Predictability Beyond the Deterministic Limit

by Brian Hoskins1

The traditional idea of a deterministic limit is questioned by considering the possibility of some predictive skill on all time-scales from hours to decades. The discussion is framed in terms of the seamless weather-climate prediction problem. The focus is on phenomena that evolve on the time-scales of interest and the predictability associated with them, as well as the bias produced by longer time-scale conditions.

How can there be prediction beyond the deterministic limit?

The title given to me for this talk reflects the seeming contradiction between the fact that predictions are increasingly being attempted for months, seasons and longer and the idea that the atmosphere is essentially unpredictable beyond about two weeks. The latter idea is well-based on theory and arose from the work of Lorenz (1969). The sensitivity to initial conditions found by him and developed in the theory of chaos means that inevitable initial condition errors must eventually influence the flow on all length scales. Turbulence arguments, based on the observed relatively slow decrease in energy as smaller scales are considered, envisage inevitable uncertainty on small scales influencing motions on larger and larger scale such that all scales reflect this uncertainty in a finite time. Experiments with high resolution global forecast models suggest that two weeks is the outside limit for deterministic prediction of even the largest scales in the atmosphere.

However there are also indications of phenomena and structures that exhibit robustness beyond what might be expected based on chaos and turbulence arguments. Every 26 months or so the equatorial winds in the stratosphere change from westerly to easterly and back again. Blocking highs in middle latitudes tend to persist with little change in structure over many typical life-cycles of synoptic lows and highs. In such cases, the dynamics in the atmosphere appears to be crucial in extending potentially predictable behaviour rather than leading to its demise.

The idea of a deterministic prediction is one based in middle latitude synoptic weather forecasting and refers to explicit determination of the synoptic scale flow. It was never expected that each convective shower would be predicted: there would always have been the notion of a probability of their occurrence. In more recent years there has been a realisation that forecasts on all scales should be probabilistic. Ensemble prediction systems have been developed based on a number of runs of the forecast model with varied initial conditions within the observational analysis error. Inevitable randomness in the representation of sub-grid-scale processes is being mimicked by adding some statistical noise (e.g. Slingo and Palmer, 2011). On longer time-scales variations in the parameters in the representations of sub-grid-scale processes are now starting to be used.

Such techniques can be applied on all time-scales with the aim of determining the likelihood of differing outcomes of phenomena evolving on the time-scale of interest and the statistical characteristics of phenomena on shorter time-scales. Over the many years since the pioneering studies of Charney & Shukla (1981), it has also been shown that conditions in parts of the interacting Earth system external to the atmosphere, such as tropical sea surface temperatures or land surface soil moisture, may evolve slowly or in predictable ways. Consequently they are able to give a bias to the subsequent behaviour of the atmosphere, and therefore provide the basis for some predictive power. Solar variability and volcanic eruptions are truly external to the interacting system and can provide possible predictive power, though volcanic eruptions during the forecast period might diminish predictive skill.

The major focus here is on the phenomena whose evolution on the time-scale of interest give hope of some predictive power. The behaviour of the atmosphere can often seem like noise, but we are looking for the patterns of behaviour: the music. The discussion is framed in terms of the seamless weather-climate prediction problem illustrated in Figure 1. Potentially predictable phenomena occur on all time-scales. Each time-scale evolves in the context of the longer time-scales and truly external conditions that may bias their evolution. Smaller scale phenomena that cannot be represented explicitly may be partially “slave” to the retained scales, like general regions of convection to a front, in which case aspects of their feedback on the retained scales may be well determined by those retained scales. They may also be “free” such as the location and nature of individual convective towers, in which case some statistical element will be required.

As indicated in Figure 1, the breadth and complexity of the Earth system model required for prediction will depend on the time-scale of that prediction. In addition to the physical atmosphere, the extent to which the ocean, land, atmospheric chemistry and ice sheets have to be included explicitly in the forecast system will depend on the time-scale of interest. Understanding, and improved simulation and prediction at one scale, can provide valuable support for prediction on longer time-scales. For example the improvement in the forecasting of individual blocking events in recent years should help in giving an improvement of the simulation of their frequency and characteristics over the 20th century by climate models, and therefore more confidence in projections for changes in blocking at the end of the 21st century.

Figure 1 – The seamless weather-climate prediction problem. The time-scales are marked along the axis in the middle and below it some phenomena that occur on the different time-scales are given. At the top are indicated the components of the Earth system that need to be represented and the extent to which this needs to be done. For time-scales to the right of the arrows even more completeness in this representation may be required.

Examples of potential predictive skill on a wide range of time-scales

Day 1 – There is good progress on developing forecast systems for the first day using kilometre scale models embedded in regional or global models. As an example, the UK Met Office has embedded a 1.5 km model covering the United Kingdom of Great Britain and Northern Ireland in various members of an ensemble forecast system based on a 24 km model for an extreme local precipitation event in October 2008. The larger scale system gives various locations for a front and the fine-scale system gives evidence that very high rainfall event can be expected somewhere within a region dictated by the larger-scale front. Designing a fine resolution ensemble which is able to provide useful predictive power for these and other events is a current challenge.

Week 1 – In the past 30 years there has been great progress in predictions on the synoptic scale in middle latitudes, which were made possible by forecast model and observational and initial data analysis improvements. In the tropics there is potential predictability associated with phenomena that are not currently well captured by forecast models. As an example, equatorial waves coupled with convection are found in data to have typical structures, to move in a coherent manner and to evolve over this one week time-scale.

1 week to 1 month – Almost all the members of the ensemble prediction system of the Japanese Meteorological Agency initialised in the middle of December 2010 showed a very cold spell starting late December and continuing through early January 2011 that actually occurred. The floods in north west Pakistan were associated with a succession of major rainfall events from July to early August. Each one of these was picked up by the European Centre for Medium-Range Weather Forecasts ensemble prediction system more than 10 days before it occurred. The predictive power in both cases was associated with the same two phenomena, a propagating Rossby wave and a blocking high. In the winter case, the wave was present in the initial conditions and propagated along the subtropical jet before reaching the Japanese region. Here the wave extended in latitude and broke to form a blocking high which persisted. In the summer case each rainfall event was initiated by a trough in a wave that propagated from near the UK along the westerlies well to the south of the blocking high over Russia which led to the heat wave there. The rainfall events occurred when the trough reached the entrance region of the strong jet near Pakistan.

In both cases it is again the predictable evolution of phenomena that underlies the predictive power. Similarly, the evolution of the Madden Julian Oscillation (MJO) gives promise of significant predictive power for the tropics and into both hemispheres. However this predictive power is not yet realised because of limitations in the simulation of the MJO.

1 month-seasons – The well-known El Niño-Southern Oscillation (ENSO) is a phenomenon associated with the coupled evolution of the tropical Pacific Ocean and the atmosphere. It has been the basis of predictive skill on seasonal time-scales in the tropics and to a greater or lesser extent in higher latitude regions. Winds associated with MJO events are important for ENSO evolution, and so better simulation of the MJO may also lead to increased skill in ENSO prediction. Also promising, but more elusive than for ENSO, is skill in predicting the North Atlantic oscillation (NAO). There have been some indications of predictability through interactions with the stratosphere, and more recently through the impact of Arctic sea ice and Asian snow cover. The impact of the NAO in the atmosphere on the underlying ocean is clear, but the reverse impact that could help in providing predictive power is less clear.

Some extreme seasons such as the European summer heat wave in 2003 and the cold winter of 2009/10 were not predicted, but some hindcasts now appear promising. However the real test will be on the prediction of future extreme seasons.

1 year to 1 decade – A number of the phenomena that are almost stationary on seasonal time-scales and give potential predictability on that time-scale may also do this on longer time-scales because of their slow, potentially predictable evolution. The NAO appears to have some persistence on these time-scales. The stratosphere also has multi-annual and perhaps decadal time-scales associated with persistent composition changes. The predictable evolution of solar activity through its impact on very short-wave radiation that is absorbed by the stratosphere is likely to influence its temperature. There is increasing evidence that such changes in the stratosphere can influence the statistics of the weather.

Skill has been demonstrated for predicting the temperature of the upper layer of the North Atlantic Ocean. In general, as said before, it is not yet clear whether this implies any predictability for the atmosphere. However tropical cyclones are strongly influenced by upper ocean temperatures and it has been shown that there is predictive skill for the 5-year average of their frequency in the North Atlantic region.

1 decade to 1 century – On these time-scales the trend implied by increasing greenhouse gases become important and should give predictive power. The focus until recent years was on changes in mean quantities, but there is now increasing interest in the possible impact on phenomena such as blocking or ENSO, or on patterns of variability such as the NAO. This impact might be seen in changing amplitude or frequency, or in changing structure.

There is variation in the NAO on multi-decadal time-scales and there are phenomena such as the Atlantic Multi-decadal Oscillation (AMO) and the Pacific Decadal Oscillation (PDO) whose evolution is on these time-scales. Current models can represent structures and their evolution that have some similarity to the observed AMO and PDO. When these representations improve and the behaviour of the NAO is better understood, it can be hoped that these phenomena will be the source of some predictive skill. To realise this will require suitable observational data and analysis and initialisation procedures. In the past these phenomena have tended to be perceived as noise that acts to obscure the climate change signal. In future they will become a major component of the projections for future decades.

Concluding comments

The background provided by the longer time-scales and by external conditions, and the phenomena that occur on each range of time-scales in the seamless weather-climate prediction problem, give the promise of some predictive power on all time-scales. The actual usefulness of this predictive power will not be clear for many time-scales before the relevant science has been done and techniques for using predictions in particular applications have been explored. I believe that a crucial aspect of the scientific approach will need to be an increased focus on the phenomena and their evolution: searching for and appreciating the music amongst all the noise of the weather-climate system. The challenge is a huge one for our science but the benefits for society may be immense.



I should like to thank the WMO and its Director General, Michel Jarraud, for the invitation to give the 2011 IMO Lecture. I acknowledge the very helpful input of many colleagues including Jagadish Shukla, Tim Palmer, Julia Slingo, Tim Woollings, David Strauss, Roberto Buizza, Mike Blackburn, Nigel Roberts, Adam Scaife, Rowan Sutton, Jon Robson and Doug Smith. A full scientific paper based on the lecture is to be published in the Quarterly Journal of the Royal Meteorological Society under the title: Predictability and the seamless weather-climate problem.



Charney, J. G. and J. Shukla, 1981: Predictability of monsoons. Monsoon Dynamics, Editors: Sir James Lighthill and R. P. Pearce, Cambridge University Press, pp. 99 109.

Lorenz, E., 1969: The predictability of a flow which posses many scales of motion. Tellus, 21, 289-307.

Slingo, J, and Palmer, T, 2011: Uncertainty in weather and climate prediction. Phil. Trans. R. Soc. A 369, 4751–4767


1 Grantham Institute for Climate Change, Imperial College London, Department of Meteorology, University of Reading

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