I extracted two drainage networks from a DEM of 30 meters resolution with two stream definition thresholds: 1000 pixels and 500 pixels.
Can you tell me what this thresholds represent in terms of scale (1/25000, 1/50000...etc)?
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The threshold is not directly related to the scale, but it controls the level of detail in your network. If you consider the scale from a cartographic point of view, the scale is more related to the size of your pixels, which is constant when you change the threshold.
In hydrology, the threshold is set on the "flow accumalution", which is a count of the number of pixels that will contribute to bringing run off water to the stream. So if you set a threshold of 500, it means that the water from at least 500 pixels (= 500 * 30*30 m²= 450000 m² in your case) will arrive there (under the assumption that there is no loss of water).
If you work at very small scales, you could consider that it is not relevant to represent a part of the network that receive water from a smallr area than the minimum mapping unit. Then your scale factor would be proportional to the square root of the threshold.