A DYNAMIC SPACE-TIME MODEL FOR PARTICULATE MATTER … · Applied a method based on space-time...
Transcript of A DYNAMIC SPACE-TIME MODEL FOR PARTICULATE MATTER … · Applied a method based on space-time...
![Page 1: A DYNAMIC SPACE-TIME MODEL FOR PARTICULATE MATTER … · Applied a method based on space-time dynamic models to fine space-time resolution air quality data. Temporal signal dominates,](https://reader033.fdocuments.in/reader033/viewer/2022060420/5f17974da055d45d0421d23b/html5/thumbnails/1.jpg)
A DYNAMIC SPACE-TIME MODEL FOR PARTICULATE MATTER AIR POLLUTIONNICHOLAS HAMM
![Page 2: A DYNAMIC SPACE-TIME MODEL FOR PARTICULATE MATTER … · Applied a method based on space-time dynamic models to fine space-time resolution air quality data. Temporal signal dominates,](https://reader033.fdocuments.in/reader033/viewer/2022060420/5f17974da055d45d0421d23b/html5/thumbnails/2.jpg)
Context AiREAS initiative Data Objectives Methods Results Conclusions
OVERVIEW
2
![Page 3: A DYNAMIC SPACE-TIME MODEL FOR PARTICULATE MATTER … · Applied a method based on space-time dynamic models to fine space-time resolution air quality data. Temporal signal dominates,](https://reader033.fdocuments.in/reader033/viewer/2022060420/5f17974da055d45d0421d23b/html5/thumbnails/3.jpg)
AiREAS civic initiative City-level air-quality monitoring and modelling Low cost sensors. High resolution of measurements in space and time. New possibilities for insights into air pollution at daily/sub-
daily time scales links to projects on traffic management and environmental epidemiology.
Large data volume. Data quality is a concern.
CONTEXT
3
![Page 4: A DYNAMIC SPACE-TIME MODEL FOR PARTICULATE MATTER … · Applied a method based on space-time dynamic models to fine space-time resolution air quality data. Temporal signal dominates,](https://reader033.fdocuments.in/reader033/viewer/2022060420/5f17974da055d45d0421d23b/html5/thumbnails/4.jpg)
Civic-initiative: local government, industry, SME's, universities, citizen groups.
Aim for a healthy city. Based in the City of Eindhoven,
The Netherlands (90 km2; 220,000 people)
Low-cost “Airboxes” housing sensors that measure different air pollutants
PM1, PM2.5, PM10 + NO2, O3, ultrafine particules
AIREAS CIVIC INIATIVE
www.aireas.com
4
![Page 5: A DYNAMIC SPACE-TIME MODEL FOR PARTICULATE MATTER … · Applied a method based on space-time dynamic models to fine space-time resolution air quality data. Temporal signal dominates,](https://reader033.fdocuments.in/reader033/viewer/2022060420/5f17974da055d45d0421d23b/html5/thumbnails/5.jpg)
32 “Airboxes” throughout the city Modified Shinyei PD42 optical
sensor Particle counts, calibrated to
PM10, PM2.5, PM1 Hourly observations
Missing data Noisy data Interpolation mapping
DATABACKGROUND
5
![Page 6: A DYNAMIC SPACE-TIME MODEL FOR PARTICULATE MATTER … · Applied a method based on space-time dynamic models to fine space-time resolution air quality data. Temporal signal dominates,](https://reader033.fdocuments.in/reader033/viewer/2022060420/5f17974da055d45d0421d23b/html5/thumbnails/6.jpg)
DATADISTRIBUTION OF AIRBOXES
6
![Page 7: A DYNAMIC SPACE-TIME MODEL FOR PARTICULATE MATTER … · Applied a method based on space-time dynamic models to fine space-time resolution air quality data. Temporal signal dominates,](https://reader033.fdocuments.in/reader033/viewer/2022060420/5f17974da055d45d0421d23b/html5/thumbnails/7.jpg)
We need a model to satisfy the following objectives1. Fill in gaps in the time-series2. Filter outliers3. Interpolate to un-sampled locations 4. Use minimal additional data.
Trial using a subset of the data: 2 weeks of observations 1-14 October 2014 32 locations, 336 observations (14 days 24 hours) Focus on PM10
OBJECTIVES
7
![Page 8: A DYNAMIC SPACE-TIME MODEL FOR PARTICULATE MATTER … · Applied a method based on space-time dynamic models to fine space-time resolution air quality data. Temporal signal dominates,](https://reader033.fdocuments.in/reader033/viewer/2022060420/5f17974da055d45d0421d23b/html5/thumbnails/8.jpg)
DATA TIME SERIES
8
![Page 9: A DYNAMIC SPACE-TIME MODEL FOR PARTICULATE MATTER … · Applied a method based on space-time dynamic models to fine space-time resolution air quality data. Temporal signal dominates,](https://reader033.fdocuments.in/reader033/viewer/2022060420/5f17974da055d45d0421d23b/html5/thumbnails/9.jpg)
Treat time as discrete and space as continuous
Measurement equation
: response (PM10) : covariates vary in space : coefficients vary in time only : space-time varying intercept ∼ 0, : uncorrelated error points in time (336) and measurement locations (32)
METHODS SPACE-TIME DYNAMIC MODEL (GELFAND ET AL 2005; FINLEY ET AL. 2012)
9
![Page 10: A DYNAMIC SPACE-TIME MODEL FOR PARTICULATE MATTER … · Applied a method based on space-time dynamic models to fine space-time resolution air quality data. Temporal signal dominates,](https://reader033.fdocuments.in/reader033/viewer/2022060420/5f17974da055d45d0421d23b/html5/thumbnails/10.jpg)
Time-varying regression coefficients
∼ 0, Σ
Space-time-varying intercept
∼ 0, ⋅; ,
; , ; exp /
METHODS TRANSITION EQUATIONS
10
![Page 11: A DYNAMIC SPACE-TIME MODEL FOR PARTICULATE MATTER … · Applied a method based on space-time dynamic models to fine space-time resolution air quality data. Temporal signal dominates,](https://reader033.fdocuments.in/reader033/viewer/2022060420/5f17974da055d45d0421d23b/html5/thumbnails/11.jpg)
Inference is performed in a Bayesian framework using MCMC Gibbs sampling with Metropolis step for Non-informative priors Normal distributions for the ’s Inverse Gamma distributions for and Uniform distribution for ’s Inverse Wishart distribution for Σ
20,000 iterations, check for convergence Implement using spBayes & coda packages in R
METHODS IMPLEMENTATION
11
![Page 12: A DYNAMIC SPACE-TIME MODEL FOR PARTICULATE MATTER … · Applied a method based on space-time dynamic models to fine space-time resolution air quality data. Temporal signal dominates,](https://reader033.fdocuments.in/reader033/viewer/2022060420/5f17974da055d45d0421d23b/html5/thumbnails/12.jpg)
Exploratory analysis found no significant relationship with meteorological data. Spatially varying covariates not currently available. Simplify the model to
Three experiments1. Isolated missing values. Remove 500 values at random and
predict them.2. Extended periods of missing values. Three sensors removed on
day 8. One sensor removed for three days.3. Predict at unsampled locations. Remove a sensor for the entire
period.
METHODSEXPERIMENTS
12
![Page 13: A DYNAMIC SPACE-TIME MODEL FOR PARTICULATE MATTER … · Applied a method based on space-time dynamic models to fine space-time resolution air quality data. Temporal signal dominates,](https://reader033.fdocuments.in/reader033/viewer/2022060420/5f17974da055d45d0421d23b/html5/thumbnails/13.jpg)
RESULTSEXPERIMENT 1 – ISOLATED MISSING VALUES
Time series of Σ 6.13 5.24, 7.19
13
![Page 14: A DYNAMIC SPACE-TIME MODEL FOR PARTICULATE MATTER … · Applied a method based on space-time dynamic models to fine space-time resolution air quality data. Temporal signal dominates,](https://reader033.fdocuments.in/reader033/viewer/2022060420/5f17974da055d45d0421d23b/html5/thumbnails/14.jpg)
RESULTSEXPERIMENT 1
Time series of Σ 6.13 5.24, 7.19 Time varying spatial
parameters Clear spatial structure
0.6
Temporal variability dominates Σ
14
![Page 15: A DYNAMIC SPACE-TIME MODEL FOR PARTICULATE MATTER … · Applied a method based on space-time dynamic models to fine space-time resolution air quality data. Temporal signal dominates,](https://reader033.fdocuments.in/reader033/viewer/2022060420/5f17974da055d45d0421d23b/html5/thumbnails/15.jpg)
RESULTSEXPERIMENT 1 – ISOLATED MISSING VALUES
Successfully fills in missing values, RMSE = 1.4 g m-3
15
Median Median
Median CI on prediction
Observed values
![Page 16: A DYNAMIC SPACE-TIME MODEL FOR PARTICULATE MATTER … · Applied a method based on space-time dynamic models to fine space-time resolution air quality data. Temporal signal dominates,](https://reader033.fdocuments.in/reader033/viewer/2022060420/5f17974da055d45d0421d23b/html5/thumbnails/16.jpg)
Median Median
Median CI on prediction
Observed values RESULTSEXPERIMENT 2 – EXTENDED PERIOD OF MISSING VALUES
Successfully fills in missing values, RMSE = 1.8 g m-3
16
![Page 17: A DYNAMIC SPACE-TIME MODEL FOR PARTICULATE MATTER … · Applied a method based on space-time dynamic models to fine space-time resolution air quality data. Temporal signal dominates,](https://reader033.fdocuments.in/reader033/viewer/2022060420/5f17974da055d45d0421d23b/html5/thumbnails/17.jpg)
Median Median
Median CI on prediction
Observed values
Extended period – 3 days at Airbox 19
RESULTSEXPERIMENT 2 – EXTENDED PERIOD OF MISSING VALUES
17
![Page 18: A DYNAMIC SPACE-TIME MODEL FOR PARTICULATE MATTER … · Applied a method based on space-time dynamic models to fine space-time resolution air quality data. Temporal signal dominates,](https://reader033.fdocuments.in/reader033/viewer/2022060420/5f17974da055d45d0421d23b/html5/thumbnails/18.jpg)
Reliability of results highly variable. Consider Airbox 19 – red dot
RESULTSEXPERIMENT 3 – PREDICTION AT UN-SAMPLED LOCATIONS
10
27
32
37
4
24
26
18
![Page 19: A DYNAMIC SPACE-TIME MODEL FOR PARTICULATE MATTER … · Applied a method based on space-time dynamic models to fine space-time resolution air quality data. Temporal signal dominates,](https://reader033.fdocuments.in/reader033/viewer/2022060420/5f17974da055d45d0421d23b/html5/thumbnails/19.jpg)
RESULTSEXPERIMENT 3 – PREDICTION AT UN-SAMPLED LOCATIONS
10
27
32
267
4
24
26
19
![Page 20: A DYNAMIC SPACE-TIME MODEL FOR PARTICULATE MATTER … · Applied a method based on space-time dynamic models to fine space-time resolution air quality data. Temporal signal dominates,](https://reader033.fdocuments.in/reader033/viewer/2022060420/5f17974da055d45d0421d23b/html5/thumbnails/20.jpg)
Applied a method based on space-time dynamic models to fine space-time resolution air quality data.
Temporal signal dominates, but spatial signal is still strong. Missing values were predicted accurately. Method is promising for data
cleaning. Prediction at un-sampled locations is inaccurate. Spatial correlation alone does not support accurate predictions Need to consider spatial and spatial-temporal covariates to support
prediction Method shows promise for outlier detection.
CONCLUSIONS
20