# 40 CFR 80.48 - Augmentation of the complex emission model by vehicle testing.

(a) The provisions of this section apply only if a fuel claims emission reduction benefits from fuel parameters that are not included in the complex emission model or complex emission model database, or if the values of fuel parameters included in the complex emission model set forth in § 80.45 fall outside the range of values for which the complex emission model is deemed valid.

(b) To augment the complex emission model described at § 80.45, the following requirements apply:

(1) The petitioner must obtain prior approval from the Administrator for the design of the test program before beginning the vehicle testing process. To obtain approval, the petitioner must at minimum provide the following information: the fuel parameter to be evaluated for emission effects; the number and description of vehicles to be used in the test fleet, including model year, model name, vehicle identification number (VIN), mileage, emission performance (exhaust THC emission level), technology type, and manufacturer; a description of the methods used to procure and prepare the vehicles; the properties of the fuels to be used in the testing program (as specified at § 80.49); the pollutants and emission categories intended to be evaluated; the precautions used to ensure that the effects of the parameter in question are independent of the effects of other parameters already included in the model; a description of the quality assurance procedures to be used during the test program; the statistical analysis techniques to be used in analyzing the test data, and the identity and location of the organization performing the testing.

(2) Exhaust emissions shall be measured per the requirements of this section and § 80.49 through § 80.62.

(3) The nonexhaust emission model (including evaporative, running loss, and refueling VOC and toxics emissions) shall not be augmented by vehicle testing.

(4) The Agency reserves the right to observe and monitor any testing that is performed pursuant to the requirements of this section.

(5) The Agency reserves the right to evaluate the quality and suitability of data submitted pursuant to the requirements of this section and to reject, re-analyze, or otherwise evaluate such data as is technically warranted.

(6) Upon a showing satisfactory to the Administrator, the Administrator may approve a petition to waive the requirements of this section and § 80.49, § 80.50(a), § 80.60(d)(3), and § 80.60(d)(4) in order to better optimize the test program to the needs of the particular fuel parameter. Any such waiver petition should provide information justifying the requested waiver, including an acceptable rationale and supporting data. Petitioners must obtain approval from the Administrator prior to conducting testing for which the requirements in question are waived. The Administrator may waive the noted requirements in whole or in part, and may impose appropriate conditions on any such waiver.

(c) In the case of petitions to augment the complex model defined at § 80.45 with a new parameter, the effect of the parameter being tested shall be determined separately, for each pollutant and for each emitter class category. If the parameter is not included in the complex model but is represented in whole or in part by one or more parameters included in the model, the petitioner shall be required to demonstrate the emission effects of the parameter in question independent of the effects of the already-included parameters. The petitioner shall also have to demonstrate the effects of the already-included parameters independent of the effects of the parameter in question. The emission performance of each vehicle on the fuels specified at § 80.49, as measured through vehicle testing in accordance with § 80.50 through § 80.62, shall be analyzed to determine the effects of the fuel parameter being tested on emissions according to the following procedure:

(1) The analysis shall fit a regression model to the natural logarithm of emissions measured from addition fuels 1, 2, and 3 only (as specified at § 80.49(a) and adjusted as per paragraph (c)(1)(iv) of this section and § 80.49(d)) that includes the following terms:

(i) A term for each vehicle that shall reflect the effect of the vehicle on emissions independent of fuel compositions. These terms shall be of the form Di × Vi, where Di is the coefficient for the term and Vi is a dummy variable which shall have the value 1.0 for the ith vehicle and the value 0 for all other vehicles.

(ii) A linear term in the parameter being tested for each emitter class, of the form Ai × (P1−P1 (avg)) × Ei, where Ai is the coefficient for the term, P1 is the level of the parameter in question, P1 (avg) is the average level of the parameter in question for all seven test fuels specified at § 80.49(a)(1), and Ei is a dummy variable representing emitter class, as defined at § 80.62. For normal emitters, E1 = 1 and E2 = 0. For higher emitters, E1 = 0 and E2 = 1.

(iii) For the VOC and NOX models, a squared term in the parameter being tested for each emitter class, of the form Bi × (P1−P1 (avg)) 2 × Ei, where Bi is the coefficient for the term and where P1 , P1 (avg), and Ei are as defined in paragraph (c)(1)(ii) of this section.

(iv) To the extent that the properties of fuels 1, 2, and 3 which are incorporated in the complex model differ in value among the three fuels, the complex model shall be used to adjust the observed emissions from test vehicles on those fuels to compensate for those differences prior to fitting the regression model.

(v) The Ai and Bi terms and coefficients developed by the regression described in this paragraph (c) shall be evaluated against the statistical criteria defined in paragraph (e) of this section. If both terms satisfy these criteria, then both terms shall be retained. If the Bi term satisfies these criteria and the Ai term does not, then both terms shall be retained. If the Bi term does not satisfy these criteria, then the Bi term shall be dropped from the regression model and the model shall be re-estimated. If, after dropping the Bi term and re-estimating the model, the Ai term does not satisfy these criteria, then both terms shall be dropped, all test data shall be reported to EPA, and the augmentation request shall be denied.

(2) After completing the steps outlined in paragraph (c)(1) of this section, the analysis shall fit a regression model to a combined data set that includes vehicle testing results from all seven addition fuels specified at § 80.49(a), the vehicle testing results used to develop the model specified at § 80.45, and vehicle testing results used to support any prior augmentation requests which the Administrator deems necessary.

(i) The analysis shall fit the regression models described in paragraphs (c)(2) (ii) through (v) of this section to the natural logarithm of measured emissions.

(ii) All regressions shall include a term for each vehicle that shall reflect the effect of the vehicle on emissions independent of fuel compositions. These terms shall be of the form Di × Vi, where Di is the coefficient for the term and Vi is a dummy variable which shall have the value 1.0 for the ith vehicle and the value 0 for all other vehicles. Vehicles shall be represented by separate terms for each test program in which they were tested. The vehicle terms for the vehicles included in the test program undertaken by the petitioner shall be calculated based on the results from all seven fuels specified at § 80.49(a). Note that the Di estimates for the petitioner's test vehicles in this regression are likely to differ from the Di estimates discussed in paragraph (c)(1)(i) of this section since they will be based on a different set of fuels.

(iii) All regressions shall include existing complex model terms and their coefficients, including those augmentations that the Administrator deems necessary. All terms and coefficients shall be expressed in centered form. The Administrator shall make available upon request existing complex model terms and coefficients in centered form.

(iv) All regressions shall include the linear and squared terms, and their coefficients, estimated in the final regression model described in paragraph (c)(1) of this section.

(v) The VOC and NOX regressions shall include those interactive terms with other fuel parameters, of the form Ci(1, j) × (P1 − P1 (avg)) × (Pj − Pj (avg)) × Ei, where Ci(1, j) is the coefficient for the term, P1 is the level of the parameter being added to the model, P1 (avg) is the average level of the parameter being added for all seven addition fuels specified at § 80.49(a), Pj is the level of the other fuel parameter, Pj (avg) is the centering value for the other fuel parameter used to develop the complex model or used in the other parameter's augmentation study, and Ei is as defined in paragraph (c)(1) of this section, which are found to satisfy the statistical criteria defined in paragraph (e) of this section. Such terms shall be added to the regression model in a stepwise manner.

(3) The model described in paragraphs (c) (1) and (2) of this section shall be developed separately for normal-emitting and higher-emitting vehicles. Each emitter class shall be treated as a distinct population for the purposes of determining regression coefficients.

(4) Once the augmented models described in paragraphs (c) (1) through (3) of this section have been developed, they shall be converted to an uncentered form through appropriate algebraic manipulation.

(5) The augmented model described in paragraph (c)(4) of this section shall be used to determine the effects of the parameter in question at levels between the levels in Fuels 1 and 3, as defined at § 80.49(a)(1), for all fuels which claim emission benefits from the parameter in question.

(d)

(1) In the case of petitions to augment the complex model defined at § 80.45 by extending the range of an existing complex model parameter, the effect of the parameter being tested shall be determined separately, for each pollutant and for each technology group and emitter class category, at levels between the extension level and the nearest limit of the core of the data used to develop the unaugmented complex model as follows:

Fuel parameter | Data core limits | |
---|---|---|

Lower | Upper | |

Sulfur, ppm | 10 | 450 |

RVP, psi | 7 | 10 |

E200, vol % | 33 | 66 |

E300, vol % | 72 | 94 |

Aromatics, vol % | 18 | 46 |

Benzene, vol % | 0.4 | 1.8 |

Olefins, vol % | 1 | 19 |

Oxygen, wt % | ||

As ethanol | 0 | 3.4 |

All others: | 0 | 2.7 |

(2) The emission performance of each vehicle on the fuels specified at § 80.49(b)(2), as measured through vehicle testing in accordance with §§ 80.50 through 80.62, shall be analyzed to determine the effects of the fuel parameter being tested on emissions according to the following procedure:

(i) The analysis shall incorporate the vehicle testing data from the extension fuels specified at § 80.49(b), the vehicle testing results used to develop the model specified at § 80.45, and vehicle testing results used to support any prior augmentation requests which the Administrator deems necessary. A regression incorporating the following terms shall be fitted to the natural logarithm of emissions contained in this combined data set:

(A) A term for each vehicle that shall reflect the effect of the vehicle on emissions independent of fuel compositions. These terms shall be of the form Di × Vi, where Di is the coefficient for the term and Vi is a dummy variable which shall have the value 1.0 for the ith vehicle and the value 0 for all other vehicles. Vehicles shall be represented by separate terms for each test program in which they were tested. The vehicle terms for the vehicles included in the test program undertaken by the petitioner shall be calculated based on the results from all three fuels specified at § 80.49(b)(2).

(B) Existing complex model terms that do not include the parameter being extended and their coefficients, including those augmentations that the Administrator deems necessary. The centering values for these terms shall be identical to the centering values used to develop the complex model described at § 80.45.

(C) Existing complex model terms that include the parameter being extended. The coefficients for these terms shall be estimated by the regression. The centering values for these terms shall be identical to the centering values used to develop the complex model described at § 80.45.

(D) If the unaugmented VOC or NOX complex models do not contain a squared term for the parameter being extended, such a term should be added in a stepwise fashion after completing the model described in paragraphs (d)(2)(i)(A) through (C) of this section. The coefficient for this term shall be estimated by the regression. The centering value for this term shall be identical to the centering value used to develop the complex model described at § 80.45.

(E) The terms defined in paragraphs (d)(2)(i)(C) and (D) of this section shall be evaluated against the statistical criteria defined in paragraph (e) of this section.

(ii) The model described in paragraph (d)(2)(i) of this section shall be developed separately for normal-emitting and higher-emitting vehicles, as defined at § 80.62. Each emitter class shall be treated as a distinct population for the purposes of determining regression coefficients.

(e)Statistical criteria.

(1) The petitioner shall be required to submit evidence with the petition which demonstrates the statistical validity of the regression described in paragraph (c) or (d) of this section, including at minimum:

(i) Evidence demonstrating that colinearity problems are not severe, including but not limited to variance inflation statistics of less than 10 for the second-order and interactive terms included in the regression model.

(ii) Evidence demonstrating that the regression residuals are normally distributed, including but not limited to the skewness and Kurtosis statistics for the residuals.

(iii) Evidence demonstrating that overfitting and underfitting risks have been balanced, including but not limited to the use of Mallow's Cp criterion.

(2) The petitioner shall be required to submit evidence with the petition which demonstrates that the appropriate terms have been included in the regression, including at minimum:

(i) Descriptions of the analysis methods used to develop the regressions, including any computer code used to analyze emissions data and the results of regression runs used to develop the proposed augmentation, including intermediate regressions produced during the stepwise regression process.

(ii) Evidence demonstrating that the significance level used to include terms in the model was equal to 0.90.

(f) The complex emission model shall be augmented with the results of vehicle testing as follows:

(1) The terms and coefficients determined in paragraph (c) or (d) of this section shall be used to supplement the complex emission model equation for the corresponding pollutant and emitter category. These terms and coefficients shall be weighted to reflect the contribution of the emitter category to in-use emissions as shown at § 80.45.

(2) If the candidate parameter is not included in the unaugmented complex model and is not represented in whole or in part by one or more parameters included in the model, the modification shall be accomplished by adding the terms and coefficients to the complex model equation for that pollutant, technology group, and emitter category.

(3) If the parameter is included in the complex model but is being tested at levels beyond the current range of the model, the terms and coefficients determined in paragraph (d) of this section shall be used to supplement the complex emission model equation for the corresponding pollutant.

(i) The terms and coefficients of the complex model described at § 80.45 shall be used to evaluate the emissions performance of fuels with levels of the parameter being tested that are within the valid range of the model, as defined at § 80.45.

(ii) The emissions performance of fuels with levels of the parameter that are beyond the valid range of the unaugmented model shall be given in percentage change terms by 100 − [(100 A) × (100 C) / (100 B)], where:

(A) “A” shall be set equal to the percentage change in emissions for a fuel with identical fuel property values to the fuel being evaluated except for the parameter being extended, which shall be set equal to the nearest limit of the data core, using the unaugmented complex model.

(B) “B” shall be set equal to the percentage change in emissions for the fuel described in paragraph (f)(3)(i) of this section according to the augmented complex model.

(C) “C” shall be set equal to the percentage change in emissions of the actual fuel being evaluated using the augmented complex model.

(g) EPA reserves the right to analyze the data generated during vehicle testing, to use such analyses to determine the validity of other augmentation petitions, and to use such data to update the complex model for use in certifying all reformulated gasolines.

(h) Duration of acceptance of emission effects determined through vehicle testing:

(1) If the Agency does not accept, modify, or reject a particular augmentation for inclusion in an updated complex model (performed through rulemaking), then the augmentation shall remain in effect until the next update to the complex model takes effect.

(2) If the Agency does reject or modify a particular augmentation for inclusion in an updated complex model, then the augmentation shall no longer be able to be used as of the date the updated complex model is deemed to take effect, unless the following conditions and limitations apply:

(i) The augmentation in question may continue to be used by those fuel suppliers which can prove, to the Administrator's satisfaction, that the fuel supplier had already begun producing a fuel utilizing the augmentation at the time the revised model is promulgated.

(ii) The augmentation in question may only be used to evaluate the emissions performance of fuels in conjunction with the complex emission model in effect as of the date of production of the fuels.

(iii) The augmentation may only be used for three years of fuel production, or a total of five years from the date the augmentation first took effect, whichever is shorter.

(3) The Administrator shall determine when sufficient new information on the effects of fuel properties on vehicle emissions has been obtained to warrant development of an updated complex model.