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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
Journal article   Open access   Peer reviewed

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 Capps
Geoscientific Model Development, v 17(2), pp 567-585
24 Jan 2024
DOI: https://doi.org/10.5194/gmd-17-567-2024
url
https://doi.org/10.5194/gmd-17-567-2024View
Published, Version of Record (VoR) Open

Abstract

Accuracy Aerosol formation Aerosols Air pollution Air pollution control Air quality Air quality models Analysis Anthropogenic factors Approximation Atmospheric models Chemical transport Chemistry Coefficients Complex variables Computer applications Computing time Data assimilation Data collection Efficiency Emissions Finite difference method Mathematical models Methods Models Number systems Outdoor air quality Pollutants Pollution control Sensitivity analysis Truncation errors Variables
Sensitivity analysis in chemical transport models quantifies the response of output variables to changes in input parameters. This information is valuable for researchers engaged 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 nonlinear 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 subtractive cancellation and truncation errors, just 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 explore 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 optimized to reduce memory and computational time overheads.

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