Alternative carbon price trajectories can avoid excessive carbon removal.

The large majority of climate change mitigation scenarios that hold warming below 2 °C show high deployment of carbon dioxide removal (CDR), resulting in a peak-and-decline behavior in global temperature. This is driven by the assumption of an exponentially increasing carbon price trajectory which is perceived to be economically optimal for meeting a carbon budget. However, this optimality relies on the assumption that a finite carbon budget associated with a temperature target is filled up steadily over time. The availability of net carbon removals invalidates this assumption and therefore a different carbon price trajectory should be chosen. We show how the optimal carbon price path for remaining well below 2 °C limits CDR demand and analyze requirements for constructing alternatives, which may be easier to implement in reality. We show that warming can be held at well below 2 °C at much lower long-term economic effort and lower CDR deployment and therefore lower risks if carbon prices are high enough in the beginning to ensure target compliance, but increase at a lower rate after carbon neutrality has been reached.

Integrated Climate-Change Assessment Scenarios and Carbon Dioxide Removal.

To halt climate change this century, we must reduce carbon dioxide (CO2) emissions from human activities to net zero. Any emission sources, such as in the energy or land-use sectors, must be balanced by natural or technological carbon sinks that facilitate CO2 removal (CDR) from the atmosphere. Projections of demand for large-scale CDR are based on an integrated scenario framework for emission scenarios composed of emission profiles as well as alternative socio-economic development trends and social values consistent with them. The framework, however, was developed years before systematic reviews of CDR entered the literature. This primer provides an overview of the purposes of scenarios in climate-change research and how they are used. It also introduces the integrated scenario framework and why it came about. CDR studies using the scenario framework, as well as its limitations, are discussed. Possible future developments for the scenario framework are highlighted, especially in relation to CDR.

Pathways limiting warming to 1.5°C: a tale of turning around in no time?

We explore the feasibility of limiting global warming to 1.5°C without overshoot and without the deployment of carbon dioxide removal (CDR) technologies. For this purpose, we perform a sensitivity analysis of four generic emissions reduction measures to identify a lower bound on future CO2 emissions from fossil fuel combustion and industrial processes. Final energy demand reductions and electrification of energy end uses as well as decarbonization of electricity and non-electric energy supply are all considered. We find the lower bound of cumulative fossil fuel and industry CO2 emissions to be 570 GtCO2 for the period 2016-2100, around 250 GtCO2 lower than the lower end of available 1.5°C mitigation pathways generated with integrated assessment models. Estimates of 1.5°C-consistent CO2 budgets are highly uncertain and range between 100 and 900 GtCO2 from 2016 onwards. Based on our sensitivity analysis, limiting warming to 1.5°C will require CDR or terrestrial net carbon uptake if 1.5°C-consistent budgets are smaller than 650 GtCO2 The earlier CDR is deployed, the more it neutralizes post-2020 emissions rather than producing net negative emissions. Nevertheless, if the 1.5°C budget is smaller than 550 GtCO2, temporary overshoot of the 1.5°C limit becomes unavoidable if CDR cannot be ramped up faster than to 4 GtCO2 in 2040 and 10 GtCO2 in 2050.This article is part of the theme issue 'The Paris Agreement: understanding the physical and social challenges for a warming world of 1.5°C above pre-industrial levels'.

Swarming in three dimensions.

We consider a three-dimensional model of active Brownian particles interacting via a Morse-type potential. The system exhibits two modes of motion: translation and a coherent rotation in a torus-shape structure. We observe noise-induced transitions in both directions between the two states. These occur at different noise intensities, thus leading to a hysteresis curve. For certain parameter regions, the system switches persistently between the states such that the center of mass alternates between ballistic and diffusive motion. The coherent rotation leads to a pronounced mean angular momentum that changes its direction diffusively. We derive an analytic expression for the diffusion of the angular momentum of one particle in an external harmonic potential and show that it is always faster than the stochastic switching of the direction of motion in the two-dimensional case.