# How exactly is the butterfly effect

## The butterfly effect

We often receive inquiries like: "We want to get married in two months. How will the weather be on our wedding day". In such cases we unfortunately have to disappoint the wedding couple, because weather forecasts are not possible for such a long period of time. But why are there limits to the forecast period and where are the limits of predictability? To answer this question, we should first briefly explain how weather forecasts are usually made. Today the meteorologist derives his weather forecast from the calculation results of various weather models. A high-performance computer calculates the state at a later point in time from a given initial state of the atmosphere with the help of complex equations. The initial state for these equations results from the station observations, measurements of buoys, ships and aircraft, balloon ascent as well as from satellite and radar data. Weather models provide the meteorologist not only with the moisture and pressure distribution at different altitudes, but also parameters such as temperature, degree of coverage and precipitation.

The problem with the calculations, however, is that the atmosphere is a chaotic system. This means that the future state of the atmosphere is heavily dependent on the initial conditions. Only slight deviations in these initial conditions can lead to a completely different weather development in the future. The American meteorologist Edward N. Lorenz, the founder of the chaos theory, illustrated this effect with the fact that a butterfly's wing beat in Brazil can possibly trigger a tornado in Texas. Today this is known as the so-called butterfly effect. Lorenz made this discovery through computer calculations that simulated the behavior of gases and liquids.

The initial state of the atmosphere for the weather models cannot be determined as precisely as desired. On the one hand, measurements are not available for every point in the atmosphere; on the other hand, all observations are flawed to a certain extent. Furthermore, some of the equations in the weather models are only approximations. The model calculations become more and more uncertain as the forecast time increases. How long the weather can still be reasonably predicted depends heavily on the weather situation. In stable weather conditions, the period is correspondingly longer, while in borderline weather conditions it is often only a few days. In general, however, the weather can currently be forecast for an average of about 7 days without going into detailed regional forecasts. A rough trend can be specified for up to 10 days.

In order to get the problem with chaos at least a little under control, so-called ensemble calculations are carried out. This means that a weather model is calculated several times, each time with slightly different initial conditions. If certain weather developments are now piling up in the calculations, these are most likely. In addition, statements can be made about the reliability of the forecast. You can find more information on this in the topics of the day from 19.12. and 20.12.2015, as well as from 24.01.2016.

Nevertheless, in spite of ever better computers and more precise measurement data, the possible forecast time will only be slightly extended in the future. Because even in the future it will not be possible to detect every flap of the wings of butterflies. The mathematician and chaos researcher Vladimir Igorwitsch Arnold found that the principle limit of weather forecasts is 2 weeks. If that seems too short for the wedding planning, the principle of hope will also apply in the future when it comes to weather.

Dipl.-Met. Christian Herold

German Weather Service Forecast and Advice Center Offenbach, February 19, 2016