30 Jun 2023
 | 30 Jun 2023
Status: this preprint is open for discussion.

The first application of a numerically-exact, higher-order sensitivity analysis approach for atmospheric modelling: implementation of the hyperdual-step method in the Community Multiscale Air Quality Model (CMAQ) version 5.3.2

Jiachen Liu, Eric Chen, and Shannon L. Capps

Abstract. Sensitivity analysis in chemical transport models quantifies the response of output variables to changes in input parameters. This information is valuable for researchers in data assimilation and model development. Additionally, environmental decision-makers depend upon these expected responses of concentrations to emissions when designing and justifying air pollution control strategies. Existing sensitivity analysis methods include the finite-difference method, the direct decoupled method (DDM), the complex variable method, and the adjoint method. These methods are either prone to significant numerical errors when applied to non-linear models with complex components (e.g., finite difference and complex step methods) or difficult to maintain when the original model is updated (e.g., direct decoupled and adjoint methods). Here, we present the implementation of the hyperdual-step method in the Community Multiscale Air Quality Model (CMAQ) version 5.3.2 as CMAQ-hyd. CMAQ-hyd can be applied to compute numerically exact first- and second-order sensitivities of species concentrations with respect to emissions or concentrations. Compared to CMAQ-DDM and CMAQ-adjoint, CMAQ-hyd is more straightforward to update and maintain while it remains free of numerical errors as those augmented models do. To evaluate the accuracy of the implementation, the sensitivities computed by CMAQ-hyd are compared with those calculated with other traditional methods or a hybrid of the traditional and advanced methods. We demonstrate the capability of CMAQ-hyd with the newly implemented gas-phase chemistry and biogenic aerosol formation mechanism in CMAQ. We also explored the cross-sensitivity of monoterpene nitrate aerosol formation to its anthropogenic and biogenic precursors to show the additional sensitivity information computed by CMAQ-hyd. Compared with the traditional finite difference method, CMAQ-hyd consumes fewer computational resources when the same sensitivity coefficients are calculated. This novel method implemented in CMAQ is also computationally competitive with other existing methods and could be further optimised to reduce memory and computational time overheads.

Jiachen Liu et al.

Status: open (extended)

Comment types: AC – author | RC – referee | CC – community | EC – editor | CEC – chief editor | : Report abuse
  • RC1: 'Comment on egusphere-2023-1017', Anonymous Referee #1, 18 Jul 2023 reply
    • AC1: 'Reply on RC1', Shannon Capps, 26 Aug 2023 reply
  • RC2: 'Comment on egusphere-2023-1017', Jixiang Li, 21 Jul 2023 reply
    • AC2: 'Reply on RC2', Shannon Capps, 26 Aug 2023 reply

Jiachen Liu et al.

Model code and software

CMAQ-hyd Jiachen Liu, Eric Chen, Shannon Capps

Jiachen Liu et al.


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Short summary
Air pollution harms human life and ecosystems, but its sources are complex. Scientists and policy makers use air pollution models to advance knowledge and inform control strategies. We implemented a recently-developed numeral system to relate any set of model inputs, like pollutant emissions from a given activity, to all model outputs, like concentration of pollutants harming human health. This approach will be straightforward to update when scientists discover new processes in the atmosphere.