   MEMORANDUM
   
   FROM:	James Warila 
   		United States Environmental Protection Agency
   		Office of Air and Radiation
   		Office of Transportation and Air Quality
   		Assessment and Standards Division
   			
   TO:	Tier 3 Docket EPA-HQ-OAR-2011-0135
   
   DATE:	February 28, 2013
   
RE:   	Statistical Analysis of the Effects of Changing Fuel Properties on CO2
	Emissions from Light-Duty Gasoline-Powered Vehicles based on EPAct/V2/E-89
	Test Program Results


The proposed change in test fuel, if finalized, could have implications for the CAFE and GHG emissions compliance programs, as well as the fuel economy labeling program.  Therefore, it is important to characterize the potential impact on CO2 emissions from the change in certification test fuel proposed in this rule.  As outlined in the preamble to the 2017 and Later Model Year Greenhouse Gas Emissions and Corporate Average Fuel Economy (CAFE) final rule, if the EPA test fuel used for certification and fuel economy vehicles changes to include ethanol, EPA is committed to address whether the fuel change has a potential to affect the stringency of Greenhouse Gas and CAFE standards.   As a result, we used data from the EPAct Program to examine the effects of changing fuel properties on CO2 emissions.  

Based on results from Phase 3 of the EPAct Program, we performed a statistical analysis of the effects of five fuel properties on the CO2 emissions of 15 late-model light-duty vehicles.  To our knowledge, this is the most comprehensive study of fuel effects of CO2 emissions available.  

The project was conducted as a controlled experiment, in which the design can be characterized as "randomized block with repeated measures", in which vehicles are treated as blocks and fuel properties as "treatments."  A statistically optimal study design was developed to represent variation in five fuel properties: ethanol volume (%), aromatic content (%), RVP (psi), T50 (°F) and T90 (°F).  These five parameters were selected based on previous studies as having potential to affect exhaust emissions, and were included in the design at the levels shown in Table 1.   A critical feature of the study design is that the properties of the test fuels are assigned to span the ranges of in-use fuel properties, with the intent of providing a basis for the development of statistical models capable of predicting emissions for the majority of in-use fuels.  Following a process in which statistical power, fuel-blending feasibility and budget were balanced, the final design included 27 test fuels.

A set of 15 test vehicles, all in model year 2008, with the majority certified to Tier-2/Bin-5 standards, was selected on the basis of sales levels, vehicle and engine sizes, and representation of manufacturers.  Emissions were measured on the LA92 test cycle at a nominal temperature of 75°F. Emissions measured include carbon dioxide (CO2), carbon monoxide (CO), total hydrocarbons (THC), methane (CH4), non-methane hydrocarbons (NMHC), oxides of nitrogen (NOx), and particulate matter (PM2.5).  Following the completion of data collection, in June 2010, construction of the dataset involved intensive evaluation and quality assurance.  

The conduction and analysis of the EPAct Phase-3 project are discussed in greater detail in the EPA project Report.

Table 1.  Levels assigned to Experimental Factors (Fuel parameters) for the Phase-3 EPAct program.
Factor
                                  No. Levels
                                    Levels

                                       
Low
                                    Middle
High
Ethanol (%)
                                       4
                                       0
                                    10, 15
                                      20
Aromatics
                                       2
                                      15
                                       
                                      35
RVP (psi)
                                       2
                                       7
                                       
                                      10
T50 (°F)
                                       5
                                      150
                                 165, 190, 220
                                      240
T90 (°F)
                                       3
                                      300
                                      325
                                      340
Analysis
Each of the vehicles was measured on each of the 27 fuels, with replication.  On most vehicle fuel combinations two replicates were performed, whereas on some combinations, 3 replicates were performed. The total dataset includes 956 observations.  More details on the vehicles, fuels, and test procedures can be found in the program report.

For purposes of this analysis, we used cycle composites for the LA92 results. Results for the 3 phases of the cycle (cold start, hot running and hot start) were averaged in the same manner as a composite calculated on the FTP cycle.
Data Review
Figure 1 shows a summary of the entire dataset as the common logarithm of the cycle composites, presented by vehicle and fuel. As expected, measurements are consistent and precise for each vehicle, with variability among vehicles considerably larger than variability within vehicles. Overall, the measurements range from 290 to 600 g CO2/mi.

 Figure 1.  Common logarithms of CO2 measurements (Composites on LA92 cycle).
                                       
As a next step, we averaged the data across all levels of each of the fuel properties in turn, and by vehicle, as shown in Figure 2 through Figure 6.  The plots make it clear that, at the scales shown, visible effects are apparent only for aromatics.  Effects may be present for the other properties, but would be too small to be visible at the scale shown.
                                       
Figure 2.  CO2 (Composite): Results averaged by four levels of ethanol and by vehicle.

                                       
Figure 3.  CO2 (Composite): Results averaged by two levels of aromatics and by vehicle.

Figure 4. CO2 (Composite): Results averaged by two levels of RVP and by vehicle.
                                       

Figure 5.  CO2 (Composite): Results averaged by five levels of T50 and by vehicle.
                                       


Figure 6.  CO2 (Composite): Results averaged by three levels of T90 and by vehicle.
                                       

In addition, we investigated whether graphing the results might indicate the possibility of an interaction effect between aromatics and ethanol.  In this case we averaged the data by both its four ethanol and two aromatics levels and plotted the means, as shown in Figure 7.  In this plot we show trends against aromatics with a different series for each ethanol level. As in Figure 3, the effect of aromatics is visible, but it is not apparent that the aromatics effect differs systematically by ethanol level.
                                       
    Figure 7.  CO2 (Composite):  Emissions vs. Aromatics by Ethanol Level.
                                       
Statistical Modeling
We followed up on the graphical presentation of the data by performing statistical modeling. 

Response variable:  As mentioned above, the response variable was CO2 emissions, as the cycle composite on the LA92 cycle.  Unlike other emissions, such as NOx, PM or NMOG, it was not necessary to perform a natural log transformation of the data before modeling, as the CO2 results are approximately normally distributed with respect to the fuel properties.

Design Model:  The properties of the test fuels form a five-dimensional study design optimized to estimate emissions as efficiently as possible for set of pre-specified model terms. These terms include a linear term for each of the five fuel properties, two squared terms for ethanol and T50, and four interaction terms, for combinations of ethanol with each of the remaining four properties.  A model including this set of 11 terms is shown in Equation 1.



                                                                     Equation 1

The model including all 11 terms will be referred to as a "full model," indicating that it contains all available candidate terms.

Standardization:  Prior to modeling, all terms were "standardized."  That is, each fuel property measurement was "centered" by subtracting its mean (for all measurements), and then "scaled" by dividing the difference by its corresponding standard deviation (for all measurements).  For the five linear terms, this process was performed using individual fuel property measurements. The resulting "Z score" has a mean of 0.0 and a standard deviation of 1.0.  For 2[nd]  - order terms, cross products terms were constructed not from the original measurements, but rather from the Z scores for the applicable linear terms.  Then the standardization process was repeated, after calculating the means and standard deviations of the cross products of the Z scores. Thus, these "two-stage" standardized values for the 2[nd]-order terms will be referred to using the notation "ZZ."  For example, the term for the etOHxetOH quadratic term is notated as ZZee, and that for the etOHxAromatics interaction as ZZea. This process is performed to neutralize any remaining correlations among terms, particularly between linear effects and corresponding 2[nd]-order terms, and is described in greater detail in section 2.3.1 of the EPAct analysis report.   Thus the models actually fit are represented in Equation 2, in which each term corresponds to its counterpart in Equation 1.


                                                                     Equation 2

Model Fitting:  Starting with a "full model" including all 11 terms in Equation 2, we performed model fitting to identify and remove terms not contributing to the fit of the model to the dataset.  This process was performed by backwards elimination.  In the first step, after fitting the full model, any terms with p-values for their Type-III tests greater than 0.10 were removed and the model refit without them.  The model with fewer terms is termed a "reduced model," which is said to be "nested" in the full model. Then, as a test of goodness of fit between the two models, a likelihood ratio test was performed.  The test statistic was the difference in the -2 log likelihood statistics between the nested and full models (known as the "reference model" for purposes of the test). This statistic is assumed to follow a χ[2] distribution with degrees of freedom equal to the difference in the number of parameters between the two models. If the test gave a p-value greater than 0.10, the null hypothesis of no difference in fit between the two models was retained, and the term(s) under consideration were dropped in subsequent model-fitting steps, under the assumption that they did not make a statistically significant improvement in the model fit. On the other hand, if the p-value was < 0.10, the null hypothesis was dropped, and one or more of the term(s) would be retained in the model, pending successive fitting steps.  In this circumstance, one or more of the terms is assumed to make a statistically significant improvement in model fit.

If terms dropped in the first step are not retained, the "reduced model" with fewer terms becomes the "reference model" and the process is repeated.  Successive model fitting steps are performed until a significant result is obtained and all remaining terms have p-values < 0.10.
Results
The process is summarized in Table 1 to Table 3.  Table 1 shows the set of reduced models fit. Table 2 shows the results of successive tests fit during the process.  Table 3 shows the coefficients, standard errors and tests of effect for the full model and the reduced model having the best fit to the dataset.


Table 2. Models fit for CO2 (composite): (all models include an intercept term).
Model Term
                                   Notation
                                     Model

                                       
                                     Full
                                    FM6[1]
                                      FM7
                                      FM8
                                     etOH
Ze
                                      ●
                                      ●
                                      ●
                                      ●
                                     Arom
Za
                                      ●
                                      ●
                                      ●
                                      ●
                                      RVP
Zr
                                      ●
                                      ●
                                      ●
                                      x
                                      T50
Z5
                                      ●
                                      ●
                                      ●
                                      ●
                                      T90
Z9
                                      ●
                                      x
                                       
                                       
                                 etOH x etOH
ZZee
                                      ●
                                      x
                                       
                                       
                                  T50 x T50
ZZ55
                                      ●
                                      x
                                       
                                       
                                 etOH x Arom
ZZea
                                      ●
                                      ●
                                      x
                                       
                                  etOH x RVP
ZZer
                                      ●
                                      x
                                       
                                       
                                  etOH x T50
ZZe5
                                      ●
                                      x
                                       
                                       
                                  etOH x T90
ZZe9
                                      ●
                                      x
                                       
                                       
[1] denotes "full minus 6."


                                       
                                       
Table 3. CO2 (Bag 1): Model Fitting History, starting with the 11-term Full model.
                                Fit Parameters

                             Test with respect to
                                Previous Model
Model
                                                                              p
-2lnL
BIC  [1]

                                                                           Dev.
                                                                              d
                                                                    Pr>χ[2]
Full
                                                                             12
                                                                       -7591.08
                                                                       -7553.17

                                                                               
                                                                               
                                                                               
FM6
                                                                              6
                                                                       -7582.70
                                                                       -7561.03

                                                                          8.380
                                                                              6
                                                                          0.212
FM7
                                                                              5
                                                                       -7580.88
                                                                       -7561.92

                                                                          1.820
                                                                              1
                                                                          0.177
FM8 [2]
                                                                              4
                                                                       -7578.22
                                                                       -7561.97

                                                                          2.660
                                                                              1
                                                                          0.103

                                                                               



                                                                               
                                                                               
                                                                               
[1] A lower value indicates a better fit.
[2] Best fit with respect to the 11-term design model.









Table 4.  CO2 (Composite): Coefficients  and Tests of Effect for the Full and Reduced Models, with respect to the 11-term design model.
Effect
                                       
                                  Full Model

                              Reduced Model (FM8)


Estimate[1]
Std.Err.[1]
d.f.
t-value
Pr> t

                                                                    Estimate[1]
Std.Err.[1]
d.f.
t-value
Pr> t
Intercept
                                                                               
                                                                          433.7
                                                                          25.59
                                                                             15
                                                                          16.95
                                                                       0.000000

                                                                          433.7
                                                                          25.59
                                                                             15
                                                                          16.95
                                                                       0.000000
Ze
                                                                               
                                                                         0.9796
                                                                         0.2043
                                                                            941
                                                                          4.795
                                                                       0.000002

                                                                         0.9877
                                                                         0.1678
                                                                            941
                                                                          5.886
                                                                       0.000000
Za
                                                                               
                                                                          7.784
                                                                         0.1424
                                                                            941
                                                                          54.67
                                                                       0.000000

                                                                          7.766
                                                                         0.1414
                                                                            941
                                                                          54.92
                                                                       0.000000
Zr
                                                                               
                                                                        -0.1993
                                                                         0.1626
                                                                            941
                                                                         -1.225
                                                                           0.22

                                                                         0.8249
                                                                         0.1730
                                                                            941
                                                                          4.768
                                                                       0.000002
Z5
                                                                               
                                                                         0.7546
                                                                         0.2051
                                                                            941
                                                                          3.679
                                                                        0.00025

                                                                               
                                                                               
                                                                               
                                                                               
                                                                               
Z9
                                                                               
                                                                        -0.0243
                                                                         0.1424
                                                                            941
                                                                         -0.170
                                                                           0.86

                                       
                                       
                                       
                                       
                                       
ZZee
                                                                               
                                                                         0.2269
                                                                         0.2741
                                                                            941
                                                                         0.8276
                                                                           0.41

                                                                               
                                                                               
                                                                               
                                                                               
                                                                               
ZZ55
                                                                               
                                                                        -0.2038
                                                                         0.2053
                                                                            941
                                                                         -0.993
                                                                           0.32

                                                                               
                                                                               
                                                                               
                                                                               
                                                                               
ZZea
                                                                               
                                                                         0.2050
                                                                         0.1393
                                                                            941
                                                                          1.472
                                                                           0.14

                                                                               
                                                                               
                                                                               
                                                                               
                                                                               
ZZer
                                                                               
                                                                        -0.1770
                                                                         0.1421
                                                                            941
                                                                         -1.246
                                                                           0.21

                                                                               
                                                                               
                                                                               
                                                                               
                                                                               
ZZe5
                                                                               
                                                                        -0.0867
                                                                         0.2942
                                                                            941
                                                                         -0.295
                                                                           0.77

                                                                               
                                                                               
                                                                               
                                                                               
                                                                               
ZZe9
                                                                               
                                                                        -0.0459
                                                                         0.1398
                                                                            941
                                                                         -0.328
                                                                           0.74

                                                                               
                                                                               
                                                                               
                                                                               
                                                                               

                                                                               
                                                                               
                                                                               
                                                                               
                                                                               
                                                                               

                                                                               
                                                                               
                                                                               
                                                                               
                                                                               

                                                                               
                                                                          9,822
                                                                               
                                                                               
                                                                               
                                                                               

                                                                          9,821
                                                                               
                                                                               
                                                                               
                                                                               

                                                                               
                                                                             18
                                                                               
                                                                               
                                                                               
                                                                               

                                                                             18
                                                                               
                                                                               
                                                                               
                                                                               

                                                                               
                                                                               
                                                                               
                                                                               
                                                                               
                                                                               

                                                                               
                                                                               
                                                                               
                                                                               
                                                                               
[1] Expressed in units of g/mi per a change in the fuel property of 1.0 standard deviation (g/mi-σ).

Interpretation
 The results presented in Table 3 are presented graphically below in Figure 8, in which the bars represent the magnitude and signs of the coefficients, excluding the intercept (434 g/mi). Error bars on the coefficients represent 90% confidence intervals based on the standard errors shown in the table. The terms dropped from the reduced model are clearly seen as those with error bars spanning 0.0.

Figure 8.  CO2 (Composite): Standardized Model Coefficients for Full and Reduced Models (Error bars represent 90% confidence intervals).
                                       

The reduced model is simple, retaining only three linear effects and no 2[nd]-order terms. It contains three linear terms, for ethanol, aromatics and T50, with the values for ethanol and T50 being similar in size, with values of approximately 1.0 g/mi-σ. The term for aromatics is considerably larger, at approximately 8.0 g/mi-σ. 

Because, as mentioned above, the fuel properties are "standardized" before model fitting, and because the response variable is CO2 emissions (g/mi), as a composite on the LA92, the coefficients represent a change in CO2 emissions corresponding to changes in the fuel properties of 1.0 standard deviation (σ), as calculated for the fuel matrix used in the study.  In addition, the coefficients represent the effect on the emission rate for each fuel property, as though the remaining properties would be held constant while varying the property under consideration. This assumption is entirely artificial but very useful in assessing the behavior of emissions in relation to changing fuel properties.

An interpretation of each of the terms is provided below:

Ethanol:  The coefficient takes a value of 0.98 g/mi-σ. As the σ for ethanol is 7.9 vol.%, the coefficient indicates an increase of ~0.124 g CO2/mi per % increase in ethanol volume, assuming aromatics and T50 are held constant. For example, with the other two properties constant, we would predict a 1.25 g/mi increase in CO2 from an E10 blend relative to an E0 blend. Note, however, that the change is very small, e.g., an average rate of 350 g/mi on E0 would increase to 351.24 g/mi on E10, which represents an increase of 0.4%.

Aromatics:  This coefficient takes a value of 7.8 g/mi-σ.   The σ for aromatics is 10.0 vol.%.  Thus, the coefficient indicates an increase of 0.78 g CO2/mi per % increase in aromatics volume, assuming ethanol and T50 are held constant.  For example, with the other two properties constant, we would predict a 7.8 g/mi increase in CO2 from a 15% aromatics to one with 25% aromatics.  While larger than the ethanol effect, this change is also small relative to the base level, e.g., an average rate of 350 g/mi on a fuel with 15% aromatics would increase to 357.8 g/mi on a fuel with 25% aromatics, which represents an increase of 2.2%.  

T50:   This coefficient takes a value of 0.83 g/mi-σ.  The σ for T50 is 28.6°F.  The coefficient thus indicates an increase of 0.029 g CO2/mi per an increase in T50 of 1.0 F°, assuming ethanol and aromatics are held constant.  For example, with the other two properties held constant, we would predict a 0.88 g/mi increase in CO2 from a fuel with T50 at 220°F relative to a fuel with T50 at 190°F.  An average rate of 350 g/mi on a fuel with T50 at 220°F would increase to 350.88 g/mi on a fuel with T50 at 190°F, which represents an increase of 0.3%.
Conclusion
The analysis of results from the EPAct program indicates that changes in fuel properties are associated with measurable changes in CO2 emissions. In particular, three fuel properties, ethanol, aromatics and T50 are associated with statistically significant changes in CO2 emissions that are, however, small to very small in absolute terms. 

Of the three properties, the effect for aromatics is clearly the most important, with the aromatics coefficient 8 times and 9.4 times larger than those for ethanol and T50, respectively (based on the standardized coefficients shown above in Figure 8).

While it is useful to consider the coefficients in isolation, it is critical to remember that in practice the fuel properties cannot be cleanly separated.  Thus, when applying the models, it is necessary to account for the effects of multiple properties varying simultaneously. 

For example, while noting that the ethanol coefficient predicts that a shift from E0 to E10 blends would result in a small increase in CO2 emissions, accounting for simultaneous decreases in aromatics (and possibly T50) due to dilution and/or octane match-blending by refiners, we would expect the aromatics effect would be opposite the ethanol effect and of an equal or greater magnitude.  For example, the model suggests that the increase in CO2 due to an increase in ethanol from 0 to 10 vol% (1.25 g/mi CO2 increase) would be offset by a reduction in aromatics of 1.6 vol% (1.25 g/mi CO2 decrease), not accounting for potential changes in T50.  Stated differently, the model predicts that a gasoline with 0 vol% ethanol and 25 vol% aromatics would have the same CO2 emissions as a fuel with 10 vol% ethanol and 23.4 vol% aromatics.

In general, we conclude that the data and analysis support a conclusion that, aside from improbable cases in which ethanol and aromatics increase simultaneously, the addition of ethanol to gasoline is expected to have no appreciable effects on CO2 emissions.
  

   

