Sankey Diagrams

I was pointed to an article on carbon footprint, that used Sankey diagrams to underline a method of carbon accounting along the supply chain. This article was part of the “first virtual global conference on climate change” CLIMATE 2008 that took place, yes, exclusively on the Internet from November 3 to 7, 2008. (I must admit that this event passed largely unnoticed by me, although reading some of the papers now gives me the impression that it would have merited more attention.)

The paper titled “Carbon Accounting and Carbon Footprint - more than just diced results?” by Prof. Mario Schmidt from Pforzheim University describes the various approaches of corporate carbon accounting, carbon footprint of products, and Life Cycle Assessment LCA. Schmidt introduces a method that allows determining “cumulative emissions … at each point of the supply chain up to the POS”, and calls this the CO2 backpack.

The four Sankey diagrams above from the article illustrate the idea. They show (1) the CO2 equivalent emisisons along the supply chain, (2) the value added in a supply chain, (3) the relative CO2 emissions per value of product, and (4) the total emissions of the products along the supply chain with sectoral gate-to-gate, cradle-to-gate or crade-to-grave approaches.

This article is well worth reading, you should do so while it is still available online.
Schmidt is an acclaimed expert in Sankey diagrams and has also published on the history and methodology of Sankey diagrams.

Came across densitydesign’s images on flickr and was really fascinated by the visualizations presented there.

Density Design is a research framework and an experimental laboratory, born as a laboratory course in the final year of the Master Degree Course in Communication Design at the Politecnico di Milano.

One of their recent projects was on social conditions and poverty in Italy. Some of the visualizations that were created in the course of this project resemble Sankey diagrams, and this is why I thought I should share them with you.

The designers had several dimensions of information they wanted to put into the visualization of statistical data on poverty in Italy. The four shown above chose bands of proportional widths to display the numbers rather than pie charts. In contrast to Sankey diagrams these are not flows, because they are not directed. The works by Luca Rossi (2nd above) and Elena Capolongo (4th above, my personal favourite) try to link the quantities to regions using a map of Italy.

A nice followup project would be to display the migration movements from Southern Italy to the North and abroad due to the social conditions, as previously reported about here.

Density Design has kindly granted permission to show these visualizations here. Read the summary (Project progress report 01. Economic statistic & Communication Design) and learn about their other projects on the Density Design blog. I am adding them to the blogroll too.

Found this Sankey-like diagram accompanying an abstract submitted for the 2001 International Conference on Thermal Engineering and Thermogrammetry. Posting it here on the blog before this site eventually vanishes. This Sankey diagram is a good example of how not to draw Sankey diagrams, I think. Or, as a Japanese friend would put it politely: “Maybe… [turn head at 30° degree angle, make slight air-sucking noise by inhaling through open mouth] … maybe not so good”.

Here’s the diagram:

The idea was to display heat losses at a slab furnace in a Turkish steel plant. Heat losses were identified in exhaust gases (22 %), at the cooling pipes (2.90 %), and at the furnace walls (0.47 %).

The fact that the widths of the arrows displaying the heat losses were chosen arbitrarily give a completely wrong idea of the proportions. The powerpointish curved arrows don’t really contribute to a better understanding.

All in all, not a very good one. Adding this to my “Lying with Sankey diagrams” mini series (see part 1, part 2), which has been neglected recently.

Never thought that Sankey diagrams would inspire artwork, but here you go.

Whitey Flagg (check out the cool ASCII navigation on the front page, based on the NYC subway map!) uses satellite images, maps, info graphics, and the like as a model for his oil on canvas or acrylic paintings.

Here are some Sankey diagram artwork samples: The first is called “Energy Flow” (60.5” x 60”), the second “Water Flow” (42” x 75”), the last one “Carbon Emissions” (64” x 80”).

All artwork is available for sale, so if you want to enjoy a real oil Sankey diagram, and have an appartment big enough to hang it, you can contact the artist. Also, check out the other paintings on his website.

The Virginia Center for Coal and Energy Research at Virgina Tech has a website on Virgina Energy Patterns and Trends (VETP).

This summary page on natural gas features a Sankey diagram for natural gas flows in Virginia in 2005.

Flows are in million cubic feet. Note that the division line between dry gas production (88.610 million cubic feet) and interstate imports (1.114.460 million cubic feet) overemphasizes VA’s own production. Also the magnitude of the “consumption” flow and “interstate exports” are not to scale, probably owed to the desire of the designer to be able to split up the consumption arrow into separate arrows. The transportation arrow is exaggerated, and would only be a thin line if to scale.

On the VETP summary page for coal, there is another interesting Sankey, also for 2005.

The second one also has some pecularities: The Sankey arrows for imports (15.764 thousand short tons) and exports (21.288 thousand short tons) of coal are not to scale, neither are the losses/unaccounted coal flows 4.951 thousand short tons.

Reminder to self: If I find the time I’ll do these two diagrams properly and to scale.

For those of you interested in some of the maths behind drawing Sankey diagrams properly, you might want to read this article on ‘Programmatic Rendering of Directed, Weighted Graphs’ submitted for SVG Open 2003 by Philip A. Mansfield and Mark Ambachtsheer of SchemaSoft.

The authors consider Sankey diagrams as directed weighted graphs but they “can be difficult, time-consuming, and uninteresting to render by hand”. However, “Sankey diagrams do add an indisputable expressive power to a standard mathematical rendering of a graph…[and] when professionally constructed, Sankey diagrams represent flow in a manner … can be understood by anyone, instantly.”

Three diagrams are presented: a simple directed, weighted graph representing a candy factory, a pen-sketched B/W Sankey diagram, and the corresponding Sankey diagram in SVG format, created using data in XML format and XSLT style sheet transformation.

They also have some interesting details on graphical problems, such as overlay, edge layout, width of Sankey arrows in curves, etc. Basically all that stuff that developers of professional Sankey software tools have to cope with.

Most of the Sankey diagrams I come across on the net focus on energy issues, followed by the topics greenhouse gases and material flows of different kinds. Display of cost Sankey diagrams (value streams) is less common, so are people/passenger flows. An interesting approach is presented with Sankey diagrams that show migration flows between countries, or in and out of a region.

The best one I have seen was in this summary report on ‘Europe’s Demographic Future’ published by Berlin Institute for Population and Development. On page 11 you can see the migration flows within Europe (with omissions). The widest Sankey arrows are for migration movements from Bulgaria and Romania, mainly to Spain. There seems to be a lower cut off threshold at approx. 10.000, which leads to smaller flows not being scaled linearly any more. A lot of interesting details in this one… [would have loved to reproduce it, but permission wasn't granted].

Here are other samples for Sankey diagrams visualizing migration flows (no quantities given, exact time range unknown).

Emigration flows to North and South America in the first half of the 20th century

Refugee flows in Middle East, Africa and Asia in 2006 (clustered quantities)

Both diagrams found on My Paris Your Paris blog

I think Sankey diagrams in this context merit more attention. Will be looking for more of these…

A followup to my last post: This thread on ‘The Oil Drum: Europe’ features similar national energy flow diagrams for UK (2007), The Netherlands (2006) and Switzerland (2007).

For the UK these Sankey diagrams are published by BERR (Department for Business, Enterprise and Regulation). Historic charts back to 1974 can be found on their website.

A commentor to Chirs Vernon’s original post added the Swiss version of this Sankey energy flow diagram:

These Sankey diagrams have some nice details, which a worth a mentioning: The UK diagram shows stock increases and decreases with circles. The size of the circle has no significance, but the magnitude of the in and out flows seem to be to scale, thus allowing to see if the stock has increased or decreased in that year. Losses at transformation steps are shown with “hanging arrows” (the flows branching off to the bottom line of the diagram). The Swiss version also shows exports this way, but visualizes losses with a pin with a big round head.

Even though your run the risk of being overwhelmed by a gloomy feeling when your read through the comments to Chris Vernon’ post, I would like to draw your attention to a comment by “realist” on Sept 5. He writes: “Deceptive graph! Why show losses for electric power generation and not transportation? The heat losses from the internal combustion engine in most transport is 70-80%”. This is true, but I have always understood that losses explicitly shown in these energy flow Sankey diagrams are the losses occuring in the energy generation, conversion and grid, while losses in the energy consumption (such as use for transport) are not shown. This let alone that they are worthwile to discuss.