The Importance of Mathematical Modeling in the Global

The Importance of Mathematical Modeling in the Global Climate Change Debate Jason Batts Department of Geosciences Virginia Tech Blacksburg, Va 24061 USA Projected temperature differences between 2080 – 2099 and 1980 - 1999 http: //www. aip. org/history/climate/GCM. htm Singapore 2012

Outline What is a mathematical model? How are models validated? What are the common models for studying climate change? What is the best climate change model? http: //www. marciotnferreira. com/blog/2010/11/30/be-rational-get-real/

A mathematical model is the use of mathematics to represent a natural system. Models are often built through the collection of components. Complex models require vast amounts of computational time, but tend to be more accurate. Simple models can be computed quickly, but tend to have less accuracy. www. ipcc. ch

In order to best ensure the quality of a particular climate model, scientists often validate their work in comparison to known data. Observed global mean near surface temperatures (black line) Calculated global mean near surface temperatures (yellow lines) Average calculated global mean (red line) http: //www. ipcc. ch/publications_and_data/ar 4/wg 1/en/faq-8 -1 -figure-1. html 58 different simulations 14 climate models

In order to best ensure the quality of a particular climate model, scientists often validate their work in comparison to known data. Observed global mean near surface temperatures (black line) Calculated global mean near surface temperatures (yellow lines) Average calculated global mean (red line) http: //www. ipcc. ch/publications_and_data/ar 4/wg 1/en/faq-8 -1 -figure-1. html 58 different simulations 14 climate models

Many factors influence regional climate changes, which results in several variables for mathematical models. www. ipcc. ch

Most models either represent several variables in little detail or fewer variables in greater detail. www. ipcc. ch

Most climate change models are based on a general circulation model, though the exact approach varies. Simplified GCM Atmospheric GCM Oceanic GCM Coupled Atmospheric-Ocean GCM Other models often used include: Upwelling Diffusion Energy Balance Radiative Convection www. noaa. gov

The Coupled Atmospheric-Ocean General Circulation Model is favored as it allows for inclusion of the most variables. Common models Hadley Centre Coupled Model, version 3 (Had. CM 3) Key model in IPCC Third Assessment Report Geophysical Fluid Dynamics Laboratory Coupled Model, version 2. x (GFDL CM 2. X) Key model in IPCC Fourth Assessment Report Ed. GCM en. wikipedia. gov

The Coupled Atmospheric-Ocean General Circulation Model is made by two individual models joined with a time loop. Calculate a step of an Atmospheric model Prepare data for input into Oceanic model. Calculate a step of an Oceanic model. Prepare data for input into Atmospheric model. Repeat www. ipcc. ch

No single model fully expresses the environment; however, some are better able to represent several variables. Models are built from a collection of mathematical formulas. Models often trade completeness for time. Validation often occurs through confirming known data. Climate involves several variables which need to be modeled. Coupled Atmospheric-Oceanic models are most often used as the primary model for climate change.