Extrapolation is how we predict the future

A blog post by Adam Mrozek, placement student with Pixalytics in October/November 2013.

I grew up in a very small village with very few inhabitants. As my father very often burned the midnight oil, my mother was the only person to look after me. But I lacked for nothing as she was both mother and father to me.

I can still see a vivid image of my mother celebrating St Andrew’s Eve. During this celebration people try to predict the future using a piece of hot wax and a bucket of cold water.

She had dipped the wax in the bucket of water and tried to interpret the shape. It was a common belief that the shape of wax reveals the future.

As I grew older I left all the superstitious beliefs behind. I practiced the subject of mathematics instead. Believe me or not, but it can help us predict the future, at least to some extent.

Let’s consider a set of points collected above a river. Each point represents a different height measured by the satellite.

Maslow's hierarchy


As the satellite orbits our planet, it provides more data.

Maslow's hierarchy

More points over time

Why do points appear in different places? Because the satellite is unable to pass over exactly the same spot twice in succession as it moves around the Earth; see polar orbits.

How is the water height going to change in the future?

I am going to show the simplest approach available. Namely, the High School approach. We can use extrapolation in order to work out this problem.

Each point can be represented by a set of three elements, i.e. x and y (position) together with height.

Let us calculate the average height at every instance in time. Therefore, we will not have to worry about the x and y coordinates any more; we represent every period of time with one value only.

It becomes easy to draw all the points on a single chart. Like this…

Maslow's hierarchy


We can now extrapolate the graph easily and tell how the height is going to change in the near future.

This is a very simple approach and will only work for small areas and short time periods.

Using this method we can predict how rivers will behave in the future. More advanced methods are used to research various areas of the Congo river letting us know whether the river will flood its surroundings or not.

EO Applications and Visualisation

I’m concluding my trio of conference blogs by focussing on Earth Observation (EO) and visualisation.

Within the data visualization session at ESA’s Living Planet conference Planetary Visions Limited gave a great talk entitled ‘Presenting Data and Telling Stories’. They highlighted the importance of knowing the audience that you’re communicating with, particularly the difference between presenting data to the general public versus fellow scientists.

The key element of communication to remember is that it’s only complete when the recipient understands the message. Scientific figures are often presented using a colour palette, which is applying artificial colours to black and white images (the rainbow palette is shown below, going from low values being purple / dark blue to high values being red). These enables scientists to easily extract values and get a detailed view of the results. Fine for scientists who understand this principle, but for anyone who doesn’t they may not understand the data presented or even worse may draw incorrect conclusions.

Rainbow Colour Palette

Rainbow Colour Palette

To make data widely understood, it needs to be presented in a way that makes it immediately clear what is being shown. This means that sometimes you need to focus only on the overall message, and sacrifice elements of the detail that allow the extraction of values, differences and trends.

Infographics is the on-trend term for the visual representation of complex data in a chart or graphic, so it’s quickly understood. There’s recently been an explosion of software, and websites, offering to create infographics for you. However, infographics aren’t new. A long running example is the London Underground Map; it isn’t a precise map of the tunnels, but it gives everyone the information they need to use the underground.

The key to a good infographic, and other graphs and charts, is keeping it simple. Focus on the information that you want to convey, rather than graphical embellishments. Edward Tufte argued in ‘The Visual Display of Quantitative Information’ that graphics should be assessed in terms of the data-to-ink ratio, such that the data should be presented with the least amount of ink.

Look at your figures and ask yourself whether the axis, grid lines, legends, numbers, borders or any other of the fancy bits in PowerPoint add anything to the image; or do they make it more confusing and less understandable?
Next time you have present, don’t just pull out the presentation you gave to the other conference last month and think it will do. Think about who is going to be listening to you? Will they understand the data as you’ve presented it? If you don’t think they will change it!

Scientists need to think about visualisation of data, as well as the raw data, if it’s going to be understood by more than those who created it. Data becomes information when it’s presented in a context that makes is useful. Always turn your data into information; your audience will thank you!

EO applications and the ESA Living Planet Symposium

Last week’s blog looked at developments in the technology providing Earth Observation (EO); however the industry is evolving and much more attention is now being paid to downstream activities. It’s no longer good enough to get a satellite to collect data, everyone has to think about how applications will, and can, use the data.

At the Living Planet Symposium there were presentations on the applications being developed from European Space Agency’s (ESA) CryoSat-2, which was launched in April 2010; it’s a replacement for Cryosat-1, which was lost due to a launch failure in 2005. CryoSat-2’s main focus is the monitoring of sea ice thickness in the polar oceans and ice sheets over Greenland and Antarctica. During its 3 years of full operation it has witnessed a continuing shrinkage of winter ice volume.

However, the on-board altimeter can also be used for many other applications, for example it doesn’t just acquire data over the polar regions. More interestingly the presenters also showed its potential for mapping coastal waters and inland water bodies with a spatial coverage that’s not possible from current low resolution altimeters.

Freshwater is a scarce resource, 97.5% of the earth’s water is saltwater, and given that almost three quarters of that freshwater is used in agriculture to grow food; the benefits of developing a method for remotely obtaining accurate river/lake water heights with frequent coverage are obvious.

No doubt there will be a variety of new applications developed using this freshwater data over the coming period. However, these applications need to have one eye on the next significant revolution in EO; data visualisation. It’s becoming vital that data is made available in a form that is understandable for non-scientists, and this will be the subject of next weeks blog!