Deep learning-based adjoint modeling for daily CO estimations

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 first validated through the adjoint test, the finite-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 flows 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 confirms that the DL-based ADM exhibits physically reasonable propagation of the observational information over time and space, offering a promising and efficient alternative to dynamic model-dependent adjoint frameworks constrained by the high computational costs.