Course Description
Basic mathematical models describing the physical, chemical, and biological interactions that affect climate. Mathematical and computational tools for analyzing these models.
Additional Requirements for Graduate Students:
Graduate students will be asked to submit additional, more
extensive homework problems requiring deeper synthesis of the
concepts and material. Graduate students' term projects will
also be expected to be more extensive, reviewing and integrating
the materials more thoroughly, and will be graded at a higher
standard than the undergraduate projects.
Athena Title
Mathematics of Climate
Prerequisite
MATH 2700
Semester Course Offered
Offered fall
Grading System
A - F (Traditional)
Course Objectives
Students will understand the basic physical, chemical, and biological interactions that affect climate. Systems of differential equations will be introduced to model these interactions. Students will learn the mathematical and computational tools needed to analyze these models.
Topical Outline
1.) Climate basics: climate versus weather; radiation and heat balance; box models; macro atmospheric structures; thermo- haline circulation; air-sea interactions; El Nino Southern Oscillation; vegetation and land interactions 2.) Low Dimensional Mathematical models: (Energy balance models; radiative-convective models; Budyko model; Daisyworld) 3.) Qualitative analysis of systems: Bifurcations (tipping points, snowball earth); fast-slow systems; critical slowing; critical noise 4.) Carbon Cycle: vegetation; ocean cycle; weathering 5.) Fluid models: stable manifolds; Lagrangian structures 6.) Global Climate models