The high-order decoupled direct method in three dimensions for particulate matter (HDDM-3D/PM) has been implemented in the Community Multiscale Air Quality (CMAQ) model to enable advanced sensitivity analysis. The major effort of this work is to develop high-order DDM sensitivity analysis of ISORROPIA, the inorganic aerosol module of CMAQ. A case-specific approach has been applied, and the sensitivities of activity coefficients and water content are explicitly computed. Stand-alone tests are performed for ISORROPIA by comparing the sensitivities (first- and second-order) computed by HDDM and the brute force (BF) approximations. Similar comparison has also been carried out for CMAQ sensitivities simulated using a week-long winter episode for a continental US domain. Second-order sensitivities of aerosol species (e.g., sulfate, nitrate, and ammonium) with respect to domain-wide SO<sub>2</sub>, NO<sub>x</sub>, and NH<sub>3</sub> emissions show agreement with BF results, yet exhibit less noise in locations where BF results are demonstrably inaccurate. Second-order sensitivity analysis elucidates poorly understood nonlinear responses of secondary inorganic aerosols to their precursors and competing species. Adding second-order sensitivity terms to the Taylor series projection of the nitrate concentrations with a 50% reduction in domain-wide NO<sub>x</sub> or SO<sub>2</sub> emissions rates improves the prediction with statistical significance.