You might read my paper on Stream Types and Management Implications. I beLieve there are some hydro tools in ArcMap that can make it easier, but even then, careful visual inspection is recommended. Stream ordering is related to branching, not drainage size or number of pixels. Look up some of the cited literature listed. GIS is not foolproof, and the level of stream ordering detail depends on the DEM detail.

I think Stream Definition and Stream Ordering are two different things.

For Stream Definition we use the Con Tool, which basically selects the stream pixels with a drainage area greater than a certain value (e.g. 500). These pixels may or may not belong to a certain Stream Order.

If you only want streams with a certain Stream Order, my suggestion is that you first define streams based on a very small threshold using the Con Tool so that all/most of the streams are definition upto a very high order. Then use the Stream Order tool in ArcGIS to define the Stream Order for each pixel (based on Strahler Stream Ordering Method). Finally, use the Con Tool again to select the stream pixels with only the desired value of Stream Order (e.g. 4). The resulting stream pixels will define the stream network only upto the desired level of Stream Order. Hope this helps

I totally agree with Dr. William. I don't think with any GIS tool one can decipher stream order. Stream order has to be done manually, as it is concerned with stream branching.

Thank you all.

I want to learn the scientific applications and the reasons why we decide to select a certain stream order to study, what to read for that?