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Sankey Flow Map

Flow diagram — instantiates Conserved Reservoir-Flux Balancing

Draws the whole flow network as ribbons whose width is proportional to quantity, so you see at a glance where a conserved flow concentrates, splits, and disappears.

The Sankey Flow Map turns a conserved quantity's journey into a picture in which magnitude is the visual variable: every channel is a ribbon whose width is proportional to how much flows through it, sources arrayed on one side and sinks on the other. Because conservation must hold at each node — the ribbons entering equal the ribbons leaving — the diagram enforces the balance visually, and any un-balanced node has to be drawn with an explicit loss ribbon. What makes it this mechanism, rather than the Stock-and-Flow Diagram, is that the diagram shows how much goes where, not the causal structure or feedback behind it. The eye lands on the thickest ribbon and the biggest loss node without reading a single number, which is exactly what makes it the fastest way to find where a flow really goes.

Example

A regional energy agency draws a year of energy as a Sankey. On the left, primary sources — coal, gas, nuclear, hydro, wind, solar — enter as ribbons sized by the energy they supply. They flow into conversion and end-use sectors: electricity generation, transport, industry, buildings. On the right the flows split into two destinations: energy services actually delivered, and rejected energy lost as waste heat.

The picture is blunt in a way a table never is: the grey ribbon of rejected energy is fatter than the ribbon of useful services — roughly two-thirds of the primary energy never does useful work, most of it lost in thermal generation and in vehicle engines. A viewer sees instantly that the largest lever is not adding supply on the left but attacking conversion losses in the middle. This is precisely the story the Lawrence Livermore National Laboratory energy flow charts tell each year, and it is the Sankey's whole gift: the biggest loss is the widest ribbon, impossible to miss.

How it works

  • Nodes are reservoirs or processes; ribbons are channels. Each ribbon's width is scaled to the flow it carries over the period.
  • Conservation is drawn, not assumed. At every node the widths in must equal the widths out; a node that "loses" quantity gets an explicit loss ribbon rather than a silent shrinkage.
  • Layout carries the topology. Sources left, sinks right, splits and merges in between — the arrangement itself reveals where flow concentrates.
  • Magnitude does the talking. The distinctive move is encoding quantity as width, so the largest flows and losses are found by eye.

Tuning parameters

  • Node granularity — a few fat ribbons or many thin ones; aggregation clarifies the headline flows but hides the small leaks, disaggregation does the reverse.
  • Flow threshold — the minimum width worth drawing; hiding trickles declutters but can bury a diffuse loss spread across many small channels.
  • Boundary and period — an instantaneous snapshot versus an annualised total; the frame decides which flows even appear.
  • Loss visibility — whether losses and leakage get their own ribbons or quietly vanish; the honesty dial of the diagram.
  • Ordering and layout — how nodes are placed to minimise crossings and make the intended story legible.

When it helps, and when it misleads

Its strength is communication: it shows where a conserved quantity concentrates and where the large losses hide, and it does so fast enough to align a room around the fattest target in seconds.

Its limits are those of a snapshot. It carries no dynamics, no feedback, no time — it says where the quantity went, never why or what happens next. And a beautiful Sankey whose widths are not actually conserved is decoration masquerading as accounting; the classic misuse is drawing it to persuade — thinning an embarrassing ribbon, omitting the loss node — so the picture flatters a decision. The discipline that keeps it honest is to source every ribbon from a closed Mass-Balance Table, so the widths genuinely sum, and to always draw the loss channel rather than letting the missing quantity leave the frame unremarked.[1]

How it implements the components

The Sankey Flow Map realises the archetype's visualisation-and-topology surface — the components a magnitude-proportional diagram produces:

  • flux_channel_definition — every ribbon names and sizes a transfer channel between reservoirs; the channels are the diagram's substance.
  • topology_map — the arrangement of nodes and channels is the network topology made visible, showing how the reservoirs connect.

It does NOT measure or reconcile the flows it draws — that's the Mass-Balance Table — nor capture the conserved quantity's stocks and feedback structure — that's the Stock-and-Flow Diagram — nor simulate change over time — that's the System Dynamics Simulation.

References

[1] The diagram is named for Captain Matthew H. P. R. Sankey, who in 1898 drew the energy flows of a steam engine as width-proportional bands to expose where its energy was wasted — conservation-of-flow visualisation from its very origin. ↩