## 1 Introduction

Secondary air pollutants like ozone (O_{3}) are formed as a result of complex nonlinear chemistry between various primary pollutants emitted directly into the atmosphere due to anthropogenic and natural activities. Understanding the responses of ambient pollutant concentrations to emission changes (sensitivity) is therefore crucial for the development of effective pollution abatement strategies. Photochemical models are used to estimate the sensitivity of secondary air pollutants to their precursor emissions, and thus serve as useful tools for determining the amount of emission reduction needed to attain ambient air-quality standards and informing the selection of control strategies.

Models for informing air-quality management are typically run deterministically with a single best-available setting for model formulation and inputs. However, there has been a growing interest in probabilistic representations of model results that account for model uncertainty [*Dennis et al*., 2010; *Hogrefe and Rao*, 2001]. Uncertainties in pollutant-emission sensitivity may arise from choices of numerical representations of atmospheric processes such as chemical mechanism, vertical mixing scheme, horizontal transport, and emission model (*structural uncertainty*), and/or from the values of input parameters such as emission rates, reaction rate constants, boundary conditions, and deposition velocities (*parametric uncertainty*) [*Deguillaume et al*., 2008; *Fine et al*., 2003; *Pinder et al*., 2009].

Recent work by *Digar and Cohan* [2010] and *Tian et al*. [2010] introduced efficient Monte Carlo techniques for characterizing *parametric* uncertainties in O_{3} and particulate matter (PM) responses to emission controls. *Pinder et al*. [2009] jointly considered *parametric* and *structural* uncertainties to develop probabilistic estimates of O_{3} concentrations. However, none of these studies evaluated the relative likelihoods of the various Monte Carlo cases.

Previous work by *Bergin and Milford* [2000] had shown that a Bayesian inference approach can weight the relative likelihood of each Monte Carlo model formulation based on its performance in simulating observed concentrations, and thus yield probability distributions for predicting the actual values of pollutant-emission sensitivities as well as model inputs. That study used a simplified two-dimensional trajectory model, and only a handful of studies have applied Bayesian Monte Carlo approaches to characterize O_{3} responsiveness in more computationally intensive three-dimensional regional models [*Beekmann and Derognat*, 2003; *Deguillaume et al*., 2008].

The aim of this study is to develop probabilistic representations of O_{3} responsiveness to emission changes constrained by actual measurements of pollutant concentrations. The Monte Carlo Reduced Form Model (RFM) approach of *Digar and Cohan* [2010] has been used to generate a large ensemble of model predictions of O_{3} concentrations and responsiveness to emission controls in the Dallas-Fort Worth (DFW) region of Texas, which is currently a nonattainment area for the 1997 eight hour O_{3} National Ambient Air Quality Standard (NAAQS). The simulated concentrations of O_{3} and its precursor nitrogen oxides (NO_{x} ≡ NO and NO_{2}) are compared against observations to yield adjusted (*observation-constrained*) probabilistic representations of photochemical model inputs and output predictions. Use of both Bayesian and non-Bayesian statistical techniques allows us to evaluate the consistency of our results across various observational metrics and methods of comparison. Sections 2 and 3 describe the modeling and measurements used for this work, and section 4 describes the statistical methodology and metrics considered here. Important findings are elaborated in Results and Discussion (section 5), followed by the Conclusion.