Cumulative Distribution Functions (CDFs) in detail
This page gives more information about when it is appropriate to use CDFs, some things to be aware of when using them and details about how the CDFs show uncertainties in the projections.
What should I use them for?
CDFs are useful to explore and to display climate projection information in certain circumstances. You might like to use them:
- To explore the probability level associated with a certain amount of climate change
CDFs show the probability level associated with climate changes greater than or less than a certain value. The probability reflects how certain we are that change will be less than (or greater than) a specified value. This information is particularly useful when climate vulnerabilities or thresholds are known.
- To explore the amount of climate change associated with a certain cumulative probability level
CDFs show the amount of climate change associated with different cumulative probability levels. These probability levels reflect different amounts of certainty we have (based on current understanding and the UKCP09 method) about different amounts of change. This information allows you to use risk-based approaches.
You can also use it to explore attitudes towards risk. In the context of climate change, for example, it allows you to ask questions such as; "what level of risk am I willing to accept?"
- To estimate the probability of projected change within user-defined intervals
CDFs allow the UKCP09 projections to be aggregated and communicated in many ways.
You may want to, for example, use CDFs to estimate probability levels associated with specific intervals of changes (e.g. 0 to 2°C, 2 to 4°C, etc.). These bands might be related to specific climate vulnerabilities or thresholds, or used to explore the probability of a variable changing by either more or less than these intervals.
Things to be aware of
When using CDFs it is important to remember that they reflect the probability ranges obtained using the UKCP09 method. The range of projections contained in a CDF captures the important known uncertainties associated with climate projections.
Other factors that you should bear in mind when using CDFs are:
- That they are less appropriate for communicating climate projections.
While CDFs are useful to explore the UKCP09 climate projections, they might not be the most powerful tool for visualising and communicating these changes.
You may find that Probability Distribution Function (PDFs) are more useful in this respect, showing more clearly and intuitively both the spread (i.e. the range of changes) and shape of a probability distribution. For more information on PDFs please see the Probability Distribution Functions (PDFs) pages.
- Each CDF shows projected change for a single time period
A single CDF shows the projected climate change associated with a single, user-defined, 30-year time period. They provide no information about the evolution of changes through time.
- CDFs show probability of climate change at a single geographic location
CDFs show the probability of climate change for a single 25 km grid square or aggregated area. If you require information about spatial patterns of change, maps from the User Interface are more appropriate.
- CDFs provide information about projected change for one climate variable
CDFs provide information about projected changes in one variable (such as temperature or precipitation). CDFs cannot be used to provide simultaneous changes for different variables, for a specific probability level. This means that, for example, you cannot assume that the change in summer temperature associated with the 90% cumulative probability will be accompanied by, say, the summer precipitation change also associated with the 90% cumulative probability level. CDFs for different climate variables must be considered independently of each other.
For decision-making purposes we advise you to use the 10% to 90% probability level range. Values falling outside of this range are less robust.
A single CDF shows projections associated with a single, user-specified, emissions scenario. Multiple CDFs are therefore needed to illustrate emissions uncertainty.
In UKCP09 emissions uncertainty is accounted for by using 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)
For more information see the Handling uncertainty in UKCP09 ' page.