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tion procedures for a model might include sensitivity testing to identify the parameters having the greatest influence on the output values and assessment of its accuracy, precision, and predictive power. Validation of a model also requires an appropriate data base.

This chapter discusses the evaluation and validation of data and models used in risk assessment. In cases where there has been an insufficient assessment of performance or quality, research recommendations are made. Although in this chapter we consider validation issues sequentially, according to each of the stages in the (modified) Red Book paradigm, our goal here is to make the assessment of data and model quality an iterative, interactive component of the entire risk-assessment and risk-characterization process.

Emission Characterization

As described in Chapter 3, emissions are characterized on the basis of emission factors, material balance, engineering calculations, established Environmental Protection Agency (EPA) protocols, and measurement. In each case, this characterization takes the structural forms of a linearly additive process (i.e., emissions equals product – [feedstock + accumulations]), a multiplicative model (i.e., emissions equals [emission factor][process rate]), or an exponential relationship (e.g., emission equals intercept + [(emission factor) (measurement)exp]).

The additive form is based on the mass-balance concept. An estimate is made by measuring the feedstock and product to determine an equipment-specific or process-specific transfer coefficient. This coefficient is used to estimate emissions to the atmosphere. The measurements available for the additive form are often not sufficiently precise and accurate to yield complete information on inputs and outputs (NRC, 1990a). For example, an NRC committee (NRC, 1990a) considered a plant that produced 5 million pounds of ethylene per day and used more than 200 monitoring points to report production with a measurement accuracy of 1%, equivalent to 50,000 lb of ethylene per day. The uncertainty in this estimate (50,000 lb) greatly exceeded a separate estimate of emissions, 191 lb, which was calculated by the plant and was confirmed by monitoring of the emission points. Thus, despite the apparently good precision of estimates within 1%, the additive method was not reliable. This seems to be generally true for complicated processes or multiple processing steps.

The other forms are based on exponential and multiplicative models. Each may be deterministic or stochastic. For example, emissions from a well-defined sample of similar sources may be tested to develop an emission factor that is meant to be representative of the whole population of sources. A general difficulty with such fits that use these functional (linear or one of several nonlinear forms) forms is that the choice of form may be critical but hard to validate. In addition, it must be assumed that data from the sources used in the calculations are directly applicable to the sources tested in process design and in the manage-

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