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  Uncertainty in Weather Forecasts

Can we offer more information?

Everyone knows that weather forecasts go wrong sometimes!  Reasons for this vary, but the chaotic nature of the atmosphere means there is always a limit to what we can predict accurately.  When we issue a forecast we usually give our best estimate of what will happen, but often we know more about the confidence or uncertainty surrounding that forecast. In television forecasts the presenter will often express some of the uncertainty in words, but time constraints limit how much detail can be given.  In many other forecasts, such as those available freely through the internet, only the best-estimate is provided. So what more can we offer?

Expressing uncertainty

Uncertainty can be expressed in several ways:

1.  Verbal Expressions

Weather forecasters express uncertainty using many forms of words. Examples for rain could include:

  • rain at times
  • scattered showers, mainly in the NW
  • up to 50mm in places
  • risk of heavy bursts  

End-users are often most interested in specific events which might disrupt their normal activities, and then the forecaster might express a risk with phrases like:

  • only a small chance of...
  • a high probability of disruption to...
  • a risk that some places might get...
  • I cannot guarantee you won't get..., but it is probably worth the risk.
In order to make a statement like the last example, the forecaster requires some knowledge of the user's application, and in particular the risks and dangers for the user of the event happening. The forecast given to one user may therefore not be appropriate for another. A second user interested in the same weather event for a different application might get:
  • I cannot be sure you'll get..., but I wouldn't risk it if I were you!
All the examples above give some impression of how likely the end-user is to experience certain types of weather, but none of them is very precise. because they are imprecise, it is difficult to say whether such forecasts are accurate or not. The following examples show how uncertainty can be expressed more precisely. Attaching numbers to the confidence or uncertainty can allow the user to assess the risks more accurately, and it also allows the forecasts to be assessed more reliably.

2. Confidence Range

A range of values can be given, such as "Temperature between 3 and 7 Celsius".  For some customers we thus provide a most-probable temperature, along with upper and lower bounds. These bounds would be given with a level of confidence agreed with the end-user, for example "We are 95% certain that the temperature will be between 3 and 7 Celsius" for which the user should expect that the actual temperature will fall outside the range given on around 5% of occasions, or once in every 20 forecasts.

The graph below gives an example of how confidence ranges can be presented to users. Maximum and minimum temperatures for each day at a given location are given a range of uncertainty. The full length of each vertical line represents the 95% confidence range, while the central bar represents a 50% confidence range. The horizontal line across this bar is the most likely temperature.Thus for the first night we can be 95% certain the minimum temperature will be between 8 and 13 Celsius, and 50% certain it will be between about 11 and 12 Celsius. It is interesting to note how the uncertainty increases further ahead in the forecast.

Example of meteogram graph.

3. Probability Forecasts

Where the end-user of a forecast is interested in the risk of a particular event occurring, this can be expressed as a probability. The second list of examples above could then become something like:

  • a 10% chance of...
  • 80% probability of disruption to...
  • a one-in-five chance that Heathrow Airport might get...
  • a 5% risk of... so it is probably worth the risk.
Note that in the 3rd example we have not only attached a number but also been specific about the risk at a particular location, which makes interpretation for the user much easier.  In the last example the risk can be justified by the number, depending of course on the user's sensitivity.

How we estimate uncertainty

The Met Office uses various techniques to estimate the uncertainty in forecasts. In particular the development of so-called "ensemble forecasts" allows us to estimate many uncertainties automatically and provide extra information to customers in routine forecast products.  In an ensemble forecast, instead of running our computer forecast model just once, we run it many times from slightly different starting conditions to assess how certain or uncertain the forecast is. We can estimate the risk or probability of a given weather event from the proportion of these forecasts which predict the event to occur.

Ensemble forecasts available at the current time are best-suited to estimating uncertainty in forecasts between 3 and 10 days ahead. For customers with shorter-range requirements 1-2 days ahead we are currently researching new ensemble methods, but we can also offer statistically-based estimates of uncertainty. Whatever the method, the types of products we can offer are similar.

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Probabilities and Odds

Use of probabilities can sometimes cause some confusion, and many people are more familiar with Odds which are commonly used for betting. The two are very closely related. For example, a probability of 10% means 10 times out of 100, or a 1 in 10 chance. Thus for every 10 occasions the event will not occur on 9 occasions and will only occur once. The Odds are therefore 9:1 against.

Working in the opposite direction, if the Odds are 4:1 against an event occurring, then this means that it will not happen 4 times as often as it happens. So it will occur on 1 occasion in 5. Turning 1 in 5 into a percentage gives 20%.

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Probabilities and False Alarms
As noted above, if the probability is 10% then the event will only occur on 1 occasion in every 10 (or equivalently 10 in 100). This means that on the other 9 out of 10 occasions the event will not occur. Thus if a user asks the Met Office to warn them every time there is a 10% risk of a particular event, then they should expect that 9 times out of 10 that a warning is issued the event will not occur. If the user does not understand this then they are likely to think the Met Office is issuing too many False Alarms, or to quote the fairy tale, "crying wolf". On the other hand, if the user is liable to suffer a large loss by being unprepared for the event, then they may well benefit from putting up with 9 out of 10 false alarms because of the large benefit from being prepared on the 1 in 10 occasion when the event does occur.

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Decision-making with Probability Forecasts

To make best use of the probability forecasts, the user must choose a probability threshold which gives the correct balance of alerts and false alarms for their particular application. Consider two examples:
  • User A is liable to suffer a loss when a particular weather event occurs so they would like to be able to protect themslves. However actually protecting themselves is also expensive (but less expensive than being unprotected when an event occurs), so they should only protect themselves when the probability of the event is high.

  • User B is sensitive to the same weather event but is liable to suffer a much larger loss than User A, but with a warning can protect themselves quite cheaply. This user should therefore protect themselves at much lower probabilities. They will get a larger number of false alarms but have the best chance of being protected when an event does occur. 
Both these users will take the same probability forecasts from the Met Office, but they will respond to them in different ways. User B will react at low probabilities, perhaps anything more than 20%, whereas User A may only take action when the probability reaches 80%. The precise level at which each user should start to react depends on their cost of protection and their potential losses - advice can be offered in how to maximise the benefit of the forecasts for any particular application.

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Examples of applications

Many users of forecasts can benefit from understanding better what the uncertainty in a forecast is.  Here are two examples:
  • In the energy business a 1-degree difference in temperature can have a huge impact on demand, and hence on the cost of gas or electricity. For a trader, knowing in advance what the risk of the temperature being one or two degrees warmer or colder than the basic forecast value can give a valuable competitive edge in the trading market. Some Met Office customers in the energy sector benefit from getting upper and lower bounds on their temperature forecasts, from which they can estimate bounds on energy demand and be better prepared for surges.

  • For an engineer planning a delicate operation in the offshore oil industry involving expensive equipment, knowing the risks of larger-than-expected waves can avoid expensive last-minute cancellations, or minimise the risk of equipment damage due to deteriorations during the operation.  Customers can be provided either with a range of uncertainty or with probabilities of waves exceeding given heights.
More Information

For more information on any of the above products, please contact the Met Office Customer Centre.

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