Chaos and ensemble forecasting

B. Geerts and E. Linacre


The atmosphere is essentially chaotic because the processes involved in its evolution, in particular advection, are non-linear. It is said that the flap of the wings of a butterfly may trigger a thunderstorm. But no particular butterfly’s wings fix the following weather, since there are untold numbers of other butterflys’ wings of equal importance. A chaotic system is not random. It is deterministic, but in a way that is too complicated to ascertain. In weather forecasting Newton’s laws of motion can be applied to a grid that is many orders of magnitude more coarse than the actual atmosphere (e.g. 100 km vs 1 mm). But such forecasts become inaccurate (not unstable) after a number of days, by which time the conversion of kinetic energy to heat becomes large.

An increasingly used method of weather forecasting allows for the uncertainties concerning initial conditions and the role of chance. It is called ‘ensemble forecasting’. The idea is that repeated forecasts are made from the same initial time, with the initial conditions varied by an error whose magnitude reflects the degree of uncertainty of the observations. In 1965, MIT meteorology professor Ed Lorenz (1) noted that forecast errors are due to at least three causes:

  1. Insufficient observations. Without considering the accuracy of weather measurements, features of the atmosphere still go unobserved because measurements cannot be made everywhere. Not even satellites and radar provide all the temperature, pressure, humidity, and wind information that are missed by standard weather balloon and surface observations.
  2. Inadequate forecasting procedures. Computer forecasts are deficient in that they neglect small scale effects, and they approximate complicated physical processes such as heat transfer, what goes on in clouds, and interaction with the Earth's surface (friction, evaporation, etc.).
  3. Inherent limits to long-range forecasting. In his seminal 1963 paper (2), Lorenz showed that, no matter how good the observational network or how good the forecasting procedures, there is almost certainly an insurmountable limit as to how far into the future one can forecast. The tiniest error in the specification of winds, pressure, temperature, humidity, etc. around the world will ultimately amplify, due to non-linear interactions at various scales, until a forecast will be worthless. The sensitivity of atmospheric behaviour to small perturbations is known as chaos. Chaos is the result of the dependence of any prediction on the precise values of the input to the prediction process. The small uncertainty concerning initial conditions eventually leads to huge uncertainty about the calculation. The forecast uncertainty can be assessed by ensemble forecasting.

The first two sources of error have become smaller since the days of Lorenz, but the fundamental reasons for forecast failure are still there. Ensemble forecasting yields a range of prognoses. The breadth of this range indicates the possible error in any forecast, and their consensus provides the best estimate. Sometimes the atmosphere behaves more chaotically, and small errors amplify rapidly. At other times the various forecasts stay within a narrow range, therefore they can be treated with more confidence. Various operational medium-range forecasting centers, including the ECMWF, use the ensemble technique. It can also be used in short-range forecasting, in particular to predict the evolution and movement of tropical cyclones (3).



  1. Lorenz, E. N., 1965. A study of the predictability of a 28-variable atmospheric model. Tellus, 17, 321-333.
  2. Lorenz, E. N., 1963. Deterministic non-periodic flow. J. Atmos. Sci., 20, 130-141.
  3. Zhang, Z. and T.N. Krishnamurti, 1997. Ensemble forecasting of hurricane tracks. Bull. Amer. Metor. Soc., 78, 2785-95.