A coarse grid three-dimensional global inverse model of the atmospheric transport - 1. Adjoint model and Jacobian matrix

TM2 is a global three-dimensional model of the atmospheric transport of passive tracers. The adjoint of TM2 is a model that allows the efficient evaluation of derivatives of the simulated tracer concentration at observational locations with respect to the tracer's sources and sinks. We describe the generation of the adjoint model by applying the Tangent linear and Adjoint Model Compiler in the reverse mode of automatic differentiation to the code of TM2. Using CO2 as an example of a chemically inert tracer, the simulated concentration at observational locations is linear in the surface exchange fluxes, and thus the transport can be represented by the model's Jacobian matrix. In many current inverse modeling studies, such a matrix has been computed by multiple runs of a transport model for a set of prescribed surface flux patterns. The computational cost has been proportional to the number of patterns. In contrast, for differentiation in reverse mode, the cost is independent of the number of flux components. Hence, by a single run of the adjoint model, the Jacobian for the approximately 8 degrees latitude by 10 degrees longitude horizontal resolution of TM2 could be computed efficiently. We quantify this efficiency by comparison with the conventional forward modeling approach. For some prominent observational sites, we present visualizations of the Jacobian matrix by series of illustrative global maps quantifying the impact of potential emissions on the concentration in particular months. Furthermore, we demonstrate how the Jacobian matrix is employed to completely analyze a transport model run: A simulated monthly mean value at a particular station is decomposed into the contributions to this value by all flux components, i.e., the fluxes into every surface model grid cell and month. This technique also results in a series of global maps.