Those of you who have already created Sankey diagrams might have come across the issue: As long as the flow data you are about to visualize is more or less in the same value range everything is fine, and there should be no problem in coming up with an nice Sankey diagram. However, sometimes we have very small flow quantities, while at the same time there are some large flows dominating the picture.

Sticking to the “golden rule” of Sankey diagrams (i.e. the width of the Sankey arrow corresponds to the flow quantity represented) and ensuring the proportionality of flows in relation to each other becomes very difficult. If you opt to show the larger flows at “normal” width, the smaller flows become difficult to perceive and are shown as hairlines (sometimes even invisible on a screen or in print). If, on the other hand, you decide to push up the scaling factor so that these smaller flow quantities can be seen in the diagram, then the large flows are really fat and spoil your diagram.

This seems to be an irresolvable issue… Nevertheless, there are some approaches to tackle this. Most of them resort to taking out the tiny flows or the very large flows of being to scale used in the Sankey diagram. You may opt to use a minimum width (e.g. 1 or 2 pixels) for arrows that carry only a small flow quantity, or you may decide to set an upper flow threshold, corresponding to a maximum width for the Sankey arrow, independent of the actual flow quantity (beyond the threshold value). In both cases I would strongly recommend to denote this decision in the diagram (e.g. in a footnote), since otherwise the person looking at the Sankey diagram will get a wrong idea of the quantities/proportions.

The Sankey diagram from the PROSUM report I recently featured in this post has another, quite unique solution. Here is a zoomed cropped section:

The metals in the end-of-life vehicle (ELV) stream of 8 million tons (in 2016) are mainly aluminium, copper and iron. This stream is on the same scale as the overall Sankey diagram (see full diagram here). However, the other metals in the stream (such as gold, silver or platinum) are contained in comparatively much smaller amounts. The authors of the Sankey diagram hence opted to emphasize them by switching to another scale (1:5.000). As a result the arrow representing the flow of approximately 660 tons of critical raw materials (CRMs) is almost a wide as the arrow that shows 6780 ktons!

The fact that the precious metal stream is highlighted and not to scale with the rest of the flows in the diagram is clearly signalled with a note, a dotted line that separates this diagram area, and even an exclamation mark symbol.

Since CRMs were the focus of the PROSUM study I think such a “trick” is justified. What are your experiences with flows on different scales? How would you handle this “dimension challenge” in a Sankey diagram? Let me know your ideas!

Up on the EUR-Lex, the European Union’s database on laws, regulations, publications and reports is a staff working paper ‘Measuring progress towards circular economy in the European Union – Key indicators for a monitoring framework’ meant as accompanying background text for a ‘Communication from the Commission to the European Parliament, the Council, the European Economic and Social Committee and the Committee of the Regions on a monitoring framework for the circular economy’.

And it shows this beautiful Sankey diagram on material flows in the EU economy (2014).

Beautifully crafted, this diagram shows that “8 billion tonnes of raw materials were processed during 2014 in the EU: of this 1.5 billion (i.e. around 20%) are imported, which indicates the EU dependency on imports of materials. Out of the 8 billion tonnes of processed materials, 3.1 billion tonnes are directed to energetic use, 4.2 to material use and 0.6 are not used in the EU but exported.”

Flows are in Gt/yr (billion tons per year. The composition of the flows is presented at certain points in the diagram as bar charts on top of the dark blue bands: metal ores, non-metallic minerals, fossil energy materials/carriers and biomass. For each of those four groups individual Sankey diagrams can also be found in the working paper.

The EU never stops to surprise me! In this case in a positive way, as Sankey diagrams seem to have arrived at the top echelons of European policy making (or at least with their staff).

Javier Dufuor on the madrid+d Energía y Sostenibilidad blog reports about a novel lignocellulose biorefinery process developed by Prof. James A. Dumesic at the University of Wisconsin-Madison. This so-called TriVersa process can yield up to 80% of biomass from birch wood as marketable products.

The Sankey diagram for the TriVersa process shows carbon in biomass flows. Values are in percent, starting with the 100% C molecules in birch wood being used as feedstock.

An interesting detail about this Sankey diagram is that it additionally uses the process “nodes” or “boxes” to indicate operating cost and annualized capital cost. No numbers are given here, but the height of the process box indicates the overall cost (in a kind of stacked bar chart).

Another example for a Sankey diagram on a map from an article ‘Exergoecology Assessment of Mineral Exports from Latin America: Beyond a Tonnage Perspective’ by Jose-Luis Palacios (Escuela Politécnica Nacional, Quito, Ecuador) et al. published in Sustainability 2018, 10(3), 723 as open access article distributed under Creative Commons Attribution (CC BY) license.

I had not heard of the term ‘exergoecology’ before:

Exergoecology is the application of the exergy analysis in the evaluation of natural fluxes and resources on earth. The consumption of natural resources implies destruction of organized systems and dispersion, which is in fact generation of entropy or exergy destruction. This is why the exergy analysis can describe perfectly the degradation of natural capital.
The thermodynamic value of a natural resource could be defined as the minimum work (exergy) needed to produce it with a specific composition and concentration…
(Source: Exergoecology Portal)

The authors of the article argue that the Material Flow Analysis (MFA) approach should be combined with a measure for the thermodynamic quality of minerals, “especially when dealing with non-fuel minerals”. They propose to use the indicator exergy replacement costs (ERC) from exergoecology because it “considers the scarcity degree of the commodities in the crust and the energy required to extract them. When a mineral is scarcer and its extraction and beneficiation processes are more difficult, its ERC value becomes higher”.

These two sets of Sankey diagrams visualize this approach:

The two Sankey diagrams on the left are for Chile, the two on the right for Mexico.

The figure at the top is a common mass-based figure, showing minerals production, imports, domestic consumption and exports for certain minerals. The unit of measure is million tonnes per year (in 2013).

The one at the bottom shows exergy replacement costs (ERC) measured in million tonnes of oil equivalent (Mtoe). For each mineral an energy indicator in GJ per tonne of element has been applied, representing the work (energy) to extract the mineral.

In the case of Chile we can see for example that iron, copper and salt are the minerals mined in largest quantities (mass-wise). However, iron and salt only make up a small fraction of ERC, while copper and potash dominate the picture. In other words: Potash has a high exergy replacement cost to produce given the work effort required to mine it and in face of its scarcity. Copper comes in second.

For Mexico the figure a the top and below look pretty similar in regard to the proportions of each of the colored flows. One could say that the minerals are similarly difficult or expensive to extract. Coal (yellow band) is comparatively wider in the mass flow diagram than in the exergy replacement costs diagram, so it is “cheaper” in regard to exergy cost to be mined.

Many more interesting details to discover and the article is well worth reading. In my oponion a fascinating blend of two approaches and a great use for Sankey diagrams.

This Sankey diagram visualizing the energy balance for the French island Réunion has already been published back in 2010 in an article on reliability of supply in future power systems. (Mathilde Drouineau, Nadia Maïzi, Vincent Mazauric, Edi Assoumou. Long term planning tools and reliability needs: focusing on the Reunion Island. 3rd IAEE Rio 2010 International Conference “The Future of Energy: Global Challenges, Diverse Solutions”, Jun 2010, Rio de Janeiro, Brazil. 14 p., 2010). Access article here.

The flows are in Mtoe for the year 2007. The authors have been using the Markal/TIMES models to obtain data and study alternatives for future energy scenarios for the Réunion Island.

The EU funded PROSUM research project looks at ‘Prospecting Secondary raw materials in the Urban mine and Mining wastes’. The more than 15 institutions participating in the project have recently published their findings in a final report.

The report has some interesting Sankey diagrams on market input, stocks, waste generation and waste flows for product groups such as vehicles, batteries, precious materials and selected critical raw materials (CRMs) contained in batteries, electrical and electronic equipment (EEE) and vehicles.

Here is the diagram for vehicles in the EU28+2 (=EU28 plus Switzerland and Norway) market. Data relates to the year 2015.

Flows are in tons and ktons, blending two scales in one diagram. This merits its own post, I think. (read it here)

The electric vehicles currently driving on the roads are shown as “Stock”, meaning that the materials are in use and that they could eventually be recovered at the end of the life of the vehicle. This is the large stackd bar between “POM” (placed on market) and “De-reg Vehicles”. Again this stacked bar uses two different scales (tons and ktons).

Official report citation: Jaco Huisman, Pascal Leroy, François Tertre, Maria Ljunggren Söderman, Perrine Chancerel, Daniel Cassard, Amund N. Løvik, Patrick Wäger, Duncan Kushnir, Vera Susanne Rotter, Paul Mählitz, Lucía Herreras, Johanna Emmerich, Anders Hallberg, Hina Habib, Michelle Wagner, Sarah Downes. Prospecting Secondary Raw Materials in the Urban Mine and mining wastes (ProSUM) – Final Report, ISBN: 978-92-808-9060-0 (print), 978-92-808-9061-7 (electronic), December 21, 2017, Brussels, Belgium

Ann Arbor based consulting firm RRS has published a Sankey diagam visualization of the plastic streams in the United States. This is from their Data Corner blog.

Breakdown is in percentage values only. The amount of 8,300 MMT seems to be an aggregated figure for a 65 year period from 1950 to 2015. And 80% has ended up on landfills.

Original data is from a study ‘Production, Use, and Fate of All Plastics Ever Made’ authored by Roland Geyer of the University of California, Santa Barbara; Jenna Jambeck of the University of Georgia; and Kara Law from the Sea Education Association.

What would daily life in a ‘zero carbon’ Great Britain look like? Since 2007 the Zero Carbon Britain (ZCB) project of the Centre for Alternative Technology (CAT) has worked to “offer the hard data and confidence required for visualising a future where we have risen to the demands of climate science; to remove fear and misunderstandings and open new positive, solution-focused conversations.”

They have presented a Sankey diagram for the energy landscape in the UK, the way it could look like if Britain’s energy production was actually carbon free and 100% renewable energy.

via Open Energy Monitor blog, original image here (under CC BY-NC 2.0 license)

Flows are in TWh/year. The largest energy sources are wind and biomass. Some of the electricity is used to produce synthetic gas, synthetic liquid fuels and hydrogen (used mainly in the transportation sector). In that scenario there is even an electricity surplus that can be exported.

While I can not judge how realistic such a vision of the UK energy landscape is, I can at least say it is very different from the current situation (see here or here), and even from this UK 2050 energy scenario.