1. Modeling CO 2 in the Atmosphere

2. Perhaps one of the most important graphs in history! Date C0 2 (ppm)

5. A Simple Equilibrium Model Assume an constant rate of change  ppm/a of CO 2 entering atmosphere and an amount in ppm leaving via oceans and biosphere over a longer time period  years. Assume an constant rate of change  ppm/a of CO 2 entering atmosphere and an amount in ppm leaving via oceans and biosphere over a longer time period  years. We can express this via: We can express this via:

6. Solution… The previous equation can be integrated directly to give: The previous equation can be integrated directly to give: Go to Excel spreadsheet simulation of this

7. A Slightly More Complex Model What if the amount of C02 entering the atmosphere is not constant? What if the amount of C02 entering the atmosphere is not constant? Let’s solve as a difference equation: Let’s solve as a difference equation: Go to Excel spreadsheet simulation of this

8. Box Models These are more complex, coupled differential equation models that account for sources and sinks These are more complex, coupled differential equation models that account for sources and sinks “Boxes” are just names given to specific sources/sinks “Boxes” are just names given to specific sources/sinks Consider a 4-Box Model Consider a 4-Box Model Boxes are: Atmosphere, Biomass, Middle Ocean Layer, Deep Ocean Layer Boxes are: Atmosphere, Biomass, Middle Ocean Layer, Deep Ocean Layer

9. 4-Box Model This can be modeled with a set of 4 coupled 1 st order differential equations This can be modeled with a set of 4 coupled 1 st order differential equations

10. Goals for this project… Create an interactive applet for model based on the variable C0 2 flux shown earlier Create an interactive applet for model based on the variable C0 2 flux shown earlier Applet should: Applet should: Provide parameters (starting concentration, time step etc) Provide parameters (starting concentration, time step etc) Give graphical and tabular output Give graphical and tabular output Allow user to enter either an equation for R(t) or a table of numerical values Allow user to enter either an equation for R(t) or a table of numerical values