MEMORANDUM

SUBJECT: Regression Analysis of Nitrous Oxide and Oxides of Nitrogen from Motor
Vehicles

FROM: David Choi
Assessment and Standards Division Office of Transportation and Air Quality

TO: Docket Number EPA-HQ-OAR-2011-0135

DATE: February 27, 2014

The purpose of this memorandum is to document the regression analysis examining the relationship between nitrous oxide (N 2 O) and oxides of nitrogen (NO
x ) from motor vehicles. The result from the analysis was used to estimate the reductions in N 2 O emissions projected from gasoline cars and trucks due to the Ti er 3 vehicle and sulfur standards.

Nitrous oxide (N 2 O) is a potent greenhouse gas with 100-year global warming potential 298 times greater than carbon dioxide (CO 2 ). A N 2 O is not formed during combustion, but in the catalyst, during catalyst warm-up, be fore the catalyst reaches the temperatures required for full effectiveness (known as “light-off”). Improveme nts to catalyst technol ogy required to meet lower emission standards reduce the time require d for the catalyst to reach light-off, which
reduces the window of N 2 O formation.

Several studies have established that reductions in tailpipe standards for NO
x result in reductions
in N 2 O. Studies conducted by EPA and Environment Canada found that N 2 O emission are lower
on vehicles certified to more stringent NO
x emission standards. 1,2 A study by Meffert, et al. established a strong correlation between improvements in NO
x catalytic conversion efficiency
and reductions in N 2 O emissions. 3 A study published by Behrentz, et al. in 2004 examined the relationship between N 2 O and NO
x from data collected by the California Air Resources Board (CARB) on 37 passenger cars and light-duty trucks ranging from the mid-1980s through early 2000’s Low Emission Vehicle (LEV) technology. 4 Another study by Winer, et al (2005) tested 134 light-duty vehicles, including pa ssenger cars and light-duty tr ucks, as part of the CARB’s

A 2007 Intergovernmental Panel on Climate Change (IPCC) Fourth Assessment Report (AR4)vehicle surveillance program, varying from Tier 0 to ULEV in emissions standards. 5 These two studies reported N 2 O: NO
x ratios of 0.06 and 0.095, respectively, and supported the application
of N 2 O: NO
x ratios to NO
x emissions as a reasonable method for estimating N 2 O emission inventories. Meszler, et al. subsequently analyzed the dataset by Behrentz and found that for vehicles equipped with more modern controls, N 2 O emissions increased with vehicle mileage, suggesting deterioration in N 2 O emissions as vehicles age. 6 The study by Winer, et al (2005)
also found that as the emissions st andards became more stringent, the N 2 O: NO
x ratios increased.

The MOVES model used to generate emissions inventory is based on a limited sample of N 2 O
emissions data and curren tly does not associate N 2 O emissions to NO
x emissions as suggested by Winer and Behrentz. Therefore, the model does not estimate the potential N 2 O reduction concurrent with the Tier 3 program since it doe s not account for the factors affecting light-duty
NO
x emissions, such as deteriorati on, aggressive driving, and lower NO X standards.

In an effort to estimate the N 2 O inventory accounting for th e factors that affect N 2 O emissions, EPA analyzed the data collected by Californi a Air Resources Board (CARB) at El Monte laboratory facilities from 2000 to 2007, as a part of CARB’s vehicle surveillance program. The
data described in Winer and Behrentz were also collected as a part of the same program. However, the data we analyzed, available as a part of this memorandum to the docket, is the most comprehensive since it includes additiona l tests that CARB collected, since the studies conducted by Winer and Behrentz. The same da taset was used to ex amine the association
between N 2 O and NO
x emissions and to apply the relationship to estimate the N 2 O benefits from the LEV III program. 7

Regression Analysis

A total of 174 vehicles were included in the an alysis, ranging in model years from 1981 to 2004. For this analysis, weighted FTP was calculate d based on the individual bag results and the regression analysis was performed on the weighted FTP results.

Before proceeding with the analysis of the da ta, EPA performed a numb er of tests to assess whether the data meets the assumptions of linear regression. First, the assumption of normality was tested. Both visual inspection of the QQplo t (Figure 1) and the Shapiro-Wilk W test of normality (p-value < .0001) indicated that the nu ll hypothesis that it is normally distributed need to be rejected. However, the failure to meet the normality assumption is not likely to affect the validity of estimation of coefficients.Figure 1. Test for normality: QQplot of Raw Data

Next, the test for heteroskedasticity was perf ormed. One of the main assumptions for the ordinary least squares regression is the homogene ity of variance of the residuals, and if the constant variance assumption is not met, it can affect the model fit. The visual inspection of the residual vs. predicted plot (Figure 2) indicate s that there is a potential heteroskedasticity showing the pattern is very narrow towards the left e nd. The White test was performed to confirm the finding and the test showed that the p-value is very small (p=0.0118) i ndicating that the null hypothesis that the variance of the residual is homogeneous needs to be rejected.Figure 2. Plot of Residual vs. Predicted: Raw Data

In an effort to fulfill the assumptions of th e ordinary least squares regression, EPA has logtransformed both the dependent and independent variables, which is a well-established method in modeling of emissions data. The QQplot tes ting for normality in Figure 3 shows that the

distribution of the residual has improved. Furthermore, the hom ogeneity of the variance of the residuals is confirmed both by vi sual inspection of Figure 4 and by the White test with p-value of

0.5706.Figure 3. Test for Normality: QQplot of Log-Transformed DataFigure 4. Plot of Residual vs. Predicted: Log-Transformed Data

After confirming the assumptions of the ordinary least squares regression have been satisfied, a regression analysis was performed to examine the relationship between N 2 O and NO X. A number of different methodologies were considered including performi ng regression analysis by bags, technology groups, and fuel types. However, the analysis did not find improvement in the model fit due to increased variability from reduced samp le size. No statistically significant difference
in N 2 O: NO
x ratio was observed between different vehicle types.

The resulting regressi on model correlating N 2 O emissions to NO
x emissions is shown in Equation 1.

Equation 1. Regression Model Correlating N 2 O Emissions to NO X Emissions

In order to evaluate the performance of the re gression, the data vs. model prediction was plotted (Figure 5). The model shows reasonable accuracy in predicting the data (R 2 =0.57).Figure 5. Plot of Data vs. Predicted – Regression with log-transformation

Conclusion

N 2 O emissions are known to be dependent on cata lyst control technology, age of the technology, operating conditions such as the drive cycle, and the fuel sulf ur levels. The many factors involved make it difficult to accurately estimate the N 2 O emissions inventory. Because the dataset the regression was based on included vehicles with differe nt emission standards, it may not be reasonable to apply the regression to estimate N 2 O emissions on a per-vehicle basis. However, since the purpose of the analysis was to examine the relationship between N 2 O and
NO
x to be applied in estimating the fleet-wide N 2 O emissions inventory, the analysis has merits. Furthermore, the future fleet to which N 2 O: NO
x emissions ratio is being applied is much cleaner than the test fleet the regre ssion is based on, and considering the previous findings that N 2 O:
NO
x emissions ratios increase with more stringe nt emission standards, the estimation of the
future N 2 O emissions inventory and the reductions in N 2 O from the Tier 3 standards, using the regression presented in this memorandum, would likely be a conservative estimates.References

1 Michaels, H. (1998) Emissions of Nitrous Oxide from Highway Mobile Sources, U.S. EPA EPA420-R-98-009.

2 Graham, L. (2006) Greenhouse Gas Emissions from 1997-2005 Model Year Light Duty Vehicles Environment Canada ERMD Report #04-44.

3 Meffert, et al (2000) Analysis of Nitrous Oxide Emissions from Light Duty Passenger Cars, SAE 2000-01-1952.

4 Behrentz, et al. (2004) Measurements of nitrous oxide emissions from light-duty motor vehicles: a pilot study, Atmospheric Environment 4291-4303.

5 Winer, et al. (2005) Estimates of Nitrous Oxide Emissi ons and the Effects of Catalyst Composition and Aging,
State of California Air Resources Board 02-313.

6 Meszler, D. (2004) Light Duty Vehicle Methane and Nitrous Oxide Emissions: Greenhouse Gas Impacts Study for
Northeast States Center for a Clean Air Future.

7 LEVIII Mobile Source Emissions Inventory Technical Support Document – Appendix T, January 2012. http://www.arb.ca.gov/regact/2 012/leviiighg2012/levappt.pdf