| |
The Concept of Ensemble
Prediction
|
 |
|
|
The concept of ensemble prediction can be illustrated using the
Lorenz attractor. This is a set of non-linear equations in 3 parameters
which is very simple compared to a numerical model of the atmosphere,
but which shares the important 
property of chaotic behaviour.The main characteristic of a chaotic
system (such as the atmosphere) is that very small differences in the
initial conditions will be amplified over time, often quite rapidly, so
that similar initial states will evolve into quite different final
states. This property means that it is impossible to have perfect
forecasts for a chaotic system. We can never know every tiny detail of
the initial state of the atmosphere, and these small uncertainties in
the initial state will always lead to large errors in the forecast at
some point in the future. Chaos thus means that there is always a finite
limit to the predictability of a chaotic system. However, we can use
the Lorenz attractor to illustrate how, with ensemble forecasts, we can
maximise the predictability on any particular occasion. |
The
Lorenz Attractor
|
|
| Ensemble prediction in the Lorenz attractor
|
|
The pictures below show three different ensemble forecasts in the
Lorenz attractor. In each case the starting point for the forecast is
known only approximately, represented by the first black circle - we
know the starting point is somewhere within this circle, but not
exactly where. This is exactly like a weather forecast where we can
analyse all the main pressure systems and the temperatures and
humidities of the air averaged over large areas, but we cannot know
every detail of the current state. From each of these circles of
possible initial states in the Lorenz attractor we calculate a whole
set of forecasts - an ensemble - of where in the attractor we expect to
be after a number of time-steps:
- In the first case in the top picture it can be seen
that the forecasts all stay close together throughout 10 time-steps, so
even quite a long way ahead we can predict quite accurately where we
will be in the attractor.
- In the lower-left figure we can similarly predict
with good accuracy for the first 5 or 6 time-steps, but after that the
forecasts diverge quite rapidly. However, by counting how many of the
forecasts go into the left lobe of the attractor, and how many go into
the right, we can at least estimate the probability that we end up in
either lobe. So although there is uncertainty, we can still extract a
lot of useful forecast information.
- In the third case in the lower-right picture the
predictability is lower still and by the 4th time-step we need to
issue a probability forecast. From about the 6th time-step onwards
there is huge uncertainty, but nevertheless there is still some useful
probability information which can be extracted.
Forecasting the weather is, of course, much more complex than
forecasting in the Lorenz attractor, but it does provide a useful
analogy. Most of the time the atmosphere behaves rather like the
lower-left picture where we can predict with confidence for a few days
and have to use probabilities thereafter. Sometimes we are lucky and get
situations like the top where we can be confident further ahead, but on
other occasions there can be great sensitivity early on like the last
case. This is discussed further below.
|
Thanks
to Tim Palmer of ECMWF for
permission to use this illustration.
|
|
Back to top
|
| Predictability in the atmosphere |
|
As noted above, chaos means there is always a finite limit to
predictability. So what is this limit in the atmosphere? In practise
the limit depends on what we are trying to predict. For the general
patterns of daily weather, such as the low and high pressure systems
often illustrated on a weather map with isobars, we can normally expect
to predict these reasonably accurately up to around 3 days ahead.
However there is a lot of variability around this average figure. As
shown above for the Lorenz model, predictability varies according to
the situation. Some days we can predict the general weather pattern
quite confidently up to a week or more ahead - this can often occur
when there is a large slow-moving high pressure system over the region.
On other occasions significant errors can occur only one or two days
ahead - fortunately the advances in NWP systems over recent years mean
that such occasions are increasingly rare, but they may never be
eliminated completely. Importantly, some of the most difficult and
unpredictable situations can be related to the rapid development of
major storms, so it is particularly important to be able to assess the
uncertainty in such situations.
While we can typically predict general weather patterns up to 3 days
ahead, predictability for detailed local weather such as rainfall or fog
formation is much less. For example we may be able to predict the
general conditions for the formation of showers a few days ahead, but we
may only be able to predict whether a particular location will get a
shower a few hours ahead or even less.
Where predictability is limited, probability forecasting can frequently
be useful to extend the times over which useful forecasts can be
provided. Use of ensemble prediction means that we can assess the
relative probabilities of different outcomes. While it is unusual that
we can make detailed predictions of daily weather more than 3-5 days
ahead, by using ensembles we can normally issue some useful
probabilities up to 7-10 days ahead.
Back to top
|
|
|
|
Home 
