Sacramento County Regression Equation Appendix X

X-1

Appendix X

Information on the Sacramento County Regression Equation

Clinton P. MacDonald

Daniel M. Alrick

Dianne S. Miller

2

1. Introduction

Ozone predictions from regression equations were used by SMAQMD to 

estimate wildland fire’s contribution to peak 1-hr ozone concentrations in Sacramento, 

California. This appendix provides background information about regression equations 

(Section 2), how Sonoma Technology, Inc. (STI) developed the regression equation 

used for the exceptional event analysis (Section 3), and how the equation was used to 

calculate the wildland fire’s contribution to ozone in Sacramento County (Section 4). 

The wildland fire’s contribution to peak 1-hr ozone concentrations is discussed in the 

main body of the report.

2. Background on Regression Equations

Regression is a statistical method for describing relationships among variables. 

For estimating air quality concentrations, regression equations are developed to 

describe the relationship between pollutant concentrations (referred to as the predictand, 

what is being predicted) and primarily meteorological variables (referred to as the 

predictors). Regression equations have been successfully used to predict daily or subdaily pollutant concentrations in many areas of the country (Cassmassi, 1987; Hubbard 

and Cobourn, 1997; Ryan, 1994; Dye et al., 1996; U.S. Environmental Protection 

Agency, 2003). 

Because regression equations are developed with several years of data, they 

represent the relationship between air quality and meteorology under typical emission 

patterns. Therefore, the difference between the predictions and observations can 

provide a reasonable estimate of the air pollution caused by unusual emissions (e.g., 

emissions from wildland fires). 

How Regression Equations Work

If two variables are correlated, a mathematical equation can generate a line or a 

curve that depicts the relationship between those variables. With this mathematical 

equation, one variable (e.g., ozone) can be predicted from other variables (e.g., 

meteorology). Multi-linear regression is most commonly used to predict ozone 

(Equation 1) from multiple variables. However, curvilinear regression (Equation 2) is 

also useful in predicting ozone because it captures the non-linear relationships of ozone 

and predictor variables. 

Ozone = c1 V1 + c2 V2 ....... cn Vn + constant (1)

Ozone = c1 V1+ c2 V2

2

+ c3 V3

3 ......, cn Vnn

+ constant (2)

where:

Ozone = predictand

c = coefficients (weighting factors)

V = meteorological predictor variables
3

An example of a multi-linear regression equation is shown in Equation 3. This 

regression model was developed for forecasting hourly ozone concentrations for 

Sacramento, California. The variables are described in Table 1. To predict ozone 

concentration on a given day, one simply inputs the value of each meteorological 

variable for that day into the equation.

 1-hr Ozone = exp (13.72 – 0.03*Clouds – 0.04*WindSpeed1 + 0.01*WindSpeed2 

+ 0.0002*WindDirection – 0.01*Pressure – 0.02*DewPoint 

+ 0.03*AloftTemperature – 0.009*AloftWindSpeed 

+ 0.009*TemperatureDifference) 

(3)

Table 1. Variables used in regression Equation 3. The surface meteorological conditions are for 

Sacramento, California. The aloft meteorological conditions are for Oakland, California.

Variable 

Abbreviations Description

Clouds Average hourly cloud cover from 6:00 a.m. PST to 6:00 p.m. PST where 

clear = 0, partly cloudy = 1, mostly cloudy = 2, and overcast = 3

WindSpeed1 Average wind speed from 6:00 a.m. PST to 12:00 p.m. PST in m/s

WindSpeed2 Surface wind speed at 00Z (4:00 p.m. PST on the previous day) in m/s

WindDirection Surface wind direction at 00Z (4:00 p.m. PST on the previous day)

Pressure Surface pressure at 12Z (4:00 a.m. PST) in mb

DewPoint Surface dew point temperature at 12Z (4:00 a.m. PST) in °C

AloftTemperature 925-mb temperature at 00Z (4:00 p.m. PST on the previous day) in °C

AloftWindSpeed 925-mb wind speed at 12Z (4:00 a.m. PST) in m/s

TemperatureDifference Temperature difference from 850 mb to the surface at 12Z (4:00 a.m. PST) in °C 

3. Regression Equation Development

As part of STI’s Forecasting and Outreach Support project with the Sacramento 

Metropolitan Air Quality Management District (SMAQMD), in 2004 STI developed a 

regression equation to assist with daily ozone forecasting for the Sacramento region. To 

develop the regression equation, STI staff completed the following tasks:

Data Processing

Obtained and processed six years (1997-2003) of May through October ozone 

data from the U.S. Environmental Protection Agency (EPA) for Sacramento 

County. The sites include Sacramento T Street, Del Paso Manor, Airport Blvd., 

North Highlands, Elk Grove, Sloughhouse, and Folsom.

Processed six years (1997-2003) of surface and upper-air meteorological data 

from the National Oceanic and Atmospheric Administration (NOAA) for the 

Sacramento area. 
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Performed general quality control of the air quality and meteorological data.

Populated a Microsoft Access database with Sacramento air quality and 

meteorological data, linked by date. New variables, such as average wind 

speeds, average cloud cover, minimum and maximum temperature, and stability 

parameters, were computed from the surface and upper-air meteorological data

that capture meteorological processes important to air quality. 

Regression Equation Development

Imported final data table from Microsoft Access into SYSTAT statistical software.

Determined proper software inputs for the regression algorithm to yield 

statistically sound equations. The software inputs included:

Tolerance – limits the similarity or collinearity of input variables. For example, 

950-mb temperature and 925-mb temperature are closely related; therefore, 

only one factor will be allowed into the equation. STI used tolerance values 

between 0.3 and 0.5.

Estimation – controls the method used to enter and remove variables from 

the equation. STI used Stepwise estimation in which variables are entered or 

removed from the model one at a time.

Stepwise options – control the entry and removal of variables. STI used the 

Forward and Automatic options:

Forward – begins with no variables in the model. At each step, SYSTAT 

adds the variable with the smallest Enter value.

Automatic – SYSTAT automatically adds a variable to the model at each 

step for the Forward option.

Probability – specifies probabilities to enter and remove a variable from the 

model. A variable is entered into the model if its alpha value is less than the 

specified Enter value, and it is removed from the model if its alpha value is 

greater than the specified Remove value. STI used probabilities between 

0.05 and 0.15.

MaxStep – dictates the maximum number of steps (variables) allowed. STI 

used a maximum of 10 variables.

Force – forces the first n variables listed to remain in the equation. STI did 

not force any variables into the equations (i.e., n = 0).

Evaluated the output variables for physical sense (i.e., higher ozone expected to 

be predicted with lower wind speeds). 

Evaluated the statistical strength of the equation. Output metrics included 

Standard error – shows the average deviation of a sample from the expected 

mean; small error is best.

T-test – shows whether each variable in the equation is statistically significant 

by comparing the mean of the predictions with and without the new variable. 

P2-tail – shows the likelihood of the equation’s performing well with a random 

sample,such as when used operationally Values less than 0.05 are desired, 

indicating a 95% probability that the model will work with a random sample.
5

Standard coefficient of a variable – shows how much the equation output 

would change by altering the variable by one standard deviation. In other 

words, it shows how heavily each variable contributes to the overall equation.

Regression Equation Testing

Compared the regression output to observations in order to evaluate accuracy. 

Metrics used for evaluation included

accuracy based on Air Quality Index (AQI) category;

accuracy based on predicted concentration;

bias; and

average error. 

Tested regression equations on independent data sets using the same metrics 

listed above.

Selected the best equation to use, basing the selection on test results.

Test Results Associated with Equation Development

The final equation used to predict daily peak 1-hr maximum ozone concentration for 

Sacramento County is shown in Equation 3. Immediately after developing the equation, 

we evaluated the equation’s performance by comparing the predictions from the 

equations to the observations from both the data set used to develop the equations and 

a data set reserved for testing only. The results for the correlation coefficient (r2) and 

bias values are shown in Table 2. The overall performance is good and is consistent 

with performance from other regression equations developed for air quality forecasting 

programs (U.S. Environmental Protection Agency, 2003).

Table 2. Sacramento County 1-hr ozone equation test results.

Metric Result

Development data set r20.75

Development data set bias 15.2 ppb

Independent data set r20.58

Independent data set bias 8 ppb

4. Application to Exceptional Event Analysis

To estimate the wildland fire contribution to ozone concentrations in Sacramento, 

the following general steps were performed:

1. STI used the Sacramento regression equation to calculate daily peak 1-hr 

ozone predictions for Sacramento County for each day during May through 

October 2007. The meteorological input data used in the regression equation 

were the output data from the National Center for Environmental Prediction’s 

(NCEP) Eta model. The Eta model is a weather forecast model that was 

used by the National Weather Service to produce daily weather forecasts 
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until it was replaced by the Weather Research and Forecast model. Several 

variations of the Eta model predictions were available. STI used three:

A. The predictions produced by the 12:00 UTC model run, which 

provided the most recent meteorological predictions each day to run 

the regression equations. We will refer to the ozone predictions that 

used this input data as the “12 Prediction.”

B. The predictions produced by the 12:00 UTC model run but adjusted 

by NCEP using statistical techniques called Model Output Statistics 

(MOS). We will refer to the ozone predictions that used this input data 

as the “12 MOS Prediction.”

C. The predictions produced by the 00:00 UTC run, which provided 

meteorological predictions that are 12 hours less recent than 12:00 

UTC model predictions. We will refer to the ozone predictions that 

used this input data as the “00 Prediction.”

Eta model weather data, rather than observed data, were used to predict 

ozone because the model did not account for the wildfire’s influence on 

meteorology; thus, the Eta predictions represent meteorological conditions 

(and ultimately ozone via the regression equations) that would be expected in 

the absence of the wildfires. 

2. STI calculated the average daily differences (bias) between the daily ozone 

predictions and the observed ozone concentrations on all non-smoke impact 

days in 2007. The average bias between the predicted and observed ozone 

was 8.4, 8.6, and +13.3 ppb for the 12 Prediction, 12 MOS Prediction, and 00 

Prediction, respectively. These positive biases mean that, on average, the 

regression equation overestimated ozone concentrations. The positive bias 

is likely due to reductions in ozone precursor emissions between the period 

for which the equations were developed (1997-2003) and the years that they 

were applied (2007 and 2008). This result was expected.

3. To correct for the positive biases, to make these equations more accurate for 

2007 and 2008, STI subtracted the average biases (8.4, 8.6, and +13.3) from 

the associated daily predictions (12 Prediction, 12 MOS Prediction, and 00 

Prediction) for May through October of 2007 and 2008.

4. SMAQMD used the “bias-adjusted” predictions from Step 3 to estimate the 

wildfire contribution to ozone. In particular, for June 23, June 27, July 7, and 

July 10, 2008, SMAQMD subtracted the “bias-adjusted” 1-hr ozone 

predictions for Sacramento County (including the 12 Prediction, 12 MOS 

Prediction, and 00 Prediction) from the peak observed 1-hr ozone 

concentration in Sacramento County. The results were three estimates of 

wildfire contribution to ozone in Sacramento County for June 23, June 27, 

July 7, and July 10, 2008. These results are presented in the main body of 

the report.

5. STI estimated the error of the 12 Prediction, 12 MOS Prediction, and 00 

Prediction methods. In particular, for each prediction method, STI

A. Calculated the difference between the daily bias-adjusted ozone 

prediction and daily observed ozone concentrations for May through 
7

October for the years 2006, 2007, 2008, except for the fire impact 

days of 2008.

B. Plotted the distribution of error and determined that the errors are 

“normally distributed” about the mean; i.e., the distribution is 

symmetric. This indicates that there is no directional bias and the 

errors are random. The distributions for the 12 Prediction, 12 MOS 

Prediction, and 00 Prediction are shown in Figures 1, 2, and 3,

respectively. As indicated by each of the three histograms, the 

majority of days had relatively small prediction errors, while very few 

days had large prediction errors.

C. Calculated the value at which 68% and 95% of the positive daily 

errors, and 68% and 95% of the negative daily errors, fall within the 

mean error for each prediction method. For a normal distribution of 

data, the 68th and 95th percentiles correspond to roughly one and two 

standard deviations from the mean, respectively. The use of the 95th

percentile (approximately two standard deviations) provides a 

conservative upper and lower bounds of the predictions. The 12 

Prediction, 12 MOS Prediction, and 00 Prediction 95% error values 

are shown in Table 3. 

Figure 1. Distribution of ozone prediction error using meteorological input data 

from the 12:00 UTC ETA model run (12 Prediction).

-100 -75 -50 -25 0 25 50 75 100

12Z ETA

0

20

40

60

80

100

Count of Days

0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

0.16

0.18

Proportion per Bar

Predicted – Observed (ppb)
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Figure 2. Distribution of ozone prediction error using meteorological input data 

from the 12:00 UTC ETA MOS model run (12 MOS Prediction).

Figure 3. Distribution of ozone prediction error using meteorological 

input data from the 00:00 UTC ETA model run (00 Prediction).

-100 -75 -50 -25 0 25 50 75 100

12Z ETA-MOS

0

20

40

60

80

100

Count of Days

0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

0.16

0.18

Proportion per Bar

Predicted – Observed (ppb)

-100 -75 -50 -25 0 25 50 75 100

00Z ETA

0

20

40

60

80

100

Count of Days

0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

0.16

0.18

Proportion per Bar

Predicted – Observed (ppb)
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Table 3. Summary of error values.

12 Prediction 12 MOS 

Prediction 00 Prediction

Error value (ppb) at which 95% of 

positive errors are within the mean +32 +33 +31

Error value (ppb) at which 68% of 

positive errors are within the mean +16 +17 +15

Error value (ppb) at which 68% of 

negative errors are within the 

mean

-18 -19 -18

Error value (ppb) at which 95% of 

negative errors are within the 

mean

-35 -39 -35

5. References

Cassmassi J.C. (1987) Development of an objective ozone forecast model for the South 

Coast Air Basin. Presented at the Air Pollution Control Association 80th Annual 

Meeting, New York, NY, June 21-26. 

Dye T.S., Ray S.E., Lindsey C.G., Arthur M., and Chinkin L.R. (1996) Summary of ozone 

forecasting and equation development for the air districts of Sacramento, YoloSolano, and Placer. Vol. I: ozone forecasting. Vol. II: equation development. 

Final report prepared for Sacramento Metropolitan Air Quality Management 

District, Sacramento, CA, by Sonoma Technology, Inc., Santa Rosa, CA, STI996210-1701-FR, December. 

Hubbard M.C. and Cobourn W.G. (1997) Development of a regression model to forecast 

ground-level ozone concentration in Louisville, KY. Atmos. Environ. (submitted).

Ryan W.F. (1994) Forecasting severe ozone episodes in the Baltimore metropolitan 

area. Atmos. Environ. 29, 2387-2398. 

U.S. Environmental Protection Agency (2003) Guidelines for developing an air quality 

(ozone and PM2.5) forecasting program. Prepared by Dye T.S., MacDonald C.P., 

Anderson C.B., Hafner H.R., Wheeler N.J.M., and Chan A.C. at Sonoma 

Technology, Inc., Petaluma, CA, STI-902461-2295-FR, EPA-456/R-03-002, 

June. Available on the Internet at 

http://www.epa.gov/airnow/aq_forecasting_guidance-1016.pdf.
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Addendum to Appendix X

Primary documentation of conditions connecting several high ozone events with 

unusual wildfires has already been developed. In response to a request from 

U.S. EPA for additional information on certain statistical methods, Sonoma 

Technology, Inc (STI) prepared a document titled “Appendix X – Information on 

the Sacramento County Regression Equation”. The analysis presented here is 

an addendum to the “Appendix X” document.

The analysis presented below provides substantial additional support for the 

conclusion that in the absence of the extensive and persistent wildfires in 2008, 

ozone values measured on June 23, 2008, June 27, 2008, and July 10, 2008 in 

Sacramento County, California would not have exceeded the federal 1-hour 

ozone standard.

Data

This analysis makes use of model outputs and observed concentrations 

described previously in Appendix X. The data include daily maximum 1-hour 

ozone values in Sacramento County, and daily predicted ozone values produced 

by Sonoma Technology, Inc. (STI). STI provided four different daily predicted 

values for ozone, each the product of a different prediction model. The 

predicted values from the model identified as “00Z Eta” were used in this 

analysis. The methods used for this addendum were designed to compensate 

naturally for multiple types of biases that may differ between the alternative 

models, so the conclusions would likely be the same if a different prediction 

model had been selected (details on page 3).

Analysis

The data are summarized and presented in two different ways to provide 

additional support concerning two vital questions:

Question #1: Is there clear evidence that the extensive and persistent 

wildfires in California in 2008 caused a net increase in measured ozone 

levels? 

Question #2: Is there strong evidence that several exceedances of the 

Federal 1-hour ozone standard would not have occurred “but for” the 

effect of wildfires on ozone levels.
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Question #1: Is there clear evidence that the extensive and persistent 

wildfires in California in 2008 caused a net increase in measured ozone 

levels?

Answer: Yes.

Ozone levels increase and decrease from one day to the next throughout the 

ozone season. These everyday ups and downs are caused by regular changes 

in meteorological conditions and in emissions of ozone precursors. Figure 1 

shows the regular, everyday behavior (typical variability) of daily maximum 

1-hour ozone values (solid triangles) in Sacramento County from May 1 through 

September 30, 2007, a season that was largely unaffected by wildfires. 

Everyday ups and downs make it hard to identify exceptional ups and downs, the 

ones caused by irregular meteorology and/or emissions. 

Figure 1 also shows predicted values for the daily observed maximum 1-hour 

ozone values (open diamonds) in Sacramento County. The predicted values 

represent the expected value for ozone based on forecasted meteorological 

conditions, so the ups and downs in these values tend to track the regular effects 

of weather on daily ozone.

Similar to Figure 1, Figure 2 shows the observed and predicted values for daily 

maximum 1-hour ozone in Sacramento County for 2008. Highlighted in figure 2 

are five dates on which measured ozone exceeded the Federal 1-hour standard 

for ozone. Further analysis provides strong evidence that these exceedances 

are the result of irregular (fires) rather than regular causes.

Figures 1 and 2 showed that the daily predicted ozone tends to rise and fall along 

with the observed ozone. By subtracting the predicted values from the observed 

values, the daily differences will have a “zero” baseline. Some days will have a 

positive difference because the measured ozone was above the predicted ozone, 

and some days will have a negative difference because the measured ozone was 

below the predicted ozone. 

Figures 4, 5, 6, 7, 8, and 9 track the daily differences between observed ozone 

and predicted ozone by month. In these figures, irregular ups and downs in daily 

ozone stand out from the regular ups and downs. To help in this regard, the 

figures include a horizontal dashed line representing a “Regular Upper Limit” 

which is exceeded by regular differences only 5% of the time, and even then the 

excursions are usually small . The value for the line is the difference (observed 

minus predicted) that separates the highest 5% from the lower 95% of regular 

daily differences. Figure 3 shows how the value of the line (27.6 ppb) was 

determined. A corresponding lower limit is not shown, as the appropriate focus is 

on high values that are potential exceptional events. Unlike regular differences, 
12

irregular differences stand out because the excursions are large or because 

there are many more than the 5% that are expected for regular days.

Figure 3, shows a histogram of the daily differences (observed ozone minus 

predicted ozone). The histogram represents regular differences because the 

data do not include June 23 to July 31, 2008, the period most strongly affected 

by wildfires in 2008. August 2008 was also not included because that month is 

considered borderline with respect to effects of lingering fires. Figure 3 is 

annotated showing that 95% of the daily differences did not exceed 27.6 ppb 

ozone. So, the “Regular Upper Limit” line in Figures 4 – 9 has a constant value 

of 27.6 ppb.

The use of a percentile cut-point (95% point) in these analyses naturally 

compensates for a variety of possible biases that could differ between the 

alternative predictive models. An overall additive bias will be built in to each of 

the daily differences, and that bias would become a part of every percentile 

drawn from the set of differences. Biases at the high end are unaffected by 

possibly different biases at the low end, because the distribution of percentiles 

does not use parametric assumptions, such as “normality”. The percentiles 

follow the data-driven shape of the distribution.

Figure 4 shows data for the month of May in 2007 and 2008 and characterizes 

regular variability in the daily differences (observed ozone minus predicted 

ozone).

Figures 5 and 6 show data for June and July in 2007 and 2008. The 2007 data 

exhibit regular differences, the typical behavior of daily maximum 1-hour ozone. 

The 2008 data show regular differences through June 22, but then the pattern 

changes. From June 23, 2008 through July 26, 2008, sixteen of the thirty-four 

daily differences exceed the regular upper limit, and some of the differences are 

quite large. Instead of the regularly expected 5%, the figures show a highly 

irregular 47% (16 of 34) of daily differences above the Regular Upper Limit. 

During this highly irregular period, northern California experienced extensive and 

pervasive wildfires. The possibility of extreme meteorology is not reasonable, 

since the daily differences are already “normalized” with respect to 

meteorological conditions known to affect ozone levels in the Sacramento area.

Figures 7 and 8 show data for August and September in 2007 and 2008. In 

these figures, the behavior of the daily differences is mostly regular, though 

August 2008 is considered borderline with respect to possible effects of lingering 

wildfires.

This analysis presents very strong statistical evidence that ozone levels in the 

Sacramento area on many days from June 23, 2008, through July 26, 2008, were 

enhanced by the well-documented wildfires that were pervasive and persistent in 

northern California during that time.
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Question #2: Is there strong evidence that several exceedances of the 

Federal 1-hour ozone standard would not have occurred “but for” the effect 

of wildfires on ozone levels?

Answer: Yes.

The preceding analysis established a causal connection between wildfires and 

high ozone levels in the Sacramento area from June 23 through July 26, 2008. 

The following analysis will show that ozone levels on four of five specific dates 

would not have exceeded the level of the Federal ozone standard but for the 

effects of the wildfires.

Figures 10, 11, 12, 13, and 14 track daily observed ozone together with a “dayspecific regular upper limit”. Each day-specific limit is that day’s predicted ozone 

plus the “regular upper limit” (27.5 ppb) used in the previous analysis.

When an observed ozone value exceeds the day-specific regular upper limit, it is 

likely that some irregular cause contributed to the measured value. When an 

irregular event known to enhance ozone formation, such as the 2008 wildfires, 

coincides with an exceedance of the day-specific limit, the convergence of the 

two events provides strong evidence that the exceedence would not have 

occurred but for irregular event, in this case the wildfires. 

During the wildfire period, observed ozone sometimes exceeds the federal 

standard when the day-specific upper limit does not exceed the federal standard. 

For those days, the evidence is strong that observed ozone would not have 

exceeded the standard “but for” the effects of the wildfires. Figures 11 and 12 

show that these conditions prevailed on June 23, June 27, July 10, and July 25, 

2008. Table 1 summarizes these results.
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Figure 1:

Sacramento County: Comparison of 00Z Eta (corrected) and 

Observed Daily Max. 1-hr Ozone Concentration for May - Sep., 2007

20

40

60

80

100

120

140

160

180

5/1 5/8 5/15 5/22 5/29 6/5 6/12 6/19 6/26 7/3 7/10 7/17 7/24 7/31 8/7 8/14 8/21 8/28 9/4 9/11 9/18 9/25

Month/Day from May 1 through September 30, 2008 Concentration (ppb)

Bias corrected Prediction SAC 1-hr Max (ppb)
15

Figure 2:

Sacramento County: Comparison of 00Z Eta (corrected) and 

Observed Daily Max. 1-hr Ozone Concentration for May - Sep., 2008

20

40

60

80

100

120

140

160

180

5/1 5/8 5/15 5/22 5/29 6/5 6/12 6/19 6/26 7/3 7/10 7/17 7/24 7/31 8/7 8/14 8/21 8/28 9/4 9/11 9/18 9/25

Month/Day from May 1 through September 30, 2008 Concentration (ppb)

Bias corrected Prediction SAC 1-hr Max (ppb)

June 23

July 10

June 27

July 7

July 25
16

Figure 3. Distribution of Deviations: (Obs. Ozone - Pred. Ozone*)

Based on Data from Sacramento County, California in

May - Sept., 2007 with May 1 - June 22 and Sept., 2008

0%

1%

2%

3%

4%

5%

6%

7%

8%

9%

10%

11%

12%

13%

14%

15%

16%

17%

18%

19%

20%

-45 -40 -35 -30 -25 -20 -15 -10 -5 0 5 10 15 20 25 30 35 40 45 50 55

Midpoint of Deviation Category (ppb ozone) Relative Frequency (%)

95th Percentile

27.6 ppb

* Predicted values are the daily predicted 1-hour maximum values forecasted for Sacramento County by Sonoma Technologies, 

Inc. using forecasted meteorology from 

Measured ozone < Predicted Ozone Measured ozone > Predicted Ozone
17

Figure 4. Comparison of May 2007 and May 2008

Regarding Observed - Predicted Daily Max Ozone

-50

-40

-30

-20

-10

0

10

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30

40

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60

70

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90

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31

Day of Month Obs Max Ozone - Pred. Max Ozone (ppb)

2007 2008 Regular Upper Limit
18

Figure 5. Comparison of June 2007 and June 2008

Regarding Observed - Predicted Daily Max Ozone

-50

-40

-30

-20

-10

0

10

20

30

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60

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90

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31

Day of Month Obs Max Ozone - Pred. Max Ozone (ppb)

2007 2008 Regular Upper Limit

June 23 2008
19

Figure 6. Comparison of July 2007 and July 2008

Regarding Observed - Predicted Daily Max Ozone

-50

-40

-30

-20

-10

0

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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31

Day of Month Obs Max Ozone - Pred. Max Ozone (ppb)

2007 2008 Regular Upper Limit

July 5 2007
20

Figure 7. Comparison of August 2007 and August 2008

Regarding Observed - Predicted Daily Max Ozone

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-40

-30

-20

-10

0

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30

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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31

Day of Month Obs Max Ozone - Pred. Max Ozone (ppb)

2007 2008 Regular Upper Limit
21

Figure 8. Comparison of September 2007 and September 2008

Regarding Observed - Predicted Daily Max Ozone

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-40

-30

-20

-10

0

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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31

Day of Month Obs Max Ozone - Pred. Max Ozone (ppb)

2007 2008 Regular Upper Limit
22

Figure 9. Comparison of October 2007 and October 2008

Regarding Observed - Predicted Daily Max Ozone

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-40

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-20

-10

0

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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31

Day of Month Obs Max Ozone - Pred. Max Ozone (ppb)

2007 2008 Regular Upper Limit
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Figure 10. Sacramento County : Possible Exceptional Events

Based on May 2008 Daily Max 1-Hour Ozone

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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31

Day of Month Daily Max 1-Hour Ozone (ppb)

Observed Day-Speciic Regular Upper Limit*

* If a day is regular, not irregular, the "odds" are 19-to-1 (95% to 5%) that the observed ozone w ill not exceed the "Regular Upper Limit"
24

Figure 11. Sacramento County : Possible Exceptional Events

Based on June 2008 Daily Max 1-Hour Ozone

0

10

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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31

Day of Month Daily Max 1-Hour Ozone (ppb)

Observed Day-Speciic Regular Upper Limit*

* If a day is regular, not irregular, the "odds" are 19-to-1 (95% to 5%) that the observed ozone w ill not exceed the "Regular Upper Limit"
25

Figure 12. Sacramento County : Possible Exceptional Events

Based on July 2008 Daily Max 1-Hour Ozone

0

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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31

Day of Month Daily Max 1-Hour Ozone (ppb)

Observed Day-Speciic Regular Upper Limit*

* If a day is regular, not irregular, the "odds" are 19-to-1 (95% to 5%) that the observed ozone w ill not exceed the "Regular Upper Limit"
26

Figure 13. Sacramento County : Possible Exceptional Events

Based on August 2008 Daily Max 1-Hour Ozone

0

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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31

Day of Month Daily Max 1-Hour Ozone (ppb)

Observed Day-Speciic Regular Upper Limit*

* If a day is regular, not irregular, the "odds" are 19-to-1 (95% to 5%) that the observed ozone w ill not exceed the "Regular Upper Limit"
27

Figure 14. Sacramento County : Possible Exceptional Events

Based on September 2008 Daily Max 1-Hour Ozone

0

10

20

30

40

50

60

70

80

90

100

110

120

130

140

150

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170

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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31

Day of Month Daily Max 1-Hour Ozone (ppb)

Observed Day-Speciic Regular Upper Limit*

* If a day is regular, not irregular, the "odds" are 19-to-1 (95% to 5%) that the observed ozone w ill not exceed the "Regular Upper Limit"
28

Regular

Observed Upper Exclude

Date Ozone Limit * from D.V. ?

23-Jun-2008 162 ppb 103 ppb yes

27-Jun-2008 130 ppb 104 ppb yes

7-Jul-2008 166 ppb 144 ppb no

10-Jul-2008 151 ppb 123 ppb yes

25-Jul-2008 128 ppb 107 ppb yes

* This "Regular Upper Limit" is day-specific, and

 the "odds" are 19 to 1 (95% to 5%) against a

 regular day exceeding its day-specific limit. So, 

 the 123 ppm limit on July 10, 2008, is already a

 hard-to-reach limit, providing strong evidence

 that the day would not exceed the Federal 1-hour

 standard if it were a regular, not an irregular, day.

Table 1. Exceptional Event Data Summary
Sacramento County Regression Equation Appendix X

X-3