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. As one common precursor for both PM2.5 and O3 pollution,NO x gains great attention because its controls can be beneficial forreducing both PM2.5 and O3 . However, the effectiveness ofNO x controls for reducing PM2.5 and O3 are largelyinfluenced by the ambient levels of NH3 and VOC, exhibiting strongnonlinearities characterized as NH3 -limited/ NH3 -poor andNO x -/VOC-limited conditions, respectively. Quantification of suchnonlinearities is a prerequisite for making suitable policy decisions butlimitations of existing methods were recognized. In this study, a new methodwas developed by fitting multiple simulations of a chemical transport model(i.e., Community Multiscale Air Quality Modeling System, CMAQ) with a setof polynomial functions (denoted as “pf-RSM”) to quantify responses ofambient PM2.5 and O3 concentrations to changes in precursoremissions. The accuracy of the pf-RSM is carefully examined to meet thecriteria of a mean normalized error within 2 % and a maximal normalizederror within 10 % by using 40 training samples with marginalprocessing. An advantage of the pf-RSM method is that the nonlinearity in PM2.5 and O3 responses to precursor emission changes can becharacterized by quantitative indicators, including (1) a peak ratio (denotedas PR) representing VOC-limited or NO x -limited conditions, (2) a suggestedratio of VOC reduction to NO x reduction to avoid increasing O3 underVOC-limited conditions, (3) a flex ratio (denoted as FR) representing NH3 -poor or NH3 -rich conditions, and (4) enhanced benefits in PM2.5 reductions from simultaneous reduction of NH3 withthe same reduction rate of NO x . A case study in the Beijing–Tianjin–Hebeiregion suggested that most urban areas present strong VOC-limited conditionswith a PR from 0.4 to 0.8 in July, implying that the NO x emissionreduction rate needs to be greater than 20–60 % to pass the transition fromVOC-limited to NO x -limited conditions. A simultaneous VOC control (the ratio of VOCreduction to NO x reduction is about 0.5–1.2) can avoid increasing O3 during the transition. For PM2.5 , most urban areaspresent strong NH3 -rich conditions with a PR from 0.75 to 0.95, implyingthat NH3 is sufficiently abundant to neutralize extra nitric acidproduced by an additional 5–35 % of NO x emissions. Enhancedbenefits in PM2.5 reductions from simultaneous reduction of NH3 were estimated to be 0.04–0.15  µ g m −3 PM2.5 per 1 % reduction of NH3 along with NO x ,with greater benefits in July when the NH3 -rich conditions are not asstrong as in January. Thus, the newly developed pf-RSM model has successfullyquantified the enhanced effectiveness of NO x control, and simultaneousreduction of VOC and NH3 with NO x can assure the controleffectiveness of PM2.5 and O3 .

atmospheric chemistry and physics

Quantification of the enhanced effectiveness of NO&amp;lt;sub&amp;gt;&amp;lt;i&amp;gt;x&amp;lt;/i&amp;gt;&amp;lt;/sub&amp;gt; control from simultaneous reductions of VOC and NH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt; for reducing air pollution in the Beijing–Tianjin–Hebei region, China