CoMIAR v1.0: a hybrid system for multi-species adjoint inversion of atmospheric emissions with online adaptive regularization

Abstract. Accurate estimates of anthropogenic emissions are fundamental to air quality and climate assessment. Satellite-based top-down inversion offers an independent constraint on bottom-up emission inventories, but two key limitations remain. First, dynamically constrained 4D-Var optimization often relies on fixed regularization parameters, which can destabilize convergence during iteration. Second, most inversions treat chemical species separately, even though atmospheric species are chemically coupled. Here, we develop CoMIAR v1.0 (Coupled Multi- species Inversion with Adaptive Regularization), a hybrid system implemented with CMAQ- Adjoint to address these limitations. CoMIAR combines mass-balance initialization with 4D- Var optimization, extends the adjoint formulation to a fully coupled multi-species control system, and incorporates an online Iterative-Adaptive Regularization (IAR) strategy that updates the species-specific regularization factor at each iteration using the L-curve criterion, thereby avoiding fixed empirical tuning. In observing system simulation experiments over China, IAR suppressed the convergence oscillations observed under fixed-parameter schemes. In the single-species SO₂ regularization experiment, IAR reduced emission NRMSE by 50.5 % from the 4D-Var starting point and achieved the lowest final error among the tested schemes. Joint multi-species inversion further exploited sulfate-nitrate-ammonium thermodynamic coupling to separate emission biases that single-species inversions could not resolve. CoMIAR remained robust under spatially heterogeneous prior errors. Together, CoMIAR provides a stable and chemically consistent approach for emission inversion in complex atmospheric systems.