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Probability Distribution Functions (PDFs) in detail

This page gives more information about when it is appropriate to use PDFs, some things to be aware of when using them and details about how the PDFs show uncertainties in the projections.

What should I use them for?

PDFs are useful to explore and to display climate projection information in certain circumstances. You might like to use them:

  • To provide a visual representation of the probabilistic climate projections

PDFs are a powerful tool for showing the nature of the UKCP09 climate projections, and for exploring the implications of different choice of, say, emissions scenario, geographical location or time period.

Things to be aware of

When using PDFs it is important to remember that they reflect the probability ranges obtained using the UKCP09 method. The range of projections contained in a PDF captures the important known uncertainties associated with climate projections.

Other factors that you should bear in mind when using PDFs are: 

  • PDFs show the relative probability associated with a specified amount of change

As a PDF plot shows the relative probability associated with a specified amount of change it is not recommended that they be used to explore the climate change associated with a certain probability level.

You may find that, in practice, it is more informative to know the probability of a change being greater or less than a specified value (for example, the probability associated with a temperature change of less than 4.0°C or greater than 4.0°C). Similarly, you may need to ascertain the amount of change associated with a specified probability level (for example the 10% probability level, which changes are very unlikely to be less than). In both these cases, it would be more appropriate to use a Cumulative Distribution Function (CDF) plots plot. .


PDFs show probability distributions which capture the important known uncertainties.

Emissions uncertainty is explored through the use of three sets of probabilistic climate projections to reflect three different scenarios of future greenhouse gas emissions:

  • Low emissions (IPCC SRES: B1)
  • Medium emissions (IPCC SRES: A1B)
  • High emissions (IPCC SRES: A1FI)

A single PDF shows projections associated with a single, user-specified, emissions scenario. Multiple PDFs are therefore needed to illustrate emissions uncertainty.

For more information see the Handling Uncertainty page.