent Excludes Norway and Sweden Statistics (ug/m 3 ) Min0.45 Max Mean12.47 Std dev5.64 Modeling method Bayesian Hierarchical Modelling Model

Pollutant NO 2 Scale Composite of global, rural and urban background Time period 2001, annual average Geographic extent Excludes Norway and Sweden Statistics (ug/m 3 ) Min1.66 Max Mean19.19 Std dev9.04 Length of 95% credible interval

Validation Performed at each scale Performed at each scale (global, rural, urban) (global, rural, urban)  RSME, MAbsE, R 2, etc…  Best results for NO 2, PM 10 and O 3 and O 3  Best results for urban scale (relationships scale (relationships with covariates) with covariates)  exception of O 3

Summary Applied spatial-temporal model to ca. 200 sites measuring SO 2 in UK ( ). Applied spatial-temporal model to ca. 200 sites measuring SO 2 in UK ( ). Assessed proportions of spatial, temporal and random variation Assessed proportions of spatial, temporal and random variation Applied spatial model to entire EU Applied spatial model to entire EU Produced predicted levels at 1km resolution for different scales Produced predicted levels at 1km resolution for different scales Produced composite maps with measures of uncertainty Produced composite maps with measures of uncertainty

Future work/considerations  Combined spatial models different site types modelling simultaneously different site types modelling simultaneously Computational aspects Computational aspects Estimation and (joint) prediction Estimation and (joint) prediction Sensitivity analysis (to priors) Sensitivity analysis (to priors) Conditional modelling Conditional modelling Neighbouring sites Neighbouring sites  Other pollutants  multi-pollutant models

More information on APMoSPHERE

Alternative approach – conditional modelling Problems handling large spatial matrices at such a high resolution. Problems handling large spatial matrices at such a high resolution. Define sites as having ‘neighbours’ (may include distance cut-off). Define sites as having ‘neighbours’ (may include distance cut-off). Allows feasibility of different resolutions to be examined. Allows feasibility of different resolutions to be examined. Can be much, much faster! Can be much, much faster! Prediction and estimation may performed together during the MCMC. Prediction and estimation may performed together during the MCMC.

Conditional model Y s ~ N(S s,v) Y s ~ N(S s,v) S s = β + W s S s = β + W s W s ~ N(ρ Σ i in δs W s /n s, n s τ) W s ~ N(ρ Σ i in δs W s /n s, n s τ) Where Σ i in δs W s /n s is the average of the neighbours of point s. Where Σ i in δs W s /n s is the average of the neighbours of point s. The number of points that constitute the neighbourhood can be varied The number of points that constitute the neighbourhood can be varied

A 100km resolution structure with 10 neighbours 372 unknown points

Predicted SO2

Variability

Higher resolutions Example of 50km resolution 418 known 1469 unknown points

Computational aspects 100,000 iterations with ca. 400 sites 100,000 iterations with ca. 400 sites Joint model – 5 days Joint model – 5 days Conditional model – 30 minutes Conditional model – 30 minutes Using 2.5GHZ PC with 1GB RAM Using 2.5GHZ PC with 1GB RAM Using conditional model with observed and prediction points together at 20km Using conditional model with observed and prediction points together at 20km 1 day (1000 iterations – 15 minutes) 1 day (1000 iterations – 15 minutes) Higher resolutions computationally feasible (but problems writing the file!) Higher resolutions computationally feasible (but problems writing the file!)