Abstract. 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.