DESCRIPTION

The r.stream.order calculates Strahler's and other stream hierarchy methods. It is a basic module for topological analysis of drainage networks.

OPTIONS

-z
Creates zero-value background instead of NULL. For some reason (like map algebra calculation) zero-valued background may be required. This flag produces zero-filled background instead of null (default).
-a
Uses accumulation map instead of cumulated stream length to determine main branch at bifurcation. Works well only with SFD networks
-m
Only for very large data sets. Use segment library to optimise memory consumption during analysis
stream_rast
Name of input stream map on which ordering will be performed produced by r.watershed or r.stream.extract. Because streams network produced by r.watershed and r.stream.extract may slightly differ in detail it is required to use both stream and direction map produced by the same module. Stream background shall have NULL value or zero value. Background values of NULL are by default produced by r.watershed or r.stream.extract. If not 0 or NULL use r.mapcalc to set background values to null.
direction
Name of input direction map produced by r.watershed or r.stream.extract. If r.stream.extract output map is used, it only has non-NULL values in places where streams occur. NULL (nodata) cells are ignored, zero and negative values are valid direction data if they vary from -8 to 8 (CCW from East in steps of 45 degrees). Direction map shall be of type CELL values. Region resolution and map resolution must be the same. Also stream_rast network and direction maps must have the same resolution. It is checked by default. If resolutions differ the module informs about it and stops. Region boundary and maps boundary may be differ but it may lead to unexpected results.
accumulation
Flow accumulation (optional, not recommended): name of flow accumulation file produced by r.watershed or r.stream.extract. This map is an option only if Horton's or Hack's ordering is performed. Normally both Horton and Hack ordering is calculated on cumulative stream length which is calculated internally. Flow accumulation can be used if user want to calculate main stream as most accumulated stream. Flow accumulation map shall be of DCELL type, as is by default produced by r.watershed or converted do DCELL with r.mapcalc.
elevation
Used to calculate geometrical properties of the network stored in the table.

OUTPUTS

At least one output map is required:

stream_vect
Vector network with table where stream network topology can be stored. Because r.stream.order is prepared to work both with r.watershed or r.stream.extract, it may be used to create correct vector from r.watershed results.
strahler
Name of Strahler's stream order output map: see notes for detail.
shreve
Name of Shreve's stream magnitude output map: see notes for detail.
horton
Name of Horton's stream order output map (require accum file): see notes for detail.
hack
Name of Hack's main streams output map : see notes for detail.
topo
Name of topological dimensions streams output map: see notes for detail.

NOTES

Module can work only if direction map, stream map and region map has same settings. It is also required that stream map and direction map come from the same source. For lots of reason this limitation probably cannot be omitted. This means if stream map comes from r.stream.extract also direction map from r.stream.extract must be used. If stream network was generated with MFD method also MFD direction map must be used. Nowadays f direction map comes from r.stream.extract must be patched by direction map from r.watershed. (with r.patch).

Stream ordering example


Strahler's stream order

Strahler's stream order is a modification of Horton's streams order which fixes the ambiguity of Horton's ordering. In Strahler's ordering the main channel is not determined; instead the ordering is based on the hierarchy of tributaries. The ordering follows these rules:
  1. if the node has no children, its Strahler order is 1.
  2. if the node has one and only one tributary with Strahler greatest order i, and all other tributaries have order less than i, then the order remains i.
  3. if the node has two or more tributaries with greatest order i, then the Strahler order of the node is i + 1.
Strahler's stream ordering starts in initial links which assigns order one. It proceeds downstream. At every node it verifies that there are at least 2 equal tributaries with maximum order. If not it continues with highest order, if yes it increases the node's order by 1 and continues downstream with new order.

Advantages and disadvantages of Strahler's ordering

Strahler's stream order has a good mathematical background. All catchments with streams in this context are directed graphs, oriented from the root towards the leaves. Equivalent definition of the Strahler number of a tree is that it is the height of the largest complete binary tree that can be homeomorphically embedded into the given tree; the Strahler number of a node in a tree is equivalent to the height of the largest complete binary tree that can be embedded below that node. The disadvantage of that methods is the lack of distinguishing a main channel which may interfere with the analytical process in highly elongated catchments

Horton's stream ordering

Horton's stream order applies to the stream as a whole but not to segments or links since the order on any channel remains unchanged from source till it "dies" in the higher order stream or in the outlet of the catchment. The main segment of the catchment gets the order of the whole catchment, while its tributaries get the order of their own subcatchments. The main difficulties of the Horton's order are criteria to be considered to distinguish between "true" first order segments and extension of higher order segments. That is the reason why Horton's ordering has rather historical sense and is substituted by the more unequivocal Strahler's ordering system. There are no natural algorithms to order stream network according to Horton' paradigm. The algorithm used in r.stream.order requires to first calculate Strahler's stream order (downstream) and next recalculate to Horton ordering (upstream). To make a decision about proper ordering it uses first Strahler ordering, and next, if both branches have the same orders it uses flow accumulation to choose the actual link. The algorithm starts with the outlet, where the outlet link is assigned the corresponding Strahler order. Next it goes upstream and determines links according to Strahler ordering. If the orders of tributaries differ, the algorithm proceeds with the channel of highest order, if all orders are the same, it chooses that one with higher flow length rate or higher catchment area if accumulation is used. When it reaches the initial channel it goes back to the last undetermined branch, assign its Strahler order as Horton order and goes upstream to the next initial links. In that way stream orders remain unchanged from the point where Horton's order have been determined to the source.

Advantages and disadvantages of Horton's ordering

The main advantages of Horton's ordering is that it produces natural stream ordering with main streams and its tributaries. The main disadvantage is that it requires prior Strahler's ordering. In some cases this may result in unnatural ordering, where the highest order will be ascribed not to the channel with higher accumulation but to the channel which leads to the most branched parts of the catchment.

Shreve's stream magnitude

That ordering method is similar to Consisted Associated Integers proposed by Scheidegger. It assigns magnitude of 1 for every initial channel. The magnitude of the following channel is the sum of magnitudes of its tributaries. The number of a particular link is the number of initials which contribute to it.

Scheidegger's stream magnitude

That ordering method is similar to Shreve's stream magnitude. It assigns magnitude of 2 for every initial channel. The magnitude of the following channel is the sum of magnitudes of its tributaries. The number of a particular link is the number of streams -1 contributing to it. Consisted Associated Integers (Scheidegger) is available only in attribute table. To achieve Consisted Associated Integers (Scheidegger) raster the result of Shreve's magnitude is to be multiplied by 2: 
r.mapcalc "scheidegger = shreve * 2.0"

Drwal's stream hierarchy (old style)

That ordering method is a compromise between Strahler ordering and Shreve magnitude. It assigns order of 1 for every initial channel. The order of the following channel is calculated according Strahler formula, except, that streams which do not increase order of next channel are not lost. To increase next channel to the higher order R+1 are require two channels of order R, or one R and two R-1 or one R, and four R-2 or one R, one R-1 and two R-2 etc. The order of particular link show the possible value of Strahler'order if the network was close to idealised binary tree. Drwal's order is aviallable only in attribute table.To achieve Drwal's raster the result of Shreve's magnitude is to be recalculated according formula: floor(log(shreve,2))+1 
r.mapcalc "drwal = int(log(shreve,2.0)) + 1.0"

Advantages and disadvantages of Drwal's hierarhy

The main advantages of Drwal's hierarchy is that it produces natural stream ordering with which takes into advantage both ordering and magnitude. It shows the real impact of particular links of the network run-off. The main disadvantage is that it minimise bifuraction ratio of the network.

Hack's main streams or Gravelius order

This method of ordering calculates main streams of main catchment and every subcatchments. Main stream of every catchment is set to 1, and consequently all its tributaries receive order 2. Their tributaries receive order 3 etc. The order of every stream remains constant up to its initial link. The route of every main stream is determined according to the maximum flow length value of particular streams. So the main stream of every subcatchment is the longest stream or stream with highest accumulation rate if accumulation map is used. In most cases the main stream is the longest watercourse of the catchment, but in some cases, when a catchment consists of both rounded and elongated subcatchments these rules may not be maintained. The algorithm assigns 1 to every outlets stream and goes upstream according to maximum flow accumulation of every branch. When it reaches an initial stream it step back to the first unassigned confluence. It assigns order 2 to unordered tributaries and again goes upstream to the next initial stream. The process runs until all branches of all outlets are ordered.

Advantages and disadvantages of main stream ordering

The biggest advantage of that method is the possibility to compare and analyze topology upstream, according to main streams. Because all tributaries of main channel have order of 2, streams can be quickly and easily filtered and its proprieties and relation to main stream determined. The main disadvantage of that method is the problem with the comparison of subcatchment topology of the same order. Subcatchments of the same order may be both highly branched and widespread in the catchment area and a small subcatchment with only one stream.

Topological dimension streams order

This method of ordering calculates topological distance of every stream from catchment outlet.

Stream network topology table description connected with vector file

EXAMPLE

g.region -p -a rast=elevation
r.watershed elevation=elevation threshold=10000 drainage=direction stream=streams
r.stream.order stream_rast=streams direction=direction strahler=riverorder_strahler \
  horton=riverorder_horton shreve=riverorder_shreve hack=riverorder_hack \
  topo=river_topodim

# vector river network
r.watershed elevation=elevation threshold=10000 accumulation=accum
r.stream.order stream_rast=streams direction=direction elevation=elevation \
  accumulation=accum stream_vect=river_vector

REFERENCES

SEE ALSO

r.watershed, r.stream.extract, r.stream.basins, r.stream.stats, r.mapcalc

AUTHOR

Jarek Jasiewicz

Last changed: $Date$