Development of the tangent linear and adjoint models of the global online chemical transport model MPAS-CO₂ v7.3

Abstract. We describe the development of the tangent linear (TL) and adjoint models of the MPAS-CO₂ transport model, which is a global online chemical transport model developed upon the non-hydrostatic Model for Prediction Across Scales-Atmosphere (MPAS-A). The primary goal is to make the model system a valuable research tool for investigating atmospheric carbon transport and inverse modeling. First, we develop the TL code, encompassing all CO₂ transport processes within the MPAS-CO₂ forward model. Then, we construct the adjoint model using a combined strategy involving re-calculation and storage of the essential meteorological variables needed for CO₂ transport. This strategy allows the adjoint model to undertake long-period integration with moderate memory demands. To ensure accuracy, the TL and adjoint models undergo vigorous verifications through a series of standard tests. The adjoint model, through backward-in-time integration, calculates the sensitivity of atmospheric CO₂ observations to surface CO₂ fluxes and the initial atmospheric CO₂ conditions. To demonstrate the utility of the adjoint model, we conduct simulations for two types of atmospheric CO₂ observations: tower-based in situ CO₂ mixing ratio and satellite-derived column-averaged (X_CO2). A comparison between the sensitivity to surface flux calculated by the MPAS-CO2 adjoint model with its counterpart from Carbon Tracker-Lagrange (CT-L) reveals spatial agreement but notable magnitude differences. These differences, particularly evident for X_CO2, likely arise from differences in vertical mixing between the two systems. Moreover, this comparison highlights the substantial loss of information in the atmospheric CO₂ observations due to CT-L’s simulation length and spatial domain limitations. Furthermore, the adjoint sensitivity analysis demonstrates that the sensitivities to both surface flux and initial CO₂ conditions spread out throughout the entire northern hemisphere within a month. MPAS-CO₂ forward, TL, and adjoint models stand out for their calculation efficiency and variable-resolution capability, making them competitive in computational cost. In conclusion, the successful development of the MPAS-CO₂ TL and adjoint models, and their integration into the MPAS-CO₂ system, establish the possibility of using MPAS’s unique features for investigating atmospheric CO₂ transport sensitivity studies and for conducting inverse modeling with advanced methods such as variational data assimilation.