A multivariate dynamic statistical model of the global carbon budget 1959-2020

We propose a multivariate dynamic statistical model of the global carbon budget (GCB) as represented in the annual data set made available by the Global Carbon Project, covering the sample period 1959-2020. The model connects four main objects of interest: atmospheric carbon dioxide (CO2) concentrations, anthropogenic CO2 emissions, the absorption of CO2 by the terrestrial biosphere (land sink), and by the ocean and marine biosphere (ocean sink). The model captures the GCB equation, which states that emissions not absorbed by either land or ocean sinks must remain in the atmosphere and constitute a flow to the stock of atmospheric concentrations. Emissions depend on global economic activity as measured by World Gross Domestic Product while sink activities depend on the level of atmospheric concentrations and the Southern Oscillation Index. We derive the time series properties of atmospheric concentrations from the model, showing that they contain one unit root and a near-second unit root. The statistical system allows for the estimation of key parameters of the global carbon cycle and for the assessment of estimation uncertainty. It also allows for the estimation and the uncertainty assessment of related variables such as the airborne fraction and the sink rate. We provide short-term forecasts of the components of the GCB.