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In ArcMap, the 'Hydrology' tool under the toolbox 'Spatial Analyst' can be used to extract the stream network, as described in detail here: extract streams from DEM. One step consists of using a conditional statement to generate a raster stream network from the flow accumulation, for which the threshold is, as far as I know, arbitrary. Therefore, the stream network obtained might vary when different thresholds are applied.

However, the definition for stream orders is definite, that is, the first-order streams are perennial streams--streams that carry water throughout the year--that have no permanently flowing tributaries. Therefore, from my understanding, we can not ensure that the smallest stream extracted from a DEM using an arbitrary (flow accumulation) threshold is actually the first-order stream by definition (using here the Strahler rule).

I am not sure whether the understanding above is correct or not. Can you clarify it?

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The definition you quote is one such definition. Another way of thinking about why you use Strahler order is to simply give your river some sort of context of where it is in the network. That network could also have been road/electrical/water. In the case of hydrological networks first order happen represents headwater streams.

Now think when does surface water become a "stream", in fact where do headwaters typically come from, seepages from the ground. So is it a stream when its a trickle 1cm wide, a foot wide or >1m. When is a stream a stream?

In the UK the definition of a stream would no doubt be influenced by our mapping agency the OS, because that is the data everyone uses. So thresholding a flow accumulation raster will creating a particular network density giving you a particular combination of headwaters. What you choose is subjective, for example the definition of a stream in a large country such as India will be quite different to the tiny island of Great Britain.

In my mind a first order stream is simply a segment at the end of the network, you can get coastal watercourses that are entirely represented as a first order segment.

You can also get first-order channels that are winterbournes and only flow in winter which would conflict with the definition you have quoted. So not all first-order streams are perennial. Remember first order is a mathematical definition of a segment in a network (or graph) not a hydrological definition.

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  • thank you for your help. Now, I understand that the stream orders are defined in a relative sense. Am I right?
    – tunar
    Commented Feb 5, 2023 at 1:37
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    Stream order is a function of scale of observation: better photos, more detailed mapping, higher-quality DEM etc can all indicate smaller streams courses previously not noticed. Even 1 small tributary added to a "First order" stream means the entire Strahler classification in that network goes up. See this short but succinct 1966 paper: tandfonline.com/doi/pdf/10.1080/02626666609493480 Commented Feb 5, 2023 at 23:35

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