This is lecture 10 in the series "Introduction to the Mathematics of Climate" offered at the University of Minnesota in 2014 with the support of MCRN and The Institute for Mathematics and its Applications.
It describes the isotopes of carbon and fractionation of isotopes during photosynthesis. We see evidence from carbon isotope ratios and atmospheric oxygen depletion that burning of fossil fuels has driven the rise in atmospheric carbon dioxide. The Paleocene-Eocene Thermal Maximum is described and compared to today's temperature rise. Earth's current energy imbalance is introduced, along with how long it would take this excess heat to bring about different changes in temperature and state in various Earth sub-systems.
Colin James Grudzien