How do I assign stream order when a river diverges?

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I'm in the process of tracing various river systems in Great Britain, and I've arrived at a problem. At the town of Earith, the Old and New Bedford Rivers diverge from the main course of the River Great Ouse (5th order), and I have no idea how to continue my stream order system from here.

Do all three distributaries retain fifth order? If so, what happens when tributaries join and how do I avoid artificial addition of stream orders downstream? How do I justify keeping the original Great Ouse course 5th order when it is clearly a smaller channel at that point (owing to drainage down the other channels)?

I should clarify I am using the Strahler number system.

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