# The Chaos of Weather

After a long break I am finally back. This is the first post of the “Weather Forecasting” posts. Roughly speaking, to forecast the weather, scientists use computer models to mimic Earth dynamics. These models are mathematical equations of the atmosphere and oceans. However, the Earth dynamics is a big complex system. On top of that some Earth natural systems have a chaotic behavior. But what is chaos? Summarizing the wikipedia definition:

Chaos is when the behavior of dynamical systems are highly sensitive to initial conditions. Thus, small differences in initial conditions (such as those due to rounding errors in numerical computation) yield widely diverging outcomes for such dynamical systems. Therefore, chaotic systems are predictable for a while and then appear to become random. In other words, the deterministic nature of these systems does not make them predictable.

Around 1960, the meteorologist Edward Lorenz (one of the fathers of chaos theory), was working on a set of differential equations describing convective processes in the atmosphere which were producing encouragingly realistic results. One day, he decided to enter data manually from a point part way through rather than waste time by starting the run over. He found that not long after the run had been restarted from this intermediate point, the forecast diverged and it was completely different. The reason behind, was the output data he used to restart the model. It had been rounded to 3 significant digits, while the computations were done to 6, an error of about 1%. With this unexpected results he discovered that the degree of numerical precision in the initial conditions provided to a numerical weather prediction (NWP) model affects the resulting forecast significantly after only a few days of forecast time (Lorenz 1963).  A good example (also from wikipedia) of chaotic behavior  is the double rod pendulum where the start of the pendulum from a slightly different initial condition would result in a completely different trajectory: Double-compound-pendulum” by CatslashOwn work. Licensed under Public Domain via Wikimedia Commons.

The Earth weather is one of the Earth natural systems with a chaotic behavior. Consequently, the use of different initial conditions in the atmospheric and oceans equations will lead to different final results. So why does not use the same initial condition always to forecast the weather and have the same results? The source of the errors in the forecasting is a more complex subject and I will explain in a post later. However if the Earth system is so unpredictable how come scientists can use computer models to reconstruct past and future climate? First it is necessary to explain the difference between weather and climate where the difference is a measure of time. Weather is what conditions of the atmosphere are over a short period of time, and climate is how the atmosphere “behaves” over relatively long periods of time. Weather is more difficult to predict and has more uncertainties than climate. An elegant demonstration of this difference can be seen in this short video from National Geographic. The astrophysicist and Cosmos host Neil deGrasse Tyson uses a dog walking to clarify the concept.

More additional information of computer models and how they are used to predict climate can be found here: Can we trust climate models?  and Numerical weather prediction.