In this presentation, I show how variations in streamflow can be viewed through dynamics in position (q) and momentum (p) space. Observed stage and flow rates for the Village Creek in the City of Fort Worth area is used from demonstration. The position is taken directly as the measured stage at a cross-section, and momentum is derived by solving the linear momentum theorem for a simplified control volume representation of the stream. By plotting historical measurements, “equilibrium” was observed as occurring within stable limits in (p,q) space and points outside stable limits extreme flooding or drought conditions. The oscillations of the water column about equilibrium is modeled with a dissipation-friction 2nd ODE with coefficients for inertia, friction and stability subject to an external forcing (rainfall) function. The receding limb of the rainfall hyetograph is shown useful as forcing function for predicting stream stage following rainfall onset.
