## Going Back in Time: The (un)Predictability of Climate

**Reference**

Lorenz, E. N. 1963. Deterministic Nonperiodic Flow.

*Journal of the Atmospheric Sciences*

**20**: 130- 139.

At the time, meteorology was interested in explaining why the mid-latitude flow (jetstream) would in an irregular fashion transition from a higher amplitude state to a more zonal state at a time scale of roughly 10-14 days on average. There was also some interest in being able to make monthly and seasonal forecasts, which during the late 1950s to 1960s were considered very-long range. During this time, numerical weather prediction was also in its infancy.

Lorenz (1963) was expressly interested in examining the behavior of periodic and non-periodic flows. Later Lorenz would describe the non-periodic behavior as "chaos," which he then termed "order without periodicity." In the paper, Lorenz (1963) uses a technique called "low order modeling" to study the behavior of convection in a geophysical fluid. He coupled the Equation of Motion and the First Law of Thermodynamics, and then represented the motion and temperature variables in terms of waves which were then characterized by the lowest wave numbers that reasonably represented these fields. Then he was able to demonstrate the solutions for the system in mathematical space, and thus, follow the evolution of the system in time. The resultant graph is commonly known today as Lorenz's butterfly (Fig. 1), and he realized that this model provided a good analogue for the behavior of mid-latitude flow.

In theory, then, if we knew the initial conditions of the system precisely such that we lay on one of the trajectories in the "butterfly," we could follow that trajectory forever and know what the state of the weather would be into the future infinitely. Computers could then make weather or climate forecasts, and meteorologists would be out of jobs. However, our best models are only a hypothesis on how we believe the atmosphere really works. It is our best representation of the physics, which in many articles archived here on the NIPCC website we've demonstrated are often inadequate. There is also numerical error, in that our differential quantities can only be estimated.

But, the crux of unpredictability lies in the fact that measurements, and thus the initial conditions, cannot be precisely known. There is always some form or degree of uncertainty in them, and thus we don't know whether or which trajectory on that we lay. Lorenz states, "when our results concerning the instability of non-periodic flow are applied to the atmosphere, which is ostensibly nonperiodic, they indicate that prediction of the sufficiently distant future is impossible by any method, unless the present conditions are known exactly. In view of the inevitable inaccuracy and incompleteness of weather observations, precise very-long-range forecasting would seem to be non-existent." This problem of not knowing the measurements precisely is called "sensitive dependence on initial conditions" (SDIC) and it is an integral characteristic of chaotic systems.

Lorenz's statement was plain that beyond the 10-14 days, which is the typical times-scale for the evolution of the mid-latitude flow, dynamic predictability is impossible. This is in spite of the fact we know the equations representing motions in the flow. Today, we understand that such limits on predictability are scale dependent, for example, we cannot dynamically predict the occurrence of individual thunderstorms on the smaller-scales beyond the 30 - 120 minute time-scale in take for them to evolve. Beyond our time limits, corresponding to the proper space-scale, only statistical prediction is possible.

Figure 1. A representation of Lorenz's butterfly developed using the model published in Lorenz (1963). This picture was adapted from an internet image.

Figure 1. A representation of Lorenz's butterfly developed using the model published in Lorenz (1963). This picture was adapted from an internet image.

One way that modelers attempt to mitigate SDIC is via the use of ensemble modeling. This technique takes the "initial conditions" and several plausible alternative (but very close by to the original) initial conditions and then runs the model several times with each set. If these trajectories all evolve toward a common trajectory, we can have high confidence that the predicted solution is highly probable. But, when these trajectories diverge (another character of chaotic systems) the probability that any one of them will be the actual prediction is small. Model runs of "climate change" scenarios exhibit this behavior. In these climate projections, the spread in the forecasts gets larger and larger as the projection time goes out. This is exactly what would be expected.

Thus, there is ample evidence that the climate does behave in a chaotic sense and that climate prediction is currently not possible, or only the development of "scenarios" is possible. There is much more that can be written on this topic, but the space is limited. The bottom line is don't trust the climate scientist who believes climate prediction is possible.

*Archived 5 December 2012*