We present the development of a multiphase adjoint for the Community Multiscale Air Quality (CMAQ) model, a widely used chemical transport model. The adjoint model provides location- and time-specific gradients that can be used in various applications such as backward sensitivity analysis, source attribution, optimal pollution control, data assimilation, and inverse modeling. The science processes of the CMAQ model include gas-phase chemistry, aerosol dynamics and thermodynamics, cloud chemistry and dynamics, diffusion, and advection. Discrete adjoints are implemented for all the science processes, with an additional continuous adjoint for advection. The development of discrete adjoints is assisted with algorithmic differentiation (AD) tools. Particularly, the Kinetic PreProcessor (KPP) is implemented for gas-phase and aqueous chemistry, and two different automatic differentiation tools are used for other processes such as clouds, aerosols, diffusion, and advection. The continuous adjoint of advection is developed manually. For adjoint validation, the brute-force or finite-difference method (FDM) is implemented process by process with box- or column-model simulations. Due to the inherent limitations of the FDM caused by numerical round-off errors, the complex variable method (CVM) is adopted where necessary. The adjoint model often shows better agreement with the CVM than with the FDM. The adjoints of all science processes compare favorably with the FDM and CVM. In an example application of the full multiphase adjoint model, we provide the first estimates of how emissions of particulate matter (PM2.5) affect public health across the US.

Air Health Effects Division Health Canada Ottawa ON K1A 0K9 Canada

Atmospheric and Environmental Systems Modeling Division U S EPA Research Triangle Park NC 27711 USA

Civil Architectural and Environmental Engineering Drexel University Philadelphia PA 19104 USA

College of Computer Mathematical and Natural Sciences University of Maryland College Park MD 20742 USA

Department of Chemical and Biochemical Engineering University of Iowa Iowa City IA 52242 USA

Department of Civil and Environmental Engineering Carleton University Ottawa ON K1S 5B6 Canada

Department of Earth and Atmospheric Sciences University of Houston Houston TX 77204 USA

Institute for Chemical Engineering Sciences Foundation for Research and Technology Hellas Patras 26504 Greece

Institute of Computer Science of the Czech Academy of Sciences Prague 182 07 Czech Republic

Mechanical Engineering Department University of Colorado Boulder CO 80309 USA

SAIC Stennis Space Center MS 39529 USA

School of Architecture Civil and Environmental Engineering École polytechnique fédérale de Lausanne 1015 Lausanne Switzerland

School of Civil and Environmental Engineering Georgia Institute of Technology Atlanta GA 30331 USA

School of Earth and Atmospheric Sciences Georgia Institute of Technology Atlanta GA 30331 USA

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A multiphase CMAQ version 5.0 adjoint