A Dynamical Systems Approach to Climate Modeling
Date of Creation
5-9-2018
Document Type
Departmental Honors Thesis - Restricted Access
Department
Mathematics
First Advisor
Gareth E. Roberts
Abstract
The goal of this project is to use low-dimensional mathematical models to better understand current climate, historical climate, and the drivers of climate change. In 1969, Mikhail Budyko developed one of the first Energy Balance Models, a differential equation that expresses the global average surface temperature of the Earth as a function of latitude. The latitude of interest in trying to model climate conditions of the past and present is that of the ice line (the latitude above which sea ice forms). Using the Widiasih extension of the Budyko model, which captures the dynamic movement of the ice line, we incorporate a land-albedo function in order to model the Snowball Earth hypothesis. We have produced several one- and two-dimensional bifurcation diagrams for different parameters to discern the possibility of extreme climate conditions in both the Neoproterozoic Era and the current climate state. These diagrams support the Snowball Earth hypothesis. Furthermore, we use a discrete dynamical system to approximate the coupled Budyko-ice line model and apply MATLAB to iterate the system numerically over time. Connections between parameter values and the length of time for major climate changes to occur are explored in this context.
Recommended Citation
Donovan, Cara, "A Dynamical Systems Approach to Climate Modeling" (2018). Math and Computer Science Honors Theses. 53.
https://crossworks.holycross.edu/math_honor/53