Orders of Magnitude in Branches in Permaculture

Permaculture Designers Manual




Section 4.16 –

Orders of Magnitude in Branches in Permaculture

Streams take up many ground patterns depending on the processes that have formed the underlying landscape (block faulting. folding, volcanism) and the erosion and permeability characteristics of the underlying rock itself (limestone, mudstone, sandstone , clay). That is, the ultimate pattern of a stream network in landscape depends on process and substrate; or we could call these process and media in terms of our model.

We can easily see that stream patterns are the sum of preceding events that gave rise to the geological processes and rock types, so that streams have a lot to tell us about such processes, a skill learned in photo interpretation. Figure 4.24 demonstrates some of the information so clearly told by stream patterns alone.

However, if we abstract a fairly normal dendritic (tree-like) stream branching pattern as in Figure 4.25, we can find out these things from the pattern alone:

The ORDER of channels; the volume, or SIZE, of branches .
The NUMBER OF BRANCHES in each order.
The TOTAL CHANNEL LENGTH in each order.
The MEANDER FREQUENCES in each order or the behavior of flow in the orders of branches.

Streams usually have from one to seven orders, depending on their age, size, or gradient (fall over distance). An easy gradient develops as streams cut back their headwaters and fill in (aggrade) their lower reaches; meanders increase, and the velocity of flow decreases.

These older streams, like a mature tree, have developed all their branches (as has an old company or an old army).

Unless stream conditions themselves change (by a process of stream capture, an increase in rainfall, or a change in landscape), streams (and businesses) maintain equilibrium of order. Looking at our dendrite, peaceful stream, we may find something as can be seen in Table 4.1.

As the branches join up to make ever larger orders of channels, then about 3 times as many smaller branches join up to make each larger group, and so on.

However, the individual lengths (of any one branch in each order) increase by 2 times as the order increases from 1-6.

This is a very general rule of stream branching, even in non-dendritic patterns, and holds true for many streams.

Similarly, meanders or bends also occur in a predictable way depending on the volume and gradient (flow). Regular meanders depend on certain velocities and stream width (as do stability of Von Karman vortex trails; Figure 4.14). The ratio for meanders or trails is about 1:3.6 (Vogel. 1981).

Such regularity in branching may remind us of PULSERS (wave fronts), and indeed as each size order changes, so does the behavior not only of the water flow, but of its associated flora and fauna and their shapes.

In the rills and runnels, streamlines and turbulent flow is observed.

High in the stream gradients (the flattened S-curve of the stream bed in profile) we find insects and fish with suctorial parts able to stick on rocks, flattened fins to press them into the stream bed, flattened bodies and very streamlined profile.

In the middle orders, we get less turbulent water flow, more spiraling, less oxygenation, and more free-swimming but very active fish of high oxygen demand; these may not live in the still water of higher order streams and low oxygen levels.

Thus, we see that gaseous exchange is affected by turbulent flow, and that this in turn determines the life forms in these areas (Vogel, 1981).


In the lower stream or estuaries, we get weak swimmers, less streamlined shapes, flat fish such as flounders, bulky mollusks, jellyfish in quiet areas and lower oxygen levels.

We can list many of these life changes which are coincidental with changes in stream order, so we see that the order of streams is very much connected to the behavior of the water, the landscape, and the shape of life forms in the watershed.

Branching of pathways therefore changes species, behavior, flow, and rates of exchange of nutrients or materials carried by the stream.

When we examine a tree, we find that birds and insects are also confined to, or modified to suit, the orders of branching.

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