Modeling Carbon Cycle through the Earth System as a Formative Tool for Learning about Systems Theory and Complexity

Climate studies regardless of their importance, in many institutions cannot be introduced as a separate course. Such a situation is motivated by a variety of reasons: tight curriculum, small to medium size student body population, preventing the opening of many general science courses, absence of specific earth science related majors, and some times bias against these topics. Despite of these challenging conditions, there is always possible to integrate climate studies into other courses. Teaching about climate and feedback between different earth's subunits might benefit from already existing approaches in life science and engineering. In this presentation, the Carbon cycle is used as a prototype situation where concepts from systems theory and complexity are applied. The present communication is based on experiences accumulated from undergraduate research projects oriented as part of the course Differential Equation, a Modeling Approach, and the Summer Research Internship between St. Thomas University and Miami Dade College, in Miami, Florida. Students applied the techniques learned within Differential Equations, and also complemented with concepts from Dynamical Systems and Chaos and Climatology. The project starts from a linear representation of the interaction between seven earth compartments: Atmosphere, Warm Surface Ocean, Cold Surface Ocean, Transition Ocean Waters, Deep Ocean Waters, Surface Soil and Deep Ground. Akira Tomizuka and Guido Fano introduced two versions of such a model in two different volumes of the American Journal of Physics in 2009 and 2010 respectively. Students are asked after the linear modeling is completed to add motifs of activator-inhibitor feedback as well as time-delayed effects. All computational details are performed in Mathematica from Wolfram Research. Deep Ocean layer results are compared with sedimentation rates obtained from deep ocean explorations. It is worth to notice that the author had intended to integrate different experiences obtained from AMS Climate Studies workshops and the MSI-REACH (Reconstructing Earth's Climate History advanced professional development program) in a course that is offered every year to a wide variety of science majors.