How the anthropogenic carbon is processed in the climate system has crucial and poorly understood components both in the short and the long term. During the next few decades, the implementation of the Paris Agreement will pose the question of whether individual countries will fulfil their pledges toward emissions reductions and whether their self-reporting is reliable. Science-based verification of reported emissions at least on a regional scale will be essential for building confidence in the treaty regime. This need for confidence-building is reminiscent of the situation prior to the Comprehensive Nuclear Test Ban Treaty (CTBT) of the early 1990s, banning all nuclear test explosions. One scientific challenge was to ensure that the seismic network could provide the information necessary for distinguishing suspected underground nuclear explosions from earthquakes. Advances in science and data processing led the CTBT's verification network to be widely considered up to its task. Similarly, climate science should be ready to support any potential future verification regime for the Paris Agreement3.

The scientific challenges are substantial. In principle, methods exist to estimate regional anthropogenic surface carbon fluxes from local flux measurements and inverse modelling relying on ground-based and space-based atmospheric concentration measurements. But identifying the anthropogenic part of changes in surface fluxes — crucial in any verification regime — is complicated by internal climate variability. For example, during an El Niño event, atmospheric carbon concentration tends to be elevated, due to the dominating reduced uptake by the land surface combined with the reduced outgassing in the warmer tropical Pacific. And the ocean carbon sink, the largest contribution to which comes from the Southern Ocean, shows substantial decadal variability, probably from variability in weather patterns8 that are difficult to simulate realistically in today's climate models.

Looking ahead to the second half of this century, the question shifts to the magnitude of the feedback between climate and the carbon cycle. There is general agreement that the feedback is amplifying — in a warmer climate, less carbon will be taken up by the land and by the ocean, and a larger fraction of the anthropogenic carbon will remain in the atmosphere, further enhancing climate change — but the magnitude of the feedback remains uncertain. The uncertainties arise somewhat differently for the ocean sink compared to the land sink9. For the ocean sink the basic processes are generally known (circulation, vertical mixing, and the sinking of biological material), but not the magnitude and sometimes even the sign of the expected changes in these processes, especially the impact of ocean acidification on ecosystems. On land there is substantial uncertainty concerning the processes that determine the carbon–climate feedback. For example, there is extensive scientific debate about the importance of nutrient limitation (nitrogen and phosphorous supply) for future land carbon uptake. Additionally the land biosphere, and associated carbon cycle, relies on water availability, but the future is unclear with uncertainty in circulation and water cycle changes — a topic we turn to next.