Category: Samples

All the world in one diagram

This post on the Pinhead’s Progress blog makes my day (if not my whole weekend!). ptuft draws the attention to a slide presented by Wes Hermann from Stanford at the SciFoo 2007 conference. You can see the original photo on flickr and the presentation slides “Earth’s Exergy Resources – Energy Quality, Flow, and Accumulation in the Natural World” by Wes Hermann here.

Slide from a presentation by Wes Herman (uploaded to flickr by zippy)

While I am not yet sure if this qualifies fully as a Sankey diagram, I find it really really fascinating! The diagram is titled “Exergy flux, accumulation, destruction, and use” and shows “where all the energy on the earth comes from, where it gets stored, and where it goes”. It distinguishes by colors the following exergy resources: Thermal, Nuclear, Radiation, Gravitational, Kinetic, Chemical.

The diagram type could be called a hybrid Sankey-Grassmann diagrams (see this post). The upper part is where radiation exergy is shown: 162000 TW of solar radiation and another 62500 TW of extra-solar radiation arriving on planet earth, being lost through atmospheric absorption, evaporation and surface heating. The green part (Chemical exergy) is what we focus on when we talk about energy consumption today. Hermann calls it “exergy destruction for energy services” (measured in ZJ). Accumulated exergy is shown with elliptic pouches on the arrow. Nuclear exergy features in the diagram as “bubbles”, most of it not accessible for human use as energy. One can find many other interesting details in this diagram.

I am tempted to challenge my e!Sankey tonight to see if I can draw this. Two different units (in this case TW and ZJ) can be displayed in one diagram. Biggest visualization issue will certainly be to handle the large differences in scale. Let’s see if I find the time, or if I prefer to enjoy radiation exergy of the summer sun at the poolside instead…

Using Sankey diagrams for visualizing web site performance

UK-based Stuart Brown at Modern Life 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.


Alternative version:

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

Guilty of Sankey Abuse?

The majority of Sankey diagrams I have come across so far show energy flow systems (see this post or this one) and material flow systems (my last post or this one). To a lesser extent the examples found on the web show flows of materials in process systems (e.g. a plant).

To show the number of people that have been accused of abuse of detainees in a Sankey diagram is a novel idea. The example below, originally published by the New York Times (and posted by Derek Cotter on Edward Tufte’s board ‘Ask E.T.’) features the distribution of the 600 cases and what the different outcomes were.

Diagram from N.Y. Times

The poster of the comment does criticize the inadequate diagram and says that “it might as well have been a pie chart instead”, however, the use of a Sankey diagram does give a kind of time line or at least a line of the decisions taken in the juridical system.

Choosing gray as the color rather than making it a colorful Sankey does reflect the topic adequately, I think.

Guilty of Sankey abuse? Or acquitted?

Lying with Sankey diagrams (2)

The below Sankey diagram of the ‘Material Flows of Japan in the FY 2000’ has been published by the Japanese Ministry of Environment (環境大臣) and has been reproduced in a number of publications and presentations (sample PPT). Similar charts, representing the inputs into the Japanese economy and the outputs are available for subsequent years.

When I copied the values of the Sankey diagram and re-designed it (see pic 1 below), it quickly became obvious that the inputs (2130 Mio. tons) don’t match the Outputs (2386 Mio. tons). After some research I finally detected the reason for the mismatch in a footnote to the diagram in a press release by the ministry. It said that, “due to intake of moisture, etc., total output shall be larger than total material input.” This footnote might have been dropped unintentionally when using the diagram in other publications. I wouldn’t really call this “lying” (as the title of the post implies), but maybe negligence. I wonder if anyboy doubted the numbers when looking at the diagram?

In the second diagram below I adjusted this difference of 256 Mio. tons on the input side.


Another rather surprising thing in this Sankey diagram is the fact that the domestic food consumption within Japan (127 Mio. tons/year in 2000) was almost as high as the total quantity of material being exported (132 Mio. tons). Taking into account, for example, the number of cars being exported from Japan, and their weight, this sounds a little unlikely. However, I think that many of the produced goods might be hidden in the “Net Addition to Stock”.

And for the readers who study Japanese … Sankey diagram : サンキーダイアグラム

Sankey Diagrams in Material Flow Accounting

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

U.S. Freshwater Withdrawals in 2000

I had bookmarked a number of Sankey diagrams a while ago when visiting the website of Lawrence Livermore National Laboratory. These diagrams on energy, CO2 and freshwater are a great source of information. You can, for example, find the typical energy Sankey diagrams (like the one in my previous post) for the U.S. all the way back to 1950, 1960 and 1970 and then from 1973 to today.

Summer is coming closer, and we can again expect water shortage in some states. So the Sankey diagram I have selected for presentation today (original PDF), is for freshwater withdrawals in the year 2000.

The overall extraction was 345.000 Mgal/day (roughly 1.3 bio litres per day) with approximately 75 % from surface water and 25 % from ground water. Another 62.300 Mgal/day of saline water is withdrawn for thermoelectric use.

The largest portion of the water is for irrigation, livestock and aquaculture, closely followed by the water used in thermoelectric power generation. Domestic self-supply is a comparatively marginal 3,590 Mgal/day (1,04 %), which makes my Mom’s call to “close the tap” sound somewhat ridiculous.

A Sankey for Energy Generation in the U.S.

Joshua Rosenau over at scienceblogs took up on the energy topic in his ‘Thoughts from Kansas‘ and presents a Sankey diagram for the U.S. energy distribution (The Problem of Energy Generation) from an article in Science (Whitesides and Crabtree: Don’t Forget Long-Term Fundamental Research in Energy, Science 9 February 2007:Vol. 315. no. 5813, 796-798). It shows that more than 55% of the energy produced is lost, mainly in transmission and distribution on the grid (approx 25%) and another 30% in transport-related combustion of petrol [Note to self: do a Sankey diagram comparison for 1911 race car and modern light vehicle].

“…over half of the energy produced for our domestic market goes to waste. Fully two thirds of the energy produced by electrical generation and distribution goes to waste.”

This Sankey diagram shows the energy carriers on the left side, the sectors where energy is consumed (noteworthy: traffic has a larger share than industry) as midpoint groups, and a breakdown to useful and lost energy on the right.