6.1 Introduction and Background

Uncertainty in the application of transport-transformation models arises not only due to uncertainty in model inputs or parameters (i.e., parametric or data uncertainty), but also due to uncertainty in model formulation (i.e., model uncertainty). As mentioned in Chapter 1, model uncertainty arises under several conditions, including the following: (a) when alternative sets of scientific or technical assumptions for developing a model exist (Model Structure), (b) when models are simplified for purposes of tractability (Model Detail), and (c) when a coarse numerical discretization is used to reduce the computation demands of the model (Model Resolution). Some of the major sources of model uncertainty in transport-transformation modeling are listed in Table 2.1.

When a model application involves both model and data uncertainties, it is important to identify the relative magnitudes of the uncertainties associated with data and model formulation. Such a comparison is useful in focusing resources where it is most appropriate (e.g., data gaps versus model refinement).

The approach followed here for characterizing model uncertainty here is based on the development of models corresponding to different model formulations subsequent comparison of the model results. The availability of the alternative models, ranging from simplified to more detailed, aids in evaluating the applicability of the low resolution models - if the results of the low resolution models agree closely with those of the high resolution models, then the low resolution models are preferable, since they typically require fewer computational resources and lesser input data. Furthermore, the availability of the alternative models aids in the characterization of the model uncertainty associated with the application of those models - the bounds on model calculations corresponding to different model formulations provide an estimate of the uncertainty associated with the model formulation. For example, if the bounds are narrow the uncertainty associated with the model formulation can be considered to be relatively small.

This chapter focuses on the model uncertainties associated with photochemical air quality modeling applications. Specifically, the uncertainties associated with model resolution and assumptions of ``well mixedness'' are addressed here. A case study is presented involving an EPA regulatory atmospheric photochemical trajectory model, the Reactive Reactive Plume Model (RPM) [195], which is briefly described in Section 5.2, and is described in more detail in the following sections.

As mentioned in Section 5.2, the RPM describes the evolution of a photochemical plume from ``point sources'' of emissions, such as the stacks of refineries and of power plants. The currently used version of RPM, RPM-IV, lacks vertical resolution, as the model assumptions include uniform mixing in the vertical direction; the lack of resolution is highlighted in Figure 6.3. Here, two aspects of the model are studied: (a) the uncertainty associated with the assumption of uniform vertical concentration profile, and (b) the uncertainty associated with the choice of horizontal resolution. In this process, the results of the RPM at varying horizontal resolutions are studied first. Then a ``three-dimensional version'' of the RPM, termed RPM-3D, is developed by incorporating vertical resolution into the RPM-IV. The results from the RPM and the RPM-3D are subsequently compared with each other in order to characterize the uncertainty associated with the vertical resolution in the RPM.

The relevant background information on photochemical modeling, required for a detailed understanding of the RPM, is presented here. That is followed by a description of the formulation of RPM-IV and RPM-3D.