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Modeling Ground Ozone for the Contiguous United States By Michael Tuffly, Ph.D. ERIA Consultants, LLC GIS in the Rockies 2013 Cable Center Denver, Colorado 10/9/2013 http://www.eriaconsultants.com [email protected]
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2013 ASPRS Track, Ozone Modeling for the Contiguous United States by Michael Tuffly

Jan 17, 2015

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Ozone (O3) is a powerful oxidizer (e.g. reacting with oxygen). Ozone in the upper atmosphere is considered beneficial due to the ability of the compound to filter harmful UV rays generated from the sun. However, ground level concentrations of ozone influence animal and plant health. In animals, one symptom of ground level ozone is lung tissue damage resulting in respiratory complications. Excess ozone in plants can cause excessive water loss; thus, emulate drought conditions. Ozone simulates the stomata cell in plant leaves so that these cells do not function properly. That is the stomata cells do not close completely, resulting in excess water loss (Smith et al. 2008). Anthropogenic ozone can be created via internal combustion engines and coal fired power plants.
Collecting data from the Environmental Protection Agency (EPA) CASTnet site for the time periods 1990 to 2010 I use spatial interpolation techniques to create an ozone surface concentration for the contiguous United States.
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Page 1: 2013 ASPRS Track, Ozone Modeling for the Contiguous United States by Michael Tuffly

Modeling Ground Ozone for the Contiguous United States

By

Michael Tuffly, Ph.D.

ERIA Consultants, LLC

GIS in the Rockies 2013

Cable Center

Denver, Colorado

10/9/2013

http://www.eriaconsultants.com

[email protected]

Page 2: 2013 ASPRS Track, Ozone Modeling for the Contiguous United States by Michael Tuffly

What is Ozone

Chemically

It is a molecule containing 3 Oxygen atoms (aka triatomic) oxygen (O3).

Ozone is a powerful oxidizer (e.g. combines with Oxygen).

Examples of Oxidation

Rust on metal objects

Fire

“Oxidation is an increase in the oxidation number or a real or apparent loss of one or more electrons.” (Miller 1981).

Miller. G. T., 1981. Chemistry: A basic Introduction Second Edition. Wadsworth Publishing Company, Belmont, Californai. USA.

Page 3: 2013 ASPRS Track, Ozone Modeling for the Contiguous United States by Michael Tuffly

Ozone’s Location

Ozone which is located in the lower stratosphere (20 – 50 km in elevation) is beneficial to life on earth.

In the lower stratosphere ozone molecules form a protective layer that filters out much of the high-energy solar ultraviolet radiation.

3O2 2 O3 Ultraviolet Radiation

Page 4: 2013 ASPRS Track, Ozone Modeling for the Contiguous United States by Michael Tuffly

Ground Ozone Ozone at ground level can be an issue to the health of plants and animals

One way ground ozone is formed is via a reaction of NOx VOC’s, and sunlight.

The primary source of NOx is from internal combustion engines (i.e. cars) and coal fire power plants.

Many sources of VOC’s

Methane, CFC, Benzene, Methylene chloride, etc…

VOC’s have a high vapor pressure which produces low boiling point temperatures

Low boiling point temperatures allows VOC’s to escape to the atmosphere

Page 5: 2013 ASPRS Track, Ozone Modeling for the Contiguous United States by Michael Tuffly

Some Effects of Ground Ozone

In animals

Lung tissue damage can result from inhalation of ozone

In plants

Leaf surface damage (oxidation)

Disruption in stomata cell functions

Causing excessive water loss emulating drought conditions (Smith et al. 2008).

Smith, G. C., J. W. Coulston, and B. M. O'Connell. 2008. Ozone Bioindicators and Forest Health: A Guide to the Evaluation, Analysis and Interpretation of the Ozone Injury Data in the Forest Inventory and Analysis Program. United States Department of Agriculture, Forest Service General Technical Report 34

Page 6: 2013 ASPRS Track, Ozone Modeling for the Contiguous United States by Michael Tuffly

Other ways ozone can be formed

Lighting (natural) (small contributor)

Shorts in electrical equipment (anthropogenic)

Provides that unique smell (very small contributor)

Ozone is also use as a replacement for Chlorine (potentially high contributor; but, really unknown)

In swimming Pools

In sewage treatment plants

In domestic water supply as a disinfectant

Page 7: 2013 ASPRS Track, Ozone Modeling for the Contiguous United States by Michael Tuffly

Modeling Ozone

Source ozone data are from EPA CASTNET

ftp://ftp.epa.gov/castnet/data/

Data are from a single year 2010

In the summer months during the “Ozone Activity Envelope” (OAE)

June – August from 1:00 PM – 5:00 PM

Base data for ozone are recorded every hour

Only 73 ground ozone collections sites were used

This is part of a larger study over a ten year time period. These 73 sites were the only sites consistent from 2002 to 2011.

Five variables were extracted from these data for the OAE and averaged:

Ozone (PPB)

Wind Speed (MS)

Relative Humidity (% * 100)

Solar Radiation (Watts per m2)

Temperature (degrees C * 10)

Page 8: 2013 ASPRS Track, Ozone Modeling for the Contiguous United States by Michael Tuffly

Modeling Methods

Four different modeling methods were investigated:

Inverse Weighted Distance (IDW)

Ordinary Kriging

Generalized Linear Model (GLM)

Geographically Weighted Regression (GWR)

Results for all four modeling methods were:

Compared with a set of sample data not used in model creation via the Mean Squared Error Predicted (MSEP) method.

Page 9: 2013 ASPRS Track, Ozone Modeling for the Contiguous United States by Michael Tuffly

Autocorrelation

First, need to know if the data are autocorrelated

If the data are autocorrelated then we can use:

IDW

Kriging

Results from Morans’I (a test for autocorrelation) (Moran 1950

Data have a strong positive autocorrelation

Data points that are close together have similar values

Index = 0.421; p-value = 0

If data were not autocorrelated

Our best estimate using IDW or Kriging would be the mean for the whole study site.

Moran, P.A.P. (1950). Notes on continuous stochastic phenomena, Biometrika 37, pp17-23.

Page 10: 2013 ASPRS Track, Ozone Modeling for the Contiguous United States by Michael Tuffly

IDW

Called a deterministic function

Using the same input parameters will get the same results.

Data needs to be spatially autocorrelated

Three Basic parameters are required

Number of nearest neighbors

Power

Study area boundary

Useful for Continuous data (e.g. rainfall, elevation)

Not useful for: Categorical, Binary, Ordinal

Page 11: 2013 ASPRS Track, Ozone Modeling for the Contiguous United States by Michael Tuffly

Identifying IDW Parameters

Cross Validation

Remove one data point at one location

Calculate a new value for that point using the neighboring points

Repeat this for all points

Calculate the mean squared error and variance

Mean Squared Error Predicted (MSEP) gives:

The best number of nearest neighbors

The best power

The fewer number of nearest neighbors produces good local estimates; but, poor global.

A larger number of nearest neighbors produces good global estimates; but, poor local.

Need to balance between local and global estimates.

Page 12: 2013 ASPRS Track, Ozone Modeling for the Contiguous United States by Michael Tuffly

IDW

1

1

1

niy

i in

yi i

ZDx

D

=

=

=∑

y = some exponent:; usually 1 or 2

Page 13: 2013 ASPRS Track, Ozone Modeling for the Contiguous United States by Michael Tuffly

Distance is calculated using the Pythagorean Theorem

A

C D

B

a2 + b2 = c2

For Distance A to x (C) 1.582 + 1.582 = 2.232

2.4964 + 2.4964 = 4.9729 4.97290.5 = 2.23

a

b

c

Page 14: 2013 ASPRS Track, Ozone Modeling for the Contiguous United States by Michael Tuffly

0 10 20 30 40 50 60 70

3540

4550

5560

Year = 2010 Power = 1, MSE Resi

num_neighbors

out.m

se

0 10 20 30 40 50 60 70

3540

4550

5560

Year = 2010 Power = 2, MSE Resd

num_neighbors

out2

.mse

41.8

8

43.3

8

Page 15: 2013 ASPRS Track, Ozone Modeling for the Contiguous United States by Michael Tuffly
Page 16: 2013 ASPRS Track, Ozone Modeling for the Contiguous United States by Michael Tuffly

Ordinary Kriging (Krige 1951) (Matheron 1962)

A stochastic or indeterminate interpolation process

Where estimates or interpolations at an unobserved location are made based upon: the weighted average of values at an observed location

Weights are base upon

The distance separating points

The function for the variogram

A variogram is used to identify key Kriging parameters:

Sill, Range, Nugget, and covariance

Assumes an unknown stationary mean.

Stationary mean refers that the mean over the area behaves predictably (e.g.. Gaussian).

Consider unbias

Mean residual sum to zero

Variance of error is minized

BLUE

Best Linear Unbias Estimator (Isaaks and Srivastava 1989)

Isaaks, E. H., and Srivastava, R (1989). An Introduction to Applied Spatial Statistics. Oxford, UK: Oxford University Press.

Krige, D. G. 1951 A statistical approach to some basic mine valuation problems on the Witwatersrand. Journal of the Chemical, Metal and Mining Society of South Africa 52 (6): 119 – 139)

Matheron, G. 1962. Traite de geostatistique appliquee. Editions Technip.

Page 17: 2013 ASPRS Track, Ozone Modeling for the Contiguous United States by Michael Tuffly

R output from Variogram Spherical Least Squares Estimate Nugget = 7.7377 Sill = 47.48165 Range = 1100000 AICC = 125.5306

Gaussian Least Squares Estimate Nugget = 13.6845 Sill = 52.25631 Range = 1100000 AICC = 128.4038

Exponential Nugget = 9.2776

Sill = 71.61078

Range = 1100000

AICC = 132.1289

Estimates: Nugget = 15 Sill = 30 Range = 1,100,000

Spherical and Gaussian have an AICC is less than 3 units apart; So there is no difference.

Page 18: 2013 ASPRS Track, Ozone Modeling for the Contiguous United States by Michael Tuffly

Graphic R Output

0e+00 2e+05 4e+05 6e+05 8e+05 1e+06

010

2030

4050

6070

Distance Meters

Ozo

ne V

alue

s

Year = 2010 Krig Raw Data

Gau

ExpSph

52.7

Nugget 13.6

Sill

Range

Page 19: 2013 ASPRS Track, Ozone Modeling for the Contiguous United States by Michael Tuffly

Number of Nearest Neighbors

5 10 15 20 25 30

3536

3738

3940

41

No. of Neighbors

var(c

ross

idw

$res

id)

Kriging Cross Validation, Gaussian Model

Page 20: 2013 ASPRS Track, Ozone Modeling for the Contiguous United States by Michael Tuffly
Page 21: 2013 ASPRS Track, Ozone Modeling for the Contiguous United States by Michael Tuffly

Generalized Linear Models (GLM) Similar to linear regression

Different than IDW and Kriging

Needs predictor input variables

solar radiation and relative humidity proved to be significant predicator variables.

Need to create the solar radiation and relative humidity surface via IDW as input into the GLM equation.

The GLM equation is:

45.35 + (SR * 0.0332) + (RH * -0.235)

R2 = 0.58

The GLM describes the “Large Scale Variability”

The “Small Scale Variability” is computed by calculating the differences between the observed values and the (GLM) predicted values.

Adding the “Large Scale Variability” to the “Small Scale Variability” can produce a good predicative surface.

Page 22: 2013 ASPRS Track, Ozone Modeling for the Contiguous United States by Michael Tuffly
Page 23: 2013 ASPRS Track, Ozone Modeling for the Contiguous United States by Michael Tuffly

Geographically Weighted Regression (GWR) A powerful modeling method that includes:

Linear Regression

Space

In a nutshell

GWR creates a series of local linear equations base upon the spatial parameters of the independent variables:

Kernel Function

Fixed Search Radius

Variable (number of neighbors)* (AKA Adaptive)

Bandwidth Method (fixed radius)

Cells located with in the search radius will have the same coefficients.

Best if sample points are located in a systematic method (e.g. no a gird with fixed distances).

Bandwidth Method (Adaptive or variable search radius)

One that uses the number of nearest neighbors from user input

One that uses a cross validation method which attempts to minimize the collinearity

Best if sample points are randomly located in the study area.

A sample point will be used multiple times to construct multiple linear equations

Each cell may contain different regression coefficients

Each linear equation (fixed radius or adaptive) uses the same global predictor variables as GLM

Solar Radiation and Relative Humidity proved to be the best global independent variables.

Page 24: 2013 ASPRS Track, Ozone Modeling for the Contiguous United States by Michael Tuffly
Page 25: 2013 ASPRS Track, Ozone Modeling for the Contiguous United States by Michael Tuffly
Page 26: 2013 ASPRS Track, Ozone Modeling for the Contiguous United States by Michael Tuffly
Page 27: 2013 ASPRS Track, Ozone Modeling for the Contiguous United States by Michael Tuffly

Results

Data Issues 1) Should have more data points to create and test the models 2) Data points should be more distributed over the study area

(e.g. no points in Oregon, Idaho, etc.. and few points in center of the nation.)

3) IDW MSE values for the observe points should not be different. This is likely due to cell size and rounding errors.

4) The variables temperature and wind speed were tested in the GWR model. Test results using these covariates included both the CV method or number of nearest neighbors. Results were very poor and not shown here.

Test Residuale Autocorrelated MSE MSE New Points GLM + IDW No 0.54 196.06 GWR using AICC and 25 nn No 21.98 265.09 GWR using CV No 38.43 241.2 IDW No 0.6 204.45 Kriging No 6.48 191.86

Page 28: 2013 ASPRS Track, Ozone Modeling for the Contiguous United States by Michael Tuffly

Take Home Message Final Statistical models are an abstraction of reality.

No statistical model is perfect. (e.g. errors)

Some models are better than other (Crawley 2007).

The correct model can never be known with complete certainty (Crawley 2007).

The simpler the model the better it is (Crawley 2007).

Models should include the Principle of Parsimony (Occam’s Razor)

Use the fewest number of variables

The correct explanation is the simplest explanation

Make sure that the assumptions of the model are followed.

Are the data IID.

Are the data spatially autocorrelated

Are the input variables correct?

Errors in measurement

Using temperature when solar radiation is a better independent variable.

How was the data collect

Random Sample, Systematic, etc…

Is there bias in the sample data?

Always as yourself does this model make sense.

Is the model predicted something where it should not

Example a fish population on land.

Crawley, M. J. 2007. The R Book. Imperial College London at Silwood Park, UK.

Page 29: 2013 ASPRS Track, Ozone Modeling for the Contiguous United States by Michael Tuffly

Final Quote

“Son you're going to drive me to drinking… if you don’t stop driving that hot rod Lincoln.” 1971.