Mathematics

A rounding error reroutes the future

Weather forecasts hit a hard limit at about two weeks: the atmosphere is chaotic, and starting differences too small for any instrument to detect are enough to send the forecast off course. A 2019 study using two of the world's most detailed weather models confirmed the two-week ceiling holds even with near-perfect data.

Sources & further reading

Journal of the Atmospheric Sciences (American Meteorological Society)Deterministic Nonperiodic FlowThe original paper proving that some fully deterministic systems still can't be predicted far into the future.WikipediaButterfly effectThe story of how a rounded number gave chaos theory its name.Journal of the Atmospheric Sciences (American Meteorological Society)What Is the Predictability Limit of Midlatitude Weather?A 2019 study using today's best weather models confirming a two-week ceiling on forecasting.Pennsylvania State UniversityPredictability limit: Scientists find bounds of weather forecastingA university news article explaining the two-week forecasting limit in plain language.European Centre for Medium-Range Weather Forecasts (ECMWF)Medium-range forecasts: the Ensemble Prediction SystemHow Europe's weather center runs 51 slightly different simulations at once instead of one.National Oceanic and Atmospheric Administration (NOAA)Global Ensemble Forecast System (GEFS)The US equivalent: 31 simultaneous weather simulations to measure forecast uncertainty.Science (American Association for the Advancement of Science), hosted via MITNumerical Evidence that the Motion of Pluto Is ChaoticThe 1988 study proving even Pluto's orbit is chaotic, not perfectly predictable clockwork.NASA Jet Propulsion Laboratory (JPL)NASA's Next-Generation Asteroid Impact Monitoring System Goes OnlineHow NASA tracks asteroid orbits that become harder to predict right after a close pass by Earth.Proceedings of the National Academy of Sciences (PNAS)Evaluation of individual and ensemble probabilistic forecasts of COVID-19 mortality in the United StatesA peer-reviewed evaluation of pooled COVID-19 forecasts, showing they tracked trends but missed sudden turns.