Chaos Theory
In 1963, meteorologist Edward N. Lorenz accidentally discovered the chaotic behavior of a system during his experiments on convection currents.
In his experiments, he heated liquids and gases on a hotplate. This creates a current in which the heated liquid rises and cools again on the surface and sinks again. The liquid rises and sinks continuously when the hotplate is switched on and convection currents or convection cells are formed.
Schematic representation of the convection experiment. (Illustration: Daniela Roth)
Lorenz then wanted to describe the flows using a predictive model. He linked the temperature and convection rate in a system of equations and used a computer to solve it. In further calculations, he specified the initial conditions for the system of equations with only 3 decimal places instead of 6. The results he now obtained differed enormously from his earlier calculations. By chance, he had now discovered the chaotic behavior of systems.
An in-depth look at chaos theory
Lorenz’s system of equations consists of three differential equations. If the solutions to Lorenz’s system of equations are now represented graphically, the result is a so-called Lorenz attractor (see teaser image). The X, Y and Z axes represent the variables in the equation. The line shows the temporal development of the variables, a so-called trajectory. The graphical solution indicates that chaos theory is not pure chaos, but rather “ordered chaos”. The trajectory circles two different points and the result is a structure that is quite similar to a butterfly. This structure is known as the Lorenz attractor.
Lorenz attractor simulated in the Brain Dynamics Toolbox program. (Source: Wikimedia Commons, Stewart Heitmann)
When the system tilts from one orbit to the other is chaotic and depends strongly on the initial conditions. This tilting is known in chaos theory as bifurcation.
Such tipping points or jumps also occur in weather forecasting. This often makes it difficult to make clear predictions because the weather models jump from one solution to another. Let’s look at an example:
(Source: MeteoSwiss)
Shown above is the 3-hour precipitation amount on Tuesday evening between 18 to 21 UTC (8-11 p.m. LT). The individual tiles show the different members of the ICON-CH2 model. The ensemble forecasts are based on albania mobile database slightly different initial conditions and sometimes show different solutions. Now the question arises: will there be rain on Tuesday evening? Individual members show clear precipitation signals (thunderstorms), while others show a dry Tuesday evening. It shows that small deviations in the initial conditions lead to different solutions – in this case to thunderstorms or dry conditions.
Capturing the initial conditions is complex
Even the recording of the initial conditions is subject to a certain degree of inaccuracy. Measurements are becoming increasingly inaccurate, and we do not have enough measuring points to record the initial conditions of the consistent messaging: adapt without losing entire atmosphere. In addition, the equations of the weather models are simplified because it is simply not possible to describe all of the processes in the atmosphere in complete physical and mathematical terms. (Moreover, no computer in the world would be able to calculate all of this in betting email list a timely manner).
This does not mean that weather forecasts are completely chaotic and unpredictable. It does show, however, that even the smallest changes in the initial conditions have a major impact on weather events.
How do we deal with the chaos?
At MeteoSwiss, as with other weather services, attempts are being made to bring some order to the chaos with ensemble forecasts.
Below you can see the ensemble predictions of the ECMWF model for the grid point Zurich. The closer the temperature and geopotential lines are together, the more certain the forecast is. It means that despite the different initial conditions, the solution is the same. It is in the nature of the system that the uncertainty increases with time.