An Adjoint Trajectory Model of the Perturbed Carbon Cycle

Here we present a new model framework for an adjoint trajectory model of the carbon cycle, which can be used to constrain carbon dioxide emission rates over a specific time interval given only a path constraint on the fraction of carbon dioxide that remains airborne over that interval. Earth's ocean and terrestrial biosphere act to quickly remove a large and variable portion of carbon dioxide emissions from the atmosphere, and thus measuring the atmospheric carbon dioxide concentra- tion at any given time provides limited insight into the global emission flux that is responsible for driving the time-dependent behavior of the atmospheric con- centration. Using the adjoint trajectory model presented here, we can, without having any information about the emission schedule, invoke the use of mathe- matical inverse methods to computationally search for an emission scenario that best reproduces a time series constraint of observed (or desired) atmospheric CO2 concentrations. This adjoint trajectory model utilizes a simple yet powerful 3-box transfer model to partition CO2 emissions between the atmosphere and ocean over time. The transfer functions that govern this 3-box model are also utilized to pro- vide a physical constraint on the acceptable set of emission scenario solutions. This thesis describes the governing mathematical framework of the adjoint trajectory model and provides a general algorithm for determining the unknown emission scenario that optimally reproduces the observed (or desired) atmospheric carbon dioxide trend. We show an example of the model performance in its current stage of development, and discuss its limitations and key areas for future development.