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: the first is a simple directed, weighted graph representing a candy factory:

Next, a pen-sketched b/w Sankey diagram of the candy factory…

… and finally 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.


UK Energy Flows 2007, by BERR, via The Oil Drum: Europe

A commentor to Chris Vernon’s original post added the Swiss version of this Sankey energy flow diagram originally published by Swiss Bundesamt für Energie (BFE):

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.

One type of Sankey diagram layout seems to get popular recently. A representation of national energy flows of a country with the energy carriers on the left side (source), and the consumption sectors on the right side (sink). The Sankey flows in between show how energy from these sources are consumed and in which sector. Wasted energy is shown, and the overall energy (in)efficient use of primary energy is made clear with such a Sankey diagram.

I just discovered the energy flow diagram for Spain for 2006 on Joan Vila’s blog.

Unfortunately I don’t speak Catalán (well, I learned that “blog” is “bloc” in Catalán!), and the image quality isn’t very good. You can see nuclear, natural gas, coal (“carbó”) and crude oil (“petroll”), as well as hydro an wind (the two green lines) on the left side. The top box on the right side that takes the big red Sankey arrow for losses from electricity generation (“pérdues”). The others are the use sectors transport, industry, and domestic / services / agriculture. Vila calculates an efficiency of 38,2% for the electric power generation.

Joan advocates Sankey diagrams for visualizing and being able to better understand the issue. He says, that you won’t understand many things about what’s going on, if you don’t study this [kind of] diagram (“No entendrem moltes coses sobre el que passa si no estudiem aquest diagrama.”).

Check out simiular diagrams for Japan, Scotland, Ireland, Canada, United States.