There can be some unusual circumstances, such as long narrow gullies may keep the same order for extended distances.  But downstream, when gullies combine, more frequent dendritic pattern may shorten branching pattern.  But generally, the higher the order, the longer the segments.  Some terrain types lend themselves to unusual branching character, such as trellis pattern.  I have used stream ordering extensively in studies and also applied as management indicator in specific circumstances.  Several of my Researchgate papers mention or applied stream ordering.  LiDAR of ground surface has been a substantial help in remote sensing of stream orders.

My paper Stream Types and Management Implecations ... may be a real good one for you.  There was an EIS on loblolly pine removal, where I analyzed 3rd and 4th order perennial streams for management intensity and potential need for mitigation.  On the Francis Marion and Sumter National Forests, we have GIS maps of stream ordering, initially from contour maps, more recently we are expanding with LiDAR - see also the 2 papers mentioning LiDAR, although ordering of streams is just one benefit.  I have many examples of using LiDAR to help explain stream size.  Also the Indian Creek Hydrologic Condition Analysis has a map of stream ordering that may be of interest in how it can be presented as a descriptive, visual tool to explain to others.

Thanks a  lot  Dr. Hansen, for your answer, I've read your papers and found what I'm looking for specially in those Indian Creek Hydrologic Condition Analysis, it was really helpful to me.

Eman:  I am glad this information has helped you.  Constructing the stream coverages out of topographic contour or LiDAR based digital elevation models require a substantial amount of manual overseeing and/or hand digitizing to get a desired layer.  All my early work on this was hand mapping and digitizing.  The hydrologic flow routing tools in GIS typically utilize a raster coverage developed from the DEM, and there are some areas that result in relatively flat gradients where the flow path cannot be easily determined.  A substantial amount of manual cleanup and review is needed as the hydrologic modeling yields areas  with straight streams that need to be reset manually.  Some GIS analysts use an infinite flow direction tool to overcome the normal 8 direction of flow that a pixel can use.  The most recent paper required a substantial amount of hand work to identify and locate streams within the coastal plain.  A substantial amount of detail is added to this subject with LiDAR because we have dense vegetation canopy.  In dry areas without canopy, LiDAR may not be so important.  Of course, hydrologic modeling tries to select the primary stream and may miss it in braided networks.  For ordering, that may be OK.  You want the main stream or at least a single stream within a braided section to order effectively.  I have examples in materials of stream ordering discussion or stream networks displayed in mountains (Chattooga River), piedmont rolling hills (Indian Creek) and marine terraces (Francis Marion National Forest Turkey Creek).  If you remember, maybe you would send me a message with a copy of your paper through Researchgate of how you were able to apply stream ordering for your situation.  Regards, Bill

I shall remember that N. S. Allah, many thanks for your interesting information about this field Dr. Hansen, and I wish you keep the hard work on. 

Sincerely,

E. Elbadry

Please refer work of Horton Strahler Schumm etc for some further work. if u need that i can share those papers.