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 Model for Prediction Across Scales (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 a 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 mixing ratio. To demonstrate the utility of the newly developed adjoint model, we conduct simulations for two types of atmospheric CO2 observations, namely the tower-based in situ CO2 mixing ratio and satellite-derived column-averaged CO2 mixing ratio (XCO2). A comparison between the sensitivity to surface flux calculated by the MPAS-CO2 adjoint model with its counterpart from CarbonTracker–Lagrange (CT-L) reveals a spatial agreement but notable magnitude differences. These differences, particularly evident for XCO2, might be attributed to the two model systems' differences in the simulation configuration, spatial resolution, and treatment of vertical mixing processes. Moreover, this comparison highlights the substantial loss of information in the atmospheric CO2 observations due to CT-L's spatial domain limitation. 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 in atmospheric CO2 transport sensitivity studies and in inverse modeling with advanced methods such as variational data assimilation.