Complex Systems

Increased levels of greenhouse gases in the atmosphere, especially carbon dioxide, are leading contributors to a significant increase in the global temperature, and the consequent global climatic changes are more noticeable in recent years than in the past. A persistent increased growth of such gases might lead to an irreversible transition or tipping of the Earth’s climatic system to a new dynamical state. A change of regimes in CO2 buildup being correlated to one in global climate patterns, predicting this tipping point becomes crucially important. We propose here an innovative conceptual model, which does just this. Using the idea of rate-induced bifurcations, we show that a sufficiently rapid change in the system parameters beyond a critical value tips the system over to a new dynamical state. Our model when applied to real-world data detects tipping points, enables calculation of tipping rates and predicts their future values, and identifies thresholds beyond which tipping occurs. The model well captures the growth in time of the total global atmospheric fossil-fuel CO2 concentrations, identifying regime shift changes through measurable parameters and enabling prediction of future trends based on past data. Our model shows two distinct routes to tipping. We predict that with the present trend of variation of atmospheric greenhouse gas concentrations, the Earth’s climatic system would move over to a new stable dynamical regime in the year 2022. We determine a limit of 10.62 GtC at the start of 2022 for global CO2 emissions in order to avoid this tipping. The Earth’s climate has seen many changes over the years, affecting the physical environment (be it terrestrial, marine, or the atmosphere). These major changes or regime shifts from one stable dynamical state of the physical environment to another, each of which may persist for several years, produce major shifts in natural ecosystems involving trophic structures, changes in composition, and abundance of species. The climatic system moves over to a new regime once it crosses a climatic tipping point—a threshold crossed irreversibly by the system’s dynamics. Anthropogenic influences brought about in the physical environment invariably contribute in a substantial way to climate change globally as the dynamics of the climatic system is governed by the coupling between the land, the atmosphere, and the oceans. An increase in levels of greenhouse gases in the atmosphere mainly caused by human activities, especially carbon dioxide, has been one of the important contributing factors leading to climate change in the last few decades. We present here a theoretical model that well captures the rate of increase of the total global concentrations of carbon dioxide, the major contributing greenhouse gas in the atmosphere. We then employ the concept of rate-induced bifurcations to demonstrate that it is possible to determine the climatic tipping points from our model. This way, we predict that the climatic system would relocate to a new stable state early in the year 2022. It has been widely accepted that tipping point mechanisms can be used to study climate change. In this paper, we shall introduce and apply a rate-induced tipping model to global fossil-fuel emissions data. Our model shows two distinct routes in which tipping can occur, and the parameters describing these can be calculated from data and are physically measurable. Through the application of this model, we identify crucial tipping points, which lead to climate change and quantify exact boundaries crossed that induce tipping. Control can be exercised over the parameters describing tipping, if desired, such that tipping can be prevented. The methods developed can further be applied to any growth curve that may have undergone rate-induced tipping.

Coauthored with Subhayan Sahu, Shriya Pai, and Naren Manjunath