The Butterfly Effect is one of the applied models in weather forecasting. It makes us understand that the reliability of forecasting drops considerably after 10 days.
Of course, the butterfly wings cannot cause a big storm, but in some cases, if the actual conditions can be studied it can have an effect, but is very hard to detect.
Professor Lovejoy, from McGill University, comments that "the Butterfly Effect treats the weather as random and uses historical data to force the forecast and reflect a realistic climate".