Return Time Plots

What are Return Time Plots?

Return time plots are a way of graphically representing the most extreme events in a big sample of data, such as weather data or river flows. These types of plot are a convenient way to look closely at the “tail” of a distribution, which is hard to see in detail when you plot the data in a more familiar way, such as in a histogram, where your attention is drawn to the middle of the distribution.

The “return time” of an event, also known as the “return period” or “recurrence interval”, is the likelihood of an event occurring, defined by a particular variable exceeding a certain threshold in a certain time interval. For example, you would say an extreme flood had occurred if rainfall exceeded 350mm during the winter season.

What does each dot represent?

Each dot on the plot represents a single model simulation which has been run on a participant’s computer. We run tens of thousands of model simulations, which are identical to each other except for their starting conditions, which are varied slightly. These slight differences result in a different outcome in each model for the risk of certain events.

When these model simulations are then put together to form large ensembles, we can look at the average risk for that particular event. We then plot all the individual models on one graph and you can see the curve that emerges, which represents the range of results from the entire ensemble.

If you look at a plot of just a small number of model simulations, and compare it to a plot with tens of thousands, you can see why it’s so important to run these large ensembles of models if you want to get clear, statistically significant results:

What does the x-axis along the bottom mean?

The x-axis tells us the chance of an event occurring in a given year, where that event is defined as the variable in question, such a seasonal rainfall, exceeding a particular threshold. With extreme weather events, we tend to talk about “1 in 10 year events”, which occur quite frequently. The chance of such an event occurring is 1 in 10, or 10%, in any given year.

The further you go to the right of the plot, the rarer the events get, all the way up to “1 in 1000 year events”, which are very rare, having a 0.1% chance of occurring in a given year.

The phrase “1 in 100 year event” does not mean that an event will occur exactly every 100 years, but that the probability is that it will occur once every 100 years.

The x-axis is logarithmic, which means that each number is 10 times bigger than the last (for example 10, 100, 1000), rather than there being the same distance between each (for example 10, 20, 30). This logarithmic scale lets us show a wide range of values more clearly in a single plot.

What does the y-axis up the side mean?

The y-axis shows the magnitude of the weather event in the form of a threshold. In this example, looking at high rainfall, the y-axis shows the total rainfall during a particular season that exceeded a threshold.

A low rainfall value, such as a winter with only 100mm or more of rain, would be a normal winter in the UK, which does not lead to widespread flooding.

A rainy season, which exceeded 350mm of rain, would be a “1 in 100 year event” and will have led to extreme flooding.

What does a dot at the bottom left indicate?

Dots at the bottom left of the plot represent model simulations where the winter in the model was a normal season with average and below average rainfall. All events are below a threshold that is frequently exceeded.

What does a dot at the top right indicate?

Dots at the top right of the plot represent model simulations where the winter had rare, extreme weather events, such as a “1 in 1000 year events”, where rainfall is above a very high threshold.

How can we use Return Time Plots to understand the influence of climate change?