Stream Order as a Measure of Sample Source Uncertainty

The Horton stream order at the outlet of a drainage basin is a direct measure of the uncertainty (entropy) of the source supplying any discrete particle or atom detected at the outlet. If m is the order of the main stream in a basin, the uncertainty that the source lies in the drainage area of an i th order tributary is given by m ‐ i . This may be interpreted as representing the minimum number of tests or samples needed to find a single contamination source in a sequential search of a drainage basin. Similarly Scheidegger's consistent stream order may be interpreted as being the number of samples required to search a basin for a single source when the link magnitude of the outlet is known. Because natural streams usually have multiple contaminant sources and cannot be expressed as a simple branching process, a convenient estimate of the average number of samples needed to find a single source is given by ( r b ‐ 1) ( m ‐ i ) where r b is the bifurcation ratio.