Introduction:

In this study, we develop a four-dimensional variational data assimilation (4DVAR)-based adjoint

modeling framework using deep learning (DL) for estimating daily carbon monoxide (CO)

concentrations over east Asia. The forward model is built on a U-Net architecture, and its adjoint

version is formulated by explicitly calculating the gradients of the cost function with respect to the

initial condition by leveraging the backpropagation algorithm. The DL-based adjoint model (ADM) was

rst validated through the adjoint test, the nite-difference gradient test. The idealized experiments

using synthetic CO increments at a single grid point over the Korean Peninsula showed that the adjoint

sensitivities spread horizontally and vertically to the upstream region along the climatological ows

with diffusive features. In addition, the idealized 4DVAR experiments using in-situ CO observations

over Korea and Japan during 2020–2022 demonstrated substantial error reduction across the Korean

Peninsula, Japan, and northeastern China. This con rms that the DL-based ADM exhibits physically

reasonable propagation of the observational information over time and space, offering a promising

and ef cient alternative to dynamic model-dependent adjoint frameworks constrained by the high

computational costs.

pdf : Lee et al. (2026)