There Is a Hard Ceiling on Weather Forecasting, and It Is 129 Days

Meteorologists have been arguing about the outer limit of weather forecasting since numerical prediction began in the late 1950s. A study published in Advances in Atmospheric Sciences now puts a number on it: even under perfect conditions, the atmosphere becomes unpredictable after about 129 days.

The figure, 129 days give or take seven, comes from a route almost nobody has tried. Nearly every previous attempt at this question examined how small errors in a forecast grow as the forecast runs forward. Lead author Wei Zhang, a climate scientist at the University of Miami and NOAA's Cooperative Institute for Marine and Atmospheric Studies, argues that approach has a hole in it. "How could we say we can make skillful, very-long-range forecasts without actually being able to demonstrate it?" Zhang said. "Unfortunately, there is no observational, theoretical or modeling experience of how errors smaller than in today's forecasts may behave." You cannot extrapolate error growth into a regime you have never measured.

So Zhang and co-author Zoltan Toth, recently retired from NOAA, changed the question. "Our question was whether there is a dramatically different, new perspective to approach the perennial questions of predictability," Toth said. They asked what the limit would be under genuinely ideal conditions: knowing the exact initial state of the atmosphere, the exact governing dynamics, and every future large-scale boundary condition.

Under those assumptions, the answer should be that forecasts never fail. Perfect knowledge of the starting state, carried forward by perfectly known physics, gives perfect forecasts forever. The team found one exception, and it is a very small one. Sunlight arriving at the atmosphere carries quantum-scale uncertainty in the phase of its photons, and that phase is unknowable. It is the only fresh ignorance entering the system.

The rest of the argument is bookkeeping on energy. Solar radiation drives every motion in the atmosphere and, given enough time, reaches every molecule in it. Once the sun's energy has worked its way through the entire atmosphere, the uncertainty riding in on those photons has contaminated everything, and whatever memory the system retained of its initial state is gone. The researchers call that moment the energy turnover point. Taking the atmosphere's total energy, the incoming solar flux and the observational uncertainty in both, the turnover lands at 129 days.

The practical reading of that number is optimistic. Operational forecast skill today runs to roughly 14 days, which leaves an enormous margin unexploited. The team found the unused time splits roughly in half: a genuine extension of useful skill, followed by a comparably long stretch of marginal, low-confidence guidance at the tail. Translated into working terms, the accuracy a five-day forecast delivers today could in principle be pushed out to around 62 days. Zhang's group is now developing independent estimates to check the result. If those hold, forecasters have something they have never had before, which is a target.