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Photochemical grid models (PGMs) are used to simulate tropospheric ozone and quantify its response to emission changes. PGMs are often applied for annual simulations to provide both maximum concentrations for assessing compliance with air quality standards and frequency distributions for assessing human exposure. Efficient methods for computing ozone at different emission levels can improve the quality of ozone air quality management efforts. This study demonstrates the feasibility of using the decoupled direct method (DDM) to calculate first- and second-order sensitivity of ozone to anthropogenic NO<sub>x</sub> and VOC emissions in annual PGM simulations at continental scale. Algebraic models are developed that use Taylor series to produce complete annual frequency distributions of hourly ozone at any location and any anthropogenic emission level between zero and 100%, adjusted independently for NO<sub>x</sub> and VOC. We recommend computing the sensitivity coefficients at the midpoint of the emissions range over which they are intended to be applied, in this case with 50% anthropogenic emissions. The algebraic model predictions can be improved by combining sensitivity coefficients computed at 10 and 50% anthropogenic emissions. Compared to brute force simulations, algebraic model predictions tend to be more accurate in summer than winter, at rural than urban locations, and with 100% than zero anthropogenic emissions. Equations developed to combine sensitivity coefficients computed with 10 and 50% anthropogenic emissions are able to reproduce brute force simulation results with zero and 100% anthropogenic emissions with a mean bias of less than 2 ppb and mean error of less than 3 ppb averaged over 22 US cities

A method to represent ozone response to large changes in precursor emissions using high-order sensitivity analysis in photochemical models