The complete governing equations of one-dimensional nonequilibrium mathematical models for alluvial rivers are presented, and the simplified equations and assumptions involved are briefly described. The characteristic celerities are analyzed to examine the lumped total-load transport capacity concept and decoupled solution approach widely incorporated in prior models. Existing celerity analyses for total-load transport capacity models are extended. It is revealed that suspended load transport does not adjust as quickly as flow changes. This strongly constraints the use of models in which the total-load transport rate is specified at a capacity value determined primarily by local hydraulic conditions. Further, it is shown that riverbed deformation does not occur instantaneously in response to flow change only within very limited ranges of small Froude number and low bed-load concentration (rather than the total-load concentration as of previous analyses). Otherwise, neither the "quasi-steady state" nor the "fixed bed" assumption implicit in most previous models is appropriate, which necessitates a coupled solution procedure.
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