A New Approach to Estimating the Limit of Predictability

We define the limit of predictability as the time period over which any information about the evolving state of a dynamical system can be retained, assuming its dynamics, the state at one point in time, and future boundary conditions are exactly known, but the quantum fluctuations of incoming energy are not. Simplistically, this time period is the sum of the period of skillful forecasts that can be made today, plus the period skill can theoretically be extended by the perfection of today’s initial conditions and models. As forecast skill is a reflection of error, predictability is contingent on the behavior of small errors never seen before. As such behavior cannot be assessed either theoretically or observationally, the limit of predictability has remained elusive. In a closed system, deterministic dynamics perfectly retains information about the state of the atmosphere, assumed to be perfectly known at the initial time, suggesting infinite predictability. In reality, incoming solar radiation, however, injects variance with unknown quantum characteristics that act as noise, destroying information first on the smallest scales. Through the upscale propagation of energy, noise eventually affects all parts of the system. When the total energy in the atmosphere is entirely replaced, any predictability as defined above is completely exhausted. Using the relatively well-measured quantities of total energy in the atmosphere and the incoming and outgoing radiation fluxes at its upper boundary, we estimate that the range of skillful forecasts could potentially be extended by 57 days at the most. Interestingly, such an extension would correspond with the addition of a similarly long, 57-day forecast period characterized by skill just below that observable in today’s forecasts. The full range of predictability then equals the sum of the two 57-day extensions and today’s skillful range of 14 days, estimated to be 129 (±7) days. By how much, and when this potential may be realized in practice, will be determined by future improvements in forecast technology.