Inverse topography—conduits, energy and stasis

Central Otago river networks

Stream order diagrams are simultaneously beautiful and illuminating. Subtle line width variations form pleasing dendritic patterns that suggest how water moves across a diverse landscape. The technique represents river networks as a hierarchy of segments, weighting downstream stretches of water more heavily than upstream tributaries. Depicting river networks this way is useful in environmental modelling because the technique offers a mathematical approximation of river strength. For cartographers, assigning order values to a network enables rivers to be mapped to line width, providing a visual indication of tributary size.

A visual overview of the effects of different stream order algorithms (source: osgeo)

Stream orders

Last week New Zealand’s Ministry for the Environment (MFE) launched a new spatial data portal built on the Koordinates platform. Among the ~50 environmental data layers currently available are a series of 15 river environment classifications that collectively describe New Zealand’s 425,000 kilometres of rivers and streams, broken down by region (see, for example, Canterbury River Environment Classifications). I was delighted to see that each attribute table includes a stream order field. Based on my reading of the metadata MFE appear to be assigning Strahler numbers to each segment.

The remainder of this post is series of rough maps I made with Tilemill at varying scales to explore these datasets. What intrigues me about these images is how they imply topographical form even though only the lowest points on the landscape are represented. The valley floors are thick with sinuous detail while, unusually, the towering peaks and ridges of our mountainous country constitute the regions of image whitespace. Although these maps only explicitly render rivers, lakes and coastlines, they imply an entire landscape, albeit from an unconventional perspective. Where traditional relief maps depict a terrain comprised of solid, seemingly unchanging landforms, these maps represent those same places in terms of conduits, movement, energy, motion and stasis.

View a 5000 x 7000 pixel version of all of New Zealand.

Every New Zealand river weighted by Strahler stream order.

All New Zealand rivers

Central North Island—note the twin “flowers” of Mount Taranaki and Mount Ruapehu.


Mount Taranaki in detail—a mountain implied by the water that flows from it.

Mount Taranaki

Mountains in the west; plains to the east.


Southland and Otago—fjords, alps and broken hills.

Southland and Otago

One Response to “Inverse topography—conduits, energy and stasis”

  1. Allan Moyle says:

    Also cool to see the strong linear feature on eastern side of Waikato showing the faulting that creates the horst & graben boundary along Katmais. Present but less distinct on Western side of Waikato too.

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