  We introduce new frameworks to study spatio-temporal patterns in carbon
dioxide emissions, demographic trends and economic patterns across 50 countries
over the past 50 years. Our analysis is broken up into four sections. First, we
introduce a new method to classify countries into one of three characteristic
emissions classes based on a one, two or three-segment piecewise linear model.
We reveal that most countries are best represented by a piecewise linear model
with one change point. Next, we perform a decade-by-decade study of carbon
dioxide trajectories. There, we demonstrate notable changes in cluster
structures in each decade. We then study the spatial propagation of emissions
over time, highlighting a peak in spatial dispersion in 2000, beyond which
there has been a gradual decline in spatial emissions variance over space.
Finally, we use carbon dioxide, GDP, and population data and apply
dimensionality reduction and clustering to group countries based on similarity
in their real and carbon economies.
