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 pas sive tracers. The adjoint of TM2 is a model that allows the efficient evalu ation 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 simulate d concentration at observational locations is linear in the surface exchang e 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 c omputed by multiple runs of a transport model for a set of prescribed surfa ce flux patterns. The computational cost has been proportional to the numbe r of patterns. In contrast, for differentiation in reverse mode, the cost i s independent of the number of flux components. Hence, by a single run of t he adjoint model, the Jacobian for the approximately 8 degrees latitude by 10 degrees longitude horizontal resolution of TM2 could be computed efficie ntly. We quantify this efficiency by comparison with the conventional forwa rd modeling approach. For some prominent observational sites, we present vi sualizations of the Jacobian matrix by series of illustrative global maps q uantifying the impact of potential emissions on the concentration in partic ular months. Furthermore, we demonstrate how the Jacobian matrix is employe d to completely analyze a transport model run: A simulated monthly mean val ue at a particular station is decomposed into the contributions to this val ue by all flux components, i.e., the fluxes into every surface model grid c ell and month. This technique also results in a series of global maps.