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Joint probability plots in detail

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

What should I use them for?

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

  • To illustrate the joint probability of changes in two variables

Joint probability plots show the range of projected changes in one variable, consistent with projected changes in another. You can use this to examine, for example, the probability of hotter and drier summers.

This is something that the other image outputs available from the UKCP09 User Interface do not allow.

  • To suggest what projected combinations of changes can effectively be ruled out

As well as showing what range of projected changes in one variable are consistent with projected changes in another, joint probability plots also show what projected changes in one variable are not consistent with projected changes in another.

You can use this information to effectively rule out certain combinations of changes.

Things to be aware of

When using joint probability plots there are some things that you should bear in mind. You should remember that joint probability plots reflect the probability ranges obtained using the UKCP09 method. The range of projections contained in a joint probability plot captures the important known uncertainties associated with climate projections.

Other things to consider when using joint probability plots are:

  • Joint probability plots show the probability associated with an exact joint occurrence.

Only exact joint occurrences of two variables are shown in joint probability plots. For example, you may want to compare a temperature change of 4˚C with a precipitation increase of 20%. This means they should not be used for exploring the joint probability associated with climate change being greater than or less than a certain amount.

In practice, you may want to know the joint probability of a change being greater or less than specified values: for example, the probability associated with a temperature change of less than 4.0ºC and a precipitation change of greater than 20%.

In this case, analysis of the sampled model output might be more appropriate. For more information please see the 'Sampled data' pages.

· Joint probability plots show changes associated with two variables

Joint probability plots show the changes associated with two variables, and provide probability contours to indicate the probability of joint occurrences. They should not be used for detailed analysis of the joint probability of changes in more than two variables.


The joint probability plots show probability distributions that capture the important known modelling uncertainties and natural climate variability.

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 joint probability plot shows projections associated with a single, user-specified, emissions scenario. Multiple joint probability plots are therefore needed to illustrate emissions uncertainty.

For more information see the 'Handling Uncertainty' page.