This thesis attempts to explain the basic principles of climate modelling and tipping points in the words of a first year mathematics student. Further, it investigates whether it is possible to overshoot tipping points for a brief period of time but still return to a healthy state.

Abstract

The IPCC (2022) predicts that with an increase in average global temperature between 3 and 4°C compared topre-industrial levels, the Amazon rainforest could experience a tipping point. One of the two main aims of this Bachelor Thesis is to analytically comprehend the existence of this bifurcation and understand its dynamics. For this it analyses a simple nonlinear ODE model of forest dieback, that was originally presented in the paper “Overshooting tipping point thresholds in a changing climate” by Ritchie et al. (2021). Their publication analyses the possibility of “shooting over” said bifurcation thresholds, but still return to a healthy and stable state by sufficiently reducing the global temperature. This thesis does this as well and numerically studies linear overshoot scenarios through a discretisation of the model. This thesis confirms that Ritchie et al.’s model brings out multiple bifurcations for forest dieback in the Amazon rainforest. Most importantly, there is a saddle-node bifurcation at 8.25°C above the current temperature. Should this bifurcation point be exceeded with a decadal temperature increase of 0.2°C, it would take the forest 19 years to shrink below 10% of its original size. This makes it a rapid tipping system. The analysis of overshoot scenarios reveals that returning to a healthy state is theoretically still possible within the model, given the global temperature is reduced ambitiously enough within a given time frame. For example, reducing the temperature by less than 0.01°C per year would not be sufficient if it has been rising by 0.02°C annually for 8 years after the tipping point. Practically, it is still up to question how and to what extent one could reduce global temperature to enable such a turnaround. Therefore, more research in the field of overshoots would help to answer these questions.