Sankey Diagrams

Just came across this video featuring a “Sankey diagram of the Taiwan economy, jobs and energy in 2010″ by ARUP (uploaded to vimeo by user Simon Roberts).

The underlying model is called “4see-TW” framework and has been created to “investigate the structure and function of an economy in a resource-constrained world”.

This is certainly exciting… howevever one must be warned that the Sankey diagram includes different “dimensions”: energy flows, value streams (money flows) and jobs. These three perspectives probably have different unit types and units (such as, e.g. TJ for energy, Euro or US$ or New Taiwan Dollar TWD for values, and persons or workplaces for jobs). Hence the width of the Sankey arrows mustn’t be compared to each other across the unit types.

Haven’t found the time yet to dig more into the 4see-TW model, but here is one starting point for those interested.

A great post on Sankey diagrams at the visualign blog led me to Sam Calisch’s PDF at github. It contains some insight on the maths behind the drawing of Sankey diagram curves, especially the type known as spaghetti diagram or distribution Sankey diagram (see discussion here).

There are some great scribbles in this paper that I wanted to share.

And I especially like this one, with the little man using the Sankey arrow as a slide…

The article is well-worth reading, so if you are into programming a Sankey software (the Mathematica workbook for Sankey might be a starting point), please download and study it.

Visited YouTube again and found this video on ‘Basic Sankey Diagrams’ … enjoy!

Typically it is quite difficult (read: expensive) to get hold of official ISO standards. It is by chance that I discovered the draft version of ISO 13579-1 on ‘Industrial furnaces and associated processing equipment — Method of measuring energy balance and calculating efficiency — Part 1: General methodology’ on the website of AFNOR, the French body of standards. The draft is open for comments as part of a public hearing process.

The draft standard ISO 13579-1 talks about energy balance (‘bilan énergétique’). Part 4.2 shows a sample Sankey diagram and explains that this is a tool that allows to represent the in and out flows of energy (‘outil permettant de représenter le flux d’entrée et de sortie de l’énergie’). In section 9 f on reporting the draft standard recommends that the report shall include a Sankey diagram (‘Il convient que le rapport de mesure du bilan énergétique contienne … Diagrammes de Sankey.’).

Didn’t have the original English version at hand, so I hope this is pretty much what it says in French.

Anyone aware of other ISO standards that mention Sankey diagrams?

Two Sankey-style diagramming tools which I have shamefully neglected until today are ParSets and Fineo. Both visualization tools have been released to the public in 2009 (first publication on ParSets in a research paper in 2006, predecessor project of Fineo, the Design Research Map project first mentioned in 2008). The main idea behind both tools is to visualize statistical data by grouping it into categories and showing bands/streams/parallelograms between the categories to represent the relationships between the categories.

ParSets and Fineo have similarities and differences. But before we go into details, let’s have a look at both tools first. Here is a screenshot from ParSets:

And here is one from Fineo:

ParSets was developed by Robert Kosara (Department of Computer Science, College of Computing and Informatics, University of North Carolina at Charlotte) and Caroline Ziemkiewicz (Brown University). The tool is open source and runs on Mac and Windows platforms. Read more about ParSets on the project page on Robert’s EagerEyes blog. The project had some funding from the U.S. Department of Homeland Security, and the tool is designed to work on census data or other statistical data.

Fineo was developed by the DensityDesign group, a Research Lab in the design department (INDACO) of the Politecnico di Milano in Italy. This is an online tool and can be used by uploading csv data files. Try the online version here, or visit the project page on the Density Design blog. This is a self-sponsored project, targeting at designers and infographers.

There are some differences in the layout and design. ParSets shows the link between categories as parallelograms, while Fineo has curved bands. The main orientation of the diagram is top-to-bottom in ParSets, and left-to-right in Fineo. Hence the nodes (representing categories) are thin horizontal lines in ParSets, and vertical black bars in Fineo. Not sure, but this is probably an option setting.

The main difference though seems to be that ParSets keeps track of subdivisions over neighbouring categories. Fineo looks more at pairs of categories (category – relation – category) and is according to the authors more inspired by this feature of Sankey diagrams (read here). On a side note I would like to add to this that both ParSets and Fineo lack one important of characteristic of Sankey diagrams, which differentiates them from Sankey diagrams: flow direction, or, in other words, a ‘from-to’ relationship. “Both of the visualizations are weighted bipartite graphs”, but not directed graphs.

Still, both tools are very good pieces of work, and I am looking forward to seeing updates in the future.

I found the idea behind the below Sankey diagrams quite compelling. Both are from the user manual of the ‘Umberto for Carbon Footprint’ software by ifu Hamburg. They are also the makers of e!Sankey, and it seems as if most of the e!Sankey software features are also included in this new software for modeling and calculating product carbon footprints.

I played with the demo models included in the trial version, one of which is for a toy parrot. The product life cycle is modeled from cradle-to-grave with the raw materials, assembly, distribution, use, and end-of-life phases. Using embodied carbon data from an LCI database for the raw materials and energy used along the life-cycle, a carbon footprint is calculated. The material and energy flows related to the product manufacturing and use are then shown as a Sankey diagram.

The Sankey view can be switched to an ‘embodied carbon’ or carbon load view, which shows the ‘carbon rucksack’ of the product as it cumulates along the supply chain.

In this second Sankey diagram the arrows representing the greenhouse gas burdens caused by the waste disposal phase are turned around, so that both the upstream supply chain as well as the downstream processing after the product use are visually added. They form one large Sankey arrow (shown in green here) for the product’s carbon footprint.

This is of course not a Sankey diagram drawing software, but rather a modeling or calcalation tool for carbon footprints. Still, I think, this is a fine use case where Sankey diagrams unfold their full visualization power. It can be immediately grasped which stage of the life cycle, or which raw material or energy supply contributes most to the carbon footprint.

Note: Have added this to the software list.

The below Sankey diagram from the JS Systems homepage tries to show the differences between a normal Otto engine and the “JS Motor”. The prototype JS rotation motor, from what I grasp, has different compression and expansion parameters and could prove to be twice as efficient.

To show the difference in efficiency, two Sankey diagrams have been superimposed. The diagram with the grey outline is for the Otto engine, the one with the red outline is for the JS engine. The diagram shows energy losses branching off to the right (e.g. thermodynamic losses 17% in a typical Otto engine, 13% only in the JS motor). Useful energy is represented by the flow to the top.

I am not endorsing this motor, nor have I seen it work. But I like the idea of presenting a comparison in one Sankey diagram instead of two separate Sankey diagrams.

Also, please check out this previous blog post on Sankey diagram overlay.

I have been presenting “bad examples” of Sankey diagram before (like this one, or this one), and I have a few more in my collection.
The following one from an PowerPoint presentation by someone from PennState. The topic of the presentation is actually quite interesting: thermoacoustic refrigeration – using sound waves for cooling. It describes the results of a research project.

Unfortunately, this Sankey diagram has some shortfalls, which qualify it as being a “bad example”. These are:

• Sankey arrow widths are not always to scale (see for example the flow of 7.6 W in the middle labelled “surface”, which is definitely not half the width of the 14.6 W flow marked “Joule loss”)
• Arrows branching out of the main flow are shown as short stubs, just as if the quantity is represented by the length (!) of the arrow, rather than its width. A completely new concept for Sankey diagrams. Have a look at the 0.9 W mini-stub “Surface” in the cone area, and at the 1.2 W stub “Surface” in the linear motor box.
• The diagram uses dotted-dashed frames to mark sections in the diagram, at the same time it uses white arrows with a simple border line for the Sankey arrows. Either colored or grey areas, or colored Sankey arrows would have helped enormously.
• Arrows branch off orthogonally, and to accomadate for the reduced quantity in the remaining flow, the border of the arrow on the opposite side curves in. This is not wrong as such, but rather uncommon, and can best be observed in the linear motor section at the left. Same phenomenon for arrows joining the main arrow. The arrow heads just overlap rather than actually joining the other arrow graphically. The receiveing arrow bulges out on the other side.
• The section between the exhaust heat exchanger and the regenerator is awkward, and probably wrong. How can you branch off 296.6 W and 5.8 from a stream of 320.5 W, and are still able to have a flow of 63.0 W lead away from the remaining flow. I have not yet figured out what the problem is, but possibly the “Carnot minimum” flow was supposed to be drawn the other way round.

When I get to figure out the last issue I might draw this Sankey diagram myself, and post it here.