The butterfly effect: or why the weather forecast goes wrong

Weather forecasts on popular websites are increasingly covering the next week or two. You can even find models predicting temperature, precipitation and cloud cover for months ahead. Every now and then, eye-catching headlines pop up in the newspapers about a sudden frost coming from the east, heavy snowfall for the holidays, a heat wave that will hit us as early as March or some other extreme weather that is expected to hit us in two weeks. Another time, we leave the house in the morning armed with an umbrella, because on the radio they were talking about fleeting rainfall, and throughout the day not a single drop fell on us. So what about the reliability of such predictions? And if they don’t work, why?

Why the weather forecast doesn’t work

Forecasts with forecasts, and then (which we can no longer find information about in the media) it turns out that the world has not been covered with ice, snow in the mountains is still scarce, and nature has not exploded with greenery after the sudden arrival of spring. And even the inquisitive, reviewing later the numerical models cited by the authors of the weather sensations, look in vain for confirmation of their predictions. It turns out that a butterfly is the “culprit” of it all, which, with the flutter of its wings, introduces a tiny change into the dynamic system that is the Earth’s atmosphere, and with it triggers a tornado on the other side of the world.

How a butterfly triggers a hurricane

Of course, the butterfly story is figurative, but this colloquial comparison illustrates two things. The first says that introducing even a small initial change to the system can cause large discrepancies at the end. And the second is a reference to the shape of the butterfly wing-like graph that Edward Lorenz obtained when simulating a weather model. This prominent American mathematician and meteorologist, whose research created the first computer models of the weather, tried to forecast it several days ahead. He developed the following in the 1960s. In the 1970s. A set of more than a dozen nonlinear differential equations that describe the relationship between temperature, pressure or wind speed.

He believed, as did most scientists at the time, that accurate input data on the state of the atmosphere would yield accurate output data, i.e. a weather forecast. However, when he entered the two input numbers into the computer with different accuracy, he got results that were increasingly different as the simulated time went on, despite the small difference in the initial values. Such sensitivity of an equation or system of equations to a small perturbation of the initial parameters was called the butterfly effect by Lorenz in a scientific article. This phenomenon was later referred to as deterministic chaos.

In the context of weather forecasting, the butterfly effect is of great importance because the atmospheric system is a dynamic and complex system in which even the smallest changes affect the whole. Minor differences in temperature, humidity or wind speed at one end of the world can affect weather conditions elsewhere. These parameters theoretically combine to form a cause-and-effect relationship, but one so distant and complex that it remains impossible to predict and capture in weather models.

In addition, it is not possible to enter a dataset at the beginning of the simulation that will describe all the initial parameters of the atmospheric state in a sufficiently accurate way. There may also be unexpected changes not included in the global model (such as tree cutting, change in shading by skyscraper construction or aircraft overflight) that will lead locally to cloud development, temperature change and de facto different weather than forecast.

So, as you can see, the slightest deviation in the initial values results in a very rapidly increasing deviation in the final results – the long-term weather forecast. This is still the case, despite the fact that specialists in numerical forecasting have more and more accurate and complete data on the state of the atmosphere. Today, weather models assimilate data from satellite imagery, radar, lightning detection systems, and even those collected on research vessels or passenger aircraft, in addition to data from ground measurements. However, the sensitivity of a system such as the atmosphere, the multitude of processes in it and the influence of the substrate on it result in the fact that an accurate weather forecast can only cover the next 2-4 days.

Accurate weather forecasting over the long term is unpredictable. In individual recalculations of the numerical model, based on new initial conditions every few hours, there may be results suggesting a weather collapse, which will certainly be picked up and described by numerous media outlets. However, this abrupt change may not be there in the next forecast. An additional factor contributing to the poor verifiability of the forecasts are local conditions that are not taken into account with sufficient accuracy, which can affect, for example, the variation in precipitation occurrence over a small area.

What instead – probabilistic and synoptic forecasting

So can’t we really determine, even if only in a simplified way, the weather over a time horizon of a few or several days or for an exact location taking into account local conditions? In part, we can. Today, an increasing number of global medium-term numerical weather models are based on a bundle forecast, which at one time generates dozens of forecasts with slightly altered initial conditions. The magnitude of the differences increases over time in the individual results of the beam let go. This allows you to determine the point up to which the forecasts in the bundle are consistent and reliable with each other. This extends the forecast accuracy period to 5-7 days. In this way, we can predict most of the meteorological parameters that are relevant to the standard viewer, such as temperature, cloud cover, precipitation, wind speed and pressure distribution.

If we need a forecast beyond the range of a few days, such as monthly or seasonal, it is worth turning to probabilistic models. They illustrate, usually in the form of maps for the country, whether a particular meteorological parameter will be below, even or above the multi-year norm. They are generally developed for basic meteorological parameters such as temperature and precipitation on a decadal, monthly or seasonal basis. Long-term models, due to the complexity of the calculations and the continuous development phase, are generally created at meteorological and research institutes.

For consumers expecting a weather forecast for the here and now, covering a wide range of meteorological parameters, several hours or 1-2 days at most and taking into account local conditions, forecasts developed by synoptics or nowcasting models will be important. Synopticians, with a wide range of meteorological data, knowledge of the specifics of the covered area, and based on calculations and comparison of model results, can create forecasts with high verifiability and tailored to audiences concerned with ensuring the safety of the population, ships or aviation.

You can also turn to the nowcasting models available on some platforms, which forecast weather over a time horizon of up to 6 hours. They use precise calculations of the movement and evolution of meteorological phenomena and parameters that determine the current state of the atmosphere, making it possible, for example, to Tracking the movement and development of individual storm cells. They make it possible to determine the weather with great precision and taking into account local conditions.

As you can see, products created by synoptics or nowcasting models, due to the short horizon of forecasts and their constant updating, resist the butterfly effect. On the other hand, if we want to reach into the more distant future with a forecast, we have to expect less accuracy.

In the article, I used, among others. From the works:

1. https://meteomodel.pl/modele-numeryczne-mapy-gfs/ (Accessed: 26.02.2024).
2. https://pl.wikipedia.org/wiki/Chaos_(math) (Accessed: 26.02.2024)
3. https://pl.wikipedia.org/wiki/Efekt_motyla (Accessed: 26.02.2024).
4. Dictionary for the media most important terms and phrases in meteorology, IMGW-PIB
5. Dictionary for the media of the most important terms and phrases in meteorological modeling, IMGW-PIB