# Shreve Order and Strahler Order

When working with watershed areas or watershed (stream) lines in hydrology it can be convenient to assign a number to each area or stream line which indicates at what level it lies within the branching hierarchy of the overall drainage system.   Assigning a number to each area or line to indicate the branching level is assigning the stream order, also called the waterbody order, of the object.  While there are various ways of assigning a stream order, the two methods most frequently used in GIS are the Shreve method and the Strahler method.   Manifold reports both Shreve and Strahler order numbers in the results tables for both Watershed Areas and Watershed Lines.

This topic should be read together with other watershed topics:

• Upstream Areas and Lines - Given a terrain image and a drawing of points, find the drainage basins and the stream lines from which water flows into each point.

• Downstream Lines - Given a terrain image and a drawing of points, find the stream line for each point by which water issuing from the point flows further downstream.

We continue with data from the Example: Create Watershed Lines  topic:

Opening the table for the lines drawing we created with the Watershed : lines  operation, we see that each line has an OrderShreve number and an OrderStrahler number.   We can show these with labels on the map to see what they mean.

We begin with a zoomed-in view that shows the lines drawing, as seen above.  The name of the lines drawing is Watershed lines 500.

In the Project pane, we right-click onto the Watershed lines 500 drawing and choose Copy.  We then press the Paste button twice, to create two copies of the Watershed lines 500 drawing.

We rename the first copy to Watershed lines Shreve and the second copy to Watershed lines Strahler.    We now have two copies of the lines drawing that can be independently opened and styled.  The two new drawings, along with the original Watershed lines 500 drawing, are all based on the same table, Watershed lines 500 Table.

## Strahler Ordering

We drag and drop the Watershed lines Strahler drawing into the map, and then in the Style pane we thematically format it based on the OrderStrahler field, using the above palette.

Next, we right-click onto the Watershed lines Strahler drawing and create a labels component called Strahler Labels, using the OrderStrahler field for the contents of the label.  We drag and drop that labels component into the map, Styling it to use a white, halo around the label so the label text shows up clearly in the map.

The result is a map that shows the stream lines colored by the Strahler order, from yellow for 1 to red for 5 or more, with stream lines labeled by their Strahler order number.

The Strahler method is simple.  If two streams with the same order number merge, the next, downstream, segment is assigned that order number plus one.   If two streams with different order numbers merge, the downstream segment is assigned the higher number of the two.

We can see that in action above, with some of the smallest streams hidden at the level of zoom used, and some of the labels hidden due to conflicts with other labels.   When a stream with an order number of 1 merges with a stream with order number 2, the downstream segment is assigned an order number of 2.    When two streams that both have an order number of 2 merge, the downstream segment is assigned an order number of 3.

Important:  Strahler order numbers are not about summing flow.  Instead, they indicate branching relationships in the topology of the stream.

## Shreve Ordering

We can repeat the above workflow in analogous fashion to see how Shreve ordering works.

We drag and drop the Watershed lines Shreve drawing into the map, and then in the Style pane we thematically format it based on the OrderShreve field, using the above palette.

Next, we right-click onto the Watershed lines Shreve drawing and create a labels component called Shreve Labels,  using the OrderShreve field for the contents of the label.  We drag and drop that labels component into the map, Styling it to use a white, halo around the label so the label text shows up clearly in the map.

The result is a map that shows the stream lines colored by the Shreve order, from yellow for 1 to red for 5 or more, with stream lines labeled by their Shreve order number.

The Shreve method is even simpler than the Strahler method.   At each juncture of two streams, add up the order numbers of both streams and assign the sum to the downstream segment.

We can see that in action above, with some of the smallest streams hidden at the level of zoom used, and some of the labels hidden due to conflicts with other labels.   When a stream with an order number of 1 merges with a stream with order number 3, the downstream segment is assigned an order number of 4.    When a stream with an order number of 5 merges with a stream with order number 3, the downstream segment is assigned an order number of 8.

Shreve order is more popular in GIS for a variety of reasons, not the least of which is that it can be used to show each downstream segment with increasing width, a nice cartographic effect.

Using a thematic format for the Size style parameter for lines, as seen above, we can create the illustration below:

If we wanted smoother growth in the thickness of lines, we could have used more intervals than five intervals, with a smaller increase in size between each interval.

Important:  Shreve order numbers also are not about summing flow.  Instead, they indicate branching relationships in the topology of the stream.

## Watershed Areas and Stream Lines

We can take a second look at the relationship between stream lines and watershed areas in the context of ordering.

We show both stream lines and watershed areas drawings together in the map.

Switching to the Shreve lines drawing that shows stream segments colored by their Shreve order number.   Adding the Shreve labels, we can see how each stream line has its own Shreve order number, and we can see how every time that order number changes, at a merge of two stream lines, we cross a watershed area boundary.

That is true even in the case of very small areas, such as the one indicated by the magenta arrow in the illustration above.

Zooming in, we see the very small line that is too small to see at the zoom level of the prior illustration.    Watershed areas can only be created at the borders of individual pixels.  The relationship between watershed areas and stream lines will not be perfect when we zoom so far into the terrain data that details become imprecise due to pixel quantization.

## Watershed Areas and Ordering

When we use the Watershed : areas operation to create a drawing of watershed areas, those areas also are assigned Strahler order and Shreve order numbers, the same as the order numbers that would be assigned to the stream line that is in that area.

In the illustration above, we have created a copy of the Watershed areas 500 drawing that we call Watershed areas Shreve, and we have styled it using the same thematic formatting intervals and palette used in the Watershed lines Shreve drawings shown earlier.  We have used the Layers pane to set 50% opacity, so the underlying terrain can be seen to provide visual context.   We have also created a new Shreve Areas Labels layer showing the OrderShreve number for each area.

In the display above, we have zoomed into the region shown in the beginning of this topic, to show areas colored by their Shreve order number and overlaid with the ValueSum (total flow) labels layer created in the Example:  Create Watershed Areas topic.  This display shows watershed areas, the Shreve number (by color) for each area, and the total flow in the area.   We can see from this display that as flow runs downhill, resulting in a greater Shreve order for each area, the total flow also increases.

A simpler display, zoomed out, showing only the watershed areas colored by Shreve number, shows how individual drainage areas are arranged overall for downhill flow.

However, the above illustration combines the colored palette used for the terrain elevations to skew the colors of the areas, showing slight orange tones in high elevation areas that should be uniformly yellow.  That may be pretty, but it could be misleading.

We can fix that by Copying the Montara image and Pasting to make a copy of the image called Montara Gray.  We can then drag and drop that image as a layer into the map, and Style it using a palette from light gray to white color.   The combined result, seen through the 50% Watershed areas Shreve drawing, provides hill shading without skewing the colors of the thematic format by Shreve order.

## Videos

Manifold vs Arc - Fifty times Faster than Spatial Analyst -  The first video in a series of comparisons. We compare Manifold Release 9 to ESRI's ArcMap with Spatial Analyst. ArcMap instead of ArcGIS Pro is used to ensure maximum possible speed with no slowdowns from AGOL connections. Starting with a terrain 5300 x 5300 elevation raster we compare Manifold workflow and speed creating streams (watershed lines) with ESRI ArcMap and Spatial Analyst doing the same task. ArcMap requires four operations calculating intermediate steps, taking a total of three minutes and 30 seconds to compute streams.  Manifold does the same job in a single operation in under four seconds, over fifty times faster than Arc, and with the convenience of a single click.  ArcMap plus Spatial Analyst cost over \$5000 per seat while Manifold costs under \$500.  As data sizes scale up, Manifold gets even faster than Arc. Works in the free Viewer, too!

Manifold vs Arc - Watersheds Sixty Five times Faster than Arc -  Another video comparing Manifold speed to ESRI ArcMap with Spatial Analyst, this time computing upstream watersheds on a 5300 x 5300 terrain elevation raster for a few dozen locations.  ArcMap requires three geoprocessing tool operations calculating intermediate steps, taking a minute and a half.  Manifold does the same job in a single click in less than 1.4 seconds, over 65 times faster than ESRI. The larger and more complex the geoprocessing, the greater Manifold's speed advantage.   ArcMap plus Spatial Analyst cost over \$5000 per seat while Manifold costs under \$500. Works in the free Viewer, too!

Manifold vs Arc - Seven Seconds vs Four Minutes - Finding basins in a 5300 x 5300 terrain elevation raster, we compare Manifold workflow speed and ease of workflow to ESRI's ArcMap with Spatial Analyst.  ArcMap Standard plus Spatial Analyst costs a total of \$5250 so it should work better than a Manifold package that sells for under \$500, right?  No way! Manifold absolutely crushes the comparison, taking only a single click and seven seconds to do what takes the \$5000+ package three geoprocessing operations and four minutes, not counting the time to setup and launch three operations. Works in the free Viewer, too!

Manifold vs Arc - 100x Faster on an Affordable Desktop - Watch Manifold do in 0.9 seconds what takes ArcMap plus Spatial Analyst over a minute and a half.  That's over 100 times faster!   Some  comments on previous comparisons have stated that Manifold was so super fast compared to ESRI because tests were run on a high-end, Threadripper machine that could run 48 threads. This video shows Manifold is faster even with fewer cores on an affordable desktop system.  We re-run Manifold trials on a  Ryzen 9 3900x computer, with three different tasks taking only 0.9 seconds, 5.4 seconds and 3 seconds.  AMD's 3900x CPU now retails for as low as \$450, setting a new baseline for affordable GIS desktop computing.  Everything shown in the video works in the free Viewer, too!

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