Sankey Diagrams

UK-based Stuart Brown at Modern Life (although the URL suggests it is about Modern Life Rubbish!) in his latest post (”The Varying Virtues of Site Performance Metrics”) uses a Sankey diagram to visualize web site performance. This is a rather novel idea of using Sankey diagrams, but hey, why not?

This nicely done Sankey diagram - in this case without any absolute or relative numbers - shows where web site visitors come from (input flows from the left side), and if their visit can be considered successful (that is, meeting the “goal” of the site operator) or not as output flows to the right side. Returning visitors are shown with a “browsing loop” in the Sankey diagram.

I really like this Sankey diagram and I would love to see web site metrics being visualized in this way. It really is a good visualization and can show how a website performs, although Brown acknowledges that “there simply isn’t any single great method of gauging a site’s performance”.

Coming back to the Sankey diagram itself, it does however have a small flaw. Look at the grey arrows for “Bounce” and “Non-goal visit”. The latter does not connect to the “Page Load” node, but rather seems to dive under the “Bounce” flow and appears where this one branches of vertically.

I have created two alternative Sankey diagrams where these two flows set off from the “Page Load” box parallel (stacked), rather than in an overlay manner. The overall quantity represented by the flows on the output side should be equal to the number of visitors on the input side. The first diagram keeps the original idea of the browsing loop coming in from the top, the second one hooks it on the left side of the box.

As for the colors of the two diagrams above, sorry Stuart, didn’t hit the right values right away…

Another field where Sankey diagrams are used widely is Material Flow Accounting, the analysis of material flows on a national or regional level. MFA focuses on bulk materials or individual substances (e.g. zinc, copper, cadmium) and the quantities in which they enter, leave or accumulate in a national economy.

The diagram below is from a peer-reviewed paper presented at the 4th LCA conference in Australia (van Beers, van Berkel, Graedel: The Application of Material Flow Analysis for the Evaluation of the Recovery Potential of Secondary Metals in Australia, 2005). It shows the copper flows within the system boundary of Australia, the unit is Gg/year (= 1000 metric tons per year).

This “clustered” Sankey has six different flow widths, grouping together flow quantities within a specific range (e.g. <10, 10 < 30,9, …). Flows larger than 999 Gg/year are not shown any wider. This avoids that very large quantities “spoil” the whole diagram, as smaller flows become less significant in Sankey diagrams to scale.

An alternative way to overcome the problem or very wide flows in a Sankey diagram spoiling the chart would be to define a cut-off quantity. Flows that are large than the cut-off quantity are excluded from the scale, and are shown with a hatch or moirée pattern. The two Sankey diagrams below were made based on the data from the above publication. The first one shows the large “Ore” flow with a cut-off level at 300 Gg/year (an additional note warns the reader that this flow is not to scale”, while the second diagram is fully to scale.

Very thin arrows additionally get explicit arrow heads to be able to identify their flow direction.

Feel free to comment

Mark Barrett, director of a UK-based energy consultancy, has developed several energy models.

The SEEScen model (Society, Energy and Environment Scenario model)…

…incorporates 11 energy end uses (motive power, lighting, heating etc.) across 15 sectors. Some of these end uses have physical models; for example, domestic space heating and cooling are estimated with a model of a house which allows the effects of parameters such as insulation and internal temperatures to be examined.

Sankey diagrams for several years have been put together to make a short “film” how energy requirements may change over the years, and what shifts might be expected between different ways of energy generation.

Here is a miniature preview of this animation.

To be able to see the details, download the Flash move or the GIF from the SEEScen webpage. Make sure you watch the film in the original size.

This is a neat idea, and it gives a whole new dimension to Sankey diagrams! On a side note: as far as I am informed, there are only two software tools capable of handling timelines in Sankey diagrams, S.DRAW and SankeyVis.

On my quest for more interesting Sankey diagrams I stumbled across a wykres Sankeya on a web page from Poland, which I reproduced here using ifu’s e!Sankey tool.

It shows the advantage of energy cogeneration plants over energy production in separate plants. From a base value of 100 a yield of 85% can be reached in cogeneration plants (35% electric energy, 50% heat energy - the original text accompanying the diagram says 30% electric energy, 55% heat energy) with 15% losses. To get the same energy amount from separate energy generation plants, the required energy feedstock is 1.48 times higher, with losses more than four times higher (63:15), especially originating from the generation of electricity.

While I am far from fostering one or the other technology with this post, I think this Sankey diagram merits special attention, because it is actually a 2-in-1 diagram (both with flow direction left-to-middle and right-to middle) and a baseline scenario comparison. A very nice idea!

I have decided to present in a loose sequence some diagrams I have found on the web that are obviously wrong. Or -let’s put it in other words- don’t reflect the numbers appropriately. Well, we all know that this happens quite often, and if you plan to do that purposely this book might be of use for you…

So, here is the first sample from an Estonian energy portal page:

I kind of like this Sankey diagram, because it is simple, colorful, and even though I don’t speak Eesti, I more or less get the meaning of it.

However, have a look at the gray flow labeled “Muu auru tarbimine” which supposedly represents 2% of the overall energy. Shouldn’t it be much thinner, compared to the other flows? I think this ‘not-to-scale’ representation is owed to the fact that in a diagram set up with a conventional drawing tool (is it Power Point they used?) would be very hard to draw and the label couldn’t be placed inside. So they decided to make it “small” but at the same time “lying” with this diagram.

It is also quite funky how the purple arrow for “Kaod” has an arrow line pretty much to scale, but the arrow head is much fatter!
Ah well, and the percentage values don’t add up to 100% and the percentage values for the green flows (”Pasöörid” and “Pihustuskuivatamine” - I love that word!) are percentiles of the yellow “Aur” flow in contrast to the other percent indications.

Here is the same Sankey diagram but with the values to scale, automatically created with a Sankey diagram software. I have adjusted the percentiles in accordance with the absolute values given.

Do you have an interesting Sankey diagram to share? Send it to phineas@sankey-diagrams.com

Researchers of the “energy flow” project at Weimar’s Bauhaus University have developed a Java applet to explore a Sankey energy diagram interactively.

We present a system that allows users to interactively explore complex flow scenarios represented as Sankey diagrams. Our system provides an overview of the flow graph and allows users to zoom in and explore details on demand. The support for quantitative flow tracing across the flow graph as well as representations at different levels of detail facilitate the understanding of complex flow situations.

The energy flow in a city serves as a sample scenario for our system. Different forms of energy are distributed within the city and they are transformed into heat, electricity, or other forms of energy. These processes are visualized and interactively explored. In addition our system can be used as a planning tool for the exploration of future scenarios by interactively manipulating different parameters in the energy flow network.

The Java-based online version (in German) allows the visitor to interactively explore the Sankey diagram. They can zoom in, move the nodes, or call additional data for individual layers.