The Global Carbon Budget as a cointegrated system

TL;DR

This paper models Earth's global carbon cycle as a cointegrated system of four time series, revealing physical relations and enabling projections consistent with climate science.

Contribution

It introduces a cointegrated system approach to analyze the global carbon budget, identifying key physical relations and validating a restricted error-correction model.

Findings

The four time series are cointegrated with rank three.

Anthropogenic CO2 emissions drive the nonstationary dynamics.

Projections using the model align with established climate science.

Abstract

The Global Carbon Budget, maintained by the Global Carbon Project, summarizes Earth's global carbon cycle through four annual time series beginning in 1959: atmospheric CO$_2$ concentrations, anthropogenic CO$_2$ emissions, and CO$_2$ uptake by land and by ocean. We analyze these four time series as a multivariate (cointegrated) system. Statistical tests show that the four time series are cointegrated with rank three and identify anthropogenic CO$_2$ emissions as the single stochastic trend driving the nonstationary dynamics of the system. The three cointegrated relations correspond to the physical relations that the sinks are linearly related to atmospheric concentrations and that the change in concentrations equals emissions minus the combined uptake by land and ocean. Furthermore, likelihood ratio tests show that a parametrically restricted error-correction model that embodies these physical relations cannot be rejected on the data. The model can be used for both in-sample and out-of-sample analysis. In an application of the latter, we demonstrate that projections based on this model, using Shared Socioeconomic Pathways scenarios, yield results consistent with established climate science.