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All stream or river-channel flows are time variant, or unsteady, in a different degree; steady flow is but an exception rather than the rule. These flows usually exist in different states, such as sub-critical, super-critical, and trans-critical flows. Alternative terms for different flow conditions are often used, such as continuous or discontinuous flows, flows through hydraulic jump or through channel constriction. A river basin, the basic geometric unit of the surface-water flow configurations, generally contains river reaches, branches, tributaries, junctions, and networks. Reasonable and rational definition and determination of all-weather, river-basin, unsteady flows, letting the last three quantifiers...