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 Air Pollution Modelling for Support to Policy on Health, Environment to Policy on Health, Environment and Risk Management in Europeand Risk Management in Europe

APMoSPHERE

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.

AAir ir PPollution ollution MModelling for odelling for SSupport upport to to PPolicy on olicy on HHealth, ealth, EEnvironment nvironment and and RRisk isk MManagement in anagement in EEuropeurope

APMoSPHERE

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.

PartnersPartners

APMoSPHERE

•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 (PM10 and black smoke)

•Nitrogen oxides (NOx and NO2)

•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 (PM10 and black smoke)

•Nitrogen oxides (NOx and NO2)

•Carbon monoxide

•Sulphur dioxideSulphur dioxide•Ozone

Geographic Information Geographic Information SystemSystem 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*

AimsAims

Provide modelled exposures (and measures Provide modelled exposures (and measures of uncertainty).of uncertainty).• Impute missing valuesImpute missing values• Unmeasured locationsUnmeasured locations

Combine information from multiple sourcesCombine information from multiple sources Investigate the spatio-temporal modelling of Investigate the spatio-temporal modelling of

pollutants.pollutants. Assessing the contribution of spatial, temporal and Assessing the contribution of spatial, temporal and

random variabilty.random variabilty.

Data dependenciesData dependencies

Relationship with covariatesRelationship with covariates Climate, e.g. temperatureClimate, e.g. temperature Local emissions, e.g. land coverLocal emissions, e.g. land cover Topography, e.g. altitudeTopography, 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 frameworkModel framework Bayesian Hierarchical Model.Bayesian Hierarchical Model.

Pollutants (log) modelled as a function of the Pollutants (log) modelled as a function of the ‘true’ underlying level with unstructured error.‘true’ underlying level with unstructured error.

Incorporate covariate informationIncorporate covariate information

True underlying level is a function of the True underlying level is a function of the previous year’s level.previous year’s level.

Missing values treated as unknown parameters Missing values treated as unknown parameters within the Bayesian framework and can be within the Bayesian framework and can be estimated.estimated.

Priors

Information from previous studies or Information from previous studies or yearsyears

Expert opinionExpert opinion Physical sciencePhysical science ‘‘vague’vague’

Posteriors and parameter estimates

In simple cases, e.g. where both prior In simple cases, e.g. where both prior and likelihood are conjugate, exact and likelihood are conjugate, exact expressions for the posterior expressions for the posterior distributions can be founddistributions can be found

In more complex cases, the posterior In more complex cases, the posterior may be intractablemay be intractable Can use simulation to ‘build up’ the Can use simulation to ‘build up’ the

posteriorposterior MCMC (WinBUGS)MCMC (WinBUGS)

Model stagesModel stages

Level 1 : Observed data stage.Level 1 : Observed data stage. YYtt = = tt + covariates + site effect + v + covariates + site effect + vtt, v, vtt ~ N(0, ~ N(0,vv))

Level 2(a) : Temporal/system stage.Level 2(a) : Temporal/system stage. tt = = ααt-1t-1 + w + wtt, w, wtt ~ N(0, ~ N(0,ww))

Level 2(b) : Spatial stageLevel 2(b) : Spatial stage Site random effects modelled as multivariate normal with Site random effects modelled as multivariate normal with

correlations proportional to the distance,d, between sites.correlations proportional to the distance,d, between sites. f(d) = exp(-f(d) = exp(-d)d)

Site effects can be estimated at unmeasured locations Site effects can be estimated at unmeasured locations conditional on the measured values.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 informationPrior information

For the spatial effectFor the spatial effect ΦΦ given a uniform (1.3-4) distribution given a uniform (1.3-4) distribution

Corresponds to correlations falling to Corresponds to correlations falling to between 0.13 and 0.52 at a distance of 50kmbetween 0.13 and 0.52 at a distance of 50km

Normal distributions for covariate Normal distributions for covariate effectseffects

Gamma distributions for (inverse of) Gamma distributions for (inverse of) variances [precisions]variances [precisions]

ResultsResults

UK data for SO2, 1997-2001UK data for SO2, 1997-2001

Components of variationComponents of variation

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

Random errorRandom error

Posterior estimates –Posterior estimates – temporal components temporal components

[1]

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box plot: theta

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Spatial effectsSpatial effects

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-1.413 - -0.15-0.15 - -0.064-0.064 - -0.024-0.024 - 00 - 0.0010.001 - 0.0110.011 - 0.0420.042 - 0.0890.089 - 0.1920.192 - 0.854

Spatial effect

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[-1.75 ,-0.14](-0.14, 0.06](0.06, 0.23](0.23, 0.48](0.48, 0.97]

SO2 median spatial effect for UK

Posterior median for Posterior median for ΦΦ : 3.79, 95% CrI (2.95-4.00) : 3.79, 95% CrI (2.95-4.00)

Predictions for UKPredictions for UK

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7.679 - 22.18

22.18 - 26.874

26.874 - 31.371

31.371 - 35.765

35.765 - 40.031

40.031 - 44.798

44.798 - 50.841

50.841 - 61.687

61.687 - 91.881

91.881 - 328.153

Length of 95% credible intervals for predictions

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1.89 - 6.404

6.404 - 6.831

6.831 - 7.12

7.12 - 7.445

7.445 - 7.742

7.742 - 8.076

8.076 - 8.508

8.508 - 9.138

9.138 - 10.267

10.267 - 23.707

Predictions

Overall mean + temporal (2001) effect + covariate effect + spatial effect

Extending methodology Extending methodology to EU levelto EU level

Increased number of sites brings Increased number of sites brings large computational burdenlarge computational burden

Following analysis performed on NO2 Following analysis performed on NO2 in 2001in 2001 75 % dataset (sites) used to build 75 % dataset (sites) used to build

modelsmodels 25 % for validation25 % for validation

Modelling at different scalesModelling at different scales

Based on theoretical and empirical environmental Based on theoretical and empirical environmental modelsmodels VariogramsVariograms

Scales defined by site type and associated covariatesScales 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)

Site type Modelling set Validation set Total

Global background 225 87 312

Rural 225 87 312

Urban 459 141 600

Eases computational burdenEases computational burden

CovariatesCovariates Global Background (1

km) Rural scale (5 km, 21 km)

Urban scale (1km)

Variable NO2 CO PM SO2

O3 NO2 CO PM SO2

O3 NO2 CO PM SO2

O3

Motorways A roads

+ + + + - + + + + -

B roads Minor roads

+ + + + - + + + + -

Railways HD residential + + + + + + + + + - LD residential + + + + + + + + + Industry + + + + Transport + + + Airports + + + Seaports + + + + Construction

+ + + + -

+ + + + Urban greenery - - - - + Forestry + - - - - + Agriculture + + Altitude - - - - + - - - + + Topex - - - - + - - - - + Distance to sea + + - + -

Combined into 5 Factors Seasonal temperature + + + + +

Annual radiation + + + + + Seasonal wind speed

+ + + + +

Seasonal calm + + + + + Annual vapour pressure

+ + + + +

Annual rainfall + + + + +

Model stagesModel stages Global modelGlobal model

YYGsGs = = GG + global covariates + global covariatesSS + site effects + v + site effects + vGsGs, v, vGsGs ~ N(0, ~ N(0,22GG))

Rural modelRural model (Y(YRsRs – predicted(Y – predicted(YRsRs) ) = ) ) = RR + rural covariates + rural covariatesSS + v + vRsRs, v, vRsRs ~ N(0, ~ N(0,22

RR))

Urban modelUrban model (Y(YUsUs – predicted(Y – predicted(YUsUs) ) = ) ) = UU + urban covariates + urban covariatesSS + v + vUsUs, v, vUsUs ~ N(0, ~ N(0,22

UU))

Predictions were made using the global models Predictions were made using the global models for every one of the 1km x 1km cells (2854116)for every one of the 1km x 1km cells (2854116) additional effects of rural (2788454 cells) additional effects of rural (2788454 cells) urban (65662 cells)urban (65662 cells) used to create an further two sets of predictions used to create an further two sets of predictions

which were then combined to create a composite which were then combined to create a composite map.map.

Results – global modelResults – global model Increases with distanceIncreases with distance from sea and for climate from sea and for climate variables 2 & 5 – areas variables 2 & 5 – areas with warm or hot summerswith warm or hot summers

Decreases with altitudeDecreases with altitude

Posterior median for Posterior median for , 0.037, , 0.037, corresponds to fall in corresponds to fall in correlation to 0.024 at 100kmcorrelation to 0.024 at 100km

Without any geograpahical Without any geograpahical covariates, covariates, much smaller much smaller (by factor of ten), indicating (by factor of ten), indicating much more ‘spatial’ residual much more ‘spatial’ residual error error

Results – rural and urbanResults – rural and urban

Rural - significant effect Rural - significant effect of major roadsof major roads

Urban - clear overall Urban - clear overall increase (intercept term)increase (intercept term)

transport (major, transport (major, minor roads)minor roads)

population population densitydensity

negative negative associationassociation with altitudewith altitude

PollutantNO2

ScaleComposite of global, rural and urbanbackground

Time period2001, annual average

Geographic extentExcludes Norway and Sweden

Statistics (ug/m3)Min 0.45Max 139.06Mean 12.47Std dev 5.64

Modeling methodBayesian Hierarchical Modelling

Model

0 150 300 450 60075Kilometers

«

APMoSPHEREAPMoSPHERE

0 150 300 450 60075

Kilometers

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APMoSPHEREAPMoSPHERE

PollutantNO2

ScaleComposite of global, rural and urbanbackground

Time period2001, annual average

Geographic extentExcludes Norway and Sweden

Statistics (ug/m3)Min 1.66Max 287.36Mean 19.19Std dev 9.04

Length of 95% credible interval

ValidationValidation Performed at each scalePerformed at each scale (global, rural, urban)(global, rural, urban)

RSME, MAbsE, RRSME, MAbsE, R22, etc…, etc…

Best results for NOBest results for NO22, , PMPM1010

and Oand O33

Best results for urbanBest results for urban scale (relationships scale (relationships with covariates)with covariates)

exception of Oexception of O33

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Predicted

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Predicted

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SummarySummary

Applied spatial-temporal model to ca. 200 sites Applied spatial-temporal model to ca. 200 sites measuring SOmeasuring SO22 in UK (1997-2001). in UK (1997-2001). Assessed proportions of spatial, temporal and random Assessed proportions of spatial, temporal and random

variationvariation

Applied spatial model to entire EUApplied spatial model to entire EU

Produced predicted levels at 1km resolution for Produced predicted levels at 1km resolution for different scalesdifferent scales

Produced composite maps with measures of Produced composite maps with measures of uncertaintyuncertainty

Future work/considerationsFuture work/considerations

Combined spatial modelsCombined spatial models different site types modelling different site types modelling

simultaneously simultaneously

Computational aspectsComputational aspects Estimation and (joint) predictionEstimation and (joint) prediction Sensitivity analysis (to priors)Sensitivity analysis (to priors) Conditional modellingConditional modelling

Neighbouring sitesNeighbouring sites

Other pollutantsOther pollutants multi-pollutant modelsmulti-pollutant models

More information on More information on APMoSPHEREAPMoSPHERE

http://www.apmosphere.orghttp://www.apmosphere.org

Alternative approach – Alternative approach – conditional modellingconditional modelling

Problems handling large spatial matrices Problems handling large spatial matrices at such a high resolution.at such a high resolution.

Define sites as having ‘neighbours’ (may Define sites as having ‘neighbours’ (may include distance cut-off).include distance cut-off).

Allows feasibility of different resolutions to Allows feasibility of different resolutions to be examined.be examined.

Can be much, much faster!Can be much, much faster! Prediction and estimation may performed Prediction and estimation may performed

together during the MCMC.together during the MCMC.

Conditional modelConditional model

YYss ~ N(S ~ N(Sss,v,v)) SSss = = ββ + W + Wss

WWss ~ N( ~ N(ρρ ΣΣi in i in δδs s WWss/n/nss, n, nssττ)) Where Where ΣΣi in i in δδs s WWss/n/nss is the average of the is the average of the

neighbours of point neighbours of point s. s. The number of points that constitute The number of points that constitute

the neighbourhood can be variedthe neighbourhood can be varied

A 100km resolution structure A 100km resolution structure with 10 neighbourswith 10 neighbours

372 unknown points

Predicted SO2Predicted SO2

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X Coord

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4.06 - 5.855.85 - 6.176.17 - 6.256.25 - 6.76.7 - 6.976.97 - 7.247.24 - 7.657.65 - 8.078.07 - 9.049.04 - 11.97

VariabilityVariability

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Length of the 95% Pred. interval

X Coord

Y C

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2.88 - 3.343.34 - 3.673.67 - 4.024.02 - 4.324.32 - 4.544.54 - 4.734.73 - 5.035.03 - 5.955.95 - 7.367.36 - 15.66

Higher resolutionsHigher resolutions• Example of 50km resolution

418 known 1469 unknown points

Computational aspectsComputational aspects

100,000 iterations with ca. 400 sites100,000 iterations with ca. 400 sites Joint model – 5 daysJoint model – 5 days Conditional model – 30 minutesConditional model – 30 minutes

Using 2.5GHZ PC with 1GB RAMUsing 2.5GHZ PC with 1GB RAM

Using conditional model with observed and Using conditional model with observed and prediction points together at 20kmprediction points together at 20km 1 day (1000 iterations – 15 minutes)1 day (1000 iterations – 15 minutes)

Higher resolutions computationally Higher resolutions computationally feasible (but problems writing the file!)feasible (but problems writing the file!)