Nonlinearity in atmospheric response: A direct sensitivity analysis approach

The decoupled direct method (DDM) is used for efficient and accurate calculation of the higher-order sensitivity coefficients in a regional photochemical air quality model with detailed chemical mechanism ( Statewide Air Pollution Research Center (SAPRC-99)). High-order DDM (HDDM) is an extension to a previous implementation of DDM in three-dimensional air quality models (DDM-3D) that directly calculates the higher-order derivatives (with respect to one parameter, as well as cross derivatives) with similar computational efficiency as the first-order implementation and is also modified for better accuracy. (H)DDM results show very good agreement with brute force (finite difference) sensitivity coefficients for the first- and second-order derivatives, but the agreement deteriorates for higher-order coefficients. The nature of the truncation errors and other inaccuracies in the brute force approximations are explored. The difference between the first- order brute force and DDM derivatives is dominated (and largely explained) by the truncation errors as calculated from HDDM results. Taylor expansion is used for parametric scaling of the response with the use of sensitivity coefficients. Use of higher-order coefficients can significantly improve the accuracy of such projections. Finally, higher-order sensitivity coefficients of ozone with respect to NOx and volatile organic compound emissions (including cross derivatives) are used to create time- and location-dependent ozone isopleths.