The stacked Sankey arrows show “the relative contribution from each land use sector”. The origins of the nutrients are cattle for dairy, cattle for beef, mixed grazing, horses, and others. From statistical data on nutrient use efficiency, which ranged from 10 to 50 %, the researchers estimated the accumulation of phosphorus in the soil and streams, and the final delivery into the ocean.

The Sankey diagram does look kind of … errh, how should I say, …. “different”. But this is mainly due to the fact that flows that accumulate in a storage branch off to the side. The arrow magnitudes are actually to scale. To check this, add the horizontal flow to the storage and the vertical flow.

The full report is here, the Sankey diagram is shown on page 8.

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.

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