In many sand-bed rivers the time dependence of stage is due to changing bed elevations in the reach, and changing flow depths which are functions of the slope of the energy gradient and the bed roughness. The time-dependence of stage with discharge is illustrated with stream-gage data collected on the Rio Caris, a meandering sand-bed river. The empirical approach to formulating the stage versus discharge relation for the Rio Caris works well for flood events that have been measured. For extreme flood events such as flood protection design discharges, the empirical method is not very satisfactory. Stages for extreme floods could be calculated by simultaneously solving appropriate water-routing and sediment routing equations. Development and use of the proposed water- and sediment-routing model will reduce the possibility that adverse river responses to extreme or design floods will go unpredicted.