Final Presentation given at the conclusion of the 2018 IMSM by the US EPA Student Working Group. Group Members: Elizabeth Herman, Jeonghwa Lee, Kartik Lovekar, Dorcas Ofori-Boateng, Fatemeh Norouzi, Benazir Rowe and Jianhui Sun

1. Splicing of Multi-Scale Downscaler Air Quality
Surfaces
Elizabeth Herman, Jeonghwa Lee, Kartik Lovekar, Dorcas
Ofori-Boateng, Fatemeh Norouzi, Benazir Rowe, and Jianhui Sun
Industrial Math/Stat Modeling Workshop 2018
July 25, 2018
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2. Motivation
In 2016,
122.5 million people
live in counties high
levels of air
pollutant
concentrations
12.1 million people
live in counties
which have high
levels of PM2.5
7 million premature
deaths caused by
ambient air
pollution.
http://www.who.int/gho/phe/air pollution mortality/en/
https://www.epa.gov/air-trends/air-quality-national-summary
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3. Data
Air Quality System (AQS):
Point-source measurements
(usually near large cities)
IMPROVE sites: Point-source
measurements (usually near
rural areas)
Downscaler Model (DS): fuses
estimates of pollutant obtained
through a model that uses
current knowledge of the
atmosphere and AQS readings
using a spatially-varying
weighted model
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4. Data
Old method: Run DS on National surface
New method: Run DS over regional surface
In DS, there is one range parameter
Run regions in parallel
Perform better
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5. Data
Run the DS on the NOAA climate regions with overlap area.
Question: How to deal with the multiple values in the overlap
region?
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6. Regions: Overlap
Question: How to deal with the multiple values in the overlap
region?
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7. Problem statement
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8. Exploratory Data Analysis: Relative Discrepancy
Let IMPROVEs be the air
pollutant readings from
IMPROVE station at
location s, and DSk be the
DS output from the k-th
grid which includes the
IMPROVE station s, then
FB(IMPROVEs, DSk) =
DSk − IMPROVEs
(IMPROVEs + DSk)/2
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9. Downscaler and IMPROVE Discrepancy
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10. Downscaler and AQS Discrepancy
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11. Methodology: Horizontal Mixed Density (HMD)
Model Assumption: For site s
fs = w1(s)f1,s + w2(s)f2,s
where fi,s is a normal density function with
µ = ˆµi,s(estimated DS mean at s),
σ = ˆσi,s(estimated DS standard error at s) from region i,
wi (s) =
e−φd(s,i)
e−φd(s,1) + e−φd(s,2)
d(s, i) is the distance of point s to region i, i = 1, 2.
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12. Methodology: Horizontal Mixed Density (HMD)
Figure 1: Distance from a site to the boundary
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13. Methodology: Horizontal Mixed Variable (HMD)
Figure 2: Weight functions with different φ values
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14. Results
HMD
Figure 3: HMD applied on the intersection of NR and NW
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15. Methodology: Horizontal Mixed Variable (HMV)
For a site s the DS random variable from region i is:
Xi,s ∼ N(ˆµi,s, ˆσi,s), i = 1, 2.
Our new variable at site s is :
Xs = w1(s)X1,s + w2(s)X2,s
where the weight wi (s) is defined as before,
wi (s) = e−φd(s,i)
/(e−φd(s,1)
+ e−φd(s,2)
).
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16. Results
HMV
Figure 4: HMV applied on the intersection of NR and NW
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17. Methodology: Adaptive Horizontal Mixed Variable
(AHMV)
Our new variable at site s is :
Xs = w1(s)X1,s + w2(s)X2,s
with
wi (s) = e−φd(s,i)
/(e−φd(s,1)
+ e−φd(s,2)
)
and
φ(d(s, c)) = β0 + β1d(s, c)
where d(s, c) is the horizontal distance of s to the vertical center line.
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18. Methodology: Adaptive Horizontal Mixed Variable
(AHMV)
Figure 5: Distance from a site to the center
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19. Results
AHMV
Figure 6: AHMV applied on the intersection of NR and NW
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20. Results
Table 1: Mean Square Error for AQS and IMPROVE sites (NW & NR)
Method
Data source HMD HMV AHMV
AQS 2.596 2.829 2.823
IMPROVE 47.913 42.588 42.250
Table 2: Mean Square Error for DS (NW & NR)
Region
Data source NW NR
AQS 3.89 3.21
IMPROVE 65.00 24.00
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21. Conclusion and Future Work
Conclusion:
Methods produce smooth surface
Future Work:
Extend to multiple zones and include latitudes
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22. THANK YOU!
Elizabeth Mannshardt, Barron Henderson, and Brett Gantt
Brian Reich
Organizers of IMSM
SAMSI
QUESTIONS
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23. References
Berrocal, V. J., Gelfand, A. E. and Holland, D. M. (2010a). A
spatio-temporal DS for outputs from numerical models. J. Agric. Biol.
Environ. Stat. 15 176197.doi:10.1007/s13253- 009-0004-z
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