What will the weather be like tomorrow, or next week or, indeed, in a month’s time? Today’s numerical weather predictions can easily answer the first two parts of this question, but they fall short beyond about 14 days. New work on predictability limits by scientists at the University of Miami and the NOAA Cooperative Institute for Marine and Atmospheric Studies (CIMAS) say that this maximum could be extended to around 129 days – but probably no further. Whether this limit can be reached in practice, however, will depend on future improvements in forecasting technologies, they say.
Numerical weather prediction was developed in the late 1940s. Indeed, it was one of the first major applications of electronic computers. As these have advanced, so have the predictions. Indeed, thanks to ever more sophisticated mathematical models capable of analysing increasing amounts of observational data, we can now predict, for example, when hurricanes will occur as far as eight days in advance – something that was deemed impossible even a few decades ago. But how far ahead can such predictions be made?
Previous attempts to determine this predictability limit have largely relied on analysing the behaviour of very small perturbations in the atmosphere. These tiny errors, however, are inaccessible either observationally or via numerical modelling, explains Zoltan Toth of the NOAA who led this new study together with his colleague Wei Zhang. “These past studies therefore had to make some assumptions about the behaviour of the small errors, and these assumptions are necessarily somewhat arbitrary.”
Analysing the energetic balance of the atmosphere
The method developed by Toth, Zhang and their colleagues makes no reference to this error behaviour and instead goes back to analysing the energetic balance of the atmosphere, which continually absorbs solar radiation on the molecular level. In their approach, the researchers began by considering how our planet’s atmosphere would behave as a closed system, the deterministic dynamics of which preserves information about its initial state, assumed to be perfectly known. In theory, such a hypothesis would allow forecasts of the atmosphere’s behaviour right out to infinity. This is not possible in reality, they explain, because the atmosphere is obviously not a closed system: it receives and emits radiation. In the real atmosphere, the phases of photons in sunlight are completely random and cannot be determined, injecting quantum-scale uncertainty into the atmosphere.
These unknown quantum characteristics act as noise and destroy any retained information, beginning first of all on the smallest scales, explain the researchers. As these scales become bigger, noise eventually affects all parts of the system. When the total energy in the atmosphere is entirely replaced, the ability to make any prediction is completely lost.
“Using the relatively well-measured quantities of total energy in the atmosphere and the incoming and outgoing solar radiation fluxes at its upper boundary, we estimate that the range of skilful forecasts could potentially be extended from 14 days as at present to 129 (±7) days at the most,” explains Toth.
Very different from the mainstream discourse
“This result is very different from the mainstream discourse about atmospheric predictability, which to this day is strongly influenced by early publications in the field,” adds Toth. “More recently even, the authors of a 2018 article in the Bulletin of the American Meteorological Society speculated on whether current forecast systems are reaching their limits for when it comes to predicting tropical cyclones. In 2020, we argued that this limit is at least decades, if not much farther away.”
The theoretical foundation for the new methodology to determine the time limit of predictability is rather simple, he says. “At its core is a conceptual realization, which came to us intuitively. This is that the energy turnover time (that is, the time it takes for all energy in the atmosphere to be replaced by incoming solar radiation) is equivalent to the upper limit of predictability.”
Physics-based models still beat AI for predicting extreme weather events
While there is no complex mathematics involved, Toth notes that he and his colleagues had to find a way to describe the technique in a readily understandable way – something that was not easy, he admits, given the complexity of the subject.
Looking ahead, the researchers, who detail their present work in Advances in Atmospheric Sciences, are now looking into several other independent ways to estimate the limit of predictability. “There is no doubt, this limit has a theoretical feel to it,” Toth tells Physics World. “Yet there are a number of very practical implications for both traditional equation- and AI-based modelling of the atmosphere following on from the theory of predictability that we are also exploring in a series of ongoing studies.”
